Simplification MCQ Questions & Answers

Simplification MCQs : This section focuses on the "Simplification". These Multiple Choice Questions (MCQs) should be practiced to improve the Simplification skills required for various interviews (campus interview, walk-in interview, company interview), placement, entrance exam and other competitive examinations.

Question 1

What is the simplified value of (sec4 A – tan2 A) – (tan4 A + sec2 A)?

A. -1

B. 1/2

C. 1

D. 0

Question 2

If a - b = 3 and ab =28, then a3 - b3 is

A. 279

B. 387

C. 513

D. 91

Question 3

The perimeter of two similar triangles is 36 units and 48 units. Find the ratio of their corresponding areas.

A. 1 : 3

B. 3 : 4

C. 4 : 9

D. 9 : 16

Question 4

If cot A = [sin B/(1 – cos B)], then what is the value of cot 2A?

A. cot(B/2)

B. cot 2B

C. cot B

D. tan B

Question 5

If a2+b2c2 = b2+c2a2 = c2+a2b2 = 1k k≠0 then k =

A. 2

B. 1

C. 0

D. 1/2

Question 6

If xy = 48 and x2 + y2 = 100, then (x + y) is

A. 12

B. 16

C. 18

D. 14

Question 7

A bag contains coins of denominations Rs.1, Rs.5 and Rs.10. Assuming there are equal number of Rs.1, Rs.5 and Rs.10, what will be the total number of coins in the bag be if the total money is Rs. 368?

A. 69

B. 96

C. 56

D. 65

Question 8

What is the value of tan 6° tan 36° tan 84° tan 54° tan 45°?

A. 1/2

B. 1/√2

C. 1

D. 1/3

Question 9

What is the value of equation a3+b3+c3-3abc if a2+b2+c2=ab+bc+ca+4 and a+b+c = 4.

A. 0

B. 1

C. 16

D. 256

Question 10

What is the value of 128 + 7232

A. 3.5

B. 7

C. 4.5

D. 9

Question 11

The value of 2.33+0.0272.33-0.69+0.09

A. 2

B. 2.27

C. 2.33

D. 2.6

Question 12

If 4x2= 152- 92, then value of x is

A. 9

B. 6

C. 3

D. 12

Question 13

If x + y = 13 and x2 + y2 = 89, then find xy is

A. 80

B. 169

C. 258

D. 40

Question 14

If a--b = 4 and ab = 45, find the value of a3 - b3

A. 604

B. 370

C. 253

D. 199

Question 15

Compute 4923 / 547 - 10

A. 1

B. -1

C. 1641/179

D. 1614/179

Question 16

Simplify 50 + 18 - 8

A. 8√2

B. 7√2

C. 6√2

D. 5√2

Question 17

If a and b are the roots of the equation Px2 – Qx + R = 0, then what is the value of (1/a2) + (1/b2) + (a/b) + (b/a)?

A. Q2-2P2R+PPR2

B. Q2-2PRR+PPR2

C. Q2-2R2P+RP2R2

D. Q2-2PR2R+2PP2R2

Question 18

If 2x + 3y3x - 4y = 117, then the value of x/y is __

A. 65/19

B. 68/19

C. 67/19

D. 64/19

Question 19

25 - 1/2{5 + 4 - (3 + 2 - 1 + 3)} = ?

A. 21

B. 23

C. 22

D. 24

Question 20

Solve : (x + 2y) (2x - y)

A. 2x2 + 5xy + 2y2

B. 2x2 + 3xy - 2y2

C. x2 + 4xy + y2

D. x2+ 4xy - y2

Question 21

112 × 54 =

A. 68947

B. 69874

C. 70000

D. 76000

Question 22

The average temperature of Monday to Wednesday was 37 C and of Tuesday to Thursday was 34 C. If the temperature on Thursday was 4/5 th of that of Monday, the temperature on Thursday was ?

A. 35 c

B. 36 c

C. 34 c

D. 32 c

Question 23

Simplify (b5x2a3z4)*(b3x2a4z5) / (a2b3z2)

A. b5x4a5z5

B. b5x4a5z7

C. b5x4a4z7

D. b4x4a5z7

Question 24

9876-?+5431=5553

A. 9754

B. 9765

C. 8754

D. 9854

Question 25

If a : b = c : d = 1 : 6, then what is the value of a2+c2b2+d2?

A. 1/600

B. 1/60

C. 1/36

D. 1/360

Question 26

Find the common factor of (3757+4357) and (3737+4337) ?

A. (43 - 37)

B. (43 + 37)

C. (37 + 37)

D. 10

Question 27

The points A(x,2), B(2,1) and C(6,3) are collinear. Find x?

A. 4

B. -2

C. -4

D. 2

Question 28

What is the value of cot210°?

A. 1/√3

B. -1/√3

C. √3

D. -√3

Question 29

40.36 - (9.347 - x ) - 29.02 = 3.68. Find x.

A. -56.353

B. 1.687

C. -17.007

D. 82.407

Question 30

If a + b + c + d = 4, then the value of 1(1-a)(1-b)(1-c) + 1(1-b)(1-c)(1-d) + 1(1-c)(1-d)(1-a) + 1(1-d)(1-a)(1-b)

A. 0

B. 1

C. 4

D. 1+ abcd

Question 31

If Cos θ = 5/13, then Cosec θ = ?

A. 5/12

B. 12/5

C. 13/5

D. 13/12

Question 32

An owner of a Dry fruits shop sold small packets of mixed nuts for Rs. 150 each and large packets for Rs. 250 each. One day he sold 5000 packets, for a total of Rs. 10.50 lakh. How many small packets were sold ?

A. 2000

B. 3000

C. 2500

D. 3500

Question 33

If cosαcosβ=m and cosαsinβ=n, then the value of m2+n2 cos2β is

A. n2

B. m2

C. mn

D. 1

Question 34

What is the reflection of the point (4, 7) in the line y = -1?

A. (-6 , 7)

B. (-4 , -9)

C. (4 , -9)

D. (-6 , -7)

Question 35

What is the value of x3-1x3+8 when 8x-8x-16=0 ?

A. 6

B. 8

C. 16

D. 22

Question 36

An angle is four times its complementary angle. What is the measure of the angle?

A. 72°

B. 108°

C. 54°

D. 36°

Question 37

If (6x - 5) = (4x + 7), then the numerical value of (x + 1)3 is

A. 216

B. 125

C. 64

D. 343

Question 38

What should be added to 8(3x - 4y) to obtain 18x - 18y?

A. 6x - 14y

B. 14y + 6x

C. 14y - 6x

D. 6xy

Question 39

Mr. Ankit is on tour to Siachin and he has Rs. 360 for his expenditure. If he exceeds his tour by 4 days, he must trim down his daily expenditure by Rs.3. Forhow many days is Mr. Ankit is on tour?

A. 20

B. 22

C. 24

D. 26

Question 40

What is the value of Cot 60°- Sec 45°?

A. (√2 - √3)/√6

B. (√3 - 3√2)/3

C. (1 - 2√2)/2

D. (1 - √3)/2

Question 41

If tan2A / (secA - 1)2 = x, then the value of x is

A. (1+cosecA) / (1-cosecA)

B. (1+cosA)(1-cosA)

C. (1+cosA) / (1-cosA)

D. (1+cosecA)(1-cosecA)

Question 42

If 22x - 40 = 207 + 3x, then x = ?

A. 14

B. 13

C. 12

D. 11

Question 43

If a - b = 4 and ab = -3, then what is the value of a3- b3?

A. 21

B. 28

C. 23

D. -20

Question 44

If (x + y)2 = xy + 1 and x3 – y3 = 1, then what is the value of x – y?

A. 1

B. 0

C. -1

D. 2

Question 45

What is the value of 1+aa1/2+a-1/2-a1/2+a-1/21+a+a-1/2 ?

A. √a

B. 1/√a

C. 0

D. √a+1

Question 46

If x - 2y = 2 and 3x + y = 20, then the value of (x,y) is

A. (6, 2)

B. (4, 1)

C. (3, 2)

D. (5, 5)

Question 47

When 2x + 2x = 3, then x3 + 1x + 2 value is

A. 2/7

B. 7/8

C. 7/2

D. 8/7

Question 48

(0.2 x 0.2 x 0.2)(0.06 x 0.06 x 0.06) / (0.12 x 0.12 x 0.12) = ?

A. 0.008

B. 0.001

C. 0.002

D. 0.006

Question 49

ΔDEF is right angled at E. If m∠F = 30 deg, then find the value of (sinD - 1/3).

A. -1/2√3

B. (3√3-2)/6

C. (√2-√3)/√6

D. (2√2-1)/√2

Question 50

ΔABC and ΔDEF are two similar triangles and the perimeter of ΔABC and ΔDEF are 30 cm and 18 cm respectively. If length of DE = 36 cm, then length of AB is

A. 60 cm

B. 40 cm

C. 45 cm

D. 50 cm

Question 51

Find the value of p if -3x - 11, x + p and 5x + 7 are in arithmetic progression.

A. 9

B. 2

C. -9

D. -2

Question 52

If x = 93 , y = 93 , z = 94 then the value of x2 - y2 + 10xz + 10yz is

A. 104784

B. 147840

C. 174840

D. 184740

Question 53

If 1/6 of x - 7/2 of 3/7 equals - 7/4, then the value of x is

A. -1.5

B. 3

C. -2.5

D. 6

Question 54

If Sin θ = 20/29, then what is the value of Cos θ?

A. 29/21

B. 21/29

C. 21/20

D. 20/29

Question 55

If sin - 5π/3 = x, then the value of x is

A. -√3/2

B. √3/2

C. -2

D. -2/√3

Question 56

If secA = x, then the value of x is

A. √(1 - cot2A)

B. √(1 - tan2A)

C. √(1 + cot2A)

D. √(1 + tan2A)

Question 57

Tan 45° + Cosec 60° =

A. (1 + 2√2)/2

B. (√3 + 2)/√6

C. 5/√3

D. (3 + 2√3)/3

Question 58

In a circle with centre O, AB is a diameter and CD is a chord which is equal to the radius OC. AC and BD are extended in such a way that they intersect each other at a point P, exterior to the circle. The measure of ∠APB is

A. 30°

B. 45°

C. 60°

D. 90°

Question 59

Find the value of 'y' if y84 = 225

A. 10

B. 12

C. 15

D. 18

Question 60

In ΔABC measure of angle B is 90 deg. If cotA = 7/24, and AB = 1.4cm, then what is the length (in cm) of side AC?

A. 5

B. 4.8

C. 4

D. 5.6

Question 61

What is the value of 99992 x 100008?

A. 9999999936

B. 9999899936

C. 9999999836

D. 9999999926

Question 62

What is the simplified value of cosec 2A + cot 2A?

A. sec A

B. sec (A/2)

C. cot A

D. cot2 A

Question 63

If cot π/3c - tan π/4c = x, then the value of x is

A. √3+2

B. (1-√3)/√3

C. (1-√2)/√2

D. (√3+4)/2√3

Question 64

If 4x = √5+ 2, then the value of x - 1/16x is

A. 1

B. -1

C. 4

D. 2√5

Question 65

If one more cobbler is hired the output of a shoe making unit will increase from 50 pairs of shoes to 55 pairs per day, but then the shoe making unit will have to reduce the price of a pair of shoes from Rs 3200 to Rs 3000 per pair to sell the additional output, the marginal revenue product of the last cobbler is

A. Rs 1000

B. Rs 5000

C. Rs 4000

D. Rs 200

Question 66

What is the value of (cos 45 - 1/3) ?

A. 2-√3

B. 2/√3

C. (3-√2)/3√2

D. 1/2√3

Question 67

If 9x+2 = 240 + 9x, the value of (8x)x is

A. 1

B. -1

C. 0

D. 2

Question 68

Expand and simplify (x + 4)2 + (x - 2)2

A. 2(x2 + 2x + 10)

B. 2(x2 + 2x - 10)

C. 2(x2 - 2x + 10)

D. 2(x2 - 2x - 10)

Question 69

Rs.7750 is divided among X, Y and Z such that 3 times of X's share is equal to 5 times of Y's share which is equal to 2 times of Z's share. What is the share (in Rs) of Z?

A. 4250

B. 3750

C. 3875

D. 4475

Question 70

10+10(9) =

A. 180

B. 110

C. 100

D. 19

Question 71

Slope of the line AB is -4/3. Co-ordinates of points A and B are (x, -5) and (-5, 3) respectively. What is the value of x?

A. -1

B. 2

C. -2

D. 1

Question 72

If x+y+z = 0, then what is the value of x23z+y33xz+z23x ?

A. 0

B. xz

C. y

D. 3y

Question 73

If a rod of length 208 45 is cut into equal pieces of length 23 15 then the total number of rods obtained is

A. 5

B. 8

C. 9

D. 7

Question 74

If a + b + c = 0 , then the value of a3 + b3+ c3 is

A. abc

B. 2abc

C. 3abc

D. 0

Question 75

If P = 99, then the value of P(P2+ 3P + 3) is

A. 9999

B. 999999

C. 99999

D. 9999999

Question 76

If 14/3 + (1/2)(x - 7/3) = -2x/3, then the value of x is?

A. -3

B. 3

C. -6

D. 6

Question 77

A man can cover a certain distance in 3 hours 36 minutes if he walks at the rate of 5 Km/hr. If he covers the same distance on cycle at the rate of 24 Km/hr, then the time taken by him in minutes is

A. 40

B. 45

C. 50

D. 55

Question 78

Which of the following value of 'x' satisfies the equation 814x+4 = 2432x+8?

A. 3

B. 4

C. 5

D. 6

Question 79

What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(-4, 0) and C(3, -4)?

A. ( 0, 3)

B. ( 0, -3)

C. ( 0, -5)

D. ( 0, 5)

Question 80

What is the equation of the line if its slope is 1/4 and y-intercept is -3?

A. x - 4y = 12

B. x + 4y = 12

C. x - 4y = -12

D. x + 4y = -12

Question 81

If a(a + b + c) = 45, b(a + b + c) = 75 and c(a + b + c) = 105, then what is the value of (a2 + b2 + c2 )?

A. 75

B. 83

C. 217

D. 225

Question 82

A man has Rs.480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

A. 45

B. 60

C. 75

D. 90

Question 83

A T.V was sold at a profit of 5% If it had been sold at a profit of 10% , the profit would have been Rs. 1000 more. What is its cost price ?

A. Rs.20000

B. Rs.5000

C. Rs.10000

D. Rs.15000

Question 84

What is the value of 0.55 x 4.5/0.81 ?

A. 3.555

B. 55/18

C. 3.05

D. 55/81

Question 85

In ΔPQR measure of angle Q is 90°. If tanP = 4/3, and PQ = 1.5cm, then what is the length (in cm) of side PR?

A. 2

B. 2.5

C. 3

D. 4.8

Question 86

x, y and z are prime numbers and x + y + z = 38. What is the maximum value of x?

A. 19

B. 23

C. 31

D. 29

Question 87

If cos2x + cos4x = 1, then tan2x + tan4x =

A. 0

B. 1

C. 2tanx

D. tanx

Question 88

ΔABC is right angled at B. If m∠C = 60°, then find the value of (cotA - 1/2).

A. -1/√3

B. (3-√2)/3√2

C. (2√3-1)/2

D. (√2-√3)/√6

Question 89

ΔABC is right angled at B. If cotA = 7/24, then what is the value of cosecC ?

A. 7/25

B. 25/7

C. 24/7

D. 7/24

Question 90

If tanA - cotA = x, then value of x is?

A. (1 + 2cos2A)/(sinA cosA)

B. (sinA cosA)/(1 - 2cos2A)

C. (sinA cosA)/(1 + 2cos2A)

D. (1 - 2cos2A)/(sinA cosA)

Question 91

A triangular prism has 9 edges. How many vertices does it have?

A. 8

B. 6

C. 12

D. 10

Question 92

In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?

A. 160

B. 175

C. 180

D. 195

Question 93

If (8x - 4) = (3x + 6), then the numerical value of (x + 1)3 is

A. 3

B. 9

C. 27

D. 81

Question 94

If 16% of an electricity bill is deducted, Rs 1806 is still to be paid. How much was the bill?

A. Rs 1557

B. Rs 2186

C. Rs 1593

D. Rs 2150

Question 95

What is the value of (-7776)25

A. 16

B. 36

C. 64

D. 21

Question 96

If 493/29 = 17, then 4.93/0.0017 = ?

A. 290

B. 0.29

C. 2.9

D. 2900

Question 97

P(3,1) and R(-7,5) are vertices of a rhombus PQRS. What is the equation of diagonal QS?

A. 5x - 2y = 16

B. 5x - 2y = -16

C. 5x + 2y = -16

D. 5x + 2y = 16

Question 98

If 14.35 - (1.956 - x ) - 83.92 = 3.858 then what is the value of x?

A. -92.456

B. 75.384

C. 71.472

D. 104.084

Question 99

Two fractions are such that their product is 2/5 and sum is 1/15. What are the two fractions.

A. 4/3, -3/10

B. 2/7, -7/5

C. 4/7, -7/10

D. 2/3, -3/5

Question 100

Simplyfiy : 314÷114-12212-14+16

A. 78

B. 88

C. 98

D. 108

Question 101

The highest score in an inning was 3/11 of the total and the next highest was 3/11 of the reminder . If the score differ by 9, the total score was :

A. 110

B. 121

C. 132

D. 143

Question 102

What is the simplified value of (cos4 A – sin4 A)?

A. 0

B. 2 cos2 A

C. cos2A

D. 1

Question 103

If a + b + c = 9, ab + bc + ca = 26, a3 + b3 = 91, b3 + c3 = 72 and c3 + a3 = 35, then what is the value of abc?

A. 48

B. 24

C. 36

D. 42

Question 104

If sin x + cos x = √2 sin x, then the value of tan x is

A. √2 - 1

B. √2 + 1

C. 1

D. √2

Question 105

A tower stands on the top of a building which is 40 metres high. The angle of depression of a point situated on the ground from the top and bottom of the tower are found to be 60 and 45 deg respectively. What is the height (in metres) of tower?

A. 20√3

B. 30(√3 + 1)

C. 40(√3 – 1)

D. 50(√3 – 1)

Question 106

If p and q are the roots of the equation x2 –15x + r = 0 and p –q = 1, then what is the value of r ?

A. 55

B. 56

C. 60

D. 64

Question 107

The value of sec217°-1tan273°-sin17°sec73°

A. 1

B. 0

C. -1

D. 2

Question 108

If in a triangle ABC, Sin A = Cos B then the value of Cos C is

A. √3/2

B. 0

C. 1

D. 1/√2

Question 109

In ΔABC, D and E are points on side AB and AC respectively. DE is parallel to BC. If lengths of AD, DB and DE are 8 cm, 6 cm and 7.2 cm respectively, find length of BC?

A. 12.6 cm

B. 9.3 cm

C. 8.1 cm

D. 5.4 cm

Question 110

If angles of measure (5y + 62°) and (22° + y) are supplementary , then value of y is

A. 16°

B. 32°

C. 8°

D. 1°

Question 111

Which of the following fractions is largest?

A. 3/4

B. 4/5

C. 5/6

D. 7/8

Question 112

There are 90 coins, comprising of 5 and 10 paisa coins. The value of all the coins is Rs. 7. How many 5 paisa coins are there?

A. 50

B. 45

C. 40

D. 35

Question 113

If M = 0.1 + (0.1)2 + (0.01)2 and N = 0.3 + (0.03)2 + (0.003)2, then what is the value of M + N?

A. 0.411009

B. 0.413131

C. 0.313131

D. 0.131313

Question 114

9997 x 10003 = ?

A. 9999991

B. 99999911

C. 99999991

D. 9999911

Question 115

If 3x - 8(2 - x) = -19, then the value of x is

A. -3/11

B. -33/11

C. -3/5

D. -33/5

Question 116

6 times a fraction is greater than 7 times its reciprocal by 11. What is the fraction?

A. 5/3

B. 7/3

C. 5/4

D. 4/5

Question 117

If secA + tanA = a, then the value of cosA is

A. a2+12a

B. 2aa2+1

C. a2-12a

D. 2aa2-1

Question 118

What is the value of 2sec2A?

A. secA/(cosecA - 1) + secA/(cosecA +1)

B. cosecA/(secA -1) + cosecA/(secA +1)

C. cosecA/(cosecA - 1) + cosecA/(cosecA +1)

D. secA/(secA - 1) + secA/(secA +1)

Question 119

Determine the value of 'x' in x = 11+2+12+3+13+2

A. -1

B. 0

C. 1

D. 2

Question 120

What is value of P+QP-Q if PQ=7 ?

A. 1/3

B. 2/3

C. 4/3

D. 5/3

Question 121

If Tan θ = 4/3, then what is the value of Sin θ?

A. 1.25

B. 0.8

C. 4/3

D. 3/4

Question 122

If x – 3 + [1/(x – 3)] = 4, what is the value of [(x – 3)3+ [1/(x – 3)3]?

A. 14

B. 18

C. 52

D. 76

Question 123

If 4x + 5y = 14 and x - 5y = 16 then the value of x and y are

A. 10 and -6/5

B. 6 and 2

C. 10 and 6/5

D. 6 and -2

Question 124

sin(A+B) - sin(A-B) is equal to

A. 2sinAcosB

B. 2cosAcosB

C. 2cosAsinB

D. 2sinAsinB

Question 125

At what point does the line 2x - 3y = 6 cuts the Y axis?

A. (0, 2)

B. (-2, 0)

C. (2, 0)

D. (0, -2)

Question 126

An aeroplane flying horizontally at a height of 3 Km. above the ground is observed at a certain point on earth to subtend an angle of 60°. After 15 sec flight, its angle of elevation is changed to 30°. The speed of the aeroplane (taking √3 = 1.732) is

A. 230.63 m/sec

B. 230.93 m/sec

C. 235.85 m/sec

D. 236.25 m/sec

Question 127

Determine the value of a+1b-1 when ab = 343.

A. 9

B. 64

C. 125

D. 216

Question 128

If (6 - 18x) - (x - 7) = 8, then the value of x is ______.

A. -5/19

B. -2/13

C. 2/13

D. 5/19

Question 129

If cos3A = X, then value of X?

A. 4cos3A - 3cosA

B. 4cos3A + 3cosA

C. 3cosA - 4cos3A

D. cosA + 4cos3A

Question 130

If x3 – 4x2 + 19 = 6(x – 1), then what is the value of [x2 + (1/x – 4)]?

A. 3

B. 5

C. 6

D. 8

Question 131

If sin = 2/3, find the value of secθ and cotθ

A. √5/2, 2/√5

B. 2/√5, 3/5

C. 3√5/5, √5/2

D. 3/5, 3√5/5

Question 132

What is the equation of a line having a slope -1/3 and y-intercept equal to 6?

A. x + 3y = 18

B. x - 3y = 6

C. x + 3y = -18

D. x - 3y = -6

Question 133

David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?

A. 19

B. 28

C. 30

D. 37

Question 134

The value of 3x9n+1+9x32n-19x32n-6x9n-1 is equal to

A. 335

B. 325

C. 315

D. 3

Question 135

If (1 + secA)/tanA = x, then x is

A. cot(A/2)

B. tan(A/2)

C. cosec(A/2)

D. sec(A/2)

Question 136

If sec2A cosec2A = x, then x is

A. sec2A + cosec2A + 2

B. tan2A + cot2A - 2

C. tan2A + cot2A + 2

D. sec2A + cosec2A - 2

Question 137

What is the value of (4a2 + 8b + 14c + 2)/2 ?

A. 2a2 + 4b + 7c + 1

B. a2 + 4b + 7c + 1

C. 2a2 + 4b + 7c + 2

D. a2 + 4b + 7c + 2

Question 138

In ΔDEF measure of angle E is 90 deg. If sinD = 15/17, and DE = 4cm, then what is the length (in cm) of side EF?

A. 8.5

B. 7.5

C. 5

D. 6

Question 139

Simplify: b-[b-(a+b)-{b-(b-a-b)}+2a]

A. 2b

B. 1

C. 0

D. 3b

Question 140

What is the value of Cot 45° + Cosec 60°?

A. (√6 + 1)/√3

B. (1 + √3)/2

C. 5/√3

D. (√3 + 2)/√3

Question 141

If θ is positive acute angle and 4sin2θ = 3, then the value of tan θ - cot θ/2 is

A. 1

B. 0

C. √3

D. 1/√3

Question 142

The point Q(a,b) is first reflected in y-axis to Q1 and Q1 is reflected in xaxis to (-5,3). The coordinates of point Q are

A. (-5,3)

B. (5,-3)

C. (-5,-3)

D. (5,3)

Question 143

Reflection of the point (-3,6) in the x-axis is

A. (3,6)

B. (6,-3)

C. (-3,-6)

D. (-6,3)

Question 144

What is the x – intercept of the linear equation 18x + 25y – 900 = 0?

A. 18

B. 25

C. 50

D. 450

Question 145

If sum of the areas of the circumcircle and the incircle of an equilateral triangle is 770 cm2, then what is the area (in cm2) of the triangle?

A. 125√3

B. 147√3

C. 156√3

D. 169√3

Question 146

What is (x-y)3+y-23+z-x33x-yy-zz-x =?

A. 1

B. 0

C. 1/3

D. 3

Question 147

Expand : S + 23

A. S3+3S2+12S+8

B. S3+3S2+6S+8

C. S3+6S2+12S+8

D. S3+6S2+6S+8

Question 148

Two labourers A and B are paid a total of Rs. 1120 per day. If A is paid 180 percent of what is paid to B, how much (in Rs) is B paid?

A. 400

B. 720

C. 500

D. 620

Question 149

The value of 1/64 is equal to square of

A. 0.125

B. 0.135

C. 0.145

D. 0.225

Question 150

If 3a+4b3c+4d = 3a-4b3c-4d, then

A. ab = cd

B. ad = bc

C. ac = bd

D. a = b = c ≠ d

Question 151

What is the value of tan 4π/3?

A. 1/2

B. √3

C. √3/2

D. 1/√2

Question 152

Find the value of 200 x 20 x 2 x 0.2 x 0.02 x 0.002 = ?

A. 0.064

B. 0.64

C. 64

D. 640

Question 153

M is the largest 4 digit number, which when divided by 4, 5, 6 and 7 leaves remainder as 2, 3, 4, and 5 respectively. What will be the remainder when M is divided by 9?

A. 2

B. 1

C. 3

D. 6

Question 154

If x+1x ≠0 and x3+1x3 = 0, then the value of x+1x4 is :

A. 9

B. 12

C. 15

D. 16

Question 155

The point R(a,b) is first reflected in origin to R1 and R1 is reflected in X-axis to (-5,1). The co-ordinates of point R are?

A. (5,-1)

B. (-1,5)

C. (1,-5)

D. (5,1)

Question 156

What is the y – intercept of the linear equation 59x + 14y – 112 = 0?

A. 8

B. 14

C. 28

D. 59

Question 157

The point R(a,b) is first reflected in origin to R1 and R1 is reflected in x-axis to (-3,4). The co-ordinates of point R are

A. (3,4)

B. (-3,-4)

C. (-3,4)

D. (3,-4)

Question 158

If x2 – 16x – 59 = 0, then what is the value of (x – 6)2 + [1/(x – 6)2]?

A. 14

B. 18

C. 16

D. 20

Question 159

What is the value of sin (630 + A) + cos A?

A. √3/2

B. 1/2

C. 0

D. 2/√3

Question 160

A = (x8 – 1)/(x4 + 1) and B = (y4 – 1)/(y2 + 1). If x = 2 and y = 9, then what is the value ofA2 + 2AB + AB2?

A. 96475

B. 98625

C. 92425

D. 89125

Question 161

Expanded and simplification of (x + 3)(x - 1) will be equal to

A. x2+ 2x - 3

B. x2 + 3x + 2

C. x2 - 2x + 3

D. x2 + 3x - 2

Question 162

Find co-ordinates of the mid point of the segment joining points C (3,-5) and D (-7,3).

A. (-2, -1)

B. (5, -4)

C. (-5, 4)

D. (2, 1)

Question 163

The average number of visitors of a library in the first 4 days of a week was 58. The average for the 2nd, 3rd, 4th and 5th days was 60.If the number of visitors on the 1st and 5th days were in the ratio 8 : 9. Then what is the number of visitors on the 5th day of the library ?

A. 54

B. 64

C. 68

D. 72

Question 164

What is the value of tan4A + tan2A?

A. sec4A - sec2A

B. sec4A + sec2A

C. cosec4A - sec2A

D. sec4A + cosec2A

Question 165

Two parallel chords on the same side of the centre of a circle are 5 cm apart. If the chords are 20 and 28 cm long, what is the radius of the circle?

A. 14.69 cm

B. 15.69 cm

C. 18.65 cm

D. 16.42 cm

Question 166

If Cos θ = 35/37 , then what is the value of Cot θ?

A. 12/35

B. 35/12

C. 37/12

D. 12/37

Question 167

If cosAcotA/(1 - sinA) = x, then the value of x is

A. 1 - cosecA

B. 1 + cosecA

C. 1 + secA

D. 1 - secA

Question 168

If a + b = 4 and ab = -5, then what is the value of a3 + b3?

A. 34

B. 36

C. 124

D. 126

Question 169

If y = √3 - √2, then find the value of 1y3 - y3.

A. 11

B. 11√2

C. 22

D. 22√2

Question 170

If sinP = 2/3, find the value of secP and cotP.

A. √5/2, 2/√5

B. 2/√5, 3/5

C. 3√5/5, √5/2

D. 3/5, 3√5/5

Question 171

Coefficient of x2 in (x + 7)(5 - 3x)(3x - 6) is

A. 96

B. -30

C. 42

D. -18

Question 172

If a:b = 3:8, find the value of (5a 3b)/(2a + b).

A. 9/14

B. 14/9

C. -9/14

D. -14/9

Question 173

If 2x+14x = 1, then the value of x2+164x2 is

A. 0

B. 1

C. 1/4

D. 2

Question 174

If Cot θ = 24/7, then Sin θ = ?

A. 24/25

B. 8/25

C. 7/25

D. 9/25

Question 175

If cosec π/4 - sin π/3 = x, then the value of x is

A. 4/√3

B. (2√2-√3)/2

C. (1-√3)/√3

D. √3+2

Question 176

Simplify 486b3x2a4z3/27a3b2z

A. 18bx2az2

B. 18bx2a2z

C. 36ba2z

D. 36bxaz

Question 177

What is the value of 299996 x 300004?

A. 89999999984

B. 89999699984

C. 89999999884

D. 89999999974

Question 178

What is the value of (cot30°+ 2/√3) ?

A. 5/√3

B. (1+2√3)/2

C. 5/6

D. 2/√3

Question 179

What is the value of {(sin 4x + sin 4y) [(tan 2x – 2y)]}/(sin 4x – sin 4y)?

A. tan 2 (2x + 2y)

B. tan2

C. cot (x – y)

D. tan (2x + 2y)

Question 180

If a = √2 + 1 and b = √2 - 1, then the value of 1a+1+1b+1 will be

A. 0

B. 1

C. 2

D. -1

Question 181

If Sec θ = 5/3, then what is the value of Cosec θ?

A. 0.8

B. 1.25

C. 4/3

D. 3/4

Question 182

What is the simplified value of cosec Acot A + tan A2 ?

A. 2cos 2A

B. 1 – sin2 A

C. sec2A

D. secA tanA

Question 183

A fraction is greater than its reciprocal by (72)/(77). What is the fraction?

A. 7/11

B. 11/7

C. 4/7

D. 7/4

Question 184

If x1/4 + x-1/4 = 2, then what is the value of x81 + (1/x81)?

A. -2

B. 0

C. 1

D. 2

Question 185

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 130 marks, the no of questions he attempts correctly is :

A. 35

B. 38

C. 40

D. 42

Question 186

If 3.5x = 0.07y, then find the result of [y-x / y+x]

A. 51/49

B. 49/53

C. 49/51

D. 53/57

Question 187

If Sinx = 4/5, then Secx/Sinx = ?

A. 23/12

B. 25/4

C. 4/5

D. 25/12

Question 188

Simplify: (213 x 213 + 187 x 187)

A. 80338

B. 80438

C. 60338

D. 60438

Question 189

If the value of √30 is approximately 5.477, then what is the approximate value of 56 ?

A. 0.853

B. 0.891

C. 0.913

D. 0.937

Question 190

Given: 2x - 4 ≤ 2 - x/3 and 2(2x + 5) > 3x - 5, then x can take which of the following values?

A. -14

B. 3

C. 4

D. 14

Question 191

ΔDEF is right angled at E. If m∠D = 45°, then find the value of (tanF + 1/3).

A. 4/3

B. 3√3/2

C. (√2+1)/√2

D. (3√2+1)/3

Question 192

If the roots of the equation a(b – c)x2 + b(c – a)x + c(a – b) = 0 are equal, then which of the following is true?

A. b = ( a + c)/ ac

B. 2/ b = (1/ a) + (1/ c)

C. 2 b = (1/ a) + (1/ c)

D. abc = ab + bc + ca

Question 193

If x + 1x = -2, then the value of x631 + 1x632?

A. -2

B. -1

C. 0

D. 2

Question 194

What is the value of Sec 30° + Tan 60°?

A. 5/√3

B. (√6 + 1)/√3

C. (√3 + 2)/√3

D. (1 + √3)/2

Question 195

N is the smallest three digit prime number. When N is divided by 13, then what will be the remainder?

A. 8

B. 9

C. 7

D. 10

Question 196

If x = 313- 3-13, then 3x2 + 9x is equal to

A. 5

B. 6

C. 7

D. 8

Question 197

If P = 22 + 62 + 102 + 142 + ... 942 and Q = 12 + 52 + 92 + ... 812, then what is the value of P – Q?

A. 24645

B. 26075

C. 29317

D. 31515

Question 198

What is the value of Tan 45° - 1/√3 Sec 60°?

A. (1 - 2√3)/2

B. (√2 - √3)/√6

C. (3 - 2√3)/3

D. (1 - 2√2)/2

Question 199

If 3√7 + √343 = 19.21, then find the value of √252 + 20√7.

A. 39.4

B. 49.9

C. 56.8

D. 92.3

Question 200

Compute : 4082 / 157 - 23

A. -3

B. 3

C. 2041/67

D. 2014/67

Question 201

On dividing a number by 38, we get 70 as quotient and 12 as remainder. What is the number?

A. 2648

B. 2636

C. 2684

D. 2672

Question 202

If Cosec θ = 25/7 , then what is the value of Cot θ?

A. 24/25

B. 7/24

C. 7/25

D. 24/7

Question 203

What is the value of 1xp-q+1+1xq-p+1?

A. 0

B. 1

C. x

D. cant determine

Question 204

2sin[(C+D)/2].cos[(C-D)/2] is equal to

A. sinC - sinD

B. cosC + cosD

C. cosC - cosD

D. sinC + sinD

Question 205

A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:

A. 22

B. 23

C. 24

D. 26

Question 206

If -5x3+2 = x-6, then find the value of x?

A. 1

B. 2

C. 3

D. 4

Question 207

What is the value of 1/√2 Cot 30° + 1/√3 Cosec 60°?

A. (3√3 + 2√2)/3√2

B. (3√3 - 2√2)/3√2

C. (3√3 + 2√2)/√2

D. (3√3 - 2√2)/√2

Question 208

If (1 - sinA)/(1 + sinA) = x, then x is

A. (cosecA - cotA)2

B. secA - tanA

C. (secA - tanA)2

D. cosecA - cotA

Question 209

Find the value of 'a' for which x+3x+a24 is a perfect square.

A. √3

B. 2√3

C. 3√3

D. 4√3

Question 210

The value of ds+t÷ds÷dt

A. 0

B. d

C. 1

D. ds+t

Question 211

If Tan A = 15/8 and Tan B = 7/24, then Tan (A - B) = ?

A. 304/297

B. 304/425

C. 416/87

D. 87/416

Question 212

Determine the value of y-1y2 when y4+1y4=34

A. 1

B. 2

C. 3

D. 4

Question 213

If 9x - [5(2x + 1)/2] = 9/2, then the value of x is?

A. 7/4

B. -7/4

C. 4/7

D. -4/7

Question 214

If sinC + sinD =X, then the value of X is?

A. 2cos[(C+D)/2]sin[(C-D)/2]

B. 2sin[(C+D)/2]cos[(C-D)/2]

C. 2cos[(C+D)/2]cos[(C-D)/2]

D. 2sin[(C+D)/2]sin[(D-C)/2]

Question 215

Common factor of 12a4b6, 18a6c2, 36a2b2 is

A. 36a2

B. 108b2

C. 6a2b2

D. 6a2

Question 216

If 2x - 5y = 5 and 2x - y = 9, then x - y is ______.

A. 2

B. 4

C. 6

D. 3

Question 217

If 3x2 - ax + 6 = ax2 + 2x + 2 has only one (repeated) solution, then the positive integral solution of a is

A. 4

B. 5

C. 2

D. 3

Question 218

If 1aa2+1 = 3, then the value of a6+1a3 is

A. 9

B. 18

C. 27

D. 1

Question 219

There are 10 dozen apples, 15 dozen mangoes and 20 dozen oranges for selling. If 1/2, 1/3 and 1/4 of them are sold respectively. How many of the total fruits are remaining?

A. 420

B. 380

C. 180

D. 360

Question 220

If 3x-y=27, 3x+y=243 then find the x value

A. 2

B. 8

C. 4

D. 1

Question 221

What is the simplified value of sin2(90–θ)–[sin(90–θ)sinθ/tanθ]?

A. 1

B. cosec θ

C. 0

D. cos θ

Question 222

A spherical lead ball of radius 6 cm is melted and small lead balls of radius 3 mm are made. The total number of possible small lead balls is

A. 4250

B. 4000

C. 8005

D. 8000

Question 223

Calculate the value of 0.77777 + 0.7777 + 0.777 + 0.77 + 0.7 + 0.07.

A. 3.86274

B. 3.80247

C. 3.85274

D. 3.87247

Question 224

The rate of discount on an article whose marked price is Rs. 170 and selling price is Rs. 130?

A. 24.26%

B. 22.45%

C. 23.53%

D. 23.60%

Question 225

x, y and z are real numbers. If x3 + y3 + z3 = 13, x + y + z = 1 and xyz = 1, then what is the value of xy + yz + zx?

A. -1

B. 1

C. 3

D. -3

Question 226

If cos 45° - sec 30° = x, then value of x is

A. (1+√2)/2

B. (2√2√3)/2

C. (√32√2)/√6

D. 4/√3

Question 227

A fraction, when taken away from 1/3 gives 1/12. The fraction is

A. 5/12

B. 1/4

C. 3/4

D. 1/9

Question 228

CAlculate : 72-6-45÷5-72-2×2÷2+2

A. -16/18

B. -14/7

C. -12/7

D. -12/18

Question 229

If ab+c=bc+a=Cb+athen which one of the following statements is correct?

A. Each fraction is equal to 1 or -1

B. Each fraction is equal to 1/2 or 1

C. Each fraction is equal to 1/2 or -1

D. Each fraction is equal to 1.2 only

Question 230

If (x – 2)2 + (y + 3)2 + (z – 15)2 = 0, then what is the value of x + y + z – 5?

A. 5

B. 9

C. 15

D. 20

Question 231

If x+1/x = 2, then the value of x7+2/x6 is equal to?

A. 0

B. 1

C. 2

D. 3

Question 232

Solve the following equation to find x: (x − 2)2 − 36 = 0 : xεN

A. 4

B. 8

C. -4

D. -8

Question 233

What is the value of (cos45° + 1/3) ?

A. 2+√3

B. (2√2+1)/√2

C. (3+√2)/3√2

D. 5/√3

Question 234

If 3n = 2187, then the value of n is:

A. 13

B. 14

C. 15

D. 16

Question 235

The Simplified form of (b3x2a4z3)*(b4x3a3z2)/(a2b4z3) is

A. b2x4a6z

B. b3x2a4z3

C. b3x5a5z2

D. bazx

Question 236

(secA - tanA)/(cosecA + cotA) is equal to

A. (secA - cotA) / (cosecA + tanA)

B. (secA - cosA) / (cosecA + sinA)

C. (cosecA - cotA) / (secA + tanA)

D. (secA + cosA) / (cosecA - sinA)

Question 237

If Sin θ = 12/13, then what is the value of Cot θ?

A. 13/12

B. 5/13

C. 5/12

D. 13/5

Question 238

217 x 217 + 183 x 183 = ?

A. 84521

B. 87487

C. 80578

D. 78458

Question 239

If sin θ + sin 5θ = sin 3θ and 0 < θ < (π/2), then what is the value of θ (in degrees)?

A. 30

B. 45

C. 60

D. 75

Question 240

If (7x - 13) (12x + 3) = 14, then the value of x is ______ .

A. -6

B. 6

C. -2/5

D. 2/5

Question 241

If x = 1 - q and y = 2q + 1, then for what value of q, x is equal to y ?

A. 0

B. 1

C. -1

D. -2

Question 242

Simplify : 213 - 112 of 35 + 125 ÷ 213

A. 1/10

B. 3/10

C. 11/10

D. 1

Question 243

There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:

A. 20

B. 80

C. 100

D. 120

Question 244

The factors of x2 + 8x + 12 are

A. (x+6)(x+2)

B. (x-6)(x+2)

C. (x-4)(x-4)

D. (x+6)(x-2)

Question 245

If x = 3+13, then the value of x-12642x-1x-233 is

A. √3/6

B. 2√3/6

C. 5/6

D. 2/3

Question 246

The value of tan(-405°)

A. 1

B. -1

C. 2

D. 0

Question 247

If XY = a+23 and YX = 13, then find the value of X2 + Y2X2 - Y2.

A. 1

B. 2

C. 3

D. 4

Question 248

If sin P + cosec P = 2, then the value of sin7P + cosec7P is

A. 1

B. 2

C. 3

D. 0

Question 249

If (x/5) + (5/x) = – 2, then what is the value of x3?

A. –125

B. 5

C. 1/125

D. 625

Question 250

The simplest value of 38-212+20318-227+45 is

A. 3/2

B. 2/3

C. 1/3

D. 2

Question 251

If xy = -18 and x2+ y2= 85, then find the value of (x + y).

A. 8

B. 10

C. 9

D. 7

Question 252

Find the value of 532+108

A. 732

B. 1732

C. 2732

D. 3732

Question 253

If 17/3 + [3(2x - 5/3)]/2 = 1/6, then what is the value of x?

A. 1

B. 3

C. -3

D. -1

Question 254

If a – (1/a) = b, b – (1/b) = c and c – (1/c) = a, then what is the value of (1/ab) + (1/bc) + (1/ca)?

A. – 3

B. – 6

C. – 1

D. – 9

Question 255

Factorise 24x2 - 54x - 15

A. 3(2x + 5)(4x - 1)

B. 3(2x - 5)(4x + 1)

C. 2(3x - 5)(4x + 1)

D. 4(2x - 5)(3x + 1)

Question 256

2cos[(C+D)/2]sin[(C-D)/2] is equal to

A. sinC + sinD

B. sinC - sinD

C. cosC - cosD

D. cosC + cosD

Question 257

Value of (4a2+ 12ab + 9b2)/(2a + 3b) is

A. 2a - 3b

B. 2a + 3b

C. 2a

D. 3b

Question 258

2sin[(C+D)/2].sin[(D-C)/2] is equal to

A. cosC + cosD

B. cosC - cosD

C. sinC - sinD

D. sinC + sinD

Question 259

If 3 tan θ = cot θ where 0 < θ < π/2, then what is the value of θ ?

A. π/6

B. π/4

C. π/2

D. 1

Question 260

If x + y + z = 0, then what is the value of (3y2 + x2 + z2 )/(2y2 – xz)?

A. 2

B. 1

C. 3/2

D. 5/3

Question 261

What is the slope of the line perpendicular to the line passing through the points (8,2) and (3,1)?

A. 5

B. 3/5

C. 5/3

D. 1/5

Question 262

In ∆ABC, ∠B=35°, ∠C=65° and the bisector of ∠BAC meets BC in D. Then ADB is

A. 40°

B. 75°

C. 90°

D. 105°

Question 263

What is the value of ( 1/√3 + cot60) ?

A. 3√3/2

B. 7/2√3

C. (4+√3)/2√3

D. 2/√3

Question 264

5 + 2 x 10 =

A. 70

B. 20

C. 25

D. 52

Question 265

If √[(1 + cosA)/2] = x, then find the value of x.

A. sin(A/2)

B. tan(A/2)

C. cot(A/2)

D. cos(A/2)

Question 266

A tank is 2/5 full. If 16 litres of water is added to the tank, it becomes 6/7 full. The capacity of the tank is:

A. 28 litres

B. 32 litres

C. 35 litres

D. 42 litres

Question 267

What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)?(55.01+16.0003)×22.01÷10.998 =?

A. 190

B. 130

C. 110

D. 142

Question 268

What is the value of cos 11π/6?

A. -1/√2

B. -√3/2

C. 2/√3

D. √3/2

Question 269

What is the value of cosecA/√(cosec2A - 1)?

A. sinA

B. secA

C. tanA

D. cosA

Question 270

If sec (4x - 50°) = cosec(50° - x), Then the value of x is

A. 45°

B. 90°

C. 30°

D. 60°

Question 271

θ is a positive acute angle and sinθ cosθ = 0, then the value of secθ + cosecθ is

A. 2

B. √2

C. 2√2

D. 3√2

Question 272

[15% of 300% of 560] × 2 ÷ 5 =

A. 100

B. 90

C. 85

D. 105

Question 273

If x = 313- 3-13, then 3x3 + 9x value is

A. 8

B. 9

C. 27

D. 16

Question 274

The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?

A. Rs. 1200

B. Rs. 2400

C. Rs. 4800

D. Cannot be determined

Question 275

What is the value of 143 + 163 + 183 + ... + 303?

A. 134576

B. 120212

C. 115624

D. 111672

Question 276

0.196 + 1.96 + 19.6 + 196 = ?

A. 217.756

B. 216.856

C. 216.756

D. 217.676

Question 277

0 is the circumference of a triangle ∆ABC. The point A and the chord BC are on the opposite side of O. If ∠BOC=150° then the value of ∠BAC is

A. 65°

B. 60°

C. 70°

D. 75°

Question 278

If 8x/3 + [7(5 - 2x/3)]/2 = 1/2 , then what is the value of x?

A. -17

B. 51

C. -51

D. 17

Question 279

If tan2A + cot2A + 2 = x, then the value of x is

A. tan2Acosec2A

B. secAcosecA

C. sec2Acosec2A

D. tanAcosecA

Question 280

If 2x/3 - [5(4x/5 - 4/3)]/2 = 1/3, then what is the value of x?

A. 9/4

B. 4/9

C. -9/4

D. -4/9

Question 281

What is the value of √2 Sec 45 - Tan 30?

A. (2√3 - 1)/3

B. (√3 - 1)/√3

C. (2√3 - 1)/√3

D. (√3 - 1)/3

Question 282

If SinX-CosX=1, where 'X' is an acute angle, the value of SinX+CosX is

A. 0

B. 1

C. 1/2

D. 2

Question 283

What is the value of 13313 + 729 - 5123

A. 15

B. 20

C. 30

D. 23

Question 284

If √(cosec2A - 1) = x, then the value of x is

A. tanA

B. sinA

C. cosA

D. cotA

Question 285

If x + y = 12 and x2 + y2 = 94, then xy is

A. 25

B. 50

C. 144

D. 238

Question 286

Factors of 48x3- 8x2- 93x- 45 are

A. (4x + 3)(4x - 3)(3x - 5)

B. (4x - 3)(4x - 3)(3x- 5)

C. (4x + 3)(4x + 3)(3x - 5)

D. (4x - 3)(4x + 3)(3x + 5)

Question 287

What is the unit digit of 15+25+35+...+205 ?

A. 0

B. 5

C. 2

D. 4

Question 288

If a2+1a2 = 38, then find the value of a-1a?

A. 2

B. 4

C. 6

D. 8

Question 289

If cosec θ + cot θ= 2, then cosec θ= ?

A. 1.5

B. 1.25

C. 1

D. 2

Question 290

Square of (7 - 4x) is

A. 16x2 - 28x + 49

B. 49 - 28x - 16x2

C. 49 - 56x - 16x2

D. 16x2 - 56x + 49

Question 291

If a - b = 6 and ab =16, then a3 - b3 is

A. 504

B. 702

C. 728

D. 511

Question 292

If x3 + y3 + z3 = 3(1 + xyz), P = y + z – x, Q = z + x – y and R = x + y – z, then what is the value of P3 + Q3 + R3 – 3PQR?

A. 9

B. 8

C. 12

D. 6

Question 293

What is the value of cos 4π/3?

A. -1/2

B. √3/2

C. - 1/√2

D. √3/2

Question 294

(secA - 1)/(secA + 1) is equal to?

A. (1 - sinA)/(1 + sinA)

B. (1 + cosA)/(1 - cosA)

C. (1 + sinA)/(1 - sinA)

D. (1 - cosA)/(1 + cosA)

Question 295

If x2+ x = 19, then what is the value of (x + 5)2+ [1/(x + 5)2]?

A. 77

B. 79

C. 81

D. 83

Question 296

If a2b+c=b2C+a=a2a+b=1 then 11+a+11+b+11+c is

A. 1

B. 2

C. 3

D. 4

Question 297

What is the value of (32 cos6x – 48 cos4x + 18 cos2x – 1)/[4 sin x cos x sin (60 – x) cos (60 – x) sin (60 + x) cos (60 + x)]?

A. 4 tan 6x

B. 4 cot 6x

C. 8 cot 6x

D. 8 tan 6x

Question 298

If a - b = 2 and ab = 8, then what is the value of a3 - b3?

A. 65

B. 34

C. 43

D. 56

Question 299

What is the value of sin(11π/6)?

A. 2/√3

B. -2/√3

C. -1/2

D. 1/2

Question 300

What is the value of [2 sin (45 + θ) sin (45 – θ)]/cos 2θ?

A. 0

B. tan 2θ

C. cot 2θ

D. 1

Question 301

What is the value of cosec 5π/3?

A. √2

B. -2/√3

C. -√2

D. 1/√3

Question 302

The value of x for which the expressions 5x + 17 and 17x - 5 become equal is _____.

A. 11/6

B. -11/6

C. 6/11

D. -6/11

Question 303

If sinC - sinD = x, then value of x is

A. 2sin[(C+D)/2]cos[(C-D)/2]

B. 2cos[(C+D)/2]cos[(C-D)/2]

C. 2cos[(C+D)/2]sin[(C-D)/2]

D. 2sin[(C+D)/2]sin[(D-C)/2]

Question 304

In ∆UVW measure of angle V is 900. If cosecU = 13/12, and UV = 2.5 cm, then what is the length (in cm) of side VW?

A. 6.5

B. 6

C. 4

D. 5.6

Question 305

The point P(a,b) is first reflected in origin to P1 and P1 is reflected in y-axis to (6,-5). The co-ordinates of point P are

A. (-6,-5)

B. (6,5)

C. (6,-5)

D. (-6,5)

Question 306

Δ ABC is right angled at B. If m∠A = 60°, then what is the value of sec C.sin A?

A. 2/√3

B. √3/2

C. 2/3

D. 1

Question 307

The two lines 4x+3y=0 and 7x+5y=0 will ______ in their graphical representation.

A. be parallel to each other

B. intersect each other at one point only

C. intersect each other at three points only

D. coincide each other

Question 308

What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)? √580×∛510+ 49.999 x 3.999=?

A. 384

B. 392

C. 410

D. 372

Question 309

The value of 2.31 x 0.34 = ?

A. 1.7854

B. 0.7854

C. 0.7845

D. 0.7584

Question 310

If 1/√(1 - sin2A) = x, then the value of x is

A. tanA

B. cosecA

C. secA

D. cosA

Question 311

Sin6A + Cos6A - 1 is equal to

A. -3Sin2ACos2A

B. 1 - 3 SinACosA

C. 1 + 3Sin2ACos2A

D. 0

Question 312

If xy = 22 and x2+ y2= 100, then what will be the value of (x + y)?

A. 12

B. 144

C. 72

D. 6

Question 313

The inradius of a equilateral triangle is 10 cm. What is the circum-radius (in cm) of the same triangle?

A. 5

B. 10√3

C. 20

D. 20√3

Question 314

What is the value of [12/(√5 + √3)] + [18/(√5 – √3)]?

A. 15(√5 – √3)

B. 3(5√5 + √3)

C. 15(√5 + √3)

D. 3(3√5 + √3

Question 315

The value of Cot17°Cot73°Cos222° + 1Cot17°Sec268° is

A. 0

B. 1

C. 2

D. √3

Question 316

Simplify : 69 X 69 X 69 -65 X 65 X 669 X 69 + 69 X 65 + 65 X 65

A. 1

B. 4

C. 0.216

D. 0.164

Question 317

If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (c/a) + (a/c), then what is the value of xyz – x2 – y2 – z2?

A. – 4

B. 2

C. – 1

D. – 6

Question 318

What is the value of [(sin 7x – sin 5x)÷(cos 7x + cos 5x)] – [(cos 6x – cos 4x)÷(sin 6x + sin 4x)]?

A. 1

B. 2 tan x

C. tan 2 x

D. tan (3 x/2)

Question 319

If pq(p+q) = 1, then the value of 1p3q3-p3-q3 is equal to

A. 1

B. 2

C. 3

D. 4

Question 320

cos3A is equal to

A. cos3A - 3sin2cosA

B. cos3A + 4sin2cosA

C. cos3A + 3sin2cosA

D. cos3A - 4sin2cosA

Question 321

If (9 - 3x) - (17x - 10) = -1, then the value of x is

A. 1

B. -1

C. 9/10

D. -0.9

Question 322

If l + m + n = 9 and l2+m2+n2 = 31, then the value of lm + mn + nl will be

A. 22

B. 50

C. 25

D. -25

Question 323

If tan θ + sec θ = (x – 2)/(x + 2), then what is the value of cos θ?

A. (x2 – 1)/(x2 + 1)

B. (2x2 – 4)/(2x2 + 4)

C. (x2 – 4)/(x2 + 4)

D. (x2 – 2)/(x2 + 2)

Question 324

Δ DEF is right angled at E. If m∠D = 45°, then what is the value of cosecF X cotD?

A. 1/√2

B. 2

C. 1/2

D. √2

Question 325

What is the value of cot 11π/6?

A. -√3

B. -1

C. √3

D. -1/2

Question 326

If a + b + c = 11 and ab + bc + ca = 17, then what is the value of a3 + b3 + c3 – 3abc?

A. 121

B. 168

C. 300

D. 770

Question 327

The zeros of the cubic polynomial 2x3-x2-2x+1 are a, b and c respectively. Find a+b+c :

A. -1

B. 2

C. 1

D. none

Question 328

If x2+1x2 = 2, then the value of x - 1x is

A. -2

B. 0

C. 1

D. -1

Question 329

The costs of daily ticket of local train is Rs. 50 and Monthly Pass costs is Rs. 1125. If I buy the Monthly Pass and travel for 30 days in a month then I save?

A. 10 percent

B. 25 percent

C. 14 percent

D. 15 percent

Question 330

If sec θ (cos θ + sin θ) = √2, then what is the value of (2 sin θ)/(cos θ – sin θ)?

A. 3√2

B. 3/√2

C. 1/√2

D. √2

Question 331

If P = 7 + 4√3 and PQ = 1, then what is the value of (1/P2) + (1/Q2)?

A. 148

B. 189

C. 194

D. 204

Question 332

Solve the following : 80÷[48−56−(60−36÷12×4)]=?

A. 5

B. 8

C. 4

D. 2

Question 333

What is the value of √[(1 - cosA)/(1 + cosA)]?

A. cosecA - cotA

B. cosecA + cotA

C. secA - cotA

D. secA + cotA

Question 334

If (4a +7b) (4c-7d) = (4a -7b) (4c +7d, then which one of the following is correct ?

A. a/b = c/d

B. a/d = c/b

C. a/b = d/c

D. none

Question 335

If 2cos2A - 1 = x, then the value of x is

A. cosec4A - sin4A

B. cos4A - sin4A

C. cos4A - tan4A

D. cosec4A - tan4A

Question 336

In ∆ABC if the median AD=1/2 BC, then ∠BAC is

A. 90°

B. 45°

C. 60°

D. 75°

Question 337

Water boils at 212°F or 100°C and melts at 32°F or 0°C . If the temparature of the particular day is 35°C , it is equal to :

A. 85°F

B. 95°F

C. 96°F

D. 97°F

Question 338

Reflection of the point (4,6) in the origin is

A. (4,6)

B. (-4,-6)

C. (-4,6)

D. (4,-6)

Question 339

Find the value of x3 - y3, if x - y = 4 and xy = 12.

A. 198

B. 208

C. 218

D. 228

Question 340

ΔABC is right angled at B. If m ∠A = 60°, then what is the value of 1/√3 Cosec C?

A. 2/√3

B. 2/3

C. √2/√3

D. √2/3

Question 341

If x = 2+32-3, then what is the value of x2+x-9 ?

A. 0

B. 3√2

C. 3√3

D. 5√3

Question 342

If A = 0.216 + 0.0080.36+0.04-0.12 & B = 0.729-0.0270.81+0.09+0.27, then what is the value of A2+B22 ?

A. 0.8

B. 1

C. 1.4

D. 2.2

Question 343

If Sec θ = 13/12, then Cot θ = ?

A. 12/5

B. 13/5

C. 5/13

D. 5/12

Question 344

For what value of k, the expression x6– 18x3 + k will be a perfect square?

A. -9

B. 81

C. 9

D. -81

Question 345

Which of the following is not a quadratic equation?

A. 2x(x + 4) -11 = x(x - 3) + 6

B. 4x(x + 4) -11 = 5x(x - 3) + 5

C. x(x + 2) -15 = x(x - 5) + 11

D. 2x2 + 8x - 11 = 0

Question 346

The average revenues of 13 consecutive years of a company is Rs 70 lakhs. If the average of first 7 years is Rs 65 lakhs and that of last 7 years is Rs 77 lakhs, find the revenue for the 7th year.

A. Rs 86 lakhs

B. Rs 84 lakhs

C. Rs 82 lakhs

D. Rs 80 lakhs

Question 347

Derivative of sinx by first principle?

A. -sinx

B. -cosx

C. cosx

D. sinx

Question 348

Sec 45% + Tan 30% =

A. (√6 + 1)/√3

B. (1 + √3)/2

C. (√3 + 2)/√3

D. 5/√3

Question 349

What is the value of (1 + cotA)2 + (1 - cotA)2?

A. 2cosec2A

B. 2sec2A

C. 1 - 2cosec2A

D. 1 - 2sec2A

Question 350

What will be the roots of the quadratic equation x2 - 25x + 156 = 0?

A. 12, 13

B. 25, 1

C. 9, 16

D. 31, 6

Question 351

If x3 – y3 = 81 and x – y = 3, then what is the value of x2 + y2?

A. 18

B. 21

C. 27

D. 36

Question 352

What is the equation of the line whose y-intercept is 3/4 and making an angle of 45° with the positive x-axis?

A. 4x - 4y = 3

B. 4x - 4y = -3

C. 3x - 3y = 4

D. 3x - 3y = -4

Question 353

Compute : (50 + 0.5 x 20) / 0.7

A. 8.571

B. 85.1

C. 85.71

D. 72.85

Question 354

2660 of 17 of 12 of 19.5 of 12 = ?

A. 1

B. 10

C. 0.1

D. 100

Question 355

In an acute-angled triangle ABC is Sin(B+A+C)=32 and tan(C+A-B)=1, then C is equal to

A. 37.5°

B. 67.5°

C. 52.5°

D. 72.5°

Question 356

If sum of the roots of a quadratic equation is -7 and product of the roots is 12. Find the quadratic equation.

A. x2 + 7x + 12 = 0

B. x2 - 7x + 12 = 0

C. x2 - 7x - 12 = 0

D. x2 + 7x - 12 = 0

Question 357

If the value 5 = 2.236,then calculate the value of 405 - 1280-125

A. 2.236

B. 4.472

C. 1.118

D. 8.994

Question 358

If Cosecθ + Cotθ = 2, then Cotθ = ?

A. 0

B. 0.5

C. 1

D. 0.75

Question 359

In an isosceles trapezium _____.

A. Diagonals are congruent

B. Opposite sides are parallel

C. Diagonals are bisectors of each other

D. Diagonals bisect opposite angles

Question 360

If a sum of money deposited in a bank at simple interest is doubled in 6 years, then after 12 years, the amount will be

A. 5/2times the original amount

B. 3times the original amount

C. 7/2times the original amount

D. 4times the original amount

Question 361

What is the simplified value of Sec ACot A + Tan A2 ?

A. 1 – cos2A

B. 2sin2A

C. sec2A

D. 0

Question 362

If α and β are roots of the equation 3x2 – 13x + 14 = 0, then what is the value of (α/β) + (β/α)?

A. 65/28

B. 53/14

C. 9

D. 85/42

Question 363

If ax= by= cz and b2= ac, then what is 1x+1z equal to ?

A. 1/y

B. -1/y

C. 2/y

D. -2/y

Question 364

If cos -225° = x, then the value of x is

A. 1/2

B. √3/2

C. -2/√3

D. -1/√2

Question 365

18800÷470÷20=?

A. 1

B. 2

C. 3

D. 4

Question 366

Δ DEF is right angled at E. If m∠F = 45°, then what is the value of 2 Sin F x Cot F?

A. √2

B. 2

C. 1/√2

D. 1/2

Question 367

Reflection of the point (1,4) in the xaxis is

A. (1,4)

B. (1,-4)

C. (-1,4)

D. (-1,-4)

Question 368

If p = 99, then the value of p(p2+3p+3) will be

A. 999999

B. 1000000

C. 1000001

D. 999998

Question 369

If cos 135° = x, then the value of x is

A. -1/√2

B. -√3/2

C. -1/2

D. 2

Question 370

If a2+b2+c2=14 and a+b+c=6, then the value of ab+bc+ca is,

A. 11

B. 12

C. 13

D. 14

Question 371

If a+1b=1 and b+1c=1 , then the value of c+1a is

A. 0

B. 1

C. -1

D. 2

Question 372

What is the value of sec 330°?

A. 2

B. -2/√3

C. -2

D. 2/√3

Question 373

What should be added to 3(x - 2y) to obtain 2(3x + y) - 5(2x + 3)?

A. 8y - 7x - 15

B. 8y - 7x + 15

C. 8y + 7x + 15

D. 8y + 7x - 15

Question 374

If 1 + (1/2) + (1/3) + ... + (1/20) = k, then what is the value of (1/4) + (1/6) + (1/8) + ... + (1/40)?

A. k/2

B. 2k

C. (k – 1)/2

D. (k + 1)/2

Question 375

78 books, 114 crayons and 141 notebooks were distributed to school children equally. It was found that 6 were left undistributed in each. What was the total number of children?

A. 9

B. 8

C. 13

D. 12

Question 376

If one root of the equation Ax2 +Bx + C = 0 is two and a half times the others, then which of the following is TRUE?

A. 7B2 = 3 CA

B. 7B2 = 4 CA

C. 7B2 = 36 CA

D. 10B2 = 49 CA

Question 377

If sin 3θ sec 2θ = 1, then what is the value of [3 tan2(5θ/2) – 1]?

A. 0

B. 1

C. 2

D. 3

Question 378

If x - y = 6 and xy = 40, then find x2 + y2 ?

A. 116

B. 80

C. 89

D. 146

Question 379

Hemavathi gets 3 marks for each right sum and loses 2 marks for each wrong sum. He attempts 35 sums and obtains 60 marks. The number of sums attempted correctly is ?

A. 23

B. 24

C. 25

D. 26

Question 380

If x + 1x = c + 1c, then the value of x =

A. C, 1/C

B. C, C2

C. C, 2C

D. 0,1

Question 381

If 7x - (3/2) * (4x - 9) = 6.5, then the value of x is?

A. 7

B. 20

C. -7

D. -20

Question 382

If a+1b = 1 and b+1c = 1 then c+1a = ?

A. 0

B. 2

C. 1

D. 3

Question 383

If a + b = 8 and ab = 15, then what is the value of a3 + b3?

A. 98

B. 152

C. 124

D. 260

Question 384

When a number is increased by 28, it becomes 107% of itself. What is the number?

A. 336

B. 420

C. 400

D. 252

Question 385

The standard deviation of the set {10, 11, 9, 11, 9} is

A. 1/√5

B. 2/√5

C. 3/√5

D. 0

Question 386

If sinA = x, then x is equal to

A. √(1 - cos2A)

B. √(1 - sin2A)

C. √(1 + cos2A)

D. √(1 + sin2A)

Question 387

A telephone bill costs Rs.13 for 19 minutes. What is the cost in rupees for 15 minutes 50 seconds?(rounded to one decimal)

A. 10.8

B. 10.7

C. 10.6

D. 10.9

Question 388

45 - [38 - {60 / 3 - (6 - 9 / 3)/ 3}]= ?

A. 24

B. 25

C. 26

D. 21

Question 389

If θ>0, be an acute angle, then the value of it in degrees satisfying cos2θ-3cosθ+2sin2θ=1 is

A. 90°

B. 30°

C. 45°

D. 60°

Question 390

The simplified form of (x + 3)2 + (x - 1)2 is

A. (x2 + 2x + 5)

B. 2(x2 + 2x + 5)

C. (x2 - 2x + 5)

D. 2(x2 - 2x + 5)

Question 391

Coefficient of x2 in (x + 9)(6 - 4x)(4x - 7) is

A. 216

B. -4

C. -92

D. 108

Question 392

If angles M and N measure 60 deg and 30 deg respectively, (sinM) x (cotN) = ?

A. 1/2

B. √3/2

C. 3/2

D. 0

Question 393

What value of 'p' will satisfy the equation p540 = 240p ?

A. 6

B. 10

C. 6√10

D. √10

Question 394

If 2x + 3y – 5z = 18, 3x + 2y + z = 29 and x + y + 3z = 17, then what is the value of xy + yz + zx?

A. 32

B. 52

C. 64

D. 46

Question 395

43% of 616.6 + 37% of 217 =?

A. 345.428

B. 354.428

C. 344.428

D. 364.428

Question 396

If a3- b3= 91 and a - b = 1, then what is the value of ab?

A. 27

B. 6

C. 9

D. 30

Question 397

In ΔABC, D and E are points on side AB and AC respectively. DE is parallel to BC. If lengths of AD, DB and DE are 9 cm, 6 cm and 5.4 cm respectively find length of BC?

A. 3.6 cm

B. 4.8 cm

C. 11.2 cm

D. 9 cm

Question 398

Compute : 28854 / 458 / 9

A. 70

B. 567

C. 7

D. 576

Question 399

The value of -261+(-380)-(-521)+821-(-121)

A. 833

B. 825

C. 822

D. 800

Question 400

If 2x+4-2x+2=3, then the value of x?

A. 0

B. 2

C. -1

D. -2

Question 401

Expand and simplify (3x + 2)2*(4x - 3) - (2x3 - 9x2 + 12x - 24)

A. 34x3 + 30x2 - 32x - 12

B. 34x3 + 30x2 - 32x + 12

C. 34x3 - 30x2 - 32x + 12

D. 34x3 - 30x2 + 32x - 12

Question 402

For what value of C, the system of equation 6x + 2y = 2 & 3x + y = C will be coincident?

A. 4

B. 0

C. 2

D. 1

Question 403

If secA/√(sec2A - 1) = x, then value of x is

A. tanA

B. cosecA

C. sinA

D. cosA

Question 404

If x + y + z = 22 and xy + yz + zx = 35, then what is the value of (x – y)2 + (y – z)2 + (z – x)2?

A. 793

B. 681

C. 758

D. 715

Question 405

The 3rd and 8th term of an arithmetic progression are -13 and 2 respectively. What is the 14th term?

A. 23

B. 17

C. 20

D. 26

Question 406

(798+579)2- (798-579)2798 x 579 =

A. 2

B. 6

C. 4

D. 8

Question 407

An angle is thrice its complementary angle. What is the measure of the angle?

A. 22.5°

B. 135°

C. 45°

D. 67.5°

Question 408

Find the products : 0.5 x 0.05 x 0.005 x 500

A. 0.0625

B. 0.00625

C. 0.06255

D. 0.625

Question 409

4 + 16 x -12 x 24 - 13 - 3 ÷ 20 - 4 = ?

A. 4

B. 6

C. 5

D. 3

Question 410

Slope of the line AB is -2/3. Co-ordinates of points A and B are (x , -3) and (5 , 2) respectively. What is the value of x?

A. 4

B. -14

C. 12.5

D. -4

Question 411

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:5 and area of ΔADE is 8 cm sq, what is the area (in sq cm) of quadrilateral BDEC?

A. 98

B. 94

C. 90

D. 86

Question 412

If sin π/6 + sec π/6 = x, then x is

A. (2√2-1)/2

B. 5/√3

C. (√6-1)/√2

D. (√3+4)/2√3

Question 413

If A/3 = B/2 = C/5, then what is the value of ratio (C + A)2 : (A + B)2 : (B + C)2?

A. 9 : 4 : 25

B. 25 : 4 : 9

C. 64 : 25 : 49

D. 49 : 25 : 64

Question 414

If Cot θ = 24/7, then what is the value of Sec θ?

A. 7/25

B. 25/24

C. 8/25

D. 9/25

Question 415

What is the value of [1 – tan (90 – θ) + sec (90 – θ)]/[tan (90 – θ) + sec (90 – θ) + 1]?

A. cot (θ/2)

B. tan (θ/2)

C. sin θ

D. cos θ

Question 416

What is the value of [tan2 (90 – θ) – sin2 (90 – θ)] cosec2 (90 – θ) cot2 (90 – θ)?

A. 0

B. 1

C. -1

D. 2

Question 417

If the expression px3 – qx2 – 7x – 6 is completely divisible by x2 – x – 6, then what is the value of p and q respectively?

A. 0, 1

B. 1, 0

C. 2, 1

D. 1, 2

Question 418

Two numbers are such that the sum of twice the first number and thrice the second number is 36 and the sum of thrice the first number and twice the second number is 39. Find the difference between the numbers?

A. 15

B. 3

C. 9

D. 6

Question 419

1$ = Rs.67.89. Money changer adds a margin of RS. 1.11. What will be the cost of $150?

A. RS. 10,183

B. RS. 10,350

C. RS. 10,330

D. RS. 10,450

Question 420

What is the simplified value of [2/(cot A – tan A)]?

A. sin A cos A

B. tan 2A

C. sin2 A

D. cos2 A

Question 421

What is the value of cos2A/(1 + sinA)?

A. 1 + sinA

B. 1 - sinA

C. 1 - secA

D. 1 + secA

Question 422

If a=x13y13+x-13y-13 then a3-3ay-x is equal to

A. y^2x

B. x^2y

C. a^2x

D. a^2y

Question 423

What is the simplified value of 22433+393-11253?

A. 593

B. 493

C. 793

D. 1193

Question 424

If sinA + sin2A =1 then what is the value of cos2A + cos4A

A. 1/2

B. 1

C. 2

D. 3

Question 425

If α and β are the roots of equation x2 – 2x + 4 = 0, then what is the equation whose roots are α3/β2 and β3/α2?

A. x2 – 4 x + 8 = 0

B. x2 – 32 x + 4 = 0

C. x2 – 2 x + 4 = 0

D. x2 – 16 x + 4 = 0

Question 426

If x = 999, y = 1000, z = 1001, then the value of x3+y3+z3-3xyzx-y+z is

A. 1000

B. 9000

C. 1

D. 9

Question 427

What is the value of 26 + 152?

A. 17

B. 19

C. 15

D. 21

Question 428

Which of the following equations has real and distinct roots?

A. 3x2 - 6x + 2 = 0

B. 3x2 - 6x + 3 = 0

C. x2 - 8x + 16 = 0

D. 4x2 - 8x + 4 = 0

Question 429

If sinA/(1 + cosA) = x, then x is

A. cosecA + cotA

B. secA - cotA

C. secA + cotA

D. cosecA - cotA

Question 430

Find k, if the line 2x- 3y = 11 is perpendicular to the line 3x + ky = -4?

A. -2

B. 1

C. -1

D. 2

Question 431

The value of (0.00000729/0.00000027) is

A. 0.27

B. 0.027

C. 2.7

D. 27

Question 432

If aq-r+br-p-cp-q, then find the value of (pa + qp + rc) is

A. 0

B. 1

C. 2

D. -1

Question 433

56/32 simplified value?

A. 1.705

B. 1.45

C. 1.75

D. 7.5

Question 434

If the two lines px + 6y+3=0 and 2x + qy+3=0 have infinite solutions then find the value of p and q respectively.

A. 2,6

B. 6,2

C. 2,2

D. 6,6

Question 435

What is the value of sin (–π/3) + cos(–π/6)?

A. 0

B. 1

C. 2

D. 3

Question 436

At what point does the line 3x + 2y = -12 intercept the Y-axis?

A. (0,6)

B. (0,-6)

C. (-4,0)

D. (4,0)

Question 437

5 sin(x)+ 12 cos(x) + r is always greater than or equal to zero. What is the smallest value satisfied by 'r' ?

A. -13

B. 11

C. 13

D. -11

Question 438

What is the equation of the line perpendicular to the line 5x + 3y = 6 and having Y-intercept -3?

A. 3x - 5y = 15

B. 3x + 5y = 15

C. 3x - 5y = -15

D. 3x + 5y = -15

Question 439

If sin(A/2) = x, then the value of x is

A. √[(1 + cosA)/2]

B. √[(1 - cosA)/2]

C. √[(1 - sinA)/2]

D. √[(1 + sinA)/2]

Question 440

What is the value of [cos (90 + A)÷sec (270 – A)] + [sin (270 + A)÷cosec (630 – A)]?

A. 3 sec A

B. tan A sec A

C. 0

D. 1

Question 441

Δ LMN is right angled at M. If m∠N = 60 deg., then Tan L =______.

A. 1/2

B. 1/√3

C. 1/√2

D. 2

Question 442

What is the value of ( 1/2 - cot45) ?

A. (2√2-√3)/2

B. 3/2

C. (3√3-1)/3

D. -1/2

Question 443

What is the value of [(sin 59° cos 31° + cos 59° sin 31° )÷(cos 20° cos 25° – sin 20° sin 25° )]?

A. 1/√2

B. 2√2

C. √3

D. √2

Question 444

What is the value of (3/5 + 7/9)?

A. 62/45

B. 31/28

C. 5/7

D. 1/7

Question 445

If Sin θ = 20/29 , then what is the value of Sec Sin θ ?

A. 29/21

B. 29/20

C. 21/20

D. 21/29

Question 446

The value of cosec260 + sec260 cot260 + tan230 will be

A. 5

B. 5 1/2

C. 5 1/3

D. 5 2/3

Question 447

If 5 - 5x < 4 - x and 2 - x < 6 - 4x, then x can take which of the following values?

A. 1

B. 2

C. -1

D. -2

Question 448

What is the reflection of the point (3,-5) in the origin?

A. (-3, -5)

B. (5,-3)

C. (-5,-3)

D. (-3, 5)

Question 449

Vishnu spends Rs. 5000 in buying 12 tables and some chairs. The cost of one table is Rs. 50 and that of one chair is Rs. 40. What is the ratio of the numbers of tables purchased?

A. 5 :2

B. 55 : 6

C. 5 : 1

D. 55 : 4

Question 450

What is the reflection of the point (-1 , 5) in the line x = 1?

A. (3 , -5)

B. (-3 , -5)

C. (3 , 5)

D. (-3 , 5)

Question 451

If (x – 2) and (x + 3) are the factors of the equation x2 + k1x + k2 = 0, then what are the values of k1 and k2?

A. k1 = 6, k2 = – 1

B. k 1 = 1, k 2 = – 6

C. k 1 = 1, k2 = 6

D. k1 = – 6, k2 = 1

Question 452

Reflection of the point (2,7) in the yaxis is

A. (2,7)

B. (-2,-7)

C. (-7,2)

D. (7,2)

Question 453

If 5x - 4 ≤ 2 - x and 4x + 5 > 2x - 5, then x can take which of the following values?

A. 3

B. 6

C. -7

D. -1

Question 454

Which of the following is correct?

A. (3x + 4y)(4x - 3y) = 12x2 + 7xy - 12y2

B. (3x + 4y)(4x - 3y) = 12x2 + 251xy - 12y2

C. (3x + 4y)(4x - 3y) = 12x2 - 7xy + 12y2

D. (3x + 4y)(4x - 3y) = 12x2 - 251xy + 12y2

Question 455

Sum of twice a fraction and its reciprocal is 17/6. What is the fraction?

A. 4/3

B. 5/4

C. 3/4

D. 4/5

Question 456

1.004 - 0.4 is equal to

A. 0.604

B. 0.006

C. 0.64

D. 1

Question 457

If x=8+215, then what is the value of x+1x?

A. 2√15

B. 3√5

C. (3√5+√3)/2

D. 3√2+3

Question 458

The orthocentre of an obtuseangled triangle lies

A. inside the triangle

B. outside the triangle

C. on one side of a triangle

D. none of these

Question 459

If x + y = 5, x3 + y3 = 35, then what is the positive difference between x and y?

A. 0

B. 1

C. 5

D. 6

Question 460

Find the value of 64344?

A. 1

B. 2

C. 3

D. 4

Question 461

If (x + y + z) = 12, xy + yz + zx = 44 and xyz = 48, then what is the value of x3 + y3+ z3?

A. 104

B. 144

C. 196

D. 288

Question 462

In ΔPQR, S and T are points on side PQ and PR respectively. ST is parallel to QR. If S divides PQ in the ratio 4:1 and length of QR is 15 cm,what is the length of ST?

A. 3 cm

B. 5 cm

C. 12 cm

D. 10 cm

Question 463

The sum of two numbers is 7 and the sum their squares is 23, their product is equal to:

A. 10

B. 11

C. 12

D. 13

Question 464

The angle of elevation of the top of a tower, vertically erected in the middle of a paddy field, from two points on a horizontal line through the foot of the tower are given to be α and β (α>β). The height of the tower is h unit. A possible distance (in the same unit) between the points is

A. h(cotβ-cotα)cos(α+β)

B. h(cotα - cotβ)

C. h(tanβ - tanα)tanα tanβ

D. h(cotα+cotβ)

Question 465

What is the value of (1/√2) Cot 45° + (1/√3) Cosec 60°?

A. (√6 + 1)/√3

B. √3

C. (1 + 3√2)/√3

D. (3 + 2√2)/3√2

Question 466

If a+b=2c then the value of aa-c+cb-c is equal to (where a≠b≠c)

A. -1

B. 1

C. 0

D. 1/2

Question 467

If Sinx = 4/5, then Sec2x - 1 = ?

A. 16/25

B. 25/9

C. 9/16

D. 16/9

Question 468

A crate of egg holds one rotten egg out of every 25 egg in it. If 5 out of 8 rotten eggs are unusable and there are total 10 unusable eggs in the crate,then calculate the number of eggs in the crate.

A. 380

B. 400

C. 420

D. 440

Question 469

If x = a + 1/a, y = a - 1/a, then the value of x4+y4-2x2y2

A. 4

B. 8

C. 16

D. 64

Question 470

∆PQR is right angled at Q. If m∠R = 45°, then find the value of (cosecP - √3/2)

A. (3√3-1)/3

B. 2/√3

C. (2-√3)/√3

D. (2√2-√3)/2

Question 471

What is the value of (cot60 + 1/√3) ?

A. 4/√3

B. (2√2+√3)/2

C. 2/√3

D. (2√2+1)/√2

Question 472

If (x+1/x) = 5, then the value of 5xx2+5x+1?

A. 1/3

B. 1/4

C. 1/2

D. 1/5

Question 473

The angle of elevation of the top of a tower from two horizontal points (in opposite sides) at distances of 25 meter and 64 meter from the base of tower are x and 90° - x respectively . The height of the tower will be

A. 39 m

B. 89 m

C. 1.6 m

D. 40 m

Question 474

You have 20 big and 16 small diaries and want to make gift packs containing both in each pack. What is the maximum number of gift packs you can make without any left over?

A. 5

B. 4

C. 3

D. 2

Question 475

The expenses of a person increase by Rs. 50000 for every month in February and March. If his expenses in January was Rs. 50000, calculate his average expenditure (in Rs.) from January to March.

A. 100000

B. 150000

C. 75000

D. 50000

Question 476

tan3A is equal to

A. 3tanA - tan3A(1 - 3tan2A)

B. 3tanA + tan3A(1 - 3tan2A)

C. 3tanA - tan3A(1 + 3tan2A)

D. 3tanA + tan3A(1 + 3tan2A)

Question 477

If x – 4y = 0 and x + 2y = 24, then what is the value of (2x + 3y)/(2x – 3y)?

A. 9/5

B. 11/5

C. 13/7

D. 9/7

Question 478

Find the value of 27a3 + 1a3, if 9a2 + 1a2 = 43

A. 240

B. 280

C. 320

D. 360

Question 479

If 5x - (1/2)(2x -7) = 5.5, then what is the value of x?

A. 3/2

B. 1/2

C. -1/2

D. -3/2

Question 480

For which value of ‘g’ the linear graph of 6x + 12y +9 = 0 and 2x + gy + 3 = 0 has infinite number of solutions?

A. 3

B. 4

C. 6

D. 9

Question 481

If 2x + 3(5-2x) > 2 - 3x < 2x - x/3, then x can take which of the following values?

A. 0

B. -2

C. -4

D. 2

Question 482

97 x 97 = ?

A. 9391

B. 9409

C. 9049

D. 9309

Question 483

If x - y = -9 and xy = -20, then find x2 + y2 ?

A. 61

B. 41

C. 81

D. 51

Question 484

If tan θ + cot θ = x, then what is the value of tan4θ + cot4θ?

A. (x3 – 3)2 + 2

B. (x4 – 2x) + 4

C. x2 (x2 – 4) + 2

D. x

Question 485

If 1/√(1+tan2A) = x, then value of x is

A. cosA

B. sinA

C. cosecA

D. secA

Question 486

If x = 5 + 15 - 1 & y = 5 - 15 + 1 , then find the value of x2 - y2.

A. √5

B. 2√5

C. 3√5

D. 4√5

Question 487

Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to ___ ?

A. 3.7

B. 2.7

C. 3.6

D. 2.9

Question 488

A, B and C are three points on a circle with centre O. The tangent at C meets BA produced at T. If ∠ATC = 30° and ∠ACT = 48°,then what is the value of ∠AOB ?

A. 78°

B. 96°

C. 102°

D. 108°

Question 489

If x = a cosθ+ b sinθ and y = b cosθ- a sinθ, then x2 + y2 is equal to

A. ab

B. a2+b2

C. a2-b2

D. 1

Question 490

In a party there are male and female members. If 15 female quit then the number of females will become double the number of males. If 45 males quit no. of female becomes five times the number of males. Find the number of females ?

A. 175

B. 145

C. 165

D. 135

Question 491

A, B and C can finish a job working alone in 72, 24 and 36 days respectively. In how many days they can finish the job if they worked together?

A. 12

B. 9

C. 15

D. 18

Question 492

In a circle, two arcs of unequal length subtend angles in the ratio 5:3. If the smaller angle is 45° then the measure of other angle in degrees.

A. 75°

B. 72°

C. 60°

D. 78°

Question 493

Find the unit place in 194102+294103

A. 0

B. 6

C. 8

D. 2

Question 494

3cosA is equal to

A. 4cos3A + 3cosA

B. 4cos3A - 3cosA

C. 3cos3A + 3cosA

D. 3cos3A - 3cosA

Question 495

If 2x + 3y = 0 and 3x - 4y = 34, then x - y = ______

A. 10

B. -10

C. 2

D. -2

Question 496

Point A (4 , 2) divides segment BC in the ratio 2:5. Co-ordinates of B are (2 , 6) and C are (7 , y). What is the value of y?

A. 8

B. -8

C. 6

D. -6

Question 497

What is the value of [sin (90 – A) + cos (180 – 2A)]/[cos (90 – 2A) + sin (180 – A)]?

A. sin (A/2) cos A

B. cot (A/2)

C. tan (A/2)

D. sin A cos (A/2)

Question 498

If x tan 60° + cos 45° = sec 45° then the value of x2 + 1 is

A. 6/7

B. 7/6

C. 5/6

D. 6/5

Question 499

If a3 + 3a2 + 9a = 1, then what is the value of a3 + (3/a)?

A. 31

B. 26

C. 28

D. 24

Question 500

What is the value of 1sin490-θ+1cos290-θ - 1 ?

A. tan2θ sec2θ

B. sec4θ

C. tan4θ

D. tan2θ sin2θ

Question 501

Factors of x2 + 7x + 10 are

A. (x-5)(x-2)

B. (x+5)(x+2)

C. (x-5)(x+2)

D. (x-4)(x+2)

Question 502

23 x 31 = 713. How much is 0.0713 / 3.1?

A. 0.23

B. 0.0023

C. 2.3

D. 0.023

Question 503

If cot A = n/(n + 1) and cot B = 1/(2n + 1), then what is the value of cot (A + B)?

A. -1

B. 0

C. 1

D. 2

Question 504

Solve the following : -1/4 { -45 - (-96) / (-32)} = ?

A. 12

B. 10.5

C. -12

D. -10.5

Question 505

A factory produced 18,58,509 cassettes in the month of January, 7623 more cassettes in the month of February and owing to short supply of electricity produced 25,838 less cassettes in March than in February. Find the total production in all?

A. 55,57,312

B. 59,83,245

C. 55,64,935

D. 56,08,988

Question 506

If cos -4π/3 = x, then the value of x is

A. √3/2

B. 1/2

C. -√3/2

D. -1/2

Question 507

If 9 * 6 = 45, 7 * 4 = 33, and 6 * 4 = 20, then what is the value of 5 * 3?

A. 24

B. 16

C. 13

D. 10

Question 508

What is the value of tan 1° tan 2° tan 3°....... tan 89°?

A. 0

B. 1

C. 2

D. infinity

Question 509

If x varies as y and x = 8 when y = 15 then the value of x when y = 10 is:

A. 5

B. 15/8

C. 8/15

D. 16/3

Question 510

If P = 7 + 4√3 and PQ = 1, then what is the value of 1/P2 + 1/Q2?

A. 196

B. 194

C. 206

D. 182

Question 511

Rehman walks at 8 km/hr and Roma cycles at 13 km/hr towards each other. What was the distance between them when they started if they meet after 36 minutes?

A. 12.6 kms

B. 18.9 kms

C. 15.8 kms

D. 9.5 kms

Question 512

If x + y = 3, then what is the value of x3 + y3 + 9xy?

A. 15

B. 81

C. 27

D. 9

Question 513

If 1/(tanA + cotA) = x, then value of x is

A. cosAsinA

B. cos2Asin2A

C. cosecAsecA

D. cosec2Asec2A

Question 514

If a = √2 + 1, b = √2 - 1 then the value of 1a+1+1b+1 ?

A. 0

B. 1

C. 2

D. 3

Question 515

If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3 is equal to :

A. 22

B. 23

C. 24

D. 25

Question 516

If x2+5x+6 = 0, then the value of 2xx2-7x+6 is

A. 1/6

B. 1/3

C. -1/6

D. -1/3

Question 517

If a-1a=7,then a2+1a2=?

A. 54

B. 51

C. 53

D. 52

Question 518

What is the value of (tan60 - 1/3) ?

A. 3-√2

B. (2√2-√3)/2

C. -1/2√3

D. (3√3-1)/3

Question 519

What is the reflection of the point (5, -2) in the line x = -1?

A. (-7 , -2)

B. (5 , 0)

C. (7 , -2)

D. (5 , 2)

Question 520

If 3x^2 + ax + 4 is perectly divisible by x - 5, then the value of a is :

A. -5

B. -15.8

C. -12

D. -15.6

Question 521

AB is the diameter of a circle with center O and P be a point on its circumference. If ∡POA = 120°, then the value of ∡PBO is

A. 30°

B. 60°

C. 50°

D. 40°

Question 522

If 123 x 356 = 43788, then 1.23 x 0.356 = ?

A. 437.88

B. 4.3788

C. 0.43788

D. 0.043788

Question 523

What is the area of the sector whose central angle is 90° and radius of the circle is 14 cm?

A. 308 sq cm

B. 77 sq cm

C. 154 sq cm

D. 231 sq cm

Question 524

If sinθ+cosecθ=2, the value of sinnθ+cosecnθ is

A. 2

B. 0

C. 1

D. 1/n

Question 525

If x - 1/x = 1 then what is the value of 1x1x-1-1x+1+1x2+1-1x2-1?

A. ±√5

B. 2/5

C. ±2/√5

D. ±√5/2

Question 526

If cos 45° - sec 60° = x, then the value of x is

A. (√3-4)/2√3

B. 1

C. (1-2√2)/√2

D. (√3+√2)/2

Question 527

What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)? 499.99 + 1999 ÷ 39.99 × 50.01=?

A. 3200

B. 2700

C. 3000

D. 2500

Question 528

In a triangle PQR, ∠Q = 90°. If PQ = 12 cm and QR = 5 cm, then what is the radius (in cm) of the circum circle of the triangle?

A. 5

B. 6

C. 6.5

D. 6√2

Question 529

ΔXYZ is right angled at Y. If m∠Z = 60°, then Cosec X =

A. 2

B. 1/2

C. 1/√2

D. 1/√3

Question 530

For triangle PQR, find equation of altitude PS if co-ordinates of P, Q and R are (1,2), (2,-1) and (0,5) respectively?

A. x - 3y = -7

B. x - 3y = -5

C. x + 3y = 4

D. x + 3y = 7

Question 531

Reciprocal of 235?

A. 235

B. 532

C. 513

D. 335

Question 532

23 x 19 = 437. How much is 0.0437 / 1.9 = ?

A. 0.0023

B. 0.23

C. 0.023

D. 2.3

Question 533

If C + 1C = 3, then what is the value of C-37+1C7?

A. 2

B. 0

C. 3

D. 1

Question 534

If 3a – (3/a) – 3 = 0, then what is the value of a3 – (1/a3) + 2?

A. 0

B. 2

C. 4

D. 6

Question 535

If a = 1/a-5, then the value of a + 1/a = ?

A. √29

B. √-29

C. - √29

D. √27

Question 536

Profit of Rs 144000 has to be divided among three partners Akram, Bipin and Chintan in the ratio 3:2:7. How much Rs. Chintan get?

A. 84000

B. 24000

C. 36000

D. 42000

Question 537

Calculate the value of √3√3 + 3, if √3 = 1.732

A. 0.366

B. 0.566

C. 0.356

D. 0.346

Question 538

The ratio of the curved surface area and total surface area of a right circular cylinder is 2 : 5. If the total surface area is 3080 cm2, then what is the volume (in cm3) of the cylinder?

A. 4312√6

B. 3822√6

C. 4522√6

D. 4642√6

Question 539

What is the value of x4+y4 when the value of x3+y3=8 and x+y=2 ?

A. 2

B. 8

C. 16

D. 32

Question 540

If 2x- 3(4-2x) < 4x - 5 < 4x + 2x/3, then x can take which of the following values?

A. 2

B. 8

C. 0

D. -8

Question 541

A 1.6 m tall observer is 45 meters away from a tower. The angle of elevation from his eye to the top of the tower is 30°, then the height of the tower in meters is

A. 25.98

B. 26.58

C. 27.58

D. 27.98

Question 542

Δ DEF is right angled at E. If m∠D = 45%., then Cosec F =

A. 1/2

B. 1/√2

C. √2

D. 1/√3

Question 543

If sin -330° = x, then the value of x is

A. √3/2

B. 1/2

C. -2/√3

D. √2

Question 544

0.296 + 2.96 + 29.6 + 296 = ?

A. 327.856

B. 328.756

C. 328.856

D. 327.756

Question 545

The sum of 6xy(2x - 4z) , 3yz(2x - 3z) and 4xz(3y - 2y2) is

A. 12x2y - 6xyz - 9yz2 + 8xy2z

B. 12x2y - 6xyz + 9yz2 - 8xy2z

C. 12x2y - 6xyz - 9yz2 - 8xy2z

D. 12x2y + 6xyz - 9yz2 - 8xy2z

Question 546

If 1/2 is added to a number and the sum is multipled by 3, the result is 21. Then the number is

A. 6.5

B. 5.5

C. 4.5

D. -6.5

Question 547

A hydrogen filled balloon ascending at the rate of 18 kmph was drifted by wind. Its angle of elevation at 10th and 15th minutes were found to be 60° and 45° respectively. The wind speed (in whole numbers) during the last five minutes, approximately, is equal to

A. 7 km/hr

B. 11 km/ hr

C. 26 km/hr.

D. 33 km/hr

Question 548

If x – y – √18 = –1 and x + y – 3√2 = 1, then what is the value of 12xy(x2 – y2)?

A. 0

B. 1

C. 512√2

D. 612√2

Question 549

If 1+121+141+161+181-131-151-17 = 1+ 1x, then what is the value of x?

A. 6

B. 8

C. 5

D. 7

Question 550

What is the slope of the line, perpendicular to the line 3x - 6y = 4?

A. -2

B. 2

C. 2/3

D. -2/3

Question 551

If x = 2 +√3, y = 2 – √3 and z = 1, then what is the value of (x/yz) + (y/xz) + (z/xy) + 2 [(1/x) + (1/y) + (1/z)]?

A. 25

B. 22

C. 17

D. 43

Question 552

A bag contains 25 paise, 50 paise and 1 Rs coins. There are 220 coinsinall and the total amount in the bag is Rs. 160. If there arethrice as many 1 Rs. coins as there are 25 paise coins, then what is the number of 50 paise coins?

A. 60

B. 40

C. 120

D. 80

Question 553

The average weight of Sudesh, Jyothi and Ritu is 89 kg. If the average weight of Sudesh and Jyothi be 98 kg and that of Jyothi and Ritu be 83 kg, then the weight of Jyothi is

A. 58

B. 56

C. 95

D. 66

Question 554

Calculate the value of 55-5, if the value of √5 = 2.236.

A. 0.809

B. 0.89

C. 0.089

D. 0.807

Question 555

If √(1 - cos2A)/cosA = x, then the value of x is

A. cotA

B. cosecA

C. tanA

D. secA

Question 556

If (1/x) + (1/y) + (1/z) = 0 and x + y + z = 9, then what is the value of x3 + y3 + z3 – 3xyz?

A. 81

B. 361

C. 729

D. 6561

Question 557

If a - b = 2 and ab = 15, then what is the value of a3- b3?

A. 152

B. 112

C. 108

D. 98

Question 558

If 3x + 5y + 7z = 49 and 9x + 8y + 21z = 126, then what is the value of y?

A. 4

B. 2

C. 3

D. 5

Question 559

What is the value of 4600+540+1280+250+36 ?

A. 69

B. 68

C. 70

D. 72

Question 560

If x+1x:x-1x=5:3 then the value of x is

A. +- 1

B. +-2

C. +-3

D. +-4

Question 561

In ΔPQR, S and T are points on side PQ and PR respectively. ST is parallel to QR. If S divides PQ in the ratio 4:3 and length of QR is 4.9 cm, find ST?

A. 5.6 cm

B. 7.2 cm

C. 2.8 cm

D. 3.6 cm

Question 562

In ΔABC measure of angle B is 90 deg. If cosA = 5/13, and AB = 10 cm, then what is the length (in cm) of side BC?

A. 26

B. 24

C. 25

D. 5

Question 563

Compute of 69696 x 9999 =

A. 696980304

B. 666890304

C. 696809304

D. 696890304

Question 564

If tanθ = 815, then 1-sinθ1+sinθ is

A. 1/5

B. 2/5

C. 3/5

D. 0

Question 565

If cosθ = x2-y2x2+y2, then the value of cotθ is

A. 2xyx2-y2

B. 2xyx2+y2

C. x2+y22xy

D. x2-y22xy

Question 566

p3 + q3 + r3 – 3pqr = 4. If a = q + r, b = r + p and c = p + q, then what is the value of a3 + b3 + c3 – 3abc?

A. 4

B. 8

C. 2

D. 12

Question 567

If x+19x=4, then 9x2+19x2 is

A. 140

B. 142

C. 144

D. 146

Question 568

Simplify 81x2 - 49y29x + 7y

A. 9x++7y

B. 9x-7y

C. 9x

D. 7y

Question 569

What is the value of [2 cot × (p – A)/2]/[1 + tan2× (2p – A)/2]?

A. 2 sin2 A/2

B. cos A

C. sin A

D. 2 cos2 A/2

Question 570

The sum of a number and 4 times its reciprocal is 5. What is the number?

A. 4

B. 5

C. 6

D. 7

Question 571

What is the simplified value of cosec6A – cot6A – 3 cosec2A cot2A?

A. -2

B. -1

C. 0

D. 1

Question 572

Calculate the angle subtended by the chord at the point on the major arc if the radius and the chord of the circle are equal in length.

A. 30°

B. 120°

C. 200°

D. 300°

Question 573

When 721+722+723+724 is divided by 25 the remainder is:

A. 5

B. 17

C. 7

D. 0

Question 574

If cosA = x, then x is

A. √(1 - cos2A)

B. √(1 + sin2A)

C. √(1 + cos2A)

D. √(1 - sin2A)

Question 575

If [a + (1/a)]2 – 2[a – (1/a)] = 12, then which of the following is a value of 'a'?

A. – 8 + √3

B. – 8 – √3

C. – 8 + √5

D. None of these

Question 576

The price of 4.5 m of cloth is Rs.60.75. Find the cost per meter.

A. 15.5

B. 13.5

C. 14.75

D. 13.75

Question 577

Given 17 x 29 = 493, then 170 x 0.029 = ?

A. 0.0493

B. 4.93

C. 0.493

D. 49.3

Question 578

If a + b = 1, then a4 + b4 - a3 - b3 - 2a2b2 + ab is equal to

A. 1

B. 2

C. 4

D. 0

Question 579

What is the value of 1.23+0.83+0.73-2.0161.351.22+0.82+0.72-0.96-0.84-0.56 =

A. 1/4

B. 1/2

C. 1

D. 2

Question 580

If a+b=3 then the value of a3+b3+9ab-27 is

A. 24

B. 25

C. 0

D. 27

Question 581

If tan A = 1/2 and tan B = 1/3, then what is the value of tan (2A + B)?

A. 1

B. 3

C. 5

D. 9

Question 582

If a + b = 8 and a2 + b2 = 34, then value of ab is

A. 30

B. 64

C. 98

D. 15

Question 583

What will be the value of r2+p2+s2-rp-ps-rs when r = 4, p = 2, s = 8?

A. 8

B. 18

C. 28

D. 38

Question 584

If a + b = 10 and ab- 13 = -ba - 11, then what is the value of 3ab + 4a2 + 5b2 ?

A. 450

B. 300

C. 600

D. 750

Question 585

If cot(A/2) = x, then the value of x is

A. √[(1 + cosA)/(1 - cosA)]

B. cosecA - cotA

C. √[(1 - cosA)/2]

D. √[(1 + cosA)/2]

Question 586

What is the value of tan 300°?

A. -1/2

B. -1/√2

C. -√3

D. -√3/2

Question 587

A line passing through the origin perpendicularly cuts the line 2x + 3y = 6 at point M. Find M?

A. (6/11, 9/11)

B. (6/7, 9/7)

C. (6/11, -9/11)

D. (-6/7, 9/7)

Question 588

If [7(5x/3 - 3/2)]/2 + 3/2 = 1/4, then what is the value of x?

A. 35/24

B. 24/35

C. -24/35

D. -35/24

Question 589

Find the degree of the polynomial 8x4 + 2x2y3 + 4

A. 4

B. 5

C. 0

D. 1

Question 590

If each median of an equilateral triangle has a length of 12cm. Then what will be the value of in-radius (in cm) of the equilateral triangle?

A. 3

B. 4

C. 5

D. 6

Question 591

(1155) +(18 − 6) × 9 =?

A. 113

B. 115

C. 100

D. 110

Question 592

If the mean of m observations out of n observations is n and the mean of remaining observations is m, then what is the mean of all n observations?

A. 2m –m^2/n

B. 2m –m/n

C. 2m

D. 2m –m

Question 593

One of the roots of the equation x2 - 4x + k = 0 is x = 3. The other root is

A. x = -1

B. x = -4

C. x = 1

D. x = 4

Question 594

Find the value of 777777?

A. 73164

B. 7164

C. 76364

D. 7764

Question 595

Compute : 1112 / 139 - 5

A. 557/67

B. -3

C. 556/67

D. 3

Question 596

If x4 + (1/x4) = 34, then what is the value of x3 – (1/x3)?

A. 0

B. 6

C. 8

D. 14

Question 597

If A = 30°, B = 60° and C = 135°, then what is the value of sin3A + cos3B + tan3C – 3sin A cos B tan C?

A. 0

B. 1

C. 8

D. 9

Question 598

What is the value of [tan (90 – A) + cot (90 – A)]2/[2 sec2(90 – 2A)]?

A. 0

B. 1

C. 2

D. – 1

Question 599

What is the value of [1 – sin (90 – 2A)] / [1 + sin (90 + 2A)]?

A. sinA cosA

B. cot2A

C. tan2A

D. sin2A cosA

Question 600

If 1/(1 + cosA) + 1/(1 - cosA) = x , then value of x is

A. 2sec2A

B. 2cosecA

C. 2cosec2A

D. 2secA

Question 601

2 sec2A is equal to

A. (1 - tanA)2 - (1 + tanA)2

B. √[(1 - tanA)2 + (1 + tanA)2 ]

C. √[(1 - tanA)2 - (1 + tanA)2]

D. (1 - tanA)2 + (1 + tanA)2

Question 602

If 2x + 6y = 3xy and 10x - 3y = 4xy, find x, y.

A. 3, 2

B. 2, 3

C. 4, 6

D. 6, 4

Question 603

If a – b = 11 and ab = 24, then value of a2 + b2 is

A. 169

B. 37

C. 73

D. 48

Question 604

If x + y = 10 and x2 + y2 = 68, then find xy

A. 21

B. 24

C. 25

D. 16

Question 605

What is the value of √[(1 + sinA)/(1 - sinA)]?

A. secA - tanA

B. cosecA + tanA

C. secA + tanA

D. cosecA - tanA

Question 606

If a - b = 3, a2+b2=29, find the value of ab.

A. 10

B. 12

C. 15

D. 18

Question 607

What is the value of 7293×16+676+169

A. 75

B. 64

C. 35

D. 60

Question 608

If x = 11, the value of x5 - 12x4 + 12x3 - 12x2 + 12x - 1 is

A. 11

B. 10

C. 12

D. -10

Question 609

The two roots of a quadratic equation are given as x = 1/7 and x = -1/8 . The equation can be written as:

A. (7x − 1)(8x − 1) = 0

B. (7x − 1)(8x + 1) = 0

C. (7x + 1)(8x − 1) = 0

D. (7x + 1)(8x + 1) = 0

Question 610

Divya and Kriti have total 46 candies. If Divya has 10 candies more than kriti, then find the total number of candies Divya have?

A. 20

B. 24

C. 28

D. 32

Question 611

If (sinA + CosA)/(sin A - cos A) = 5/4, the value of (tan2A + 1)/(tan2A - 1) = ?

A. 41/40

B. 12/13

C. 40/41

D. -31/49

Question 612

If P + 1P+2 = 1, then the value of P+23+1P+23-3 ?

A. 12

B. 16

C. 18

D. 15

Question 613

If sinA + sin2A = 1 then what is the value of cos2A + cos4A ?

A. 1

B. 2

C. 1/2

D. 1/4

Question 614

D and E are the points on the sides AB and AC respectively of a ΔABC and AD = 8 cm, DB = 12 cm, AE= 6 cm and EC = 9 cm, then BC is equal to:

A. 2/5 DE

B. 5/2 DE

C. 3/2 DE

D. 2/3 DE

Question 615

What is the simplified value of (cosec A – sin A)(sec A – cos A)(tan A + cot A)?

A. -1

B. 0

C. 1

D. 2

Question 616

ΔDEF is right angled at E. If cosD = 8/17, then what is the value of secF ?

A. 17/8

B. 8/17

C. 17/15

D. 15/17

Question 617

A and B are positive integers. If A + B + AB = 65, then what is the difference between A and B (A, B ≤ 15)?

A. 3

B. 4

C. 5

D. 6

Question 618

What is the reflection of the point (5, -2) in the line y = -1?

A. (-7 , -2)

B. (-5 , 0)

C. (5 , 0)

D. (-7 , 2)

Question 619

Simplify : 132 - 142 + 172 - 250 = ?

A. 196

B. 169

C. 121

D. 144

Question 620

If x/2 - [4(15/2 - x/3)]/3 = -x/18, then what is the value of x?

A. -10

B. 9/8

C. 10

D. -9/8

Question 621

If sinθ x cosθ = 1⁄2 . The value of sinθ - cosθ is where 0°< θ< 90°

A. 0

B. √2

C. 2

D. 1

Question 622

When [x + (1/x)] = 5, then what is the value of [x – (1/x)]?

A. 11

B. ± √22

C. 21

D. ± √21

Question 623

tan(A/2) is equal to

A. tanA/(1 + secA)

B. 1/(cosecA + cotA)

C. tanA/(1 + cosecA)

D. 1/(secA + cotA)

Question 624

The slope of the line passing through the points (7,-2) and (x,1) is -3/10. Find x.

A. 4

B. 2

C. -4

D. -3

Question 625

If cos 27° = x, the value of tan 63° is

A. x1-x2

B. x1+x2

C. 1-x2x

D. 1+x2x

Question 626

If x1x2x3 = 4(4 + x1 + x2 + x3 ), then what is the value of [1/(2 + x1 )] + [1/(2 + x2 )] + [1/(2 + x3 )]?

A. 1

B. 1/2

C. 2

D. 1/3

Question 627

If 4(2x + 3) > 5 - x and 5x - 3(2x - 7) > 3x - 1, then x can take which of the following values?

A. 6

B. -1

C. 5

D. -6

Question 628

If x = at2 and y = 2at then

A. x2 = 4ay

B. y2 = 4ax

C. x2 + y 2 = a2

D. x 2 - y2 = a 2

Question 629

What is the value of {[sin (x + y) – 2 sin x + sin (x – y)]/[cos (x – y) + cos (x + y) – 2 cos x]} × [(sin 10x – sin 8x)/(cos 10x + cos 8x)]?

A. 0

B. tan2x

C. 1

D. 2 tan x

Question 630

If cosecA + cotA = x, then value of x is

A. 1/(cosecA - cotA)

B. 1/(secA - tanA)

C. 1/(secA - cosA)

D. 1/(sinA - cosA)

Question 631

The two roots of an quadratic equation are given as x = 1/2 and x = -1/3. The equation can be written as

A. (2x - 1)(3x - 1) = 0

B. (2x + 1)(3x - 1) = 0

C. (2x - 1)(3x + 1) = 0

D. (2x + 1)(3x + 1) = 0

Question 632

If 27x + 27[x–(1/3)] = 972, then what is the value of x?

A. 2

B. 3

C. 4

D. 5

Question 633

The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a distance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 60°. The height of the tower in meters is

A. √3

B. 5√3

C. 10√3

D. 20√3

Question 634

If a/(a+b) = 15/21, what is (a+b)/(a-b) is equal to?

A. 13/9

B. 23/11

C. 14/5

D. 21/9

Question 635

If 4(4x + 5) > 2x - 1 > 4x - 3, then the value of x is

A. 2

B. 3

C. -2

D. 0

Question 636

The value of cos220°+cos270° is

A. 0

B. 1

C. 1/2

D. 13

Question 637

If sec2θ+tan2θ=3, then sec4θ-tan4θ =

A. 1/√3

B. 1

C. √3

D. 0

Question 638

What is the value of (1+cosA)/(1-cosA)?

A. (cosecA - cotA)2

B. (cosecA + cotA)2

C. (secA + cotA)2

D. (secA - cotA)2

Question 639

If xy = 56 and x2+ y2= 113, then what will be the value of (x + y)?

A. 29

B. 21

C. 36

D. 15

Question 640

If 13x2 = 172 - 92, find the value of x?

A. 16

B. 12

C. 8

D. 4

Question 641

Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 4 cm, then what is the area (in cm2) of an equilateral triangle with side equal to the bigger diagonal of the rhombus?

A. 6

B. 9√3

C. 12

D. 12√3

Question 642

The number of solutions of the pair of linear equations x + 2y - 8 = 0 and 2x + 4y = 16 is

A. 0

B. 1

C. Infinitely many

D. 2

Question 643

Simplify 4(x-1) -3x

A. 7x - 4

B. 7x + 4

C. x + 4

D. x - 4

Question 644

In each of the following questions two equations I and II are given. Solve both the equations and give answer: I. x2+2x-195=0II. y2+30y+225=0

A. x = y or relation can’t be established between x and y

B. x > y

C. x < y

D. x ≥ y

Question 645

[63 - (-3){-2 - 8 - 3}] / 3{6 + (-2) (-1)} = ?

A. 0

B. 3

C. 1

D. 2

Question 646

If Cot θ = 21/20, then what is the value of Sec θ?

A. 29/21

B. 21/29

C. 29/20

D. 20/29

Question 647

64/12 in simplest form?

A. 19/6

B. 32/4

C. 16/3

D. None of the above

Question 648

If (4x - 5) = (3x - 1), then the numerical value of (x + 4)2

A. 16

B. 64

C. 32

D. 8

Question 649

If a+bab=21 , then the value of (a-b) is

A. 1

B. 0

C. -1

D. 2

Question 650

1422 ÷ 1260.25 = ?

A. 586

B. 578

C. 568

D. 566

Question 651

The line passing through the point (5,a) and point (4,3) is perpendicular to the line x - 6y = 8. What is the value of 'a'?

A. -3

B. -2

C. 4

D. 5

Question 652

If 56 × 75 × 60 × 84 × 210 = 2p × 3q × 5r × 7s, then what is the value of [(p + q)/s] + r?

A. 6

B. 8

C. 12

D. 10

Question 653

If the sum of the digits of any integer between 100 and 1000 is subtracted from the same integer , the resulting number is always divisibleby

A. 2

B. 5

C. 6

D. 9

Question 654

One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?

A. Rs. 30,000

B. Rs. 50,000

C. Rs. 60,000

D. Rs. 90,000

Question 655

If 2/3(6x/5 - 1/4) + 1/3 = 9x/5, then what is the value of x?

A. 1/6

B. -1/6

C. 1/5

D. -1/5

Question 656

If a1-2a+b1-2b+c1-2c = 12, then 11-2a+11-2b+11-2c value is

A. 1

B. 2

C. 3

D. 4

Question 657

The value of 8(sin6θ + cos6θ) - 12(sin4θ + cos4θ) is equal to

A. 20

B. -20

C. 4

D. -4

Question 658

What is the value of sin 75°+ sin 15°?

A. √3

B. 2√3

C. √(3/2)

D. 3/√2

Question 659

What is the value of 4cos90-A sin390+A - 4sin90+A cos390-Acos180+8A2 ?

A. 1

B. -1

C. 0

D. 2

Question 660

If x and y are natural numbers such that x + y = 2017, then what is the value of (– 1)x+ (– 1)y?

A. 2

B. – 2

C. 0

D. 1

Question 661

What is the value of (cosec45 + √3/2) ?

A. 5/6

B. (4+√3)/2√3

C. (2√2+√3)/2

D. 3√3/2

Question 662

If cosec4A - cosec2A = x, then value of x is?

A. tan4A + tan2A

B. cot4A + cot2A

C. cot4A - cot2A

D. tan4A - tan2A

Question 663

If (x - 2) (x - p) = x2 - ax + 6, then the value of (a - p) is

A. 0

B. 1

C. 2

D. 3

Question 664

What is the value of cosec 11π/6?

A. -2/√3

B. √2

C. -2

D. -√2

Question 665

In the first 10 overs of a cricket game, the run rate was only 3.2. The run rate in the remaining 40 overs to reach the target of 282 runs is

A. 6.4

B. 6.3

C. 6.25

D. 6.5

Question 666

cosA/(1 - sin A) is equal to

A. (secA - tanA)

B. (secA + tanA)

C. √[(secA + tanA)]

D. √[(secA - tanA)]

Question 667

2sinAsinB is equal to

A. sin(A+B) + sin(A-B)

B. cos(A-B) - cos(A+B)

C. sin(A+B) - sin(A-B)

D. cos(A+B) + cos(A-B)

Question 668

Expand and simplify (x + 5)2 + (x - 3)2

A. 2(x2 + 2x - 17)

B. 2(x2 - 2x + 17)

C. 2(x2 - 2x - 17)

D. 2(x2 + 2x + 17)

Question 669

The diagonal of a square equals the side of an equilateral triangle. If the area of the square is 12 sq cm, what is the area of the equilateral triangle?

A. 12√3 sq cm

B. 6√3 sq cm

C. 12√2 sq cm

D. 24 sq cm

Question 670

3x2-14x+16=05y2-16y+12=0

A. x > y

B. x < y

C. x=y or relation cannot be established between x and y

D. x ≥ y

Question 671

50.003% of 99.8÷49.988 = ?

A. 2

B. 0

C. 1

D. 50

Question 672

Simplify the equation 0.733+0.2730.732+0.272-0.73×0.27

A. 1

B. 0.4087

C. 0.73

D. 0.27

Question 673

If x = 1.1, then what is the value of 4x2 -4x + 1 ?

A. 1.21

B. 1.331

C. 2.21

D. 1.2

Question 674

If 4x + 3y = 11 and 3x + 2y = 8, then (x,y) is

A. 2, 0

B. 1, 6

C. 2, 1

D. 5, 6

Question 675

What is the simplified value of (sin A – cosec A)(sec A – cos A) (tan A + cot A)?

A. 1

B. -1

C. 0

D. 2

Question 676

If tan π/3c + cosec π/6c = x, then x is

A. (1-√2)/√2

B. (√3+4)/2√3

C. √3+2

D. (2√2-1)/2

Question 677

Calculate the sum of squares from 1 to 9.

A. 284

B. 285

C. 385

D. 380

Question 678

If ab+ba=1, then the value of a3+b3 is

A. 1

B. 0

C. -1

D. 2

Question 679

78 of 448 + 67 of 3374 = ?

A. 3084

B. 3184

C. 3584

D. None of these

Question 680

If Tan A = 15/8 and Tan B = 7/24, then Cos(A - B) = ?

A. 297/425

B. 304/425

C. 87/425

D. 416/425

Question 681

The quadratic equation 1+a2x2+2abx+b2-c2=0 has only one root. What is the value of c21+a2 ?

A. a2

B. b2

C. c2

D. ab

Question 682

What is the sum of a3+b3+c3-3abc, when the value of a=4, b=2 and c=-6?

A. 0

B. 2

C. 4

D. 6

Question 683

If a3 + b3 = 19 and ab = -6 , then what is the value of a + b?

A. 5

B. 7

C. 1

D. -5

Question 684

What is the square root of 5041?

A. 79

B. 81

C. 71

D. 69

Question 685

If (1 + cosA)/(1 - cosA) = x, then x is

A. cot2A/(secA - 1)2

B. cot2A/(secA + 1)2

C. tan2A/(secA + 1)2

D. tan2A/(secA - 1)2

Question 686

If 3sinθ+4cosθ=5 (0<θ<90°) then the value of sinθ is

A. 1/5

B. 2/5

C. 3/5

D. 4/5

Question 687

Which of the following points lies on the line 3x - 4y = -13?

A. (5,7)

B. (-5,7)

C. (5,-7)

D. (-5,-7)

Question 688

Along a yard 225 metres long, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees

A. 8

B. 9

C. 10

D. 11

Question 689

A box weighs 8.5 kg when full of sand and weighs 5.5 kg when it is half filled with sand . Weight of the empty box is

A. 5 kg

B. 6 kg

C. 2.5 kg

D. 4.5 kg

Question 690

If X + Y = 19 and X - Y = 7, then XY = ?

A. 13

B. 48

C. 78

D. 72

Question 691

2*[0.3(1.3 + 3.7)] of 0.8 = ?

A. 1.92

B. -0.72

C. 2.16

D. -2.4

Question 692

If 2cosec2A = x, then the value of x is

A. 1/(1 - cosecA) - 1/(1 + cosecA)

B. 1/(1 + sinA) + 1/(1 - tanA)

C. 1/(1 + cosA) + 1/(1 - cosA)

D. 1/(1 - tanA) - 1/(1 + sinA)

Question 693

If the selling price is Rs 1680 after getting a discount of 16%, what was the marked price?

A. Rs 2000

B. Rs 1948.8

C. Rs 1411.2

D. Rs 1448

Question 694

What is the value of 7293 + 441 - 3433 ?

A. 48

B. 23

C. 7

D. 41

Question 695

Reduce 3596 / 4292 to lowest terms.

A. 29/37

B. 17/43

C. 31/37

D. 19/23

Question 696

If (x + y)/z = 2, then what is the value of [y/(y – z)] + [x/(x – z)]?

A. 0

B. 1

C. 2

D. – 1

Question 697

If Sec θ = 13/12, then what is the value of Sin θ?

A. 5/13

B. 12/5

C. 12/13

D. 5/12

Question 698

If x + y = 10 and xy = 4, then what is the value of x4 + y4?

A. 8464

B. 8432

C. 7478

D. 6218

Question 699

What is the x-intercept of line joining (4, 2) and (6, 3)?

A. 0

B. 1

C. 2

D. 3

Question 700

What is the slope of the line 4x - 8y = 3?

A. -1/2

B. 2

C. 1/2

D. -2

Question 701

The line passing through (-2,5) and (6,b) is perpendicular to the line 20x + 5y = 3. Find b?

A. -7

B. 4

C. 7

D. -4

Question 702

Product of 9b2, 3a2 and 4ab is

A. 108a2b2

B. 108a3b3

C. 108a3b2

D. 108a4b4

Question 703

If a3+ b3 = 19 and a + b = 1, then what is the value of ab?

A. 5

B. -6

C. 7

D. -9

Question 704

The price of 2 oranges, 3 bananas and 4 apples is Rs. 15. The price of 3 oranges, 2 bananas and 1 apple is Rs. 10. What will be price of 4 oranges, 4 bananas and 4 apples ?

A. Rs. 10

B. Rs. 15

C. Rs. 20

D. Rs. 25

Question 705

If x = √2+1, then the value of x4-1/x4

A. 8√2

B. 18√2

C. 6√2

D. 24√2

Question 706

ΔUVW is right angled at V. If secU = 5/3, then what is the value of tanW ?

A. 3/4

B. 5/3

C. 4/5

D. 4/3

Question 707

If (1/4 of x) - (4/5 of 6/7) equals - 9/7, then value of x is

A. -12

B. -2.4

C. -3.6

D. -14

Question 708

Find the common factor of 3757+ 4357 and 3737+ 4337

A. (43 - 37)

B. (43 + 37)

C. 37

D. 10

Question 709

To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?

A. 10

B. 35

C. 62.5

D. Cannot be determined

Question 710

If (4x - 3) - (2x + 1) = 4, then the value of x is

A. 0

B. 1

C. 2

D. 3

Question 711

If a+1/a = 3, then a3+1a3?

A. 12

B. 18

C. 9

D. 6

Question 712

Find the greatest number that will divide 390, 495 and 300 without leaving a remainder

A. 5

B. 15

C. 25

D. 35

Question 713

The length of a chord which is at a distance of 12 cm from the centre of a circle of radius 13 cm is

A. 10 cm

B. 5 cm

C. 6 cm

D. 12 cm

Question 714

If sec2A + cosec2A = X, then the value of X is

A. tan2A cot2A

B. sinA cosA

C. secA cosecA

D. sec2A cosec2A

Question 715

What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(4, 0) and C(-2, 2)?

A. (1 , -1)

B. (-1 , 1)

C. (2 , -2)

D. (-2 , 2)

Question 716

The sum of two positive integers is 80 & difference between them is 20. Then what is difference of squares of those numbers ?

A. 1400

B. 1600

C. 1800

D. 2000

Question 717

If X + 2Y = 27 and X - 2Y = -1, find the value of Y.

A. 13

B. 14

C. 7

D. 26

Question 718

What is the perimeter of the sector whose central angle is 60° and radius of the circle is 21 cm?

A. 128 cm

B. 96 cm

C. 64 cm

D. 32 cm

Question 719

What is the value of |3(1) - 6|?

A. 3

B. 0

C. -3

D. 4

Question 720

If x2 + (1/x2) = 31/9 and x > 0, then what is the value of x3 + (1/x3)?

A. 70/9

B. 154/27

C. 349/27

D. 349/7

Question 721

If (cotAcotB - 1) / (cotB + cotA) = x, then the value of x is

A. cot(A - B)

B. tan(A + B)

C. cot(A + B)

D. tan(A - B)

Question 722

In ∆XYZ measure of angle Y is 90 deg. If cosecX = 13/12, and XY = 1cm, then what is the length ( in cm ) of side YZ?

A. 2.6

B. 1.5

C. 2.4

D. 2

Question 723

What is the value of Tan 45° + 4/√3 Sec 60°?

A. (√3 + 8)/√3

B. (√3 + 8)/3

C. (√3 - 8)/√3

D. (√3 - 8)/3

Question 724

If X = 423 + 32 then find the value of ( X + 1X ).

A. 103 + 15212

B. (103 - 52)12

C. -103 - 33212

D. (103+332)12

Question 725

What is the simplified value of 12-13 ?

A. 5√3

B. 5/√3

C. 3√5

D. 3/√5

Question 726

ΔPQR is right angled at Q. If m∠R = 45°, then find the value of (tanP - 1/2).

A. (2-√3)/√3

B. (2√3-√6)/2√2

C. 1/2

D. (√6-6)/3√3

Question 727

If x - y = 7 and xy = 32, then value of (x2 + y2) is

A. 49

B. 64

C. 113

D. 15

Question 728

The cost of 15 kg of groundnuts and 4 kg of cashews is Rs.7,000. The cost of 10 kg of cashews is equal to 25 kg of groundnuts. Find the cost of groundnut per kg.

A. Rs.320

B. Rs.700

C. Rs.540

D. Rs.280

Question 729

If 3x + 4y – 2z + 9 = 17, 7x + 2y + 11z + 8 = 23 and 5x + 9y + 6z – 4 = 18, then what is the value of x + y + z – 34?

A. – 28

B. – 14

C. – 31

D. – 45

Question 730

If a - b = 3 and a^2 + b^2 = 29, find the value of ab.

A. 10

B. 12

C. 15

D. 18

Question 731

If x, y, z are the three factors of a3 -7a - 6, then value of x+y+z will be

A. 3a

B. 3

C. 6

D. a

Question 732

What is the value of 12 + 3(-2 x 3) - (18 / 6) ?

A. -5

B. 9

C. -9

D. 5

Question 733

5 + 2 x 10/2 = ?

A. 15

B. 35

C. 10

D. 20

Question 734

If 1/(cosecA cotA) = x, then the value of x is

A. cosecA + cotA

B. cosecA - cotA

C. cosec2A + cot2A

D. √[cosec2A + cot2A]

Question 735

2 - (cosA + sinA)2 is equal to

A. (cosecA - sinA)2

B. cosA - sinA

C. cosecA - sinA

D. (cosA - sinA)2

Question 736

At what point does the line 3x + 2y = 12 cuts the Y-axis?

A. (0, 6)

B. (0, -6)

C. (6, 0)

D. (-6, 0)

Question 737

1747 + 13212 - ? = 1123

A. 16

B. 17

C. 18

D. 19

Question 738

Simplify 0.1x0.1x0.1 + 0.3x0.3x0.30.3x0.3 - 0.3x0.1 + 0.1x0.1

A. 0.09

B. 0.03

C. 0.05

D. 0.04

Question 739

If M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) and N = (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), then what is the value of M/N?

A. 207/560

B. 339/1120

C. 113/350

D. 69/175

Question 740

If tanθ = 43, then the value of 3sinθ+2cosθ3sinθ-2cosθ ?

A. 1/2

B. 3/2

C. 3

D. -3

Question 741

If Sin 31° = xy, then the value of Sec 31° - Sin 59° is

A. x2yy2-x2

B. -x2yy2-x2

C. -y2y2-x2

D. x

Question 742

What is the value of sin 46 cos 44+ cos 46 sin 44?

A. 2

B. sin 2

C. 1

D. 0

Question 743

If x + y = 12 and xy = 32, then what is the value of x2 + y2 ?

A. 24

B. 144

C. 128

D. 80

Question 744

If the value of 3-1.732, then calculate the value of 243-12108-147

A. 1.732

B. -1.464

C. 3.464

D. -1.732

Question 745

P(4,2) and R(-2,0) are vertices of a rhombus PQRS. What is the equation of diagonal QS.

A. x - 3y = -2

B. 3x + y = 4

C. 3x + y = -4

D. x - 3y = 2

Question 746

If xy+yz+zx = 1, then the value of (1+y2)(x+y)(y+z) ?

A. 2

B. 3

C. 4

D. 1

Question 747

What is the equation of the line passing through the point (1,3) and making an angle of -45° with the positive x-axis?

A. x + y = 4

B. x + y = 2

C. x - y = 4

D. x - y = 2

Question 748

Find equation of the perpendicular bisector of segment joining the points (2,6) and (4,0)?

A. x + 3y = 6

B. x + 3y = -6

C. x - 3y = -6

D. x - 3y = 6

Question 749

If x +y = √3 and x - y = √2, then the value of 8xy (x2 + y2) is

A. 6

B. √6

C. 5

D. √5

Question 750

If xy = -30 and x2 + y2 = 61, then find the value of (x + y).

A. 2

B. 3

C. 1

D. 4

Question 751

Determine the value of a/b + b/a when a + b = 8 and ab = 4.

A. 4

B. 8

C. 12

D. 14

Question 752

If sin -240° = x, then the value of x is

A. 2/√3

B. √2

C. 2

D. √3/2

Question 753

If ( x - 5)2 + (y - 2)2 + (z - 9)2 = 0 , then value of (x + y - z) is

A. 16

B. -1

C. -2

D. 12

Question 754

If tan2A - sin2A = x, then value of x is

A. tan2A sin2A

B. cot2A cosec2A

C. tanA sinA

D. cotA cosecA

Question 755

If x + 1x = 3, then x18 + x12 + x6 + 1 value is

A. 0

B. 1

C. 2

D. 3

Question 756

If 'Q ' means ' +', 'J ' means ' X',T ' ' means '- ' and 'K ' means '÷ ', then what is the value of18K3Q7J ?

A. 15

B. 10

C. 18

D. 12

Question 757

Find length of the arc whose central angle is 45° and radius of the circle is 28 cm?

A. 11 cm

B. 33 cm

C. 44 cm

D. 22 cm

Question 758

On dividing 221a2b2 by 13b2, we get _____.

A. 17a2

B. 17b2

C. 13a2b2

D. 13

Question 759

Find the value of 0.0112 - 0.0012 of 0.14 + 0.25 × 0.20.02 × 0.01

A. 257

B. 25.7

C. 2.57

D. 0.0257

Question 760

If cosec 240° = x, then the value of x is

A. √2

B. 2

C. -2/√3

D. -√2

Question 761

Simplify 11.9983 = ?

A. 1727.136

B. 1331.136

C. 1685.136

D. 1700.136

Question 762

If x + 3 ≤ 4x + 4 and 3(4 - x) - 4 ≥ 2x - 2, then x can take which of the following values?

A. 1

B. 3

C. -1

D. -3

Question 763

The solution set of 4x - 3y = 47 and 3x + y = 32 is

A. {(15, 3)}

B. {(4, 12)}

C. {(11, -1)}

D. {(12, 3)}

Question 764

If a + b = 9 and a2+ b2= 61, then ab is

A. 20

B. 10

C. 81

D. 142

Question 765

If x + [1/(4x)] = 5/2, then what is the value of (64x6+ 1)/8x3?

A. 110

B. 115

C. 125

D. 140

Question 766

Point A divides segment BC in the ratio 4:1. Co-ordinates of B are (6 , 1) and C are (7/2 , 6). What are the co-ordinates of point A?

A. (4 , 3)

B. (4 , 5)

C. (2 , 5)

D. (3 , 5)

Question 767

What is the value of sec 5π/4?

A. 1/√3

B. -√2

C. √3

D. 1

Question 768

Simplify : -21973 × -1253 ÷ 275123

A. 492/7

B. 520/3

C. 554/7

D. 571/5

Question 769

6.651 - (148.6 - x ) - 57.22 = 6.098. Find x.

A. 205.267

B. 90.827

C. -91.933

D. 218.569

Question 770

A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter were to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?

A. 10 m

B. 14 m

C. 12 m

D. 8 m

Question 771

The total of 324 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is :

A. 50

B. 100

C. 150

D. 200

Question 772

If πsinθ= 1, πcosθ= 1, then (3tan 23θ+1) is

A. 1

B. √3

C. 2

D. 1/√3

Question 773

Find the value of 1006×994?

A. 999932

B. 999964

C. 1000032

D. 1000064

Question 774

In a farm, in addition to 48 hens there are 42 sheep and 11 oxen with some shepherds. If the total number of feet be 224 more than the number of heads, find the number of shepherd.

A. 11

B. 13

C. 15

D. 17

Question 775

8 x {5 - (-2) x (-3)} = ?

A. 8

B. -168

C. 88

D. -8

Question 776

Factorise x2 + 3x - 18

A. (x+18)(x-1)

B. (x-1)(x+18)

C. (x+6)(x-3)

D. (x-6)(x+3)

Question 777

Solve the following : 27 - [38 - {46 - (15 - 13 - 2)}]

A. 31

B. 35

C. 30

D. 29

Question 778

What is the simplified value of 1-sin A1+sin A ?

A. tan A

B. sec A

C. sec A + tan A

D. sec A – tan A

Question 779

If 2x+13x = 5, the value of 5x6x2+20x+1 is

A. 1/4

B. 1/6

C. 1/5

D. 1/7

Question 780

What is the value of sinAtanA/(1 - cosA)?

A. 1 - secA

B. 1 + secA

C. 1 + cotA

D. 1 - cotA

Question 781

If √3 = 1.732, then the value of 9+233?

A. 7.169

B. 7.196

C. 5.198

D. 7.296

Question 782

If a - b = -6 and a2 + b2 = 44, then ab is

A. -4

B. 8

C. 4

D. -8

Question 783

What is the value of tan 7π/4?

A. √3

B. -1/2

C. √3/2

D. -1

Question 784

If 3P/5 = 7Q/2 = 7R/5, then what is the ratio of p, Q and R respectively?

A. 3 : 2 : 5

B. 3 : 35 : 14

C. 5 : 7 : 5

D. 35 : 6 : 15

Question 785

If a + b = 4 and ab = 3, then what is the value of a3 + b3?

A. 21

B. 17

C. 28

D. 31

Question 786

The cost of one dozen bananas is Rs.5. The cost of one dozen oranges is Rs.75. What will the cost of one and a quarter dozen bananas and three-fourth dozen oranges?

A. Rs. 109.25

B. Rs. 87.25

C. Rs. 71.75

D. Rs. 62.50

Question 787

What is the value of Cot 45° - (1/√3)Cosec 60°?

A. 1/√3

B. 1/2

C. 1/√2

D. 1/3

Question 788

If xy (x + y) = m, then the value of x3 + y3 + 3m is:

A. m3xy

B. m3x+y3

C. m3x3y3

D. mx3y3

Question 789

Simplify 437bxaz / 23ab.

A. 17xzb

B. 9xz

C. 19xz

D. 19ab

Question 790

If 5x - 40 = 3x, then the numerical value of 2x - 11 is

A. 29

B. 39

C. 19

D. 9

Question 791

Which of the following numbers is completely divisible by 99?

A. 57717

B. 57627

C. 55162

D. 56982

Question 792

XYZ is a right angled triangle and ∠Y = 90°. If XY = 2.5 cm and YZ = 6 cm then the circumradius of ∆XYZ is

A. 6.5 cm

B. 3.25 cm

C. 3 cm

D. 2.5 cm

Question 793

What is the equation of the line which has 3/2 and -4/7 as x and y intercept respectively?

A. 8x - 21y = -12

B. 8x + 21y = 14

C. 8x - 21y = 12

D. 8x + 21y = -14

Question 794

What is the equation of line whose slope is -1/2 and passes through the intersection of the lines x - y = -1 and 3x - 2y = 0?

A. x + 2y = 8

B. 3x + y = 7

C. x + 2y = -8

D. 3x + y = -7

Question 795

If x = 1/(√2+1) then the value of x2 + 2x - 1 is

A. 2√2

B. 4

C. 0

D. 2

Question 796

What is the value of cosec -7π/6?

A. -2

B. 2

C. 2/√3

D. -2/√3

Question 797

If (-1/2) * ( x - 5) + 3 = -5/2, then what is the value of x?

A. 16

B. 4

C. -6

D. -4

Question 798

In ΔUVW measure of angle V is 90 deg. If sinU = 24/25, and UV = 0.7cm, then what is the length (in cm) of side VW?

A. 2.5

B. 3

C. 2.4

D. 4

Question 799

Triangle DEF is right angled at E. If cot D = 5/12, then what is the value of sin F?

A. 5/12

B. 13/5

C. 5/13

D. 13/12

Question 800

If a(x + y) = b(x - y) = 2ab, then the value of 2(x2 + y2)

A. 2(a2 - b2)

B. 2(a2 + b2)

C. 4(a2 - b2)

D. 4(a2 + b2)

Question 801

If a+1a2 = 3, then the value of a3+1a3 is

A. 0

B. a

C. 1/a

D. 1

Question 802

∆DEF is right angled at E. If cosD = 5/13, then what is the value of tanF?

A. 5/13

B. 5/12

C. 13/5

D. 13/12

Question 803

If x/3 - [5(7x/5 - 4/3)]/2 = -x/6, then what is the value of x?

A. 10/9

B. -10/9

C. -9/10

D. 9/10

Question 804

The simplest form of 3774/2958 is

A. 43/19

B. 37/29

C. 31/13

D. 31/23

Question 805

If 4(2x - 4) - 2 > 3x - 1 ≥ 4x - 7, then x can take which of the following values?

A. 7

B. 6

C. 2

D. 0

Question 806

If 5/2 - (6/5)(x - 15/2) = -x/5, then what is the value of x?

A. -23/2

B. 13/2

C. -13/2

D. 23/2

Question 807

What is the value of [(cos 7A + cos 5A)÷(sin 7A – sin 5A)]?

A. tan A

B. tan 4 A

C. cot 4 A

D. cot A

Question 808

Solve this inequality 3b - 7 < 32?

A. b = 13

B. b < 13

C. b > = 13

D. b < = 13

Question 809

If u : v = v : w, then what is the value of u4 : v4?

A. u2 : wv

B. u2 : w2

C. u2 v : w3

D. u : w

Question 810

∆XYZ is right angled at Y. If m ∠Z = 60. What is the length (in cm) of YZ, if ZX = 9√3 cm?

A. 3√3

B. 3√3/2

C. 9√3/2

D. √3

Question 811

If (tanA - tanB)/(1 + tanAtanB) = x, then the value of x is

A. tan(A - B)

B. tan(A + B)

C. cot(A - B)

D. cot(A + B)

Question 812

If (23)2= 4x then 3x is equal to

A. 3

B. 6

C. 9

D. 27

Question 813

If cosec θ + sinθ = 5/2 then the value of cosecθ - sinθ is

A. -3/2

B. 3/2

C. −√3/2

D. √3/2

Question 814

ΔPQR is right angled at Q. If m∠P = 45°, then find the value of (cosecR + 1/3).

A. (√3+2)/2√3

B. (√3+2)/2

C. (3√2+1)/3

D. (2+2√3)/√3

Question 815

If x - y = -8 and xy = 45, then (x2 + y2) is

A. 154

B. 64

C. 90

D. 26

Question 816

If x/y = 4/9, then what is the value of (7x2 – 19xy + 11y2)/y2 ?

A. 59/81

B. 100/27

C. 319/81

D. 913/81

Question 817

If x+1x=5, then the value of x1+x+x2 is

A. 1/5

B. 1/6

C. 5

D. 6

Question 818

What is the square root of 9409?

A. 83

B. 87

C. 89

D. 97

Question 819

1/(tanA + cotA) is equal to

A. (cosecA + sinA)(secA - cosA)

B. √[(cosecA - sinA)(secA - cosA)]

C. √[(cosecA + sinA)(secA - cosA)]

D. (cosecA - sinA)(secA - cosA)

Question 820

Out of the 60 students of a class, 29 took Mathematics, 32 took Biology and 8 took none of the two subjects. How many students took both Mathematics and Biology?

A. 8

B. 9

C. 7

D. 6

Question 821

The value of sinθ+sin∅cosθ+cos∅ + cosθ-cos∅sinθ-sin∅ is

A. 1

B. 2

C. 1/2

D. 0

Question 822

What is the equation of a line which has 3 as x-intercept and -5 as y-intercept?

A. 3x - 5y = 15

B. 5x - 3y = 15

C. 5x + 3y = 15

D. 3x + 5y = 15

Question 823

A and B together have Rs. 6300. If 5/19 of A's amount is equal to 2/5 of B's amount. The amount of 'B' is

A. Rs. 2500

B. Rs. 3800

C. Rs.2300

D. Rs. 4000

Question 824

What is the value of tan3A?

A. (3tanA - tan3A)/(1 - 3tan2A)

B. (3tanA + tan3A)/(1 + 3tan2A)

C. (3tanA - tan3A)/(1 + 3tan2A)

D. (3tanA + tan3A)/(1- 3tan2A)

Question 825

If x = 1 + √2 + √3 , then the value of 2x4 - 8x3 - 5x2 + 26x - 28 is

A. 2√2

B. 3√3

C. 5√5

D. 6√6

Question 826

Reflection of the point (3,-6) in the y-axis is

A. (3,6)

B. (3,-6)

C. (-3,-6)

D. (-3,6)

Question 827

The value of 122 + 345 - 3 / 1116 x 372 is

A. 466

B. 469

C. 446

D. 460

Question 828

If 5x + 1/x = 10, then x2 + 125x2 is equal to

A. 215

B. 335

C. 315

D. 235

Question 829

A man has only 20-paise and 25-paise coins in a bag. If he has 50 coins in all totaling to Rs.10.25, then the number of 20-paise coins is

A. 42

B. 45

C. 38

D. 36

Question 830

-70 + 28 / (7 - 3) = ?

A. -9

B. -69

C. -10.5

D. -63

Question 831

What is the value of tanπ4+A×tan3π4+A ?

A. 1

B. 0

C. cot A/2

D. – 1

Question 832

If tanθ = 724 then find the value of p such that tanθ - secθsinθ = -p28

A. 25

B. 75

C. 50

D. 100

Question 833

The slopes of two lines are 1 and √3. What is the angle between these two lines?

A. 15°

B. 30°

C. 45°

D. 60°

Question 834

If x – (1/x) = 3, then what is the value of (2x4 + 3x3 + 13x2 – 3x + 2) / (3x4 + 3)?

A. 1/3

B. 2/3

C. 4/3

D. 5/3

Question 835

On dividing 111a2b2c2 by 37a2, we get ______.

A. 2c2

B. 2b2

C. 3

D. 3b2c2

Question 836

What is the reflection of the point (4 , -3) in the line y = 1?

A. (4, -5)

B. (4, 5)

C. (-4, -5)

D. (-4, 5)

Question 837

A 12 m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle?

A. 12/π+4

B. 6/π+4

C. 3/π+4

D. 6/π+2√2

Question 838

The value of 16 - [5 - 2{14 of 2 - (8 ÷ 4 x 2 - 1 + 3}] is

A. -12

B. -9

C. -10

D. -14

Question 839

If 3x + [1/(5x)] = 7, then what is the value of 5x/(15x2+ 15x + 1)?

A. 1/5

B. 1/10

C. 2/5

D. 10

Question 840

Which of the following equations has the sum of its roots as 11?

A. x2 - 11x + 18 = 0

B. x2 - 7x + 10 = 0

C. x2 + 2x - 26 = 0

D. x2 + 5x - 6 = 0

Question 841

What is the value of 13×7+17×11+111×15+...+1899×903 ?

A. 21/509

B. 18/403

C. 25/301

D. 29/31

Question 842

If √(1 - sin2A) = x, then the value of x is

A. tanA

B. cosA

C. cosecA

D. secA

Question 843

ΔPQR is right angled at Q. If tanP = 24/7, then what is the value of cosR ?

A. 25/7

B. 24/25

C. 24/7

D. 7/24

Question 844

Reflection of the point (4,-5) in the y-axis is

A. (4,5)

B. (-4,-5)

C. (4,-5)

D. (-4,5)

Question 845

Sumit and Amit undertook a work for Rs 7200. Sumit alone can do the work in 5 days and Amit alone can do the work in 4 days. If they work together,then what will be the difference (in Rs.) in the amount they receive?

A. 800

B. 1600

C. 1200

D. 1400

Question 846

The distance between the points (11,5) and (k,0) is 13. Find k.

A. k = 1 or 23

B. k = -1 or 23

C. k = 1 or -23

D. k = -1 or -23

Question 847

What is the value of tan 7π/6?

A. 1/√3

B. -1/√3

C. √3

D. -√3

Question 848

What is the sum of the first 12 terms of an arithmetic progression if the 3rd term is -13 and the 6th term is -4?

A. 67

B. 45

C. -30

D. -48

Question 849

What is the total number of points in the plane of triangle ABC which is equidistant from the vertices of the triangle?

A. 0

B. 1

C. 2

D. 3

Question 850

What is the value of (√3 - sec60) ?

A. √3-2

B. (1-√6)/√2

C. (2√3-√6)/2√2

D. (1-3√2)/3

Question 851

If a3 + b3 = 28 and a + b = 4, then what is the value of ab?

A. -3

B. 2

C. 8

D. 3

Question 852

If cosC + cosD = x, then value of x is

A. 2cos[(C+D)/2]cos[(C-D)/2]

B. 2sin[(C+D)/2]sin[(C-D)/2]

C. 2cos[(C+D)/2]sin[(C-D)/2]

D. 2sin[(C+D)/2]cos[(C-D)/2]

Question 853

72 ÷ 52 × 3272 ÷ 52 of 32 ÷ 5.25

A. 3/5

B. 3/6

C. 3/7

D. 3/8

Question 854

∆LMN is right angled at M. If m ∠N = 45°. What is the length (in cm) of MN, if NL = 6√2 cm?

A. 3

B. 4

C. 2

D. 6

Question 855

If x2+1x2 = 98, then x3+1x3 = ?

A. 970

B. 1030

C. -970

D. -1030

Question 856

If secA - tanA = x, then the value of x is

A. √[(1 + sinA)/(1 - sinA)]

B. √[(1-sinA)/(1+sinA)]

C. (1-sinA)/(1+sinA)

D. (1 + sinA)/(1 - sinA)

Question 857

If (tanA + tanB)/(1 tanAtanB) = x, then the value of x is

A. tan(A + B)

B. tan(A - B)

C. cot(A + B)

D. cot(A - B)

Question 858

If a2+b2=80 and ab = 32, then calculate the value of a-b/a+b.

A. 0.337

B. 0.339

C. 0.333

D. 0.335

Question 859

If secA + tanA = x, then find the value of x.

A. √[(1 - sinA)/(1 + sinA)]

B. (1 + sinA)/(1 - sinA)

C. (1 - sinA)/(1 + sinA)

D. √[(1 + sinA)/(1 - sinA)]

Question 860

What is the value of tan -240°?

A. -√3

B. 1/√3

C. -1/√3

D. √3

Question 861

If 3+12=x+3y, then the x+y is

A. 2

B. 4

C. 6

D. 8

Question 862

23x12+49x15312+50 = ?

A. 0.5

B. 1

C. 2

D. 3

Question 863

If a+1b= b+1c = c+1a (a , b, c are not equal) then the value of abc =

A. + 1

B. - 1

C. +1 & -1

D. None of the options

Question 864

If a3+1a3 = 2, then the value of a2+1a?

A. 1

B. 2

C. 3

D. 4

Question 865

If 3x - 7 = 5x - 1, then the numerical value of (x - 4)2 is

A. 1

B. 49

C. -1

D. -49

Question 866

If cosec2 θ = 625/576, then what is the value of [(sin θ – cos θ)/(sin θ + cos θ)]?

A. 1

B. 31/17

C. 17/31

D. 14/25

Question 867

If a + b = 11 and a2+ b2= 61, then value of ab is

A. 12

B. 96

C. 24

D. 30

Question 868

What is the value of 96+21624?

A. 8

B. 4

C. 5

D. 10

Question 869

The difference between two numbers is 1146. When we divide the larger number by smaller we get 4 as quotient and 6 as remainder. Find the larger number

A. 1526

B. 1431

C. 1485

D. 1234

Question 870

If α and βare the zeros of the polynomial 5x2 - 7x + 2 then the sum of their reciprocals is

A. 5/2

B. 7/5

C. 2/5

D. 7/2

Question 871

What is the value of Sin 30° - Cosec 45°?

A. (2√6 - 1)/√3

B. (1 - 2√3)/2

C. (√2 - √3)/√6

D. (1 - 2√2)/2

Question 872

The areas of two similar triangles ΔABC and ΔPQR are 121 sq cms and 64 sq cms respectively. If PQ = 12 cm, what is the length (in cm) of AB?

A. 7.25

B. 6.25

C. 16.5

D. 5.25

Question 873

If ax + by = 1 and bx + ay = 2aba2+b2 then x2+y2a2+b2 is equal to

A. 1

B. 2

C. 0.5

D. 0

Question 874

If cos 2π/3c = x, then the value of x is

A. -1/2

B. 1/2

C. -√3/2

D. √3/2

Question 875

If a3 + b3 = 35 and ab = 6, then what is the value of a + b?

A. 5

B. 8

C. 2

D. -8

Question 876

P is a point outside the circle at distance of 6.5 cm from centre O of the circle. PR be a secant such that it intersects the circle at Q and R. If PQ = 4.5 cm and QR = 3.5 cm, then what is the radius (in cm) of the circle?

A. 1.5

B. 2

C. 2.5

D. 3

Question 877

What is the value of √[(1 - sinA)/(1 + sinA)]?

A. cosA/(1 - sinA)

B. cosecA/(1 + sinA)

C. cosA/(1 + sinA)

D. cosecA/(1 - sinA)

Question 878

If √20 + √125 = 15.65, then what is the value of √45 + √5?

A. 6.98

B. 8.94

C. 9.98

D. 11.27

Question 879

Coefficient of x2 in 6x3 + 4x2 + 2x + 3 is

A. 4

B. 6

C. 3

D. 2

Question 880

For real a, b and c if a2 + b2 + c2 = ab + bc + ca, then find the value of a+b+c2.

A. 9a2

B. 81a2

C. 27a2

D. 243a2

Question 881

A bag contain equal number of 1 rupee, 50 paisa and 25 paisa coins. If the total amount is Rs 105, then how many coins of each type are there?

A. 15

B. 45

C. 60

D. 80

Question 882

If 2x -3(x + 2) < 5 - 2x < -x + 2, then find the value of x.

A. 2

B. 0

C. 10

D. 12

Question 883

If a.sin 45°.cos 45°.tan60° = tan 245° cos60° then find the value of a ?

A. 13

B. 3

C. 1

D. 32

Question 884

Simplify 413 + 215 + 414 = ?

A. 10 47/60

B. 11 45/73

C. 11 47/36

D. 10 35/48

Question 885

Cost of 4 pens, 6 note books and 9 files is Rs 305. Cost of 3 pens, 4 notebooks and 2 files is Rs 145. What is the cost (in Rs) of 5 pens, 8 notebooks and 16 files?

A. 415

B. 465

C. 440

D. Cannot be determined

Question 886

A complete factorisation of x4 + 64 is

A. (x2 + 8)2

B. (x2 + 8)(x2 - 8)

C. (x2 - 4x + 8)(x2 -4x - 8)

D. (x2 + 4x + 8)(x2 - 4x + 8)

Question 887

If sec -5π/4 = x, then the value of x is

A. -1/√3

B. -√2

C. -1

D. √3

Question 888

If ab = 21 and a+b2a-b2 = 254,then the value of a2+b2+3ab

A. 115

B. 121

C. 125

D. 127

Question 889

If C+1C = 3, then what is the value of C3+1C3 = ?

A. 0

B. 3√3

C. 1/√3

D. 6√3

Question 890

If Cos θ = 15/17 , then what is the value of Cosec θ?

A. 17/8

B. 8/17

C. 8/15

D. 17/15

Question 891

If 51.97 (81.18 - x ) - 59.39 = 5.268, then value of x will be

A. - 24.912

B. - 68.492

C. 93.868

D. 197.808

Question 892

If sin3A = x, then value of x is

A. 3sinA + 4sin3A

B. 4sin3A - 3sinA

C. 4sin3A + sinA

D. 3sinA - 4sin3A

Question 893

What is the equation of the line if its slope is 2/5 and y-intercept is 6?

A. 2x + 5y = 6

B. 2x + 5y = 30

C. 2x - 5y = 6

D. 2x + 5y = -30

Question 894

If x = 222, y = 223, z = 225 then the value of x3 + y3 + z3 - 3xyz is

A. 4590

B. 4690

C. 4950

D. 4960

Question 895

Find the value of 491321973

A. 17/13

B. 13/17

C. 13/7

D. 17/7

Question 896

If sec 300° = x, then value of x is

A. √2

B. 1/√3

C. 2

D. 1

Question 897

If a3+ b3 = 341 and ab = 30, then what is the value of a + b?

A. 1

B. 9

C. 7

D. 11

Question 898

If price of oranges is increased by 30%, then a person can buy 12 oranges less for Rs 208. What is the original price (in Rs) of an orange?

A. 2

B. 4

C. 8

D. 3

Question 899

Coefficient of x in (x + 8)(6 - 3x) is

A. 18

B. 30

C. -18

D. -30

Question 900

Which of the following is a Pythagorean triplet?

A. 8, 15, 17

B. 17, 21, 29

C. 7, 9, 11

D. 2, 3, 5

Question 901

How many times the keys of a typewriter have to be pressed in order to write numbers from 121 to 1346?

A. 3675

B. 4018

C. 4021

D. 4025

Question 902

If p/q = (x+3)/(x-3), then what is the value of p2+q2p2-q2 ?

A. x+9

B. x2+96x

C. x2+186x

D. 0

Question 903

If sin (3x 20°) = cos (3y + 20°), then find the value of (x + y).

A. 90°

B. 60°

C. 120°

D. 30°

Question 904

If 3x= 4y= 12, then z is equal to

A. xy

B. x + y

C. xy/x+Y

D. 4x +3y

Question 905

The value of (sec245 - cot245) - (sin230 + sin260) is

A. 1

B. 2√3

C. 0

D. 1/√2

Question 906

The point P (a,b) is first reflected in origin to P1 and P1 is reflected in Yaxis to (4,3). The co-ordinates of point P are

A. (4,3)

B. (-4,3)

C. (-3,4)

D. (3,-4)

Question 907

Simplify : (-4.6)x(-4.6)/(-4.6+0.6)

A. -5.29

B. -0.529

C. -4.06

D. 5.01

Question 908

If Tan θ = 7/24, then what is the value of Sec θ?

A. 24/25

B. 24/7

C. 25/7

D. 25/24

Question 909

What is the reflection of the point (2, 3) in the line y = 4?

A. (2, 5)

B. (2, -5)

C. (-2, -5)

D. (-2, 5)

Question 910

What is the value of sin 330°?

A. 2

B. 2/√3

C. √2

D. -1/2

Question 911

What is the value of sin 5π/3?

A. √3/2

B. 2/√3

C. 1/√3

D. -2/√3

Question 912

Solve the following: (−18)[36÷7−(−2)]÷{}(−4)19−(−3)×(−5)={}?

A. -4.5

B. 4.5

C. -2.5

D. 2.5

Question 913

Square root of 0.9 is equal to

A. 0.03

B. 0.3

C. 0.9487

D. 0.9463

Question 914

If α + β = 90° and α:β = 2:1, then the ratio of cosα to cosβ is

A. 1:√3

B. 1:3

C. 1:√2

D. 1:2

Question 915

Which of the following is TRUE?

A. 1123>1294>15

B. 1294>1123>15

C. 15>1123>1294

D. 15>1294>1123

Question 916

tanAcosec2A is equal to

A. (1 + tan2A)cotA

B. (1 - tan2A)cotA

C. √[(1 + tan2A)cotA]

D. √[(1 - tan2A)cotA]

Question 917

The value of cos0 deg is

A. 0

B. infinite

C. not defined

D. 1

Question 918

[sinA/(1 + cosA)] + [(1 + cosA)/sinA] is equal to

A. 2secA

B. 2cosecA

C. 2tanA

D. 2cotA

Question 919

If 3x - 10 = -(2x + 5), then the numerical value of (x - 4)3 is

A. 27

B. 125

C. -125

D. -27

Question 920

If 2 cos θ = 2 – sin θ, then what is the value of cos θ?

A. 1 or 3/5

B. 1 or –1/2

C. –1 or–1/2

D. –1 or 3/5

Question 921

Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?

A. 4/5

B. 9/4

C. 4/9

D. 5/4

Question 922

PQR is an equilateral triangle whose side is 10 cm. What is the value (in cm) of the inradius of triangle PQR?

A. 5/√3

B. 10√3

C. 10/√3

D. 5√2

Question 923

What is the simplified value of (1– sin A cos A)(sin A + cos A)?

A. sin2A – cos2A

B. sin3A + cos3A

C. 0

D. 1

Question 924

What is the area (in sq cm) of a regular hexagon of side 9 cm?

A. 50√3

B. 300√3

C. 243√3/2

D. 200√3

Question 925

If cosA/(1 - sinA) = x, then the value of x is

A. secA - tanA

B. cosecA + tanA

C. secA + tanA

D. cosecA - tanA

Question 926

If (cosecA - 1)/(cosecA + 1) = x, then the value of x is

A. (sinA/(1 + cosA))2

B. cosA/(1 + sinA)

C. (cosA/(1 + sinA))2

D. sinA/(1 + cosA)

Question 927

Find the unit place digit in 192102 + 193103

A. 0

B. 1

C. 3

D. 5

Question 928

If x - y = 7 and x + y = 13, then x2 - y2 is

A. 91

B. -30

C. 30

D. -91

Question 929

If tan(A/2) = x, then the value of x is

A. sinA/(1 - cosA)

B. sinA/(1 + cosA)

C. √[sinA/(1 + cosA)]

D. √[sinA/(1 - cosA)]

Question 930

tan2Asin2A is equal to

A. tan2A - sin2A

B. tan2A + sin2A

C. cot2A - sin2A

D. cot2A + sin2A

Question 931

If x = 1 + √2 + √3, then the value of x2-2x-4=0

A. √6

B. 2√3

C. 3√2

D. 2√6

Question 932

A man spends in 8 months as much as he earns in 6 months. He saves Rs. 6000 in a year. His average monthly income is

A. Rs. 2400

B. Rs. 2000

C. Rs. 2150

D. Rs. 1800

Question 933

The solution set of 4x - 3y = 10 and 3x + y = 14 is

A. {(5, 3)}

B. {(4, 2)}

C. {(11, 1)}

D. {(2, 3)}

Question 934

If (6x - 1) - (8x - 5) = 7, then the value of x is _______ .

A. -3/2

B. 3/2

C. 11/2

D. -11/2

Question 935

If the zeroes of the polynomial x2 - ax + b are 3 and 4, then 'a' and 'b' are respectively equal to

A. 4, 3

B. 12, 7

C. 3, 4

D. 7, 12

Question 936

Find the value of x if 1-x24 = 1318

A. 155

B. 157

C. 159

D. 161

Question 937

What is the value of sin225°+ sin265°?

A. 0

B. 1

C. 2

D. 4

Question 938

If x2-3x+1=0, then x+1x is (x≠0)

A. 1

B. 0

C. 3

D. 2

Question 939

If cosec 45° - sin 30° = x, then x is

A. 5/√3

B. (√6-1)/√2

C. √3+2

D. (2√2-1)/2

Question 940

What is the value of (cos30° + 1/2) ?

A. (√3+1)/√3

B. (√2+1)/√2

C. (√3+1)/2

D. (2√3+1)/√3

Question 941

What is the area (in square units) of the figure enclosed by the x-axis, the y-axis and the line x + 2y = 6 ?

A. 3

B. 6

C. 9

D. 12

Question 942

If tanA + tanB = X, then the value of X is

A. (tanA - tanB)/(1 + tanAtanB)

B. (tanA + tanB)/(1 - tanAtanB)

C. (tanA + tanB)/(1 + tanAtanB)

D. (tanA - tanB)/(1 - tanAtanB)

Question 943

What is the value of cosec 120°

A. 2/√3

B. 2

C. -2/√3

D. -2

Question 944

If tanα = 2 - 1, then the value of tanα - cotα = ?

A. -2

B. √2 + 1

C. 1

D. 2√2

Question 945

If a - b = 2 and ab = 24, then what is the value of a3- b3?

A. 280

B. 124

C. 140

D. 152

Question 946

If x + (1/x) = 2, then what is the value of x21 + (1/x1331)?

A. 0

B. 1

C. 2

D. 3

Question 947

If A and B are the roots of the equation Ax2 – A2x + AB = 0, then what is the value of A and B respectively?

A. 1, 0

B. 1, 1

C. 0, 2

D. 0, 1

Question 948

P + Q = 2(P-Q). If Q = 10, what is the value of P?

A. 10

B. 40

C. 20

D. 30

Question 949

Mayur can complete a work in 27 hours. If he is joined by Jayantika who is 100% more efficient, in what time will they together finish the work?

A. 6 hours

B. 3 hours

C. 9 hours

D. 10 hours

Question 950

Find the value of 6813+6413314

A. 5

B. 6

C. 36

D. 216

Question 951

If cosec 135° = x, then the value of x is

A. √2

B. 2

C. -√2

D. 1/√3

Question 952

ΔXYZ is right angled at Y. If m∠X = 30 deg, then find the value of (sinZ + √3).

A. 4/√3

B. 5/√3

C. 4/3

D. 3√3/2

Question 953

A circle is inscribed in a square. If the length of the diagonal of the square is 14√2 cm, what is the area of the circle?

A. 308 sq cm

B. 462 sq cm

C. 154 sq cm

D. 616 sq cm

Question 954

In ΔPQR measure of angle Q is 90°. If cosP = 5/13, and PQ = 2.5cm, then what is the length (in cm) of side PR?

A. 6

B. 6.5

C. 4

D. 5.6

Question 955

What is the simplified value of 0.042+0.212-0.00840.043+0.213

A. 0.5

B. 2

C. 10.25

D. 10.3

Question 956

If Cos θ = 35/37, then what is the value of Cosec θ?

A. 37/12

B. 33/12

C. 35/12

D. 12/35

Question 957

If 1/√(cosec2A - 1) = x, then value of x is

A. cotA

B. tanA

C. sinA

D. cosA

Question 958

AB is a diameter of a circle. C is a point on the tangent drawn at A . If AB = 8 cm and AC = 6 cm , then the length of BC is

A. 10 cm

B. 14 cm

C. 5 cm

D. 7 cm

Question 959

If the expression px3 – 2x2 – qx + 18 is completely divisible by (x2 – 9), then what is the ratio between p and q respectively?

A. 1:9

B. 1:3

C. 3:1

D. 9:1

Question 960

If a2+b2+c2=83 and a+b+c=15 then the value of ab+bc+ca is

A. 69

B. 70

C. 71

D. 72

Question 961

What is the value 32cos 39sin 51-sin239 + sin251

A. 1/2

B. 5/2

C. 0

D. Both 1/2 and 5/2

Question 962

Shaan got a total of Rs. 912 in the denomination of equal numbers of Rs. 1, Rs. 5 and Rs. 10 coins. How many coins do Shaan posses?

A. 16

B. 57

C. 171

D. 323

Question 963

If 2sec2x - tan2x = 5 and 0° ≤ x ≤ 90° , then x = ?

A. 60°

B. 90°

C. 30°

D. 45°

Question 964

If cosθ + sinθ = m, secθ + cosecθ = n, what is m/n?

A. 1

B. sinθ cosθ

C. secθ cosecθ

D. cotθ tanθ

Question 965

If (x/a) + (y/b) = 3 and (x/b) – (y/a) = 9, then what is the value of x/y?

A. ( b + 3 a)/( a – 3 b)

B. ( a + 3 b)/( b – 3 a)

C. (1 + 3 a)/( a + 3 b)

D. ( a + 3 b2)/( b – 3 a2)

Question 966

Geetha weighs 11.235 kg. Her sister weighs 1.4 times her weight. Find their combined weight?

A. 15.729 kg

B. 25.964 kg

C. 26.964 kg

D. 26.946 kg

Question 967

If 1p+1q = 1p+q, then the value of p3-q3

A. p-q

B. pq

C. 1

D. 0

Question 968

What is the value of Sin 60° + (1/2)Cosec 45°?

A. (√3 + 2)/2

B. (√3 + √2)/√2

C. (√3 + 2)/√2

D. (√3 + √2)/2

Question 969

Point P (-2, 5) is the midpoint of segment AB. Co-ordinates of A are (-5, y) and B are (x, 3). What is the value of x?

A. 1

B. -1

C. 2

D. -2

Question 970

What is the value of 2 - 2z + z22 + 2z - z2, when z+2z = 2 ?

A. 0

B. 2

C. 4

D. 8

Question 971

For triangle ABC, what would be the equation of median AD if co-ordinates of A, B and C are (-5,4), (-4,0) and (-2,2) respectively?

A. 3x - 2y = -11

B. 3x + 2y = 7

C. 3x + 2y = -7

D. 3x - 2y = 11

Question 972

Determine the value of a2+b2a3+b3 when a = 2+√3 and b = 2-√3.

A. 0.27

B. 0.42

C. 0.58

D. 0.93

Question 973

For triangle ABC, find equation of median AD if co-ordinates of points A, B and C are (2,4), (3,0) and (5,2) respectively?

A. 3x - 2y = 14

B. 3x - 2y = 2

C. 3x + 2y = 14

D. 3x + 2y = 2

Question 974

Simplify 576b3x2a4z3/36a3b2z

A. 16bx2az2

B. 8bx2az2

C. 32ba2 z

D. 32bxa2

Question 975

If one root of the equation (1-m)x2 + 1 = 0 is double the other and 'I' is a real number, then which of the following is true?

A. m > 9/8

B. m> 8/9

C. m = 8/9

D. m <= 9/8

Question 976

What is the value of [(cos 3θ + 2cos 5θ + cos 7θ)÷(cos θ + 2cos 3θ + cos 5θ)] + sin 2θ tan 3θ?

A. cos 2θ

B. sin 2θ

C. tan 2θ

D. cot θ sin 2θ

Question 977

What is the value of 34+122 ?

A. 13

B. 15

C. 17

D. 19

Question 978

If x + √5 = 5 + √y, and x, y are positive integers, then the value of x+yx + y

A. 1

B. 2

C. √5

D. 5

Question 979

If cotA + cotB = x, then value of x is

A. (cotAcotB + 1)/(cotB - cotA)

B. (cotAcotB + 1)/(cotB + cotA)

C. (cotAcotB - 1)/(cotB + cotA)

D. (cotAcotB - 1)/(cotB - cotA)

Question 980

If x + 3y - 2z4 = 6, x + 232y + 3z = 33 and 17x + y +z + 2z =9, then what is the value of 46x+ 131y ?

A. 414

B. 364

C. 384

D. 464

Question 981

The difference of 18 and its reciprocal is equal to :

A. 1/8

B. 4/3

C. 15/16

D. 105/304

Question 982

What is the value of 36+729381+643

A. 5/12

B. 5/9

C. 4/9

D. 4/15

Question 983

If 11-13xx + 11-13yy + 11-13zz = 5 then what is the value of 1x + 1y + 1z = ?

A. 1

B. 13/11

C. 13/5

D. 4

Question 984

If x = (√2 + 1)/(√2 – 1), then what is the value of (x5 + x4 + x2 + x)/x3 ?

A. 5

B. 2

C. 2√3

D. 2√2

Question 985

∆XYZ is right angled at Y. If tanX = 24/7, then what is the value of cotZ ?

A. 25/7

B. 24/25

C. 7/24

D. 24/7

Question 986

Product of 6ab, 3b and 4a is

A. 72a2b2

B. 144ab

C. 72ab

D. 144a2b2

Question 987

What is the simplified value of sec6 A – tan6 A – 3 sec2 A tan2 A?

A. -1

B. 0

C. 1

D. sec A tan A

Question 988

The sum of 4x + 3y 7z, x y z and 2x 3y + 4z is

A. 3x - y - 4z

B. 3x - y + 4z

C. 3x + y - 4z

D. 3x + y + 4z

Question 989

If the equation 4x + 3y + 5 = 0 and 6x - ky - 7 = 0 have no solution, then the value of k is

A. -4.5

B. -8

C. 8

D. 4.5

Question 990

19 x 23 = 437. Then 190 x 0.023 = ?

A. 43.7

B. 4.37

C. 0.0437

D. 0.437

Question 991

The sum of the parallel sides of a trapezium is 12.4 cm. If the distance between the parallel sides is 3.5 cm, what is the area of this trapezium?

A. 43.4 sq cm

B. 86.8 sq cm

C. 130.2 sq cm

D. 21.7 sq cm

Question 992

If Cot θ = 21/20, then what is the value of Cosec θ?

A. 21/29

B. 29/21

C. 20/29

D. 29/20

Question 993

If (cotA - cosecA)2 = x, then the value of x is

A. (1 - cosA)/(1 + cosA)

B. (1 - sinA)/(1 + sinA)

C. (1 - secA)/(1 + secA)

D. (1 - cosecA)/(1 + cosecA)

Question 994

If a=101 then the value of a(a2-3a+3) is

A. 1000000

B. 1010101

C. 1000001

D. 999999

Question 995

If 10x/3 + 5/2(2 - x/3) = 7/2, then the value of x is?

A. 3/5

B. -5/3

C. 5/3

D. -3/5

Question 996

If [√(a2 + b2 + ab)] + [√(a2 + b2 – ab)] = 1, then what is the value of (1 – a2 )(1 – b2 )?

A. 1/4

B. 4/7

C. 5/4

D. 3/4

Question 997

The square root of 4096 is

A. 56

B. 68

C. 74

D. 64

Question 998

If α and β are the roots of the equation x2+ x – 1 = 0, then what is the equation whose roots are α5 and β5?

A. x2 + 7x – 1 = 0

B. x2 – 7x – 1 = 0

C. x2 – 11x – 1 = 0

D. x2 + 11x – 1 = 0

Question 999

The sum of 2xy(3x + 4y - 5z) and 5yz(2x - 3y) is

A. 6x2y - 8xy2 + 15y2z

B. 6x2y + 8xy2 - 15y2z

C. 6x2y + 8xy2 - 15y2z - 20xyz

D. 6x2y - 8xy2 + 15y2z + 20xyz

Question 1000

What is the reflection of the point (5, 2) in the line x = -3?

A. (-11 ,2)

B. (-11 ,-2)

C. (11 ,-2)

D. (11 ,2)

Question 1001

Solve the following : 3/4+{3/4 + 3/4 ÷ (3/4 + 3/4)} = ?

A. 0

B. 3/4

C. 1

D. 2

Question 1002

If (x + 1/x) = 3, then x8+1x8 is equal to

A. 2201

B. 2203

C. 2207

D. 2213

Question 1003

If √(1+tan2A) = x, then the value of x is

A. sinA

B. cosecA

C. secA

D. cosA

Question 1004

If 9x - 6(3 - x) = 12, then the value of x is

A. 2

B. 4

C. 6

D. 9

Question 1005

If 3x + 2y = 7 and 4x - y = 24, then x - y = ______.

A. 9

B. 1

C. -9

D. -1

Question 1006

What is the value of Sin 30- √2 Cos 30

A. (1 - √6)/√2

B. (1 - √6)/2

C. (3 - √6)/2

D. (3 - √6)/√2

Question 1007

If 5 sin2θ+ 4 cos2θ= 9/2 and 0 <θ<Π/2 then tanθ is equal to?

A. 1

B. 0

C. -1

D. 1/4

Question 1008

The value of x for which the expressions 15x + 4 and 13x - 2 become equal is ______

A. -1

B. 1

C. -3

D. 3

Question 1009

1/(secA + tanA) is equal to

A. cosecA - cotA

B. sinA - cosA

C. secA - tanA

D. sinA + cosA

Question 1010

If 12x = 192- 112, what is the value of x?

A. 20

B. 17

C. 13

D. 11

Question 1011

Two points P and Q are at the distance of x and y (where y > x) respectively from the base of a building and on a straight line. If the angles of elevation of the top of the building from points P and Q are complementary, then what is the height of the building?

A. xy

B. √( y/ x)

C. √( x/ y)

D. √( xy)

Question 1012

What is the value of (sinA - 2sin3A)/(2cos3A - cosA)?

A. cotA

B. cosecA

C. secA

D. tanA

Question 1013

If 2x+29x = 4, then the value of 27x3+127x3

A. 180

B. 198

C. 234

D. 252

Question 1014

In a farm, there are goats and peacocks. If the number of heads are 60 and the number of feet are 170, then the number of goats = ?

A. 18

B. 20

C. 23

D. 25

Question 1015

The value of (1 - √2) + (√2 - √3) + (√3 - √4) + ..... + (√15 - √16) is

A. 0

B. 1

C. -3

D. 4

Question 1016

The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:

A. Rs. 3500

B. Rs. 3750

C. Rs. 3840

D. Rs. 3900

Question 1017

Δ XYZ is right angled at Y. If m∠Z = 60°, what is the length of YZ (in cm), if ZX = 3√3 cm?

A. 3√3/2

B. 3√3

C. 9

D. 6

Question 1018

If a - b = 1 and ab = 6, then what is the value of a3- b3?

A. 21

B. 23

C. 19

D. 25

Question 1019

If x2-2x+1=0, then the value of x4+1x4 is

A. 0

B. 1

C. 2

D. 3

Question 1020

If a4 + 1 = [a2 /b2 ] (4b2 – b4 – 1), then what is the value of a4 + b4?

A. 2

B. 16

C. 32

D. 64

Question 1021

What is the value of sin6θ + cos6θ + 3 sin2θ cos2θ –1?

A. 0

B. 1

C. 2

D. 4

Question 1022

∆ABC is right angled at B. If m∠A = 30°., then Sec C =?

A. 1/2

B. 1/√2

C. 2

D. 1/√3

Question 1023

Find the value of '?' in 512 × 125 ÷ 15625 = 3125 × 25?

A. 4

B. 3

C. 2

D. 1

Question 1024

What is the value of Cot 45°+ 1/3 Cosec 60°?

A. √3 + 2

B. (9 + 2√3)/9

C. √3

D. (2√2 + 3)/√6

Question 1025

What is the value of [(sin x + sin y) (sin x – sin y)]/[(cosx + cosy) (cosy – cosx)]?

A. 0

B. 1

C. – 1

D. 2

Question 1026

If √(1 + cot2A) = x, then the value of x is

A. secA

B. sinA

C. cosecA

D. cosA

Question 1027

If x(2x + 3) = 90 and 7y-1/2+ 2y-1/2= y1/2 (x and y are positive numbers), then what is the value of x2+ y2?

A. 45

B. 109

C. 117

D. 126

Question 1028

If (8 - 10x) - (13x - 2) = -9, then the value of x is

A. -19/23

B. 19/23

C. -1/23

D. 1/23

Question 1029

If a + b = 1 and ab = -6, then what is the value of a3+ b3?

A. 17

B. 15

C. 19

D. 13

Question 1030

For triangle PQR, what is the equation of altitude PS if coordinates of P, Q and R are (5,1), (0,4) and (2,3) respectively?

A. 7x + 2y = 33

B. 2x - 7y = 9

C. 2x - 7y = -3

D. 7x + 2y = -33

Question 1031

If 2x-12x = 5, then what is the value x2 + 116x2 - 2

A. 19/4

B. 23/4

C. 27/4

D. 31/4

Question 1032

The value of the expression 2(sin6θ+cos6θ) - 3(sin4θ+cos4θ) + 1 is

A. -1

B. 0

C. 1

D. 2

Question 1033

If 7x - 5y = 13 and 2x - y = 5, then (x - y) is

A. 3

B. 4

C. 5

D. 1

Question 1034

The value of cos (1110°) is

A. √3/2

B. 1/2

C. 1/√2

D. 1

Question 1035

What is the value of Tan 60 + Cosec 60?

A. 5/3

B. 2/√3

C. 5/√3

D. 2/3

Question 1036

If cosec 4π/3 = x, then the value of x is

A. √2

B. 2/√3

C. √2

D. -1/√3

Question 1037

The average of 100 observations was calculated as 35.It was found later, that one of the observation was misread as 83 instead of 53. The correct average is :

A. 32.7

B. 34.7

C. 35.7

D. 36.7

Question 1038

Reduce 2530/1430 to lowest terms.

A. 47/17

B. 23/13

C. 47/19

D. 29/17

Question 1039

Find x, if 5x-6+5x+6 = 6

A. -4

B. 0

C. 2

D. 4

Question 1040

If Cosec θ = 17/8, then Cot θ = ?

A. 17/8

B. 15/8

C. 8/15

D. 17/15

Question 1041

If Sec θ = 25/24 , then what is the value of Sin θ?

A. 24/25

B. 7/25

C. 24/7

D. 25/7

Question 1042

If (333 + 333 + 333) (233 + 233) = 6x, then what is the value of x?

A. 34

B. 35

C. 33

D. 33.5

Question 1043

199994 x 200006 = ?

A. 39999799964

B. 39999999864

C. 39999999954

D. 39999999964

Question 1044

Solve : 12 - [26 - {2 + 5 x (6 - 3)}]

A. 2

B. 3

C. 7

D. 8

Question 1045

The first and last terms of an arithmetic progression are 37 and 18. If the sum of the series is 114, then it has how many terms?

A. 13

B. 12

C. 14

D. 15

Question 1046

If 3x + 4y – 11 = 18 and 8x – 6y + 12 = 6, then what is the value of 5x – 3y – 9?

A. 18

B. – 9

C. – 27

D. – 18

Question 1047

A root of equation ax2 + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3√3. What is the value of (a2 + b2 + c2)/(a + b + c)?

A. 35/3

B. 37/3

C. – 105/11

D. – 105/13

Question 1048

If x+1x=5, then 6xx2+x+1 value is

A. 3

B. 2

C. 1

D. 0

Question 1049

Coefficient of x2 in (x + 9)(6 - 4x) is

A. 54

B. -4

C. 30

D. 4

Question 1050

If (x - 4) (x2 + 4x + 16) = x3 - P, then P is equal to

A. 27

B. 8

C. 64

D. 0

Question 1051

If (x – y) = 7, then what is the value of (x – 15)3 – (y – 8)3?

A. 0

B. 343

C. 392

D. 399

Question 1052

If a3 + b 3 = 35 and ab = 6, then what is the value of a + b?

A. 5

B. 8

C. 2

D. -8

Question 1053

If a+b=5 then the value of a-37+b-27 is

A. 27

B. 37

C. 1

D. 0

Question 1054

Calculate the value of 61681x61681-31681x3168130000

A. 93352

B. 94362

C. 93362

D. 95362

Question 1055

What is the value of √2 Sec 45° + (1/√3)Tan 30°?

A. (1 + √3)/2

B. (1 + 3√2)/√3

C. 7/3

D. (3 + 2√2)/3√2

Question 1056

What is the simplest form of (1 + cosA)(cosecA cotA)?

A. cosA

B. tanA

C. cotA

D. sinA

Question 1057

If cot 240° = x, then the value of x is

A. -1

B. -1/√3

C. 1/√3

D. √3

Question 1058

If 2(3x-2) < 6-3x and 6x + 2(6-x) > 2x-2, then x can take which of the following values?

A. -8

B. 5

C. 8

D. -5

Question 1059

If x = a + 1a, y = a - 1a ,(a>0), then the value of x4+y4-2x2y2 is

A. 16

B. 20

C. 10

D. 5

Question 1060

If a+b+c = 0, then (a^3 + b^3 + c^3)^2 = ?

A. 27abc

B. 9abc

C. 3abc

D. 9a^2b^2c^2

Question 1061

If 5(4 - x) - 4 > 5x -2 > 2x - 6, then the value of x is

A. -2

B. 2

C. -1

D. 3

Question 1062

If secθ = cosecq with 0° < θ , q < 90°, then the value of sin (θ + q) is

A. 1

B. 0

C. 2

D. 4

Question 1063

If 4x - 7y = 3 and 2x - y = 9, then x - y is.

A. 3

B. 4

C. 5

D. 6

Question 1064

If ab-1b=cb-1c=ac-1a, then ac+ba+cb

A. 1

B. 2

C. 3

D. 4

Question 1065

∆ABC is right angled at B. If m∠A = 45°, then find the value of (coseC + 1/√3).

A. (3√2+1)/3

B. (2+√3)/2

C. 5/√3

D. (√6+1)/√3

Question 1066

If x2+ y2+ z2= xy + yz + zx, then what is the value of (7x + 3y – 5z)/5x?

A. 0

B. 1

C. 5

D. 33/5

Question 1067

If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ?

A. 500

B. 1000

C. 1500

D. 2000

Question 1068

The sum of a fraction and 4 times its reciprocal is 13/3. What is the fraction?

A. 4/3

B. 3/4

C. 5/4

D. 4/5

Question 1069

Which of the following is correct?

A. (3x - 2y)2 = 9x2 - 12xy + 4y2

B. (3x - 2y)2 = 9x2 - 6xy + 4y2

C. (3x + 2y)2 = 9x2 - 12xy + 4y2

D. (3x + 2y)2 = 9x2 - 6xy + 4y2

Question 1070

38% of 7500 + ?% of 375 = 50% of 6000

A. 50

B. 40

C. 60

D. 45

Question 1071

If 9x2 + 16y2 = 60 and 3x + 4y = 6, then the value of xy is

A. -1

B. 1

C. -2

D. 2

Question 1072

If a = 299, b = 298, c = 297 then the value of 2a3 + 2b3 + 2c3 - 6abc is

A. 5154

B. 5267

C. 5364

D. 5456

Question 1073

Δ LMN is right angled at M. If m∠N = 60°, then Tan L =______.

A. 1/2

B. 1/√3

C. 1/√2

D. 2

Question 1074

α and β are the roots of quadratic equation. If α + β = 8 and α – β = 2√5, then which of the following equation will have roots α4 and β4?

A. x2 – 1522x + 14641 = 0

B. x2 + 1921x + 14641 = 0

C. x2– 1764x + 14641 = 0

D. x2+ 2520x + 14641 = 0

Question 1075

Which of the following quadratic equations has real roots?

A. 4x2 - 3x + 6 = 0

B. 2x2 + 7x + 6 = 0

C. x2 - 2x + 4 = 0

D. 3x2 - 4x + 3 = 0

Question 1076

If a-b=1 and a3-b3 = 61, then the value of ab will be

A. -20

B. 20

C. 30

D. 60

Question 1077

Simplify (533bxaz)/(41ab)

A. 17xzb

B. 19xz

C. 13xz

D. 31ab

Question 1078

If x = 6+26, then what is the value of x-1 + 1x-1 ?

A. 2√3

B. 3√2

C. 2√2

D. 3√3

Question 1079

Find the sum of interior angles of a dodecagon?

A. 1620°

B. 1800°

C. 1440°

D. 1260°

Question 1080

If (1 - cosA)/(1 + cosA) = x, then the value of x is

A. (cotA + cosecA)2

B. (cotA - cosecA)2

C. cotA - cosecA

D. cotA + cosecA

Question 1081

What is the value of sin (90° + 2A)[4 – cos2(90° – 2A)]?

A. 2(cos3 A – sin3 A)

B. 2(cos3 A + sin3 A)

C. 4(cos6 A+ sin6 A)

D. 4(cos6 A – sin6 A)

Question 1082

If 2x-y2+(3y-2z)2=0, then the ratio of x:y:z is

A. 1 : 3 : 2

B. 1 : 2 : 3

C. 3 : 1 : 2

D. 3 : 2 : 1

Question 1083

If √(1 - cos2A) = x, then the value of x is

A. cosecA

B. sinA

C. tanA

D. secA

Question 1084

If x2 + y2 + 6x + 5 = 4(x - y) then x - y is

A. 1

B. -1

C. 0

D. 4

Question 1085

Solve : 1000x - 5 = -6

A. 1/1000

B. -1/1000

C. -11/1000

D. 11/1000

Question 1086

A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook ?

A. 15

B. 20

C. 10

D. 8

Question 1087

The measures of the three angles of a triangle are in the ratio 1:2:3. What is the measure of the biggest angle?

A. 30°

B. 60°

C. 90°

D. 120°

Question 1088

ABCD is a parallelogram. Co-ordinates of A, B and C are (5,0), (-2,3) and (-1,4) respectively. What will be the equation of line AD?

A. y = 2x - 5

B. y = x + 5

C. y = 2x + 5

D. y = x - 5

Question 1089

Find the value of x if 0.08x + 0.04y = 10 and 0.2(x-1) + 0.4y = 24.8

A. 125

B. 150

C. 1.25

D. 12.5

Question 1090

What is the value of z2+1z2 when z = 5+26 ?

A. 49

B. 50

C. 98

D. 100

Question 1091

10 dozen apples, 15 dozen mangoes & 20 dozen oranges are kept for sale. 1/2, 1/3rd & 1/4th of each item respectively have been added. What is the total number of fruits kept for sale now?

A. 720

B. 600

C. 580

D. 820

Question 1092

If 31x + 31y = 403, then what is the average of x and y?

A. 3.5

B. 5

C. 6.5

D. 13

Question 1093

At what point does the line 2x + 5y = -6 cuts the X-axis?

A. (3, 0)

B. (0, 3)

C. (-3, 0)

D. (0, -3)

Question 1094

If sec (3x – 20°) = cosec (3y + 20°), then what is the value of tan (x + y)?

A. 1

B. √3

C. 1/√3

D. 2√3

Question 1095

If √[(1 - cosA)/2] = x, then the value of x is

A. cos(A/2)

B. tan(A/2)

C. sin(A/2)

D. cot(A/2)

Question 1096

What is the value of {sin (90 – x) cos [π – (x – y)]} + {cos (90 – x) sin [π – (y – x)]}?

A. -cos y

B. -sin y

C. cos x

D. tan y

Question 1097

Two equal circles intersect such that each passes through the centre of the other. If the length of the common chord of the circles is 10√3 cm, then what is the diameter of the circle?

A. 10 cm

B. 15 cm

C. 20 cm

D. 30 cm

Question 1098

The value of cos(1110) is

A. √3/2

B. 1/2

C. 1/√2

D. 1

Question 1099

For triangle PQR, find equation of altitude PS if co-ordinates of P, Q and R are (6,2), (0,3) and (-4,5) respectively?

A. 2x - y = 14

B. 2x + y = 10

C. 2x - y = 10

D. 2x + y = 14

Question 1100

If 11+11+11+1x = 58, then what is the value of x?

A. 2

B. 3

C. 1

D. 4

Question 1101

cot2A + cos2A is equal to

A. (cosecA - sinA)2(cosecA + sinA)

B. (cosecA + sinA)(cosecA - sinA)

C. (secA + sinA)(secA - sinA)

D. (secA - sinA)2(secA + sinA)

Question 1102

If A = (-14 + 4) and B = 4 - 14, then AB =

A. 0

B. -100

C. 100

D. -1

Question 1103

On dividing 8a2b2c2 by 4a2, we get

A. 2b2

B. 2c2

C. 2b2c2

D. 2

Question 1104

If a + b = 8 and ab =15, then a3 + b3 is

A. 224

B. 244

C. 152

D. 128

Question 1105

If secθ + tanθ = 4, then secθ - tanθ = ?

A. 1

B. 0.25

C. 0.5

D. 0.75

Question 1106

ABC is a right angled triangle. ∠BAC = 90 deg and ∠ACB = 60 deg. What is the ratio of the circum radius of the triangle to the side AB?

A. 1 : 2

B. 1 : √3

C. 2 : √3

D. 2 : 3

Question 1107

If √(1 + cot2A)/cotA = x, then the value of x is

A. sinA

B. cosecA

C. secA

D. cosA

Question 1108

5 bottles cost as much as 2 bags. The cost of 15 bottles and 4 bags is Rs 2,000. What is the price (in Rs.) of a single bag?

A. 200

B. 215

C. 240

D. 250

Question 1109

Value of (cos 53° - sin 37°) is

A. 2 sin 37 ̊

B. 2 cos 53 ̊

C. 0

D. 1

Question 1110

If a = 2 , b = 3 then the value of 27a3 - 54a2b + 36ab2 - 8b3 is

A. 1562

B. 1616

C. 1676

D. 1728

Question 1111

The value of x for which the expressions 15 7x and 15x + 7 become equal is _____.

A. -4/11

B. 11/4

C. -11/4

D. 4/11

Question 1112

If (1 + sinA)/cosA + cosA/(1 + sinA) = x, then the value of x is

A. 2cosecA

B. 2cosec2A

C. 2sec2A

D. 2secA

Question 1113

What is the simplified value of sec4θ – sec2θ tan2θ?

A. cosec2θ

B. Cot2θ

C. sec2 θ

D. secθ tan θ

Question 1114

If (1/cos θ) – (1/cot θ) = 1/P, then what is the value of cos θ?

A. (P + 1)/(P – 1)

B. (P2+ 1)/2P

C. 2(P2+ 1)/P

D. 2P/(P2+ 1)

Question 1115

What is the value of cos (90 – B) sin (C – A) + sin (90 + A) cos (B + C) – sin (90 – C) cos (A + B)?

A. 1

B. sin ( A + B – C)

C. cos ( B + C – A)

D. 0

Question 1116

Calculate the value of 61681 x 61681 - 31681 x 3168130000?

A. 93352

B. 94362

C. 93362

D. 95362

Question 1117

The sum of a fraction and 3 times its reciprocal is 37/10. What is the fraction?

A. 5/2

B. 2/5

C. 5/4

D. 4/5

Question 1118

What is the equation of a line of slope 1/3 and y-intercept 5?

A. x - 3y = -15

B. x - 3y = 15

C. x + 3y = -15

D. x + 3y = 15

Question 1119

If secA + tanA = x, then the value of x is

A. cosA/(1 + sinA)

B. √[cosA/(1 - sinA)]

C. √[cosA/(1 + sinA)]

D. cosA/(1 - sinA)

Question 1120

For x > 0, what is the minimum value of x + x+22x?

A. 1

B. 2

C. 2.5

D. 1.5

Question 1121

An army lost 10% of its men in war, 10% of the remaining died due to disease and 10% of the rest were declared disabled. Thus the strength of the army was reduced to 7,29,000 active men. The original strength of the army was

A. 1500000

B. 1000000

C. 1200000

D. 1100000

Question 1122

A ship is full of cargo containers. It drops 2/3 of cargo containers at the first port and takes 60 more, at the second port it drops two third of the new total and takes eleven more. On arriving at the third port it is found that it have 48 cargo containers. Find the number of cargo containers in the ship at the starting?

A. 189

B. 159

C. 161

D. 153

Question 1123

A tetrahedron has 4 vertices. How many edges does it have?

A. 8

B. 12

C. 6

D. 10

Question 1124

If a = 73, b = 74 and c = 75, then what is the value of a3 + b3 + c3 – 3abc?

A. 365

B. 444

C. 666

D. 999

Question 1125

If tanA - tanB = X, then the value of X is

A. (tanA + tanB)/(1 - tanAtanB)

B. (tanA + tanB)/(1 + tanAtanB)

C. (tanA - tanB)/(1- tanAtanB)

D. (tanA - tanB)/(1 + tanAtanB)

Question 1126

Point P is the midpoint of seg AB. Co-ordinates of P are (-1,1) and A are (4,3). What are the co-ordinates of point B?

A. (6, 1)

B. (-6, 1)

C. (6, -1)

D. (-6, -1)

Question 1127

Square of (3x – 5xy) is

A. 9x2 - 30x2y + 25x2y2

B. 9x2 - 15x2y + 25x2y2

C. 25x2 - 15x2y + 9x2y2

D. 25x2 - 30x2y + 9x2y2

Question 1128

There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:

A. 20

B. 80

C. 100

D. 200

Question 1129

ΔDEF is right angled at E. If secD = 25/7, then what is the value of cosecF ?

A. 7/25

B. 24/7

C. 25/7

D. 7/24

Question 1130

Coefficient of x in (x + 9)(8 - 5x) is

A. 37

B. -53

C. -37

D. 53

Question 1131

If a + b = 10 and ab = 24, then what is the value of a3 + b3?

A. 280

B. 152

C. 140

D. 72

Question 1132

What is the value of (sin60° - 2/√3) ?

A. -1/2√3

B. -1/2

C. 1/√3

D. (1-2√3)/2

Question 1133

If Tan θ = 7/24, then what is the value of Cosec θ?

A. 25/24

B. 25/7

C. 24/7

D. 24/25

Question 1134

ΔPQR is right angled at Q. If cosP = 5/13, then what is the value of cosecR ?

A. 13/5

B. 5/12

C. 5/13

D. 13/12

Question 1135

sinA/(1 + cos A) is equal to

A. (cosecA - cotA)

B. (cosecA + cotA)

C. √[(cosecA - cotA)]

D. √[(cosecA + cotA)]

Question 1136

If √x - √y = 1 , √x + √y = 17 then √xy = ?

A. √72

B. 72

C. 32

D. 24

Question 1137

What is the equation of the line which passes through the points (3,2) and (5,3)?

A. 5x - 2y = -19

B. 5x - 2y = 19

C. 5x + 2y = 31

D. 5x + 2y = -31

Question 1138

What is the value of (1/√3 + sin45 ) ?

A. √3+2

B. (√2+√3)/√6

C. (1+√6)/√3

D. (4+√3)/2

Question 1139

If α and β are the roots of equation x2 – x + 1 = 0, then which equation will have roots α3 and β3?

A. x2 + 2x + 1 = 0

B. x2 – 2x – 1 = 0

C. x2 + 3x – 1 = 0

D. x2 – 3x + 1 = 0

Question 1140

If P2+1P2 = 47, then the value of P + 1P is

A. 5

B. 6

C. 7

D. 8

Question 1141

What is the value of [(cos32θ + 3 cos 2θ)÷(cos6θ – sin6θ)]?

A. 0

B. 1

C. 2

D. 4

Question 1142

If (4x - 3) = (3x + 8), then the numerical value of(x + 1)3 is

A. 1331

B. 1000

C. 1728

D. 729

Question 1143

What is the value of (cosec30 - 1/√3)?

A. (2√3-1)/√3

B. (√3-4)/2√3

C. -1/√3

D. 2/√3

Question 1144

What is the value of xy if x - y = 3 and x2+y2=15?

A. 1

B. 3

C. 5

D. 7

Question 1145

If √(sec2A - 1)/secA = x, then the value of x is

A. cosecA

B. cosA

C. sinA

D. tanA

Question 1146

If the value of √42 is approximately 6.480, then what is the approximate value of √(6/7)?

A. 0.925

B. 0.935

C. 0.945

D. 0.955

Question 1147

If 310 × 272 = 92 × 3n then the value of n is

A. 10

B. 12

C. 15

D. 20

Question 1148

The pair of linear equations 3x + y = 1 and px + 2y = 5 has no finite solution if

A. p>=6

B. p = 6

C. 0 < p < 6

D. p = 0

Question 1149

∆PQR is right angled at Q. If sinP = 12/13, then what is the value of tanR?

A. 5/13

B. 13/5

C. 13/12

D. 5/12

Question 1150

Anuj runs 1 2/3 laps of 7 laps race, find the remaining laps to be run.

A. 16/3

B. 14/3

C. 11/3

D. 10/3

Question 1151

If 2x + 3 = 9 then find the value of 3x + 2

A. 12

B. 16

C. 13

D. 11

Question 1152

By how much is three-fifth of 350 greater than four-seventh of 210 ?

A. 90

B. 100

C. 110

D. 120

Question 1153

If x = cosecθ - sinθ and y = secθ - cosθ, then the relation between x and y is

A. x2+ y2+ 3 =1

B. x2y2 (x2+ y2+3)=1

C. x2 (x2+ y2 - 5)=1

D. y2 (x2+ y2 - 5)=1

Question 1154

If cosx.cosy + sinx.siny = -1 then cosx + cosy is

A. -2

B. 1

C. 0

D. 2

Question 1155

What is the difference between the total sale of English newspapers and the total sale of Hindi newspapers in all the localities together.

A. 7500

B. 5600

C. 6500

D. 5700

Question 1156

What is the value of [sin (90– 10θ) – cos (p – 6θ)]/ [cos (p/2 – 10θ) – sin (p – 6θ)]?

A. tan 2θ

B. cot 2θ

C. cot θ

D. cot 3θ

Question 1157

Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:

A. 1/7

B. 1/8

C. 1/9

D. 7/8

Question 1158

√(1 + tan2A)/tanA is equal to

A. secA

B. sinA

C. cosecA

D. cosA

Question 1159

If 60/75 is equivalent to 4/x, then the value of x is

A. 5

B. 4

C. 15

D. 18

Question 1160

Coefficient of x in (x + 11)(3 - 5x) is _____.

A. 33

B. -5

C. 3

D. -52

Question 1161

What is the simplified value of 31253 + 4253 + 36753

A. 18253

B. 5253

C. 9√125

D. 1253

Question 1162

A sum of Rs. 1360 has been divided among A, B and C such that A gets 2/3 of what B gets and B gets 1/4 of what C gets. B's share is:

A. Rs. 120

B. Rs. 160

C. Rs. 240

D. Rs. 300

Question 1163

If cos -300° = x, then the value of x is

A. 1/2

B. -1/√2

C. -1/2

D. √3/2

Question 1164

If a + b = 10 and ab = 21, then the value of (a - b)2 is

A. 15

B. 16

C. 17

D. 18

Question 1165

If cos 21° = x/y, then cosec 21° - cos 69° is equal to

A. x2yy2-x2

B. y2xy2-x2

C. y2xx2-y2

D. x2yx2-y2

Question 1166

If tan2θ + cot2θ = 2, then what is the value of 2sec θ cosec θ?

A. 0

B. 1

C. 2

D. 4

Question 1167

If 3x2 = 102 - 52, find the value of x?

A. 7

B. 5

C. 9

D. 11

Question 1168

Given w = -2, x = 3, y = 0 & z = -1/2. Find the value of (z/w) + x.

A. 13/4

B. -13/4

C. 3.2

D. 3.5

Question 1169

If cotA = x, then the value of x is

A. √(sec2A + 1)

B. √(cosec2A + 1)

C. √(sec2A - 1)

D. √(cosec2A - 1)

Question 1170

What is the value of sec 30° + cot 30°?

A. (√6-1)/√2

B. √3+2

C. 5/√3

D. (√3-2√2)/√6

Question 1171

What are the components of X6 - X4 - X5 - X4 + X2 - 4?

A. (X - 1)

B. (X + 2)

C. Both 1 and 2

D. Neither 1 nor 2

Question 1172

If cot(A/2) = x, then the value of x is

A. cosecA - cotA

B. cosecA + cotA

C. secA + cotA

D. secA - cotA

Question 1173

If x + 1/x = √13, then 3x(x2-1) equal to

A. 3√13

B. √13/3

C. 1

D. 3

Question 1174

If x = 1 – y and x2 = 2 – y2, then what is the value of xy?

A. 1

B. 2

C. -1/2

D. -1

Question 1175

If P=9, Q=17 then the value of p2-q2-13

A. 4

B. 1/4

C. 3

D. 1/3

Question 1176

What are the coordinates of the centroid of a triangle, whose vertices are A(2,5), B(4,4) and C(7,3)?

A. (4,-3)

B. (-1,0)

C. (-3,-3)

D. (3,-2)

Question 1177

Δ PQR is right angled at Q. If m√R = 30°, then what is the value of Cot P?

A. 1/2

B. 1/√2

C. 1/√3

D. 2

Question 1178

Reflection of the point (2,5) in the x axis is

A. (2,5)

B. (-2,5)

C. (2,-5)

D. (-2,-5)

Question 1179

What is the simplified value of 18 - 12 ?

A. 5/√2

B. 5√2

C. 2√5

D. 2/√5

Question 1180

If 23x + 23y = 184, then what is the average of x and y?

A. 2

B. 4

C. 3

D. 2.5

Question 1181

If cot -4π/3 = x, then the value of x is

A. -1

B. -1/√3

C. √3

D. 1

Question 1182

If (x – 2)2 + (y + 3)2 + (z – 15)2 = 0, then what is the value of x + y + z – 5?

A. 5

B. 9

C. 15

D. 20

Question 1183

If x+y+z = 1, 1/x + 1/y + 1/z = 1 and xyz = -1, then x3+y3+z3 is equal to

A. -1

B. 1

C. -2

D. 2

Question 1184

If cos -11π/6 = x, then the value of x is

A. -√3/2

B. 1/2

C. -2

D. √3/2

Question 1185

The distance between the points (7,7) and (k,-5) is 13. Find k?

A. -2

B. 4

C. -4

D. 2

Question 1186

What is the value of cosec 3π/4?

A. -√2

B. √2

C. 2/√3

D. -2/√3

Question 1187

When x2+ax+b is divided by (x-1), the remainder is 15 and when x2+bx+a is divided by (x+1), the remainder is -1, then the value of a2+b2 is

A. 10

B. 20

C. 8

D. 16

Question 1188

If cosθ1-sinθ+cosθ1+sinθ = 4, then the value of θ (0°<θ<90°)?

A. 60°

B. 45°

C. 30°

D. 35°

Question 1189

What is the value of the expression a3 - 5 + 2816a, when a = 2?

A. 2

B. 5

C. 7

D. 8

Question 1190

ΔPQR is right angled at Q. If secP = 13/5, then what is the value of sinR ?

A. 5/13

B. 5/12

C. 13/5

D. 13/12

Question 1191

The co-ordinates of the centroid of a triangle ABC are (3,-2). What are the co-ordinates of vertex C if co-ordinates of A and B are (-2,5) and (6,-2) respectively?

A. (-5,-9)

B. (5,-9)

C. (5,9)

D. (-5,9)

Question 1192

What is the value of a2 + b2a3 - b3, when a + b = 8 and a - b = 2?

A. 0.313

B. 0.347

C. 0.368

D. 0.381

Question 1193

If tan -5π/3 = x, then the value of x is

A. √3

B. 1

C. -1/2

D. √3/2

Question 1194

What is the value of 5.6x0.36+0.42x3.20.8 x 2.1 ?

A. 2

B. 1

C. 3

D. 3/2

Question 1195

What is the value of cot 5π/3?

A. 1/√3

B. -1/√3

C. √3

D. -√3

Question 1196

The least value of tan2x + cot2x is

A. 3

B. 2

C. 0

D. 1

Question 1197

A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:

A. 30 birds

B. 60 birds

C. 72 birds

D. 90 birds

Question 1198

Δ XYZ is right angled at Y. If m∠Z = 60°, then what is the value of (1/√2) Sec X?

A. 2/√3

B. 1/√6

C. 1/√3

D. 2/√6

Question 1199

Which of the following pair of numbers is the solution of the equation 3x+2+ 3–x= 10 ?

A. 0, 2

B. 0, -2

C. 1, -1

D. 1, 2

Question 1200

If 1/3(12x/5 - 1/2) + 6/5 = 7/6, then what is the value of x?

A. 1/6

B. -1/6

C. 1/5

D. -1/5

Question 1201

If 2cosAsinB = x, then the value of x is?

A. sin(A+B) + sin(A-B)

B. cos(A+B) + cos(A-B)

C. sin(A+B) - sin(A-B)

D. cos(A-B) - cos(A+B)

Question 1202

A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed :

A. 30 birds

B. 60 birds

C. 72 birds

D. 90 birds

Question 1203

If 1 = 2, 3 = 6, 4 = 8, and + = -, what would be the value of 41 + 34 + 13 = ?

A. -88

B. 88

C. 12

D. -12

Question 1204

If m n = 2 , mn = 15 , (m , n > 0) then the value of m2-n2m3-n3

A. 1856

B. 1658

C. 1586

D. 1568

Question 1205

Which of the following is not a quadratic equation?

A. 3x(x + 5) 11 = 2x(x - 2) + 6

B. 4x(x + 3) + 7 = 4x(x - 11) + 9

C. x(x + 2) 15 = x(2x - 5) + 11

D. 4x - 6x + 9 = 0

Question 1206

If 9x = 24311, then what is the value of x?

A. 5/11

B. 5/22

C. 5/7

D. 5/33

Question 1207

If cos 240° = x, then value of x is

A. -1/√2

B. -√3/2

C. 1/2

D. -1/2

Question 1208

Determine the value of z in the equation: z = 20+20+20+20+...∞

A. 4

B. 5

C. 20

D. 25

Question 1209

If x2 – 4x + 1 = 0, then what is the value of x9 + x7 – 194x5 – 194x3?

A. 4

B. – 4

C. 1

D. – 1

Question 1210

If a + b = 10 and ab = 24, then the value of a3 + b3 is

A. 280

B. 370

C. 520

D. 730

Question 1211

A 8 cm long perpendicular is drawn from the centre of a circle to a 12 cm long chord. The diameter of the circle is

A. 10 cm

B. 12 cm

C. 16 cm

D. 20 cm

Question 1212

What is the value of Cot 60 - Sec 30?

A. -1/3

B. -1/√3

C. 1/√3

D. 1/3

Question 1213

Point P is the midpoint of segment AB. Co-ordinates of P are (5, -1) and A are (2, -4). What are the co-ordinates of point B?

A. (6, 4)

B. (8, 2)

C. (1,-2)

D. (-6, -2)

Question 1214

The slope of the line passing through the points (2,-1) and (x,5) is -1. Find x?

A. 4

B. -4

C. 8

D. -8

Question 1215

The first and last terms of an arithmetic progression are 25 and 52. What is the sum of the series if it has 12 terms?

A. -162

B. -110

C. 162

D. 110

Question 1216

What is the equation of the line whose y-intercept is 4 and making an angle of 45° with the positive x-axis?

A. x + y = -4

B. x - y = 4

C. x + y = 4

D. x - y = -4

Question 1217

What is the value of 23+5252-23 ?

A. 9

B. 49

C. 561

D. 571

Question 1218

What is the slope of the line 2x - 5y = 12?

A. 2/5

B. 5/2

C. -2/5

D. -5/2

Question 1219

If X + Y + Z = 9 then the value of (X - 4)3 + (Y - 2)3 + (Z - 3)3 - 3 (X - 4) (Y - Z) (Z - 3) is

A. 6

B. 9

C. 0

D. 1

Question 1220

A line passing through the origin perpendicularly cuts the line 3x - 2y = 6 at point M. Find M?

A. (18/13, 12/13)

B. (18/13, -12/13)

C. (-18/13, -12/13)

D. (-18/13, 12/13)

Question 1221

If sin - 4π/3 = x, then the value of x is

A. -2

B. -2/√3

C. √3/2

D. √2

Question 1222

Solve the following 7 x {4 + (-2) x (-3)} = ?

A. 14

B. -42

C. -14

D. 70

Question 1223

If 5x - 5(3x - 2) < 4x - 1 < 2 + 2x, then x can take which of the following values?

A. 2

B. 1

C. -1

D. -2

Question 1224

Simplify (b2x 3a2z4 ) × (b2x 4a4z3 )/(a3b2z4 )

A. b2x7a3z3

B. b3x7a3 z3

C. b2x5a3 z3

D. b2x7a3z2

Question 1225

What is the simplified value of (sec A + cos A)(sec A – cos A)?

A. 2 tan2A

B. 2 sin2 A

C. sin2 A tan2 A

D. sin2A + tan2 A

Question 1226

If (5/9 of x) - (2/5 of 9/4) equals -4/5 then find x.

A. 0.18

B. 0.12

C. 2

D. 0.54

Question 1227

If a = 3+23-2, b = 3-23+2 then a2+b2-ab ?

A. 97

B. (2√3) + 2

C. (4√6) + 1

D. 98

Question 1228

If x2 + (1/x2) = 1, then what is the value of x48 + x42 + x36 + x30 + x24 + x18 + x12 + x6 + 1?

A. -9

B. 0

C. 1

D. 9

Question 1229

Determine the value of “s” for which the equation 5x + 35 = 60x + s has infinite number of solutions.

A. 420

B. 440

C. 460

D. 480

Question 1230

In a slip test, K got the 15th rank and he was 44th from the bottom of the list of passed students. 4 students did not take up the slip test and 3 students were failed. What is the total strenght of the class ?

A. 63

B. 62

C. 64

D. 65

Question 1231

If x = (√5) + 1 and y = (√5) – 1, then what is the value of (x2/y2) + (y2/x2) + 4[(x/y) + (y/x)] + 6?

A. 31

B. 23√5

C. 27√5

D. 25

Question 1232

Simplify x5 ÷ x43 ÷ x

A. x3

B. x2

C. X

D. 1/X

Question 1233

If ab+ba = -1, then the value of a2b-b2a is

A. 1

B. -1

C. 0

D. 2

Question 1234

PQ is a tangent to the circle at T. If TR = TS where R and S are points on the circle and ∠RST = 65°, the ∠PTS =

A. 65°

B. 130°

C. 115°

D. 55°

Question 1235

If Cosec θ = 17/8, then what is the value of Cos θ?

A. 15/8

B. 15/17

C. 8/15

D. 17/15

Question 1236

If [4(2x/5 - 3/2)]/3 + 7/5 = 37/5, then what is the value of x?

A. -15

B. 7/5

C. 15

D. -7/5

Question 1237

If u+v = 10 and uv = 16, then find the value of u2-v2uv

A. 0

B. 15/8

C. 15/4

D. 15/2

Question 1238

If x3+ 2x2– 5x + k is divisible by x + 1, then what is the value of k?

A. -6

B. -1

C. 0

D. 6

Question 1239

If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what is the value of (a + c)/b?

A. 9/5

B. 11/7

C. 7/11

D. 7/4

Question 1240

What is the value of sec 4π/3?

A. 2

B. -2

C. 2/√3

D. -2/√3

Question 1241

If n + n2 + n4 + n8 = 45, then find the value of 'n' which will satisfy the equation.

A. 16

B. 24

C. 36

D. 48

Question 1242

Which of the following quadratic equations has equal roots?

A. x2 - 14x - 49 = 0

B. x2 + 7x + 49 = 0

C. x2 - 7x - 49 = 0

D. x2 + 14x + 49 = 0

Question 1243

If -3/2 + (2/3)(3x + 9) = x/2, then what is the value of x?

A. -9

B. 11

C. 9

D. -3

Question 1244

If 2x - 6 ≤ x - 3 and 1+3x < 4x + 4, then x can take which of the following values?

A. 4

B. -4

C. -6

D. 2

Question 1245

If cot(A/2) = x, then x is equal to

A. tanA/(1 + secA)

B. 1/(secA + cotA)

C. tanA/(1 + cosecA)

D. 1/(cosecA - cotA)

Question 1246

If 5 3x < 4 x and 5(2 x) > 2 2x, then x can take which of the following values?

A. 0

B. 1

C. 3

D. -1

Question 1247

What are the co-ordinates of the mid point of the segment joining points C(0,-3) and D(8,5)?

A. (4, 1)

B. (-4, 1)

C. (4, -1)

D. (-4, -1)

Question 1248

If 7x + 6y = 5xy and 10x - 4y = 4xy, then value of x and y is

A. 3, 2

B. 2, 3

C. 4, 2

D. 5, 6

Question 1249

What are the roots of the quadratic equation: x2 + 3x - 154 = 0

A. 11, 14

B. 11, -14

C. 14, -11

D. 14, -22

Question 1250

The points A(3,-2), B(1,4) and C(-2,x) are collinear. What is the value of x?

A. 13

B. -2

C. 5

D. 3

Question 1251

If √(sec2A 1) = x, then the value of x is

A. cotA

B. tanA

C. cosecA

D. cosA

Question 1252

What is the value of (cos 40° – cos 140°)/(sin 80° + sin 20°)?

A. 2√3

B. 2/√3

C. 1/√3

D. √3

Question 1253

Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?

A. 256

B. 432

C. 512

D. 640

Question 1254

The square root of 6084 is

A. 82

B. 78

C. 74

D. 76

Question 1255

Consider a regular hexagon ABCDEF. Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is 30 deg, and the angle of elevation to the top of the tower at C is 45 deg. What is the ratio of the height of towers at B and C?

A. 1:√3

B. 1:3

C. 1:2

D. 1:2√3

Question 1256

If (x/y)a-4 = (y/x)2a-5, then what is the relation between x and y?

A. x > y

B. Cannot be determined

C. x < y

D. x = y

Question 1257

If 3x+22x+1 = a2x+1+bx+2 be an identity, then the value of b

A. 0

B. -1

C. 2

D. 3

Question 1258

An angle is greater than its complementary angle by 30°. Find the measure of the angle?

A. 30°

B. 90°

C. 60°

D. 120°

Question 1259

If x-1x = 10, then find the value of x4+1x2

A. 98

B. 100

C. 102

D. 106

Question 1260

If 4(x+y) = 256 and (256)(x-y) = 4, then what is the value of x and y?

A. 17/8, 15/8

B. 17/4, 15/4

C. 9/17, 15/17

D. 8/17, 8/15

Question 1261

If cot2A - cos2A = x, then value of x is

A. tan2Asec2A

B. cotAcosA

C. cot2Acos2A

D. tanAsecA

Question 1262

ΔXYZ is right angled at Y. If m∠Z = 45°, then find the value of (cosecX - 2/√3).

A. (2-√3)/2√3

B. (1-√6)/√2

C. (√6-2)/√3

D. -1/√3

Question 1263

If x - y = -6 and x + y = 16, then x2- y2 is?

A. 96

B. -96

C. 22

D. -22

Question 1264

A tailor has 37.5 metres of cloth and he has to make 8 pieces out of a metre of cloth. How many pieces can he make out of half of the cloth he has ?

A. 300

B. 150

C. 175

D. 200

Question 1265

If 2secA - (1 + sinA)/cosA = x, then the value of x is

A. cosecA/(1+sinA)

B. cosA/(1+sinA)

C. cosA(1+sinA)

D. cosecA(1+sinA)

Question 1266

If (36 - 16x) - (4x - 8) = 4, then the value of x is

A. 4

B. 2

C. 6

D. 3

Question 1267

If 2x+2x=3, then the value of x3+1x3+2 is

A. 3/4

B. 4/5

C. 5/8

D. 7/8

Question 1268

If a + b = 3 and ab = -4, then what is the value of a3 + b3?

A. 36

B. 63

C. 12

D. -15

Question 1269

Point P is the midpoint of segment AB. Co-ordinates of P are (5,-4) and A are (7,0). What will be the co-ordinates of point B?

A. (3, -8)

B. (-3, -8)

C. (3, 8)

D. (-3, 8)

Question 1270

ΔDEF is right angled at E. If cosecD = 5/4, then what is the value of cosecF?

A. 5/3

B. 3/4

C. 4/5

D. 4/3

Question 1271

If 2x + (9/x) = 9, then what is the minimum value of x2+1x2 = ?

A. 95/36

B. 97/36

C. 87/25

D. 623/27

Question 1272

If secA/(secA - 1) + secA/(secA + 1) = x, then x is

A. 2cosec2A

B. 2sec2A

C. 2cosecA

D. 2secA

Question 1273

If Sin x = 4/5, then Cosec x + Cot x =

A. 31/12

B. 35/12

C. 2

D. 1/2

Question 1274

If Tan θ = 9/40, then Sec θ = ?

A. 40/41

B. 9/41

C. 41/40

D. 41/9

Question 1275

∆XYZ is right angled at Y. If tanX = 15/8, then what is the value of sinZ ?

A. 15/17

B. 17/8

C. 17/15

D. 8/17

Question 1276

What is the equation of the line passing through the point (-1,3) and having x-intercept of 4 units?

A. 3x - 5y = 12

B. 3x + 5y = 12

C. 3x + 5y = -12

D. 3x - 5y = -12

Question 1277

If a - b = 10 and ab =-21, then what is the value of a3-b3 ?

A. 316

B. 370

C. 185

D. 158

Question 1278

If 4x + 1x = 5, (x≠0), then the value of 5x4x2+10x+1 is

A. 1/2

B. 1/3

C. 2/3

D. 3

Question 1279

Find k, if the line 4x - y = 1 is perpendicular to the line 5x - ky = 2?

A. 20

B. -20

C. 4

D. -4

Question 1280

How many 18' s are there in 3712?

A. 300

B. 400

C. 500

D. 600

Question 1281

The point Q(a,b) is first reflected in yaxis to Q1 and Q1 is reflected in xaxis to (6,2). The coordinates of point Q are

A. (-6,2)

B. (2,-6)

C. (6,-2)

D. (-2,6)

Question 1282

If 2x + 5 > 2 + 3x and 2x - 3 ≤ 4x - 5, then x can take which of the following values?

A. -2

B. 2

C. -4

D. 4

Question 1283

What is the value of (4a2 - 9b2 )/(2a + 3b) is

A. 2a - 3b

B. 2a + 3b

C. 2a

D. 3b

Question 1284

If 5x + 6(3-2x) = 4, then what is the value of x?

A. 1

B. 2

C. 3

D. 4

Question 1285

Compute 33800/520/5

A. 31

B. 325

C. 13

D. 352

Question 1286

What is the slope of the line parallel to the line passing through the points (-4,-6) and (2,-3)?

A. -1/2

B. -2

C. 2

D. 1/2

Question 1287

If √5 = 2.236, then √5/2 is

A. 1.851

B. 1.118

C. 2.236

D. 1.782

Question 1288

Which of the following quadratic equations has real roots?

A. 4x2 - 9x + 6 = 0

B. 3x2 - 2x + 6 = 0

C. 2x2 - 7x + 6 = 0

D. x2 - 2x + 2 = 0

Question 1289

The point R(a,b) is first reflected in origin to R1 and R1 is reflected in xaxis to (-4,2). The co-ordinates of point R are

A. (4,-2)

B. (-4,2)

C. (4,2)

D. (-4,-2)

Question 1290

The simplest form of 3565/1495 is

A. 31/13

B. 43/19

C. 23/13

D. 31/23

Question 1291

Δ ABC is right angled at B. If m∠A = 60°, then what is the value of 2 Sec C x 1/2 Sin A?

A. 1/2

B. 1/3

C. 1

D. 1/√2

Question 1292

In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group ?

A. 6

B. 10

C. 8

D. 12

Question 1293

What is the equation of the line which intercepts xaxis and yaxis at 3/4 and 2/3 respectively?

A. 8x + 9y = 6

B. 9x + 8y = 12

C. 8x - 9y = 6

D. 9x + 8y = -12

Question 1294

If cot 60° + cosec 60° = x, then the value of x is

A. (1-2√2)/√2

B. (√3-4)/2√3

C. 1

D. √3

Question 1295

Find the value of 6732.8 + 673.28 + 67.328 + 6.7328 + 0.67328 ?

A. 74808.1408

B. 7480.78408

C. 74808.2408

D. 7480.81408

Question 1296

On dividing 256a2b2c2 by 64a2, we get

A. 2cxc

B. 2bxb

C. 4 bxb.cxc

D. 4

Question 1297

What are the coordinates of the mid point of the segment joining points C(5,-2) and D(-1,8).

A. (-2, 3)

B. (2, 3)

C. (2, -3)

D. (-2, -3)

Question 1298

Arrange them in ascending order 64, 33 and 43

A. 33 < 64 > 43

B. 33 > 64 > 43

C. 33 > 43 > 64

D. 33 < 64 < 43

Question 1299

If cot2A = x, then x is

A. 2cotA/(cot2A - 1)

B. (cot2A - 1)/2cotA

C. (cot2A + 1)/2cotA

D. 2cotA/(1 - cot2A)

Question 1300

A sphere of radius 5 cm is melted to form a cone with base of same radius. The height (in cm) of the cone is

A. 5

B. 10

C. 20

D. 22

Question 1301

If A = (1/0.4) + (1/0.04) + (1/0.004) + ... upto 8 terms, then what is the value of A?

A. 27272727.5

B. 25252525.5

C. 27777777.5

D. 25555555.5

Question 1302

Which of the following quadratic equations has real roots?

A. 3x2 - 5x + 2 = 0

B. 3x2 - 4x + 2 = 0

C. 4x2 - 3x + 2 = 0

D. 5x2 - 2x + 2 = 0

Question 1303

What is the distance between the points (4,-8) and (-2,0)?

A. 100 units

B. 5 units

C. 25 units

D. 10 units

Question 1304

What is the value of (cosecA - cotA) / (secA + tanA)?

A. (secA + tanA)/(cosecA - cotA)

B. √[(secA - tanA)/(cosecA + cotA)]

C. (secA - tanA)/(cosecA + cotA)

D. √[(secA + tanA)/(cosecA - cotA)]

Question 1305

What is the value of ( 1/3 + cosec30)?

A. (√6+1)/√3

B. 7/3

C. (4+√3)/2

D. (√3+1)/2

Question 1306

If x=2+3, then the value of x2-x+1x2+x+1 is

A. 2/3

B. 3/4

C. 4/5

D. 3/5

Question 1307

The value of x13+x-13x23-1+x-23

A. x-1+x23

B. x+x-13

C. x13+x-1

D. x+x-1

Question 1308

125 - 73 + 48 - 137 + 99 = ?

A. 237

B. 62

C. -37

D. 52

Question 1309

Solve this inequality 3p - 16 < 20?

A. p >= 12

B. p <= 11/3

C. p < 12

D. p > 11/3

Question 1310

If 7x - [3(2x - 3)]/2 = 1/2, then what is the value of x?

A. -1

B. 1

C. 3

D. -3

Question 1311

A bag has Rs 30.8 in the form of 1 rupee, 50 paise and 10 paise coins in the ratio of 6:3:2. What is the number of 50 paise coins?

A. 8

B. 24

C. 12

D. 4

Question 1312

What is the value of cos [(180 – θ)/2] cos [(180 – 9θ)/2] + sin [(180 – 3θ)/2] sin [(180 – 13θ)/2]?

A. sin 2θ sin 4θ

B. cos 2θ cos 6θ

C. sin 2θ sin 6θ

D. cos 2θ cos 4θ

Question 1313

If (1 + cosA)/2 = x, then the value of x is

A. sin(A/2)

B. √sin(A/2)

C. √cos(A/2)

D. cos2(A/2)

Question 1314

Given a - b = 2, a3 - b3=26 then (a + b)2 is

A. 9

B. 4

C. 16

D. 12

Question 1315

On dividing 24a2b2 by 6b2, we will get

A. 4b

B. 4ab

C. 4

D. 4a2

Question 1316

If tan(A/2) = x, then the value of x is

A. √[(1 + cosA)/(1 - cosA)]

B. (1 - cosA)/(1 + cosA)

C. (1 + cosA)/(1 - cosA)

D. √[(1 - cosA)/(1 + cosA)]

Question 1317

If x2 – 12x + 33 = 0, then what is the value of (x – 4)2 + [1/(x – 4)2]?

A. 16

B. 14

C. 18

D. 20

Question 1318

If A + B = 90 deg and Cos B = 1/3, then the value of Sin A is

A. 1/2

B. 1/4

C. 1/3

D. 2/3

Question 1319

(1 + sec 20° + cot 70°)(1 - cosec 20° + tan70°) is equal to

A. 0

B. 1

C. 2

D. 3

Question 1320

Twenty times a positive integer is less than its square by 96. What is the integer ?

A. 42

B. 36

C. 48

D. 24

Question 1321

What is the value of sin -300°?

A. 1

B. √3/2

C. 1/2

D. √3/2

Question 1322

What is the simplified value of 0.072+0.292-0.02030.073+0.293

A. 0.6

B. 0.06

C. 1/0.6

D. 1/0.06

Question 1323

If a2sec2x - b2tan2x = c2 then the value of sec2x + tan2x is equal to (assume b2 ≠ a2 )

A. b2-a2+2c2b2+a2

B. b2+a2-2c2b2-a2

C. b2-a2-2c2b2+a2

D. b2-a2b2+a2+2c2

Question 1324

What is the value of [(tan 5θ + tan 3θ)/4 cos 4θ (tan 5θ – tan 3θ)]?

A. sin 2θ

B. cos 2θ

C. tan 4θ

D. cot 2θ

Question 1325

Which of the following is correct?

A. (4x + 5y)(5x - 4y) = 20x2 + 9xy - 20y2

B. (4x + 5y)(5x - 4y) = 20x2 + 41xy - 20y2

C. (4x + 5y)(5x - 4y) = 20x2 - 9xy + 20y2

D. (4x + 5y)(5x - 4y) = 20x2 - 41xy + 20y2

Question 1326

If 5x/2 - [7(6x - 3/2)]/4 = 5/8, then what is the value of x?

A. 1/4

B. -1/4

C. 4

D. -4

Question 1327

If a-1a=1, then a2 + 1a2 ?

A. 1

B. 3

C. 2

D. 4

Question 1328

For triangle ABC, find equation of median AD if coordinates of points A, B and C are (2,4), (3,0) and (5,2) respectively?

A. 3x - 2y = 14

B. 3x - 2y = 2

C. 3x + 2y = 14

D. 3x + 2y = 2

Question 1329

Determine the value of ‘r’ for which the equation 13x + 5 = rx + 18 has no solution.

A. 0

B. 5

C. 13

D. 18

Question 1330

The value of x for which the expressions 7x + 13 and 13x - 7 become equal is _____

A. -10/3

B. 3/10

C. -3/10

D. 10/3

Question 1331

What is the value of 3.6×1.62+0.48×3.61.8×0.8+10.8×0.3-2.16 ?

A. 2.4

B. 2

C. 4

D. 3

Question 1332

If 2x+ 4(x - 3) < -2 - x < 2x - 1, then find the value of x.

A. -1

B. 1

C. 2

D. -2

Question 1333

If tan 45° + cosec 30° = x, then find the value of x.

A. √3

B. (1-2√2)/√2

C. (√3-4)/2√3

D. 3

Question 1334

If 5x = 30-y = 6z, then what is the value of (xy + yz + zx)/xyz?

A. 0

B. 1

C. 2

D. 3

Question 1335

If (4a-3)2=0, then the value of 64a3+12a+13 is

A. 0

B. 11

C. 22

D. 33

Question 1336

If -3[1-(x/2)] + 5x/3 = 1/6, then what is the value of x?

A. 2

B. -1

C. 1

D. -2

Question 1337

If x3 = 62 - 32, then the value of x is

A. 9

B. 6

C. 3

D. 1

Question 1338

√[(1 sinA)/(1 + sinA)] is equal to?

A. secA - tanA

B. cosecA - cotA

C. secA + tanA

D. cosecA + cotA

Question 1339

What is the smplified value of Sin2A/1+Cos2A ?

A. tan A

B. cot A

C. sin A

D. cos A

Question 1340

The two roots of an quadratic equation are given as x = 2/3 and x = -1/2. The equation can be written as

A. (2x - 1) (3x + 2) = 0

B. (2x + 1) (3x + 2) = 0

C. (2x + 1) (3x - 2) = 0

D. (2x - 1) (3x - 2) = 0

Question 1341

Ifab=45andbc=1516, then c2-a2c2+a2 is :

A. 7/5

B. 7/25

C. 7/125

D. 7

Question 1342

Find the roots of the quadratic equation 27x2 + 57x - 14 = 0

A. 2/9, 7/3

B. 2/9, -7/3

C. 9/2, -3/7

D. -9/2, 3/7

Question 1343

If x=aCosθCosΦ, y = aCosθSinΦ and z= aSinθ, then the value of x2+ y2 + z2 is

A. 2a2

B. 0

C. 4a2

D. a2

Question 1344

Triangle PQR is inscribed in a circle such that P, Q and R lie on the circumference. If PQ is the diameter of the circle and ∠PQR = 40°, then what is the value (in degrees) of ∠QPR?

A. 40

B. 45

C. 50

D. 55

Question 1345

If 1 + secA = x, then the value of x is

A. sinAtanA/(1 + cosA)

B. √[sinAtanA/(1 - cosA)]

C. sinAtanA/(1 - cosA)

D. √[sinAtanA/(1 + cosA)]

Question 1346

Determine the value of 'a' which satisfies the equation 9a + 40a = 41a

A. 1

B. 2

C. 3

D. 4

Question 1347

If a + b = 5 and ab = 6, then what is the value of a3 + b3?

A. 32

B. 38

C. 35

D. 34

Question 1348

If a + b + c = 13, a2+b2+c2=69 then find the ab + bc + ca :

A. 10

B. 30

C. 50

D. 70

Question 1349

What is the value of tan150°?

A. -√3

B. 1/√3

C. √3

D. -1/√3

Question 1350

What is the value of 13 x 4932?

A. 4369

B. 4459

C. 4549

D. 4639

Question 1351

The distance between the points (2, 7) and (k, -5) is 13. What is the value of k?

A. -7

B. 7

C. 6

D. -6

Question 1352

If θ is positive acute angle and 7cos2Ɵ + 3sin2Ɵ = 4, then the value of θ is

A. 60°

B. 30°

C. 45°

D. 90°

Question 1353

If 5 sec θ – 3 tan θ = 5, then what is the value of 5 tan θ – 3 sec θ?

A. 1

B. 2

C. 3

D. 4

Question 1354

What is the value of sec2θ + 1sec2θ - 1 x 12cotθ - tanθ ?

A. 0

B. 1

C. cosec θ

D. sec θ

Question 1355

What is the value of sin (B – C) cos (A – D) + sin (A – B) cos (C – D) + sin (C – A) cos (B – D)?

A. 3/2

B. – 3

C. 1

D. 0

Question 1356

The number whose square is equal to the difference of the squares of 37 and 23 is:-

A. 45.09

B. 28.98

C. 47.09

D. 28

Question 1357

A class consists of both boys and girls along with a teacher. After a class, the teacher drinks 9 litres of water, a boy drinks 7 litres of water and a girl drinks 4 litres of water. If after a class 42 litres of water was consumed, find the number of girls in the class ?

A. 8

B. 6

C. 5

D. 3

Question 1358

If a - b = 5 and a2 + b2 = 97, ab = ?

A. 48

B. 32

C. 36

D. 72

Question 1359

The value of tan 315° cot ( -405° ) is equal to

A. -1

B. 1

C. 0

D. 2

Question 1360

cot3A is equal to

A. 3cotA - cot3A(1 - 3cot2A)

B. 3cotA + cot3A(1 - 3cot2A)

C. 3cotA - cot3A(1 + 3cot2A)

D. 3cotA + cot3A(1 + 3cot2A)

Question 1361

If (5x – y)/(5x + y) = 3/7, then what is the value of (4x2 + y2 – 4xy)/(9x2 + 16y2 + 24xy) ?

A. 0

B. 3/7

C. 18/49

D. 1/6

Question 1362

In an examination, a student scores 4 marks for every correct answer and loses I mark for every wrong answer. If he attempts in all 60 questions and secures 130 marks, the number of questions he attempts correctly, is:

A. 35

B. 38

C. 40

D. 42

Question 1363

If the difference between the roots of the equation Ax2 – Bx + C = 0 is 4, then which of the following is TRUE?

A. B2 – 16A2 = 4AC + 4B2

B. B2 – 10A2 = 4AC + 6A2

C. B2 – 8A2 = 4AC + 10A2

D. B2 – 16A2 = 4AC + 8B2

Question 1364

Which of the following is correct?

A. (4x - 5y)2 = 16x2 - 20xy + 25y2

B. (4x - 5y)2 = 16x2 + 40xy - 25y2

C. (4x - 5y)2 = 16x2 - 40xy + 25y2

D. (4x - 5y)2 = 16x2 - 20xy - 25y2

Question 1365

If x , y, and z are real numbers such that (x - 3)2 + (y - 4)2 + (z - 5)2 = 0 then (x+y+z) is equal to

A. -12

B. 0

C. 8

D. 12

Question 1366

ΔABC is right angled at B. If m∠A = 45 deg, then find the value of (tanC + √3/2).

A. 4/√3

B. (2+√3)/2

C. (√2+2)/2√2

D. (2+√3)/3

Question 1367

∆ABC is right angled at B. If m∠A = 30°, then find the value of (sinC + 1/3).

A. 4/3

B. (√3+1)/2

C. (√3+2)/√3

D. (3√3+2)/6

Question 1368

If 3.352 - (9.759 - x ) - 19.64 = 7.052, then what is the value of x?

A. -6.181

B. 13.581

C. 33.099

D. 39.803

Question 1369

If x = x2+11 2 - 2, then x3 + 5x2 + 12x is

A. 0

B. 3

C. 7

D. 11

Question 1370

Simplify (2/7 + 3/5) / (2/5 + 2/7)

A. 31/24

B. 24/31

C. 26/25

D. 12/13

Question 1371

If tan4θ + tan2θ = 1 then the value of cos4θ + cos2θ is

A. 2

B. 0

C. 1

D. -1

Question 1372

ax + 3y = 6 has slope -2/3. What is the value of a?

A. -2

B. 2

C. 3

D. -3

Question 1373

Common factor of 24b6c8d2, 18a6c2d4, 12a4b4 is

A. 72a2b2c2d2

B. 72a6b6c8d4

C. 6a2b2

D. 6

Question 1374

The value of (0.3)2/100=?

A. 0.09

B. 0.0009

C. 0.009

D. 0.9

Question 1375

In ΔUVW measure of angle V is 90 deg. If cosecU = 13/12, and UV = 2.5cm, then what is the length (in cm) of side VW?

A. 6.5

B. 6

C. 4

D. 5.6

Question 1376

What is the value of (sin60° + 2/√3) ?

A. (2√3+1)/√3

B. 7/2√3

C. 3

D. 2+√3

Question 1377

What is the value of (cot45 - √2) ?

A. (√3-1)/2√3

B. (√3-1)/2

C. 1-√2

D. 1-√3

Question 1378

If 2+aa + 2+bb + 2+cc = 4, then the value of ab+bc+caabc is

A. 2

B. 1

C. 0

D. 1/2

Question 1379

You purchased two pieces of cloth measring 1.2 m and 1.3 m each at Rs. 330 and Rs. 270 per meter respectively and gave Rs. 1000 at the payment counter. How much cash will you get back?

A. Rs. 253

B. Rs. 604

C. Rs. 649

D. Rs. 235

Question 1380

If cot 135° = x, then the value of x is

A. -1/√3

B. -√3

C. -1

D. -1/2

Question 1381

If p/q = r/s = t/u = √5, then what is the value of [(3p2 + 4r2 + 5t2)/(3q2 + 4s2 + 5u2)]?

A. 1/5

B. 5

C. 25

D. 60

Question 1382

If a + b + c = 27, then what is the value of (a – 7)3 + (b – 9)3 + (c – 11)3 – 3(a – 7)(b – 9)(c – 11)?

A. 0

B. 9

C. 27

D. 3

Question 1383

In the given figure, AB is a diameter of the circle with center O and XY is the tangent at a point C. If ACX = 35 deg, then what is the value (in deg) of CAB?

A. 45

B. 35

C. 55

D. 65

Question 1384

What is the value of (tan60 + 1/3) ?

A. (2√2+1)/2

B. (√3+1)/√3

C. (3√3+1)/3

D. (3+√2)/3√2

Question 1385

If a - b = -7 and a2+ b2= 85, then find ab.

A. 18

B. -30

C. -44

D. 60

Question 1386

Which of the following conditions is TRUE for the two line segments AB and CD to be congruent?

A. AB=CD

B. AB>CD

C. AB

Question 1387

For which value of ‘g’ the linear graph of 6x + 12y +9 = 0 and 2x + gy + 3 =0 has infinite number of solutions?

A. 3

B. 4

C. 6

D. 9

Question 1388

If x2+y2+z2-8x+6y-4z+29 = 0, then find the value of z(x+y).

A. 1

B. 2

C. 3

D. 4

Question 1389

If 3x+7=x2+p=7x+5, what is the value of P ?

A. 17/2

B. 25/3

C. 33/4

D. 41/5

Question 1390

For the inequation x^2–7x + 12 > 0, which one of the following is correct ?

A. 3 < x < 4

B. –∞ < x < 3 only

C. 4 < x < ∞ only

D. –∞ < x < 3 or 4 < x < ∞

Question 1391

If 2x - 3 = 3x - 5, then the numerical value of (x - 3)2 is

A. 5

B. 1

C. -5

D. -1

Question 1392

The value of aa-b+bb-a is

A. a+b/a-b

B. -1

C. 2ab

D. 1

Question 1393

What is the value of sin 300°?

A. -1/2

B. 2

C. 2/√3

D. -√3/2

Question 1394

What is the value of (1/2) Sec 30° + √2 Tan 60°?

A. (1 + 3√2)/√3

B. (√3 + 2)/√3

C. √3 + 2

D. (√3 + 2)/2

Question 1395

What is the value of S = 11x3x5 + 11x4 + 13x5x7 + 14x7 + 15x7x9 + 17x10 + ... upto 20 terms. Then what is the value of S?

A. 6179/15275

B. 6070/14973

C. 7191/15174

D. 5183/16423

Question 1396

What is the value of [sin (y – z) + sin (y + z) + 2 sin y]/[sin (x – z) + sin (x + z) + 2 sin x]?

A. cos x sin y

B. (sin y)/(sin x)

C. sin z

D. sin x tan y

Question 1397

If 5+x+5-x5+x-5-x = 3,then what is the value of x ?

A. 5/2

B. 25/3

C. 4

D. 3

Question 1398

If tan2A - tan2B = x, then the value of x is

A. (sin2A - sin2B)/(cos2A cos2B)

B. (sin2A sin2B)/(cos2A - cos2B)

C. (sin2A + sin2B)/(cos2A cos2B)

D. (sin2A sin2B)/(cos2A + cos2B)

Question 1399

What should be added to 5(2x-y) to obtain 4(2x - 3y) + 5(x + 4y)?

A. 3x - 13y

B. 3x + 13y

C. 13x - 3y

D. 13x + 3y

Question 1400

What is the value of ( 1/3 - cosec30°) ?

A. (√6-1)/√3

B. -1/2

C. -5/3

D. 3/2

Question 1401

The value of 14 ÷ 5 of 2 - 3 x 47 - 2 is

A. 44

B. 40

C. 1/10

D. 14/19

Question 1402

What is the value of Sin 30° + Cos 30°?

A. (√6 + 1)/√3

B. (√3 + 2)/√3

C. (1 + √3)/2

D. 5/√3

Question 1403

What is the equation of the line passing through the point (0,4) and making an angle of 45° with the positive xaxis?

A. x + y = 4

B. x - y = - 4

C. x + y = -4

D. x - y = 4

Question 1404

In ∆DEF measure of angle E is 90°. If secD = 25/7, and DE = 1.4cm, then what is the length (in cm) of side DF?

A. 5

B. 4.8

C. 4

D. 5.6

Question 1405

Given that tan(θ + 15°) = √3. Then the value of θ is?

A. 15°

B. 75°

C. 45°

D. 65°

Question 1406

What is the reflection of the point (-1 , 3) in the line x = -4?

A. (-7 ,-3)

B. (-7 ,3)

C. (7 ,-3)

D. (7 ,3)

Question 1407

If cotA/√(1 + cot2A) = x, then the value of x is

A. sinA

B. cosecA

C. secA

D. cosA

Question 1408

To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ?

A. 52.5

B. 62.5

C. 72.5

D. 82.5

Question 1409

The value of sec2θ + 2tanθcotθ - tan2θ is

A. 0

B. 1

C. 2

D. 3

Question 1410

What is the value of cosec -150°?

A. -2

B. 2/√3

C. 2

D. -2/√3

Question 1411

What is the value of sec -2π/3 ?

A. -2

B. 2

C. 2/√3

D. -2/√3

Question 1412

If [2(4x/5 - 3/4)]/3 - 5/3 = -1/6, then the value of x is?

A. 4/15

B. -15/4

C. -4/15

D. 15/4

Question 1413

If x = y + 2 then x3 - y3 - z3 is

A. 0

B. 3xyz

C. -3xyz

D. 1

Question 1414

What is the slope of the line perpendicular to the line passing through the points (-2, 3) and (2, 0)?

A. 4/3

B. 3/4

C. -3/4

D. -4/3

Question 1415

What is the value of Sin 30° + 2 Cos 30° ?

A. (2√2 + 3)/√6

B. (9 + 2√3)/9

C. (1 + 2√3)/2

D. (2√6 + 1)/√3

Question 1416

Find the value of 62532+18

A. 1635

B. 2635

C. 3635

D. 4635

Question 1417

In a school there are 1500 students, 44% of them are girls. Monthly fee of each boy is 540 and fee of each girl is 25% less than that of a boy. The sum of fees of boys & girl is

A. Rs. 720600

B. Rs. 720800

C. Rs. 720900

D. Rs. 721000

Question 1418

If θ is acute angle and sin(θ+18°)= 1/2, then the value of θ in circular measure is

A. Π/12 radians

B. Π/15 radians

C. 2Π/5 radians

D. 3Π/13 radians

Question 1419

If a + b + c = 7/12, 3a – 4b + 5c = 3/4 and 7a – 11b – 13c = – 7/12, then what is the value of a + c?

A. 1/2

B. 5/12

C. 3/4

D. 1/4

Question 1420

If x = 4aba+b, then what is the value of x+2ax-2a+x+2bx-2b ?

A. 0

B. 2

C. 4

D. 1

Question 1421

What is the equation of the line if its slope is 4/3 and it passes through the point (-7 , 2)?

A. 4x - 3y = -22

B. 4x + 3y = -34

C. 4x + 3y = -22

D. 4x - 3y = -34

Question 1422

ΔABC is right angled at B. If m∠A = 45°, then find the value of (cosecC + 1/√3).

A. (3√2+1)/3

B. (2+√3)/2

C. 5/√3

D. (√6+1)/√3

Question 1423

What is the equation of the line passing through the point (2,-3) and making an angle of -45°with the positive X-axis?

A. x - y = -5

B. x - y = -1

C. x + y = -5

D. x + y = -1

Question 1424

If the simple interest on Rs. 1 for 1 month is 1 paisa, then the rate percent per annum will be

A. 10%

B. 8%

C. 12%

D. 6%

Question 1425

If 2560.256 = 25.6x, then what will be the value of x?

A. 2.56

B. 25.6

C. 0.256

D. 0.0256

Question 1426

If 3√2 + √18 + √50 = 15.55, then what is the value of √32 + √72?

A. 13.22

B. 10.83

C. 14.13

D. 16.54

Question 1427

The value of Sin 60 is

A. √1/2

B. √3/2

C. 1/√2

D. 1/2

Question 1428

The value of 2 Tan53°Cot37°-Cot80°Tan10° ?

A. 3

B. 2

C. 1

D. 0

Question 1429

What is the value of 2+2+2+2.......

A. 1

B. 2

C. 3

D. 4

Question 1430

If cotθ = 4, then the value of 5sinθ+3cosθ5sinθ-3cosθ is

A. 1/9

B. 1/3

C. 3

D. 9

Question 1431

If secA - tanA = x, then the value of x is

A. 1/(sec2A - tan2A)

B. 1/(sec2A + tan2A)

C. 1/√[(sec2A - tan2A)]

D. 1/(secA + tanA)

Question 1432

The value of sinθ1+cosθ + sinθ1-cosθ

A. 2sinθ

B. 2cosθ

C. 2secθ

D. 2cosecθ

Question 1433

If a+b=5 and ab=3, then the value of (a2+b2) is

A. 17

B. 18

C. 19

D. 20

Question 1434

Find the unit digit in the given product (4211)102 x (361)52.

A. 3

B. 1

C. 4

D. 7

Question 1435

Δ DEF is right angled at E. If m∠F = 45, then what is the value of Sin F x Tan F?

A. √2

B. 1/√3

C. 1/√2

D. 2/√3

Question 1436

What is the slope of the line, parallel to the line 3x - 6y = 4?

A. -1/2

B. 1/2

C. 2

D. -2

Question 1437

In ΔXYZ measure of angle Y is 90 deg. If cot X = 5/12, and XY = 2.5 cm, then what is the length (in cm) of side XZ?

A. 6

B. 4

C. 5.6

D. 6.5

Question 1438

Find the value of sin230 cos245 + 4 tan230 + 1/2sin290 - 2 cos290 + 1/24

A. 3

B. 4

C. 2

D. 1

Question 1439

If 3 dozen guavas cost Rs. 90, how many guavas can be bought for Rs. 240?

A. 98

B. 96

C. 102

D. 90

Question 1440

The value of(1(p-n)(n-q)+1(n-q)(q-p)+1(q-p)(p-n)) is

A. 1

B. 0

C. p+q+n

D. 2np+q

Question 1441

What is the value of a-b when a2+b2-6a-6b+18 = 0 ?

A. 0

B. 3

C. 6

D. 9

Question 1442

If the angle of elevation of the sun decreases from 45° to 30°, then the length of the shadow of a pillar increases by 60m. The height of the pillar is

A. 60(√3+1) m

B. 30(√3-1) m

C. 30(√3+1) m

D. 60(√3-1) m

Question 1443

If x + 1/x = 6, then value of x2 + 1/x2 is

A. 23

B. 16

C. 34

D. 32

Question 1444

tan(A/2) is equal to

A. cosecA + cotA

B. secA - cotA

C. cosecA - cotA

D. secA + cotA

Question 1445

If (x2/yz) + (y2/zx) + (z2/xy) = 3, then what is the value of (x + y + z)3?

A. 0

B. 1

C. 2

D. 3

Question 1446

If a2b+c=b2c+a=c2a+b=1 then the value of 21+a+21+b+21+c

A. 0

B. 1

C. 2

D. 3

Question 1447

A secret can be told to only 3 persons in 3 minutes. Each person in turn tells 3 other persons in the next 3 minutes and the processes continues accordingly. In 30 minutes how many persons can be told this secret in this way ?

A. 88572

B. 77854

C. 99584

D. 55654

Question 1448

∆XYZ is right angled at Y. If CosecX = 17/15, then what is the value of CotZ?

A. 17/15

B. 8/17

C. 17/8

D. 15/8

Question 1449

If (x+a) is the H.C.F of 2x2+5x-12 and x2+x-12 then find the value of a.

A. -3

B. -2

C. 4

D. 5

Question 1450

What is the value of 643 × 121289 - 169 ?

A. 12

B. 11

C. 1/11

D. 1/12

Question 1451

If 1/√(1 + cot2A) = x, then value of x is

A. sinA

B. cosecA

C. cosA

D. secA

Question 1452

Coefficient of x2 in 4x3 - 2x2 + 2x - 3 are

A. 6

B. -2

C. 3

D. -3

Question 1453

In a Rhombus ABCD, measure of angle CAB is 35°, what is the measure of angle ABC?

A. 70°

B. 40°

C. 50°

D. 110°

Question 1454

If cosπ/4c - tanπ/4c = x, then x is

A. (√3+4)/2√3

B. (2√2-1)/2

C. (1-√2)/√2

D. 5/√3

Question 1455

The length of a median of an equilateral triangle is 12√3 cms. Then the area of the triangle is

A. 144 sq. cms

B. 288√3 sq. cms

C. 144√3 sq. cms

D. 288sq.cms

Question 1456

If tanA = x, then x is

A. √(cosec2A + 1)

B. √(sec2A + 1)

C. √(cosec2A - 1)

D. √(sec2A - 1)

Question 1457

If a + b + c = 9 and ab + bc + ca = 18, then what is the value of a3 + b3 + c3 – 3abc?

A. 189

B. 243

C. 361

D. 486

Question 1458

The coordinates of the point that divides the line segment joining the points (-5, 5) and (7,-3) internally in the ratio 3 : 1 are given by

A. (-2, 3)

B. (4, -1)

C. (5/2, 0)

D. (1, 1)

Question 1459

sec2Acosec2A is equal to

A. sec2A - cosec2A

B. √[sec2A + cosec2A]

C. sec2A + cosec2A

D. √[sec2A - cosec2A]

Question 1460

If xa+b+1=xa-b+a-ba+b, then x is equal to

A. 2a-b

B. a+b

C. a-b

D. 2a+b

Question 1461

What is the reflection of the point (6, -1) in the line y = 2?

A. (-2 , -1)

B. (-6 , 5)

C. (-2 , 1)

D. (6 , 5)

Question 1462

What is the value of (4/3) cot2 (p/6) + 3 cos2 (150) – 4 cosec2 45 + 8 sin (p/2)?

A. 25/4

B. 1

C. – 7/2

D. 13/2

Question 1463

5.16 x 3.2 =

A. 15.502

B. 16.512

C. 17.772

D. 17.52

Question 1464

For x = 462+3, what is the value of x+22x-22+x+23x-23

A. 1

B. √2

C. √3

D. 2

Question 1465

If y = 2x - 1x + 3, find x when y = 1

A. 4

B. -4

C. 3/2

D. 4/3

Question 1466

If x3-2x=3x, then the value of x2+1x2 will be

A. 3 1/9

B. 3 2/9

C. 2 1/9

D. 2 4/9

Question 1467

If sinθ + cosθ = 1, then the sinθ cosθ is equal to

A. 0

B. 1

C. 1/2

D. -1/2

Question 1468

In a rectangle _____.

A. Consecutive angles are congruent as well as supplementary

B. Diagonals are perpendicular to each other

C. Diagonals bisect opposite angles

D. Diagonals are not equal

Question 1469

If a - b = -1 and ab = 6, then what is the value of a3- b3?

A. 33

B. -19

C. 18

D. 35

Question 1470

If θ is acute angle and tan θ – cot θ = 0, then what is the value of tan26θ + cot100θ?

A. -2

B. 0

C. 1

D. 2

Question 1471

Find the value of y(y4 - y2 - y) when y = 5.

A. 2900

B. 2975

C. 2925

D. 2995

Question 1472

If sinθ+cosθsinθ-cosθ=3, then the value of sin4θ-cos4θ is

A. 4/3

B. 3/4

C. 5/3

D. 3/5