# 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

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

A. 10
B. 12
C. 15
D. 18

Question 2

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

A. 1/4
B. 1/6
C. 1/5
D. 1/7

Question 3

What is the value of the expression a3 - 5 + 2816a, when a = 2?

A. 2
B. 5
C. 7
D. 8

Question 4

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

A. 0
B. 1
C. 2
D. 3

Question 5

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 6

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 7

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

A. 8
B. 10
C. 9
D. 7

Question 8

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 9

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

A. 31
B. 26
C. 28
D. 24

Question 10

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 11

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 12

If Tan θ = 7/24, then what is the value of Cosec θ?

A. 25/24
B. 25/7
D. 24/25

Question 13

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

A. 0
B. 1
C. 2
D. 3

Question 14

If Sinx = 4/5, then Sec2x - 1 = ?

A. 16/25
B. 25/9
C. 9/16
D. 16/9

Question 15

The value of ds+t÷ds÷dt

A. 0
B. d
C. 1
D. ds+t

Question 16

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 17

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 18

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 19

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 20

If cotθ = 4, then the value of 5sinθ+3cosθ5sinθ-3cosθ is

A. 1/9
B. 1/3
C. 3
D. 9

Question 21

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

A. √3
B. 1
C. -1/2
D. √3/2

Question 22

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 23

Simplify 50 + 18 - 8

A. 8√2
B. 7√2
C. 6√2
D. 5√2

Question 24

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 25

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 26

(1155) +(18 − 6) × 9 =?

A. 113
B. 115
C. 100
D. 110

Question 27

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 28

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 29

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

A. tan2A sin2A
B. cot2A cosec2A
C. tanA sinA
D. cotA cosecA

Question 30

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 31

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 32

If a + b = 10 and ab = 21, then the value of (a - b)2 is

A. 15
B. 16
C. 17
D. 18

Question 33

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 34

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 35

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 36

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

A. 1/2
B. 1
C. 2
D. 3

Question 37

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 38

If a-b=1 and a3-b3 = 61, then the value of ab will be

A. -20
B. 20
C. 30
D. 60

Question 39

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 40

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 41

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 42

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

A. 9
B. 64
C. 125
D. 216

Question 43

If a-1a=7,then a2+1a2=?

A. 54
B. 51
C. 53
D. 52

Question 44

If tanA = x, then x is

A. √(cosec2A + 1)
B. √(sec2A + 1)
C. √(cosec2A - 1)
D. √(sec2A - 1)

Question 45

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 46

Simplify 11.9983 = ?

A. 1727.136
B. 1331.136
C. 1685.136
D. 1700.136

Question 47

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

A. 2cosecA
B. 2cosec2A
C. 2sec2A
D. 2secA

Question 48

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 49

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

A. C, 1/C
B. C, C2
C. C, 2C
D. 0,1

Question 50

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

A. 2/7
B. 7/8
C. 7/2
D. 8/7

Question 51

What is the value of 2+2+2+2.......

A. 1
B. 2
C. 3
D. 4

Question 52

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 53

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 54

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 55

The value of 2 Tan53°Cot37°-Cot80°Tan10° ?

A. 3
B. 2
C. 1
D. 0

Question 56

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 57

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

A. 1
B. -1
C. 0
D. 2

Question 58

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 59

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 60

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

A. cosecA
B. cosA
C. sinA
D. tanA

Question 61

If y = 2x - 1x + 3, find x when y = 1

A. 4
B. -4
C. 3/2
D. 4/3

Question 62

Simplify 81x2 - 49y29x + 7y

A. 9x++7y
B. 9x-7y
C. 9x
D. 7y

Question 63

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 64

If ab+ba = -1, then the value of a2b-b2a is

A. 1
B. -1
C. 0
D. 2

Question 65

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 66

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 67

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

A. 3/2
B. 2/3
C. 1/3
D. 2

Question 68

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

A. -6
B. 6
C. -2/5
D. 2/5

Question 69

What is the value of cot210°?

A. 1/√3
B. -1/√3
C. √3
D. -√3

Question 70

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

A. √2
B. 2
C. -√2
D. 1/√3

Question 71

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 72

If x + 1/x = 6, then value of x2 + 1/x2 is

A. 23
B. 16
C. 34
D. 32

Question 73

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 74

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

A. 11
B. 11√2
C. 22
D. 22√2

Question 75

∆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 76

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 77

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 78

What is the simplified value of 31253 + 4253 + 36753

A. 18253
B. 5253
C. 9√125
D. 1253

Question 79

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 80

If 11+11+11+1x = 58, then what is the value of x?

A. 2
B. 3
C. 1
D. 4

Question 81

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 82

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 83

[sinA/(1 + cosA)] + [(1 + cosA)/sinA] is equal to

A. 2secA
B. 2cosecA
C. 2tanA
D. 2cotA

Question 84

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 85

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 86

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 87

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

A. √3/2
B. 1/2
C. 0
D. 2/√3

Question 88

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

A. 13
B. 48
C. 78
D. 72

Question 89

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 90

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 91

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 92

Given that tan(θ + 15°) = √3. Then the value of θ is?

A. 15°
B. 75°
C. 45°
D. 65°

Question 93

0.296 + 2.96 + 29.6 + 296 = ?

A. 327.856
B. 328.756
C. 328.856
D. 327.756

Question 94

If x -­ y = ­7 and x + y = 13, then x2 - y2 is

A. 91
B. -30
C. 30
D. -­91

Question 95

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 96

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

A. 2
B. 3
C. 1
D. 4

Question 97

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 98

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 99

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 100

If a+b=5 and a­b=3, then the value of (a2+b2) is

A. 17
B. 18
C. 19
D. 20

Question 101

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 102

What is the value of (4a2 - 9b2 )/(2a + 3b) is

A. 2a - 3b
B. 2a + 3b
C. 2a
D. 3b

Question 103

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 104

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

A. 2
B. 3
C. 4
D. 1

Question 105

ΔPQR is right angled at Q. If tanP = 24/7, then what is the value of cosR ?

A. 25/7
B. 24/25
D. 7/24

Question 106

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

A. 1/√5
B. 2/√5
C. 3/√5
D. 0

Question 107

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

A. 1
B. -1
C. 9/10
D. -0.9

Question 108

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

A. 27
B. 6
C. 9
D. 30

Question 109

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 110

If Tan θ = 9/40, then Sec θ = ?

A. 40/41
B. 9/41
C. 41/40
D. 41/9

Question 111

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

A. -1
B. 1
C. 3
D. -3

Question 112

If a = 2 , b = ­3 then the value of 27a3 - 54a2b + 36ab2 - 8b3 is

A. 1562
B. 1616
C. 1676
D. 1728

Question 113

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 114

If sinA = x, then x is equal to

A. √(1 - cos2A)
B. √(1 - sin2A)
C. √(1 + cos2A)
D. √(1 + sin2A)

Question 115

If sec2A cosec2A = x, then x is

A. sec2A + cosec2A + 2
B. tan2A + cot2A - 2
C. tan2A + cot2A + 2
D. sec2A + cosec2A - 2

Question 116

The value of (sec245 - cot245) - (sin230 + sin260) is

A. 1
B. 2√3
C. 0
D. 1/√2

Question 117

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

A. 36a2
B. 108b2
C. 6a2b2
D. 6a2

Question 118

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 119

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 120

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

A. cosecA + cotA
B. cosecA­ - cotA
C. cosec2A + cot2A
D. √[cosec2A + cot2A]

Question 121

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 122

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 123

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 124

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 125

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 126

If 2sec2x - tan2x = 5 and 0° ≤ x ≤ 90° , then x = ?

A. 60°
B. 90°
C. 30°
D. 45°

Question 127

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 128

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

A. 7/25
B. 25/7
D. 7/24

Question 129

If 310 × 272 = 92 × 3n then the value of n is

A. 10
B. 12
C. 15
D. 20

Question 130

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 131

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

A. (43 - 37)
B. (43 + 37)
C. 37
D. 10

Question 132

Find the value of 777777?

A. 73164
B. 7164
C. 76364
D. 7764

Question 133

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

A. 9
B. 12
C. 15
D. 16

Question 134

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 135

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 136

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

A. -5
B. 9
C. -9
D. 5

Question 137

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 138

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. ABD. None of these

Question 139

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

A. 65
B. 34
C. 43
D. 56

Question 140

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 141

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 142

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 143

The value of cos(1110) is

A. √3/2
B. 1/2
C. 1/√2
D. 1

Question 144

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 145

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 146

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 147

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 148

What is the value of (cot30°+ 2/√3) ?

A. 5/√3
B. (1+2√3)/2
C. 5/6
D. 2/√3

Question 149

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 150

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 151

What is the value of (sin60° + 2/√3) ?

A. (2√3+1)/√3
B. 7/2√3
C. 3
D. 2+√3

Question 152

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 153

If 2x+ 4(x - 3) < -2 - x < 2x - 1, then find the value of x.

A. -1
B. 1
C. 2
D. -2

Question 154

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

A. 1
B. 2
C. 3
D. 4

Question 155

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 156

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

A. cosecA -­ cotA
B. cosecA + cotA
C. secA + cotA
D. secA -­ cotA

Question 157

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 158

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 159

If Sec θ = 25/24 , then what is the value of Sin θ?

A. 24/25
B. 7/25
D. 25/7

Question 160

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 161

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

A. 21
B. 24
C. 25
D. 16

Question 162

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 163

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 164

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 165

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 166

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 167

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

A. -4
B. 8
C. 4
D. -8

Question 168

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 169

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 170

If 4x2= 152- 92, then value of x is

A. 9
B. 6
C. 3
D. 12

Question 171

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 172

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 173

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 174

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 175

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

A. 2√2
B. 4
C. 0
D. 2

Question 176

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 177

What is the value of ( 1/3 - cosec30°) ?

A. (√6-1)/√3
B. -1/2
C. -5/3
D. 3/2

Question 178

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 179

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

A. secA -­ tanA
B. cosecA + tanA
C. secA + tanA
D. cosecA -­ tanA

Question 180

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 181

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

A. √29
B. √-29
C. - √29
D. √27

Question 182

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

A. 1
B. 2
C. 3
D. 4

Question 183

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 184

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

A. 466
B. 469
C. 446
D. 460

Question 185

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 186

If (4a-3)2=0, then the value of 64a3+12a+13 is

A. 0
B. 11
C. 22
D. 33

Question 187

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 188

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 189

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 190

What is the value of cos 11π/6?

A. -1/√2
B. -√3/2
C. 2/√3
D. √3/2

Question 191

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 192

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

A. 0
B. 1
C. 2
D. 3

Question 193

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 194

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 195

199994 x 200006 = ?

A. 39999799964
B. 39999999864
C. 39999999954
D. 39999999964

Question 196

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 197

1 - [5 - {2 + (- 5 + 6 - 2) 2}] is equal to:

A. -4
B. 2
C. 0
D. 2

Question 198

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 199

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 200

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 201

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

A. tanA
B. cosecA
C. secA
D. cosA

Question 202

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

A. 1331
B. 1000
C. 1728
D. 729

Question 203

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 204

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 205

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 206

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 207

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 208

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

A. 25
B. 50
C. 144
D. 238

Question 209

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 210

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

A. 1
B. 0
C. cot A/2
D. – 1

Question 211

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 212

Simplify : 213 - 112 of 35 + 125 ÷ 213

A. 1/10
B. 3/10
C. 11/10
D. 1

Question 213

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 214

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

A. tan2Acosec2A
B. secAcosecA
C. sec2Acosec2A
D. tanAcosecA

Question 215

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 216

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

A. 2cosec2A
B. 2sec2A
C. 2cosecA
D. 2secA

Question 217

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 218

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 219

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 220

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 221

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 222

18800÷470÷20=?

A. 1
B. 2
C. 3
D. 4

Question 223

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 224

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 225

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 226

What is the value of sec 330°?

A. 2
B. -2/√3
C. -2
D. ­2/√3

Question 227

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 228

The least number that must be subtracted from 63522 to make the result a perfect square is = ?

A. 18
B. 20
C. 24
D. 30

Question 229

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 230

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 231

The square root of 6084 is

A. 82
B. 78
C. 74
D. 76

Question 232

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

A. 36
B. 63
C. 12
D. -15

Question 233

If x - y = -6 and x + y = 16, then x2- y2 is?

A. 96
B. -96
C. 22
D. -22

Question 234

Which of the following fractions is largest?

A. 3/4
B. 4/5
C. 5/6
D. 7/8

Question 235

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 236

Find the sum of interior angles of a dodecagon?

A. 1620°
B. 1800°
C. 1440°
D. 1260°

Question 237

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 238

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 239

What is the value of cot 11π/6?

A. -√3
B. -1
C. √3
D. -1/2

Question 240

What is the value of 99992 x 100008?

A. 9999999936
B. 9999899936
C. 9999999836
D. 9999999926

Question 241

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 242

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

A. 5
B. 6
C. 7
D. 8

Question 243

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

A. 31
B. 35
C. 30
D. 29

Question 244

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 245

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

A. 1
B. 2
C. 1/2
D. 1/4

Question 246

What is the value of 299996 x 300004?

A. 89999999984
B. 89999699984
C. 89999999884
D. 89999999974

Question 247

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 248

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

A. a2+12a
B. 2aa2+1
C. a2-12a
D. 2aa2-1

Question 249

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

A. (4,6)
B. (­-4,­-6)
C. (­-4,6)
D. (4,­-6)

Question 250

If (x + 1/x) = 3, then x8+1x8 is equal to

A. 2201
B. 2203
C. 2207
D. 2213

Question 251

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 252

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 253

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

A. 0.366
B. 0.566
C. 0.356
D. 0.346

Question 254

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 255

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 256

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 257

Compute : 1112 / 139 - 5

A. 557/67
B. -3
C. 556/67
D. 3

Question 258

The value of (1 - √2) + (√2 - √3) + (√3 - √4) + ..... + (√15 - √16) is

A. 0
B. 1
C. -3
D. 4

Question 259

If 5(4 - x) - 4 > 5x -2 > 2x - 6, then the value of x is

A. -2
B. 2
C. -1
D. 3

Question 260

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 261

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

A. 0.0023
B. 0.23
C. 0.023
D. 2.3

Question 262

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

A. 4
B. 8
C. 12
D. 14

Question 263

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 264

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 265

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

A. 1
B. 2
C. 4
D. 0

Question 266

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 267

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 268

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

A. 0
B. xz
C. y
D. 3y

Question 269

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 270

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

A. 62/45
B. 31/28
C. 5/7
D. 1/7

Question 271

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 272

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 273

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

A. 205.267
B. 90.827
C. -­91.933
D. 218.569

Question 274

Solve : 1000x - 5 = -6

A. 1/1000
B. -1/1000
C. -11/1000
D. 11/1000

Question 275

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 276

If x2-2x+1=0, then the value of x4+1x4 is

A. 0
B. 1
C. 2
D. 3

Question 277

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

A. 5
B. 8
C. 4
D. 2

Question 278

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 279

Compute 4923 / 547 - 10

A. 1
B. -1
C. 1641/179
D. 1614/179

Question 280

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 281

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 282

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

A. 18
B. 25
C. 50
D. 450

Question 283

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 284

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 285

Solve the following : 3/4+{3/4 + 3/4 ÷ (3/4 + 3/4)} = ?

A. 0
B. 3/4
C. 1
D. 2

Question 286

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 287

∆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 288

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

A. 0.23
B. 0.0023
C. 2.3
D. 0.023

Question 289

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 290

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 291

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

A. 1/√3
B. 1/2
C. 1/√2
D. 1/3

Question 292

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 293

How many  18' s are there in  3712?

A. 300
B. 400
C. 500
D. 600

Question 294

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 295

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 296

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 297

What is the value of a-b when a2+b2-6a-6b+18 = 0 ?

A. 0
B. 3
C. 6
D. 9

Question 298

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 299

Compute : 4082 / 157 - 23

A. -3
B. 3
C. 2041/67
D. 2014/67

Question 300

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 301

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

A. 999999
B. 1000000
C. 1000001
D. 999998

Question 302

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 303

What is the value of ( 1/3 + cosec30)?

A. (√6+1)/√3
B. 7/3
C. (4+√3)/2
D. (√3+1)/2

Question 304

(98764 + 89881 + 99763 + 66342) ÷ (1186 + ? + 1040 + 1870) = 55

A. 2254
B. 2354
C. 2368
D. 2404

Question 305

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 306

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

A. 12
B. 10.5
C. -12
D. -10.5

Question 307

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

A. 1 -­ cosecA
B. 1 + cosecA
C. 1 + secA
D. 1 -­ secA

Question 308

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 309

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 310

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 311

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 312

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 313

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 314

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 315

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 316

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 317

If a - b = 5 and a2 + b2 = 97, ab = ?

A. 48
B. 32
C. 36
D. 72

Question 318

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 319

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 320

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

A. 2cos 2A
B. 1 – sin2 A
C. sec2A
D. secA tanA

Question 321

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 322

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 323

Find the value of 64344?

A. 1
B. 2
C. 3
D. 4

Question 324

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 325

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 326

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 327

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 328

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 329

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 330

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 331

Reflection of the point (4,-5) in the y-axis is

A. (4,5)
B. (-4,-5)
C. (4,-5)
D. (-4,5)

Question 332

Simplify 576b3x2a4z3/36a3b2z

A. 16bx2az2
B. 8bx2az2
C. 32ba2 z
D. 32bxa2

Question 333

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 334

If 1/√(1 + cot2A) = x, then value of x is

A. sinA
B. cosecA
C. cosA
D. secA

Question 335

What is the value of tan 4π/3?

A. ­1/2
B. √3
C. √3/2
D. ­1/√2

Question 336

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

A. 54
B. -4
C. ­30
D. 4

Question 337

What is the value of z2+1z2 when z = 5+26 ?

A. 49
B. 50
C. 98
D. 100

Question 338

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 339

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 340

Given a -­ b = 2, a3 - b3=26 then (a + b)2 is

A. 9
B. 4
C. 16
D. 12

Question 341

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 342

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 343

The square root of 4096 is

A. 56
B. 68
C. 74
D. 64

Question 344

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

A. 12
B. 16
C. 18
D. 15

Question 345

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

A. sinA cosA
B. cot2A
C. tan2A
D. sin2A cosA

Question 346

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 347

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 348

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 349

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

A. 7.169
B. 7.196
C. 5.198
D. 7.296

Question 350

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 351

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 352

∆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 353

112 × 54 =

A. 68947
B. 69874
C. 70000
D. 76000

Question 354

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 355

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 356

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

A. √2
B. 2
C. -2/√3
D. -√2

Question 357

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 358

Simplify : (-4.6)x(-4.6)/(-4.6+0.6)

A. -5.29
B. -0.529
C. -4.06
D. 5.01

Question 359

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

A. 110
B. 115
C. 125
D. 140

Question 360

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 361

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 362

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 363

Find the value of 62532+18

A. 1635
B. 2635
C. 3635
D. 4635

Question 364

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 365

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 366

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 367

Solve this inequality 3p - 16 < 20?

A. p >= 12
B. p <= 11/3
C. p < 12
D. p > 11/3

Question 368

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 369

Calculate the value of 61681x61681-31681x3168130000

A. 93352
B. 94362
C. 93362
D. 95362

Question 370

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 371

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 372

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 373

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 374

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 375

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 376

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

A. -1
B. -1/√3
C. √3
D. 1

Question 377

Which of the following is TRUE?

A. 1123>1294>15
B. 1294>1123>15
C. 15>1123>1294
D. 15>1294>1123

Question 378

sec2Acosec2A is equal to

A. sec2A -­ cosec2A
B. √[sec2A + cosec2A]
C. sec2A + cosec2A
D. √[sec2A -­ cosec2A]

Question 379

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 380

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 381

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 382

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 383

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 384

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 385

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 386

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 387

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 388

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 389

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 390

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 391

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

A. 2
B. sin 2
C. 1
D. 0

Question 392

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 393

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 394

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

A. 1
B. √3
C. 2
D. 1/√3

Question 395

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 396

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 397

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 398

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 399

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 400

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 401

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 402

What is the value of 96+21624?

A. 8
B. 4
C. 5
D. 10

Question 403

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 404

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 405

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 406

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

A. 22
B. 23
C. 24
D. 25

Question 407

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 408

Product of 9b2, 3a2 and 4ab is

A. 108a2b2
B. 108a3b3
C. 108a3b2
D. 108a4b4

Question 409

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 410

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 411

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 412

Square of (3x – 5xy) is

A. 9x2 - 30x2y + 25x2y2
B. 9x2 - 15x2y + 25x2y2
C. 25x2 - 15x2y + 9x2y2
D. 25x2 - 30x2y + 9x2y2

Question 413

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 414

64/12 in simplest form?

A. 19/6
B. 32/4
C. 16/3
D. None of the above

Question 415

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 416

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

A. 504
B. 702
C. 728
D. 511

Question 417

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 418

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 419

The value of tan(-405°)

A. 1
B. -1
C. 2
D. 0

Question 420

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 421

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 422

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

A. 0
B. 1
C. 2
D. infinity

Question 423

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 424

56/32 simplified value?

A. 1.705
B. 1.45
C. 1.75
D. 7.5

Question 425

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

A. 16
B. 12
C. 8
D. 4

Question 426

If cot2A -­ cos2A = x, then value of x is

A. tan2Asec2A
B. cotAcosA
C. cot2Acos2A
D. tanAsecA

Question 427

The least value of tan2x + cot2x is

A. 3
B. 2
C. 0
D. 1

Question 428

Find the value of x if 1-x24 = 1318

A. 155
B. 157
C. 159
D. 161

Question 429

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 430

9997 x 10003 = ?

A. 9999991
B. 99999911
C. 99999991
D. 9999911

Question 431

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

A. -2
B. -1
C. 0
D. 1

Question 432

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

A. 2
B. 0
C. 3
D. 1

Question 433

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 434

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 435

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

A. -√3/2
B. √3/2
C. -2
D. -2/√3

Question 436

What is the value of tan 300°?

A. -1/2
B. -1/√2
C. -√3
D. -√3/2

Question 437

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 438

The simplest form of 3774/2958 is

A. 43/19
B. 37/29
C. 31/13
D. 31/23

Question 439

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 440

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 441

If 4x - 7y = 3 and 2x - y = 9, then x - y is.

A. 3
B. 4
C. 5
D. 6

Question 442

What is the value of (1/√3 + sin45 ) ?

A. √3+2
B. (√2+√3)/√6
C. (1+√6)/√3
D. (4+√3)/2

Question 443

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 444

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

A. 240
B. 280
C. 320
D. 360

Question 445

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 446

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 447

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 448

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 449

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 450

If tan4θ + tan2θ = 1 then the value of cos4θ + cos2θ is

A. 2
B. 0
C. 1
D. -1

Question 451

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 452

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 453

What is the value of tan 7π/6?

A. 1/√3
B. -1/√3
C. √3
D. -√3

Question 454

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

A. 116
B. 80
C. 89
D. 146

Question 455

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 456

The value of tan 315° cot (­ -405° ) is equal to

A. -1
B. 1
C. 0
D. 2

Question 457

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 458

If 1p+1q = 1p+q, then the value of p3-q3

A. p-q
B. pq
C. 1
D. 0

Question 459

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 460

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

A. 0
B. 5
C. 2
D. 4

Question 461

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 462

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 463

Solve this inequality 3b - 7 < 32?

A. b = 13
B. b < 13
C. b > = 13
D. b < = 13

Question 464

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 465

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 466

If θ is acute angle and sin(θ+18°)= 1/2, then the value of θ in circular measure is

Question 467

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 468

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 469

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

A. x1-x2
B. x1+x2
C. 1-x2x
D. 1+x2x

Question 470

Reduce 2530/1430 to lowest terms.

A. 47/17
B. 23/13
C. 47/19
D. 29/17

Question 471

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

A. tanA
B. sinA
C. cosA
D. cotA

Question 472

Simplify (533bxaz)/(41ab)

A. 17xzb
B. 19xz
C. 13xz
D. 31ab

Question 473

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 474

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 475

∆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

Question 476

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 477

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 478

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 479

If  tan2θ + cot2θ = 2, then what is the value of 2sec θ cosec θ?

A. 0
B. 1
C. 2
D. 4

Question 480

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 481

Find the unit place digit in 192102 + 193103

A. 0
B. 1
C. 3
D. 5

Question 482

What is (x-y)3+y-23+z-x33x-yy-zz-x =?

A. 1
B. 0
C. 1/3
D. 3

Question 483

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

A. cosecA ­- cotA
B. cosecA + cotA
C. secA -­ cotA
D. secA + cotA

Question 484

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 485

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 486

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 487

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 488

What is the value of xy if x - y = 3 and x2+y2=15?

A. 1
B. 3
C. 5
D. 7

Question 489

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

A. 2a - 3b
B. 2a + 3b
C. 2a
D. 3b

Question 490

If ab = 21 and a+b2a-b2 = 254,then the value of a2+b2+3ab

A. 115
B. 121
C. 125
D. 127

Question 491

If x3 = 62 - 32, then the value of x is

A. 9
B. 6
C. 3
D. 1

Question 492

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 493

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 494

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 495

If sinθ + cosθ = 1, then the sinθ cosθ is equal to

A. 0
B. 1
C. 1/2
D. -1/2

Question 496

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 497

Determine the value of  'a' which satisfies the equation 9a + 40a = 41a

A. 1
B. 2
C. 3
D. 4

Question 498

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 499

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

A. 16
B. 4
C. -6
D. -4

Question 500

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 501

Common factor of 24b6c8d2, 18a6c2d4, 12a4b4 is

A. 72a2b2c2d2
B. 72a6b6c8d4
C. 6a2b2
D. 6

Question 502

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 503

If 9x - 6(3 - x) = 12, then the value of x is

A. 2
B. 4
C. 6
D. 9

Question 504

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

A. b2x4a6z
B. b3x2a4z3
C. b3x5a5z2
D. bazx

Question 505

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

A. (1,4)
B. (1,­-4)
C. (­-1,4)
D. (-­1,-­4)

Question 506

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 507

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

A. 134576
B. 120212
C. 115624
D. 111672

Question 508

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 509

If x2-3x+1=0, then x+1x is (x≠0)

A. 1
B. 0
C. 3
D. 2

Question 510

If 3x= 4y= 12, then z is equal to

A. xy
B. x + y
C. xy/x+Y
D. 4x +3y

Question 511

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

A. 2b
B. 1
C. 0
D. 3b

Question 512

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 513

Find the value of 6813+6413314

A. 5
B. 6
C. 36
D. 216

Question 514

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

A. 0
B. a
C. 1/a
D. 1

Question 515

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 516

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 517

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 518

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

A. 216
B. -4
C. -92
D. 108

Question 519

What is value of P+QP-Q  if PQ=7 ?

A. 1/3
B. 2/3
C. 4/3
D. 5/3

Question 520

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

A. 0
B. 6
C. 8
D. 14

Question 521

What is the value of 34+122 ?

A. 13
B. 15
C. 17
D. 19

Question 522

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

A. cosecA
B. sinA
C. tanA
D. secA

Question 523

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 524

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 525

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 526

∆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 527

Compute 33800/520/5

A. 31
B. 325
C. 13
D. 352

Question 528

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 529

If cos ­-11π/6 = x, then the value of x is

A. -√3/2
B. 1/2
C. -2
D. √3/2

Question 530

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 531

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 532

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 533

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 534

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 535

sinA/(1 + cos A) is equal to

A. (cosecA -­ cotA)
B. (cosecA + cotA)
C. √[(cosecA ­- cotA)]
D. √[(cosecA + cotA)]

Question 536

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

A. 2xyx2-y2
B. 2xyx2+y2
C. x2+y22xy
D. x2-y22xy

Question 537

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 538

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 539

If 2x + 3 = 9 then find the value of 3x + 2

A. 12
B. 16
C. 13
D. 11

Question 540

If cos3A = X, then value of X?

A. 4cos3A - 3cosA
B. 4cos3A + 3cosA
C. 3cosA - 4cos3A
D. cosA + 4cos3A

Question 541

What is the value of (sinA -­ 2sin3A)/(2cos3A -­ cosA)?

A. cotA
B. cosecA
C. secA
D. tanA

Question 542

ΔDEF is right angled at E. If secD = 25/7, then what is the value of cosecF ?

A. 7/25
C. 25/7
D. 7/24

Question 543

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 544

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 545

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

A. 25
B. 75
C. 50
D. 100

Question 546

Simplify : 132 - 142 + 172 - 250 = ?

A. 196
B. 169
C. 121
D. 144

Question 547

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

A. abc
B. 2abc
C. 3abc
D. 0

Question 548

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 549

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

A. -1
B. 1/2
C. 1
D. 0

Question 550

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 551

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 552

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

A. sinC + sinD
B. sinC - sinD
C. cosC - cosD
D. cosC + cosD

Question 553

Square root of 0.9 is equal to

A. 0.03
B. 0.3
C. 0.9487
D. 0.9463

Question 554

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 555

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 556

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 557

If cosx.cosy + sinx.siny = -1 then cosx + cosy is

A. -2
B. 1
C. 0
D. 2

Question 558

What is the value of cosec 120°

A. 2/√3
B. 2
C. -2/√3
D. -2

Question 559

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 560

If 2x - 3 = 3x - 5, then the numerical value of  (x - 3)2 is

A. 5
B. 1
C. -5
D. -1

Question 561

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 562

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 563

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 564

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 565

72 ÷ 52 × 3272 ÷ 52 of 32 ÷ 5.25

A. 3/5
B. 3/6
C. 3/7
D. 3/8

Question 566

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 567

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 568

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 569

∆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 570

What is the value of cosec -7π/6?

A. -2
B. 2
C. 2/√3
D. -2/√3

Question 571

If  P2+1P2 = 47, then the value of P + 1P is

A. 5
B. 6
C. 7
D. 8

Question 572

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 573

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 574

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

A. 8
B. -168
C. 88
D. -8

Question 575

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 576

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 577

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 578

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 579

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

A. sinA
B. cosecA
C. secA
D. cosA

Question 580

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 581

What is the value of sec2θ + 1sec2θ - 1 x 12cotθ - tanθ ?

A. 0
B. 1
C. cosec θ
D. sec θ

Question 582

If x+1x=5, then 6xx2+x+1 value is

A. 3
B. 2
C. 1
D. 0

Question 583

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 584

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

A. (cosecA - cotA)2
B. secA - tanA
C. (secA - tanA)2
D. cosecA - cotA

Question 585

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 586

If 23x + 23y = 184, then what is the average of x and y?

A. 2
B. 4
C. 3
D. 2.5

Question 587

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 588

Find the value of sin230 cos245 + 4 tan230 + 1/2sin290 - 2 cos290 + 1/24

A. 3
B. 4
C. 2
D. 1

Question 589

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 590

What is the value of sin 300°?

A. -1/2
B. 2
C. 2/√3
D. -√3/2

Question 591

P + Q = 2(P-Q). If Q = 10, what is the value of P?

A. 10
B. 40
C. 20
D. 30

Question 592

If a + b = 11 and a2+ b2= 61, then value of ab is

A. 12
B. 96
C. 24
D. 30

Question 593

If tanθ = 815, then 1-sinθ1+sinθ is

A. 1/5
B. 2/5
C. 3/5
D. 0

Question 594

What is the value of sec 5π/4?

A. 1/√3
B. -√2
C. √3
D. 1

Question 595

What is the simplest form of (1 + cosA)(cosecA ­ cotA)?

A. cosA
B. tanA
C. cotA
D. sinA

Question 596

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

A. 0
B. 1
C. 2
D. 3

Question 597

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 598

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 599

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 600

What is the value of 7293×16+676+169

A. 75
B. 64
C. 35
D. 60

Question 601

50.003% of 99.8÷49.988 = ?

A. 2
B. 0
C. 1
D. 50

Question 602

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

A. 23/12
B. 25/4
C. 4/5
D. 25/12

Question 603

CAlculate : 72-6-45÷5-72-2×2÷2+2

A. -16/18
B. -14/7
C. -12/7
D. -12/18

Question 604

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

A. 2
B. 1
C. 0
D. 1/2

Question 605

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 606

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 607

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

A. 49
B. 64
C. 113
D. 15

Question 608

√[(1 ­ sinA)/(1 + sinA)] is equal to?

A. secA -­ tanA
B. cosecA -­ cotA
C. secA + tanA
D. cosecA + cotA

Question 609

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

A. 17a2
B. 17b2
C. 13a2b2
D. 13

Question 610

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 611

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 612

If sec -5π/4 = x, then the value of x is

A. -1/√3
B. -√2
C. -1
D. √3

Question 613

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

A. m3xy
B. m3x+y3
C. m3x3y3
D. mx3y3

Question 614

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

A. 335
B. 325
C. 315
D. 3

Question 615

If a + b = 5 and ab = 6, then what is the value of a3 + b3?

A. 32
B. 38
C. 35
D. 34

Question 616

If √(sec2A ­ 1) = x, then the value of x is

A. cotA
B. tanA
C. cosecA
D. cosA

Question 617

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

A. 152
B. 112
C. 108
D. 98

Question 618

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 619

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 620

Coefficient of x in (x + 8)(6 -­ 3x) is

A. 18
B. 30
C. -18
D. -30

Question 621

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 622

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 623

The value of cosec260 + sec260  cot260 + tan230 will be

A. 5
B. 5 1/2
C. 5 1/3
D. 5 2/3

Question 624

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 625

What is the value of sin ­-300°?

A. 1
B. √3/2
C. ­1/2
D. √3/2

Question 626

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 627

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 628

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 629

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. 19th floor
B. 28th floor
C. 30th floor
D. 37th floor

Question 630

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 631

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 632

If Cosecθ + Cotθ = 2, then Cotθ = ?

A. 0
B. 0.5
C. 1
D. 0.75

Question 633

If a3+ b3 = 341 and ab = 30, then what is the value of a + b?

A. 1
B. 9
C. 7
D. 11

Question 634

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

A. 2
B. 8
C. 4
D. 1

Question 635

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

A. 24/25
C. 25/7
D. 25/24

Question 636

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 637

If x2+1x2 = 98, then x3+1x3 = ?

A. 970
B. 1030
C. -970
D. -1030

Question 638

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 639

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 640

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 641

If Cosec θ = 17/8, then Cot θ = ?

A. 17/8
B. 15/8
C. 8/15
D. 17/15

Question 642

The value of aa-b+bb-a is

A. a+b/a-b
B. -1
C. 2ab
D. 1

Question 643

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 644

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

A. 45°
B. 90°
C. 30°
D. 60°

Question 645

If (x - 4) (x2 + 4x + 16) = x3 - P, then P is equal to

A. 27
B. 8
C. 64
D. 0

Question 646

The value of sinθ1+cosθ + sinθ1-cosθ

A. 2sinθ
B. 2cosθ
C. 2secθ
D. 2cosecθ

Question 647

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

A. 34
B. 36
C. 124
D. 126

Question 648

If a + b = 8 and ab =15, then a3 + b3 is

A. 224
B. 244
C. 152
D. 128

Question 649

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 650

23x12+49x15312+50 = ?

A. 0.5
B. 1
C. 2
D. 3

Question 651

1.004 - 0.4 is equal to

A. 0.604
B. 0.006
C. 0.64
D. 1

Question 652

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 653

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 654

What is the square root of 9409?

A. 83
B. 87
C. 89
D. 97

Question 655

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 656

Compute : (50 + 0.5 x 20) / 0.7

A. 8.571
B. 85.1
C. 85.71
D. 72.85

Question 657

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 658

If a3 + b3 = 28 and a + b = 4, then what is the value of ab?

A. -3
B. 2
C. 8
D. 3

Question 659

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 660

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 661

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 662

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 663

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 664

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

A. 1/5
B. 1/6
C. 5
D. 6

Question 665

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 666

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 667

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 668

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 669

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 670

Find the value of 1006×994?

A. 999932
B. 999964
C. 1000032
D. 1000064

Question 671

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 672

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 673

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

A. 0
B. 1
C. 2
D. √3

Question 674

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 675

Solve the following 7 x {4 + (-2) x (-3)} = ?

A. 14
B. -42
C. -14
D. 70

Question 676

3cosA is equal to

A. 4cos3A + 3cosA
B. 4cos3A - 3cosA
C. 3cos3A + 3cosA
D. 3cos3A - 3cosA

Question 677

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 678

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 679

Coefficient of x2 in 4x3 - 2x2 + 2x -­ 3 are

A. 6
B. -2
C. 3
D. -3

Question 680

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

A. 279
B. 387
C. 513
D. 91

Question 681

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 682

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

A. 8
B. 9
C. 27
D. 16

Question 683

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 684

Coefficient of x2 in 6x3 + 4x2 + 2x + 3 is

A. 4
B. 6
C. 3
D. 2

Question 685

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

A. 0
B. 1
C. 2tanx
D. tanx

Question 686

What is the value of 13 x 4932?

A. 4369
B. 4459
C. 4549
D. 4639

Question 687

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 688

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

A. ­2/√3
B. √2
C. 2
D. √3/2

Question 689

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

A. 0
B. 3
C. 1
D. 2

Question 690

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 691

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 692

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 693

If √5 = 2.236, then √5/2 is

A. 1.851
B. 1.118
C. 2.236
D. 1.782

Question 694

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 695

If x = x2+11 2 - 2, then x3 + 5x2 + 12x is

A. 0
B. 3
C. 7
D. 11

Question 696

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 697

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 698

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

A. 0
B. 1
C. 2
D. 3

Question 699

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 700

If (36 - 16x) - (4x - 8) = 4, then the value of x is

A. 4
B. 2
C. 6
D. 3

Question 701

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 702

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 703

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 704

If the sum of two numbers is 22 and the sum of their squares is 404, then the product of two numbers is = ?

A. 40
B. 44
C. 80
D. 88

Question 705

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 706

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 707

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 708

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

A. 8
B. 14
C. 28
D. 59

Question 709

The simplest form of 3565/1495 is

A. 31/13
B. 43/19
C. 23/13
D. 31/23

Question 710

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

A. -56.353
B. 1.687
C. -17.007
D. 82.407

Question 711

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

A. cosAsinA
B. cos2Asin2A
C. cosecAsecA
D. cosec2Asec2A

Question 712

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 713

If a3 + b3 = 35 and ab = 6, then what is the value of a + b?

A. 5
B. 8
C. 2
D. -8

Question 714

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 715

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 716

5 - [4 - {3 - (3 - 3 - 6)}] is equal to:

A. 10
B. 6
C. 4
D. 0

Question 717

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 718

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 719

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 720

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 721

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

A. 1/2
B. 3/2
C. 3
D. -3

Question 722

10+10(9) =

A. 180
B. 110
C. 100
D. 19

Question 723

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 724

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

A. 1/2
B. √3/2
C. -2/√3
D. -1/√2

Question 725

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 726

What is the simplified value of sec4θ – sec2θ tan2θ?

A. cosec2θ
B. Cot2θ
C. sec2 θ
D. secθ tan θ

Question 727

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 728

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

A. 1
B. 2
C. 3
D. 4

Question 729

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

A. 6x -­ 14y
B. 14y + 6x
C. 14y -­ 6x
D. 6xy

Question 730

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 731

What is the value of tan150°?

A. -√3
B. 1/√3
C. √3
D. -1/√3

Question 732

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 733

If cotA = x, then the value of x is

A. √(sec2A + 1)
B. √(cosec2A + 1)
C. √(sec2A - 1)
D. √(cosec2A - 1)

Question 734

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 735

What is the value of 643 × 121289 - 169 ?

A. 12
B. 11
C. 1/11
D. 1/12

Question 736

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 737

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 738

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 739

If x2 + y2 + 6x + 5 = 4(x - y) then x - y is

A. 1
B. -1
C. 0
D. 4

Question 740

If ab-1b=cb-1c=ac-1a, then ac+ba+cb

A. 1
B. 2
C. 3
D. 4

Question 741

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 742

If x+19x=4, then 9x2+19x2 is

A. 140
B. 142
C. 144
D. 146

Question 743

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 744

Find the value of 'y' if y84 = 225

A. 10
B. 12
C. 15
D. 18

Question 745

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 746

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 747

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 748

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 749

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 750

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 751

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 752

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

A. 0
B. 1
C. 2
D. 3

Question 753

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 754

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 755

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

A. √2
B. 2/√3
C. √2
D. -1/√3

Question 756

The value of 2.33+0.0272.33-0.69+0.09

A. 2
B. 2.27
C. 2.33
D. 2.6

Question 757

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 758

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 759

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 760

∆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 761

What is the value of (cot45 - √2) ?

A. (√3-1)/2√3
B. (√3-1)/2
C. 1-√2
D. 1-√3

Question 762

On dividing 8a2b2c2 by 4a2, we get

A. 2b2
B. 2c2
C. 2b2c2
D. 2

Question 763

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 764

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 765

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 766

Let a = (4 ÷ 3) ÷ 3 ÷ 4, b = 4 ÷ (3 ÷ 3) ÷ 4, c = 4 ÷ 3 ÷ (3 ÷ 4), The maximum value among the above three is?

A. a
B. b
C. c
D. All equal

Question 767

What is the value of (-7776)25

A. 16
B. 36
C. 64
D. 21

Question 768

(1 + sec 20° + cot 70°)(1 - cosec 20° + tan70°) is equal to

A. 0
B. 1
C. 2
D. 3

Question 769

If cot2A = x, then x is

A. 2cotA/(cot2A -­ 1)
B. (cot2A -­ 1)/2cotA
C. (cot2A + 1)/2cotA
D. 2cotA/(1 -­ cot2A)

Question 770

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 771

(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 772

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 773

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 774

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

A. 24
B. 25
C. 0
D. 27

Question 775

The value of 2.31 x 0.34 = ?

A. 1.7854
B. 0.7854
C. 0.7845
D. 0.7584

Question 776

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

A. 4
B. 6
C. 5
D. 3

Question 777

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 778

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 779

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 780

If a - b = 10 and ab =-21, then what is the value of a3-b3 ?

A. 316
B. 370
C. 185
D. 158

Question 781

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

A. 1
B. 0
C. -1
D. 2

Question 782

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 783

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 784

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 785

What is the value of 2 - 2z + z22 + 2z - z2, when z+2z = 2 ?

A. 0
B. 2
C. 4
D. 8

Question 786

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 787

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 788

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 789

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 790

If cosA = x, then x is

A. √(1 - cos2A)
B. √(1 + sin2A)
C. √(1 + cos2A)
D. √(1 - sin2A)

Question 791

What is the simplified value of 18 - 12 ?

A. 5/√2
B. 5√2
C. 2√5
D. 2/√5

Question 792

∆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 793

What is the value of sin(11π/6)?

A. 2/√3
B. -2/√3
C. -1/2
D. 1/2

Question 794

What is the value of 1xp-q+1+1xq-p+1?

A. 0
B. 1
C. x
D. cant determine

Question 795

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

A. 20
B. -20
C. 4
D. -4

Question 796

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 797

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 798

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 799

5 + 2 x 10/2 = ?

A. 15
B. 35
C. 10
D. 20

Question 800

2*[­0.3(1.3 + 3.7)] of 0.8 = ?

A. ­1.92
B. -0.72
C. 2.16
D. -­2.4

Question 801

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 802

If 12x = 192- 112, what is the value of x?

A. 20
B. 17
C. 13
D. 11

Question 803

If a + b + c = 13, a2+b2+c2=69 then find the ab + bc + ca :

A. 10
B. 30
C. 50
D. 70

Question 804

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 805

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 806

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

A. 11
B. ± √22
C. 21
D. ± √21

Question 807

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 808

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 809

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 810

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

A. -1/√2
B. -√3/2
C. -1/2
D. 2

Question 811

If √(1 + cot2A)/cotA = x, then the value of x is

A. sinA
B. cosecA
C. secA
D. cosA

Question 812

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

A. 1 - secA
B. 1 + secA
C. 1 + cotA
D. 1 - cotA

Question 813

The value of cos220°+cos270° is

A. 0
B. 1
C. 1/2
D. 13

Question 814

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 815

Compute : 28854 / 458 / 9

A. 70
B. 567
C. 7
D. 576

Question 816

ax + 3y = 6 has slope -2/3. What is the value of a?

A. -2
B. 2
C. 3
D. -3

Question 817

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

A. 10
B. -10
C. 2
D. -2

Question 818

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 819

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 820

Simplify x5 ÷ x43 ÷ x

A. x3
B. x2
C. X
D. 1/X

Question 821

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

A. tanA
B. cosecA
C. sinA
D. cosA

Question 822

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 823

If 3+12=x+3y, then the x+y is

A. 2
B. 4
C. 6
D. 8

Question 824

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 825

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 826

(798+579)2- (798-579)2798 x 579 =

A. 2
B. 6
C. 4
D. 8

Question 827

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 828

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 829

sin(A+B) -­ sin(A-­B) is equal to

A. 2sinAcosB
B. 2cosAcosB
C. 2cosAsinB
D. 2sinAsinB

Question 830

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 831

If cos 240° = x, then value of x is

A. -1/√2
B. -√3/2
C. 1/2
D. -1/2

Question 832

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 833

If x-1x = 10, then find the value of x4+1x2

A. 98
B. 100
C. 102
D. 106

Question 834

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 835

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 836

217 x 217 + 183 x 183 = ?

A. 84521
B. 87487
C. 80578
D. 78458

Question 837

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 838

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 839

Find the unit digit in the given product (4211)102 x (361)52.

A. 3
B. 1
C. 4
D. 7

Question 840

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 841

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

A. 6
B. 8
C. 16
D. 22

Question 842

The value of sec2θ + 2tanθcotθ - tan2θ is

A. 0
B. 1
C. 2
D. 3

Question 843

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 844

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

A. secA - tanA
B. cosecA + tanA
C. secA + tanA
D. cosecA - tanA

Question 845

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 846

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 847

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 848

What is the value of cosec -150°?

A. -2
B. 2/√3
C. 2
D. -2/√3

Question 849

If a3+1a3 = 2, then the value of a2+1a?

A. 1
B. 2
C. 3
D. 4

Question 850

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 851

The value of 14 ÷ 5 of 2 - 3 x 47 - 2 is

A. 44
B. 40
C. 1/10
D. 14/19

Question 852

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

A. (2,7)
B. (­-2,-­7)
C. (­-7,2)
D. (7,­2)

Question 853

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 854

The value of the expression 2(sin6θ+cos6θ) - 3(sin4θ+cos4θ) + 1 is

A. -1
B. 0
C. 1
D. 2

Question 855

What is the smplified value of Sin2A/1+Cos2A ?

A. tan A
B. cot A
C. sin A
D. cos A

Question 856

What is the value of tan4A + tan2A?

A. sec4A - sec2A
B. sec4A + sec2A
C. cosec4A - sec2A
D. sec4A + cosec2A

Question 857

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

A. 5
B. 7
C. 1
D. -5

Question 858

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

A. cosecA + cotA
B. secA - cotA
C. secA + cotA
D. cosecA - cotA

Question 859

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 860

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

A. 80
B. 169
C. 258
D. 40

Question 861

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 862

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 863

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 864

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

A. 24/25
B. 7/24
C. 7/25

Question 865

If secθ + tanθ = 4, then secθ - tanθ = ?

A. 1
B. 0.25
C. 0.5
D. 0.75

Question 866

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 867

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

A. -1/2
B. 2
C. 1/2
D. -2

Question 868

What is the value of 7293 + 441 - 3433 ?

A. 48
B. 23
C. 7
D. 41

Question 869

Simplify : -21973 × -1253 ÷ 275123

A. 492/7
B. 520/3
C. 554/7
D. 571/5

Question 870

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

A. 21
B. 17
C. 28
D. 31

Question 871

Find the value of 491321973

A. 17/13
B. 13/17
C. 13/7
D. 17/7

Question 872

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

A. 215
B. 335
C. 315
D. 235

Question 873

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 874

tan(A/2) is equal to

A. cosecA + cotA
B. secA - cotA
C. cosecA - cotA
D. secA + cotA

Question 875

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 876

If  a+1/a = 3, then a3+1a3?

A. 12
B. 18
C. 9
D. 6

Question 877

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

A. 3
B. 9
C. 27
D. 81

Question 878

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 879

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 880

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 881

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 882

What is the value of tan­ -240°?

A. -√3
B. 1/√3
C. -1/√3
D. √3

Question 883

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 884

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 885

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 886

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

A. 21
B. 23
C. 22
D. 24

Question 887

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

A. 8√2
B. 18√2
C. 6√2
D. 24√2

Question 888

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 889

What is the value of sin 5π/3?

A. √3/2
B. 2/√3
C. 1/√3
D. -2/√3

Question 890

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 891

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 892

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

A. 24
B. 25
C. 26
D. 21

Question 893

If a + b = 10 and ab = 24, then the value of a3 + b3 is

A. 280
B. 370
C. 520
D. 730

Question 894

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

A. 7
B. 20
C. -7
D. -20

Question 895

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 896

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 897

The value of (0.00000729/0.00000027) is

A. 0.27
B. 0.027
C. 2.7
D. 27

Question 898

The value of  (0.3)2/100=?

A. 0.09
B. 0.0009
C. 0.009
D. 0.9

Question 899

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

A. 20
B. 10
C. 81
D. 142

Question 900

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 901

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 902

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

A. 24
B. 144
C. 128
D. 80

Question 903

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 904

Simplify: (213 x 213 + 187 x 187)

A. 80338
B. 80438
C. 60338
D. 60438

Question 905

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

A. 15
B. 81
C. 27
D. 9

Question 906

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

A. -1
B. -1/√3
C. 1/√3
D. √3

Question 907

What is the value of 23+5252-23 ?

A. 9
B. 49
C. 561
D. 571

Question 908

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

A. 3
B. 0
C. -3
D. 4

Question 909

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 910

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 911

If a-1a=1, then a2 + 1a2 ?

A. 1
B. 3
C. 2
D. 4

Question 912

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 913

If 7x ­- 5y = 13 and 2x -­ y = 5, then (x -­ y) is

A. 3
B. 4
C. 5
D. 1

Question 914

If cos -300° = x, then the value of x is

A. 1/2
B. -1/√2
C. -1/2
D. √3/2

Question 915

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 916

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 917

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 918

If A = (-14 + 4) and B = 4 - 14, then AB =

A. 0
B. -100
C. 100
D. -1

Question 919

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 920

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 921

Simplify (2/7 + 3/5) / (2/5 + 2/7)

A. 31/24
B. 24/31
C. 26/25
D. 12/13

Question 922

By how much is three-fifth of 350  greater than four-seventh of 210 ?

A. 90
B. 100
C. 110
D. 120

Question 923

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 924

Which of the following numbers is completely divisible by 99?

A. 57717
B. 57627
C. 55162
D. 56982

Question 925

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 926

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 927

If a - b = -1 and ab = 6, then what is the value of a3- b3?

A. 33
B. -19
C. 18
D. 35

Question 928

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 929

1747 + 13212 - ? = 1123

A. 16
B. 17
C. 18
D. 19

Question 930

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 931

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 932

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 933

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 934

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 935

Simplify 4(x-1) -3x

A. 7x - 4
B. 7x + 4
C. x + 4
D. x - 4

Question 936

If √x ­- √y = 1 , √x + √y = 17 then √xy = ?

A. √72
B. 72
C. 32
D. 24

Question 937

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

A. 1
B. -1
C. 0
D. 2

Question 938

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 939

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 940

If sinθ+cosθsinθ-cosθ=3, then the value of sin4θ-cos4θ is

A. 4/3
B. 3/4
C. 5/3
D. 3/5

Question 941

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

A. 1
B. 0
C. -1
D. 2

Question 942

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

A. 3, 2
B. 2, 3
C. 4, 6
D. 6, 4

Question 943

Given that ( 12 + 22 + 32 + .......... + 102 ) = 385, then the value of ( 22 + 32 + 42 + .......... + 202 ) is equal to = ?

A. 770
B. 1155
C. 1540
D. (385)2

Question 944

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 945

If a + b = 1 and ab = -6, then what is the value of a3+ b3?

A. 17
B. 15
C. 19
D. 13

Question 946

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 947

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 948

If cosθ1-sinθ+cosθ1+sinθ = 4, then the value of θ (0°<θ<90°)?

A. 60°
B. 45°
C. 30°
D. 35°

Question 949

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 950

On dividing 24a2b2 by 6b2, we will get

A. 4b
B. 4ab
C. 4
D. 4a2

Question 951

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 952

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 953

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 954

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

A. 1
B. 2
C. 1/2
D. 0

Question 955

If 60/75 is equivalent to 4/x, then the value of x is

A. 5
B. 4
C. 15
D. 18

Question 956

Simplify 486b3x2a4z3/27a3b2z

A. 18bx2az2
B. 18bx2a2z
C. 36ba2z
D. 36bxaz

Question 957

Calculate the value of 61681 x 61681 - 31681 x 3168130000?

A. 93352
B. 94362
C. 93362
D. 95362

Question 958

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

A. 198
B. 208
C. 218
D. 228

Question 959

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 960

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 961

2660 of 17 of 12 of 19.5 of 12 = ?

A. 1
B. 10
C. 0.1
D. 100

Question 962

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 963

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 964

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 965

38% of 7500 +  ?% of 375 = 50% of 6000

A. 50
B. 40
C. 60
D. 45

Question 966

If x + (1/x) = 2, then what is the value of x21 + (1/x1331)?

A. 0
B. 1
C. 2
D. 3

Question 967

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 968

Find the value of  y(y4 - y2 - y) when y = 5.

A. 2900
B. 2975
C. 2925
D. 2995

Question 969

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 970

Reciprocal of 235?

A. 235
B. 532
C. 513
D. 335

Question 971

Simplify 437bxaz / 23ab.

A. 17xzb
B. 9xz
C. 19xz
D. 19ab

Question 972

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

A. 90°
B. 45°
C. 60°
D. 75°

Question 973

Square of (7 ­- 4x) is

A. 16x2 - 28x + 49
B. 49 -­ 28x ­- 16x2
C. 49 - ­ 56x -­ 16x2
D. 16x2 - 56x + 49

Question 974

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

A. 3
B. 4
C. 5
D. 6

Question 975

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 976

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 977

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 978

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 979

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

A. 21
B. 28
C. 23
D. -20

Question 980

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 981

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 982

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

A. (3,6)
B. (3,-6)
C. (-3,-6)
D. (-3,6)

Question 983

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 984

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 985

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 986

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 987

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 988

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 989

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 990

The value of Sin 60 is

A. √1/2
B. √3/2
C. 1/√2
D. 1/2

Question 991

If (23)2= 4x then 3x is equal to

A. 3
B. 6
C. 9
D. 27

Question 992

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 993

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 994

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 995

Reduce 3596 / 4292 to lowest terms.

A. 29/37
B. 17/43
C. 31/37
D. 19/23

Question 996

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

A. –125
B. 5
C. 1/125
D. 625

Question 997

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 998

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 999

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 1000

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 1001

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

A. 16
B. 64
C. 32
D. 8

Question 1002

What is the value of sin225°+ sin265°?

A. 0
B. 1
C. 2
D. 4

Question 1003

If 3n = 2187, then the value of n is:

A. 13
B. 14
C. 15
D. 16

Question 1004

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 1005

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 1006

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 1007

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 1008

If a - b = 2 and ab = 24, then what is the value of a3- b3?

A. 280
B. 124
C. 140
D. 152

Question 1009

If a=101 then the value of a(a2-3a+3) is

A. 1000000
B. 1010101
C. 1000001
D. 999999

Question 1010

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 1011

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

A. (3,6)
B. (6,-3)
C. (-3,-6)
D. (-6,3)

Question 1012

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 1013

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 1014

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 1015

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 1016

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 1017

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 1018

What is the value of cosec 3π/4?

A. -√2
B. √2
C. 2/√3
D. -2/√3

Question 1019

The difference of 18 and its reciprocal is equal to :

A. 1/8
B. 4/3
C. 15/16
D. 105/304

Question 1020

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 1021

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 1022

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 1023

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

A. -1
B. 0
C. 1
D. 2

Question 1024

If tanα = 2 - 1, then the value of  tanα - cotα = ?

A. -2
B. √2 + 1
C. 1
D. 2√2

Question 1025

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

A. 833
B. 825
C. 822
D. 800

Question 1026

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

A. 1
B. 2
C. 3
D. 4

Question 1027

Ifab=45andbc=1516, then c2-a2c2+a2 is :

A. 7/5
B. 7/25
C. 7/125
D. 7

Question 1028

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 1029

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

A. 604
B. 370
C. 253
D. 199

Question 1030

What is the value of cosec 5π/3?

A. √2
B. -2/√3
C. -√2
D. 1/√3

Question 1031

(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 1032

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 1033

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 1034

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

A. 593
B. 493
C. 793
D. 1193

Question 1035

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 1036

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 1037

Product of 6ab, 3b and 4a is

A. 72a2b2
B. 144ab
C. 72ab
D. 144a2b2

Question 1038

If (333 + 333 + 333) (233 + 233) = 6x, then what is the value of x?

A. 34
B. 35
C. 33
D. 33.5

Question 1039

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 1040

Find x, if 5x-6+5x+6 = 6

A. -4
B. 0
C. 2
D. 4

Question 1041

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 1042

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 1043

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 1044

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

A. 8464
B. 8432
C. 7478
D. 6218

Question 1045

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 1046

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 1047

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 1048

78 of 448 + 67 of 3374 = ?

A. 3084
B. 3184
C. 3584
D. None of these

Question 1049

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

A. -2
B. 0
C. 1
D. -1

Question 1050

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 1051

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

A. 2cosec2A
B. 2sec2A
C. 1 -­ 2cosec2A
D. 1 -­ 2sec2A

Question 1052

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 1053

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 1054

Find the value of '?' in 512 × 125 ÷ 15625 = 3125 × 25?

A. 4
B. 3
C. 2
D. 1

Question 1055

If x2 – 4x + 1 = 0, then what is the value of x9 + x7 – 194x5 – 194x3?

A. 4
B. – 4
C. 1
D. – 1

Question 1056

What is the value of sin6θ + cos6θ + 3 sin2θ cos2θ –1?

A. 0
B. 1
C. 2
D. 4

Question 1057

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 1058

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 1059

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 1060

Coefficient of x in (x + 11)(3 -­ 5x) is _____.

A. 33
B. -5
C. 3
D. -52

Question 1061

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 1062

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

A. 4
B. 8
C. -4
D. -8

Question 1063

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

A. tan2θ sec2θ
B. sec4θ
C. tan4θ
D. tan2θ sin2θ

Question 1064

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 1065

5 + 2 x 10 =

A. 70
B. 20
C. 25
D. 52

Question 1066

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

A. 5
B. 15
C. 25
D. 35

Question 1067

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 1068

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 1069

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

A. cosA
B. sinA
C. cosecA
D. secA

Question 1070

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 1071

Reflection of the point (­2,5) in the x­ axis is

A. (2,5)
B. (-2,­5)
C. (­2,-5)
D. (­-2,­-5)

Question 1072

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 1073

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

A. √3/2
B. 1/2
C. -2/√3
D. √2

Question 1074

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

A. 9999
B. 999999
C. 99999
D. 9999999

Question 1075

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 1076

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 1077

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 1078

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

A. 1
B. 0
C. -1
D. 2

Question 1079

If secA = x, then the value of x is

A. √(1 -­ cot2A)
B. √(1 -­ tan2A)
C. √(1 + cot2A)
D. √(1 + tan2A)

Question 1080

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 1081

The distance between the points (7,7) and (k,-5) is 13. Find k?

A. -2
B. 4
C. -4
D. 2

Question 1082

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

A. 2
B. 3
C. -2
D. 0

Question 1083

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

A. n2
B. m2
C. mn
D. 1

Question 1084

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 1085

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 1086

If 31x + 31y = 403, then what is the average of x and y?

A. 3.5
B. 5
C. 6.5
D. 13

Question 1087

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 1088

A tetrahedron has 4 vertices. How many edges does it have?

A. 8
B. 12
C. 6
D. 10

Question 1089

Calculate the sum of squares from 1 to 9.

A. 284
B. 285
C. 385
D. 380

Question 1090

If 2x -3(x + 2) < 5 - 2x < -x + 2, then find the value of x.

A. 2
B. 0
C. 10
D. 12

Question 1091

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

A. 8
B. 6
C. 12
D. 10

Question 1092

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 1093

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 1094

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

A. 10
B. 12
C. 15
D. 18

Question 1095

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 1096

What is the simplified value of 12-13 ?

A. 5√3
B. 5/√3
C. 3√5
D. 3/√5

Question 1097

If 3x + 2y = 7 and 4x - y = 24, then x - y = ______.

A. 9
B. 1
C. -9
D. -1

Question 1098

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

A. b5x4a5z5
B. b5x4a5z7
C. b5x4a4z7
D. b4x4a5z7

Question 1099

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

A. 2
B. 4
C. 6
D. 8

Question 1100

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 1101

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 1102

125 - 73 + 48 - 137 + 99 = ?

A. 237
B. 62
C. -37
D. 52

Question 1103

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 1104

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 1105

If sin3A = x, then value of x is

A. 3sinA + 4sin3A
B. 4sin3A -­ 3sinA
C. 4sin3A + sinA
D. 3sinA -­ 4sin3A

Question 1106

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 1107

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 1108

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 1109

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 1110

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 1111

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 1112

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 1113

What is the value of tan 7π/4?

A. √3
B. -1/2
C. √3/2
D. -1

Question 1114

[15% of 300% of 560] × 2 ÷ 5 =

A. 100
B. 90
C. 85
D. 105

Question 1115

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 1116

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

A. 2
B. 3
C. 4
D. 5

Question 1117

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 1118

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 1119

For x > 0, what is the minimum value of  x + x+22x?

A. 1
B. 2
C. 2.5
D. 1.5

Question 1120

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 1121

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

A. tan4A + tan2A
B. cot4A + cot2A
C. cot4A -­ cot2A
D. tan4A -­ tan2A

Question 1122

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 1123

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

A. 216
B. 125
C. 64
D. 343

Question 1124

(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 1125

If Cos θ = 5/13, then Cosec θ = ?

A. 5/12
B. 12/5
C. 13/5
D. 13/12

Question 1126

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 1127

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 1128

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 1129

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 1130

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 1131

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

A. 98
B. 152
C. 124
D. 260

Question 1132

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

A. tanA
B. cosA
C. cosecA
D. secA

Question 1133

If √(1 + cot2A) = x, then the value of x is

A. secA
B. sinA
C. cosecA
D. cosA

Question 1134

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 1135

If sec2θ+tan2θ=3, then sec4θ-tan4θ =

A. 1/√3
B. 1
C. √3
D. 0

Question 1136

Solve the following: (−18)[36÷7−(−2)]÷{}(−4)19−(−3)×(−5)={}?

A. -4.5
B. 4.5
C. -2.5
D. 2.5

Question 1137

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 1138

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 1139

Expand : S + 23

A. S3+3S2+12S+8
B. S3+3S2+6S+8
C. S3+6S2+12S+8
D. S3+6S2+6S+8

Question 1140

What is the value of cosec 11π/6?

A. -2/√3
B. √2
C. -2
D. -√2

Question 1141

What is the value of sec -2π/3 ?

A. -2
B. 2
C. 2/√3
D. -2/√3

Question 1142

If 2x+29x = 4, then the value of 27x3+127x3

A. 180
B. 198
C. 234
D. 252

Question 1143

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

A. 69
B. 68
C. 70
D. 72

Question 1144

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

A. 290
B. 0.29
C. 2.9
D. 2900

Question 1145

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 1146

If a+b=5 then the value of a-37+b-27 is

A. 27
B. 37
C. 1
D. 0

Question 1147

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 1148

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 1149

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 1150

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 1151

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 1152

What is the value of (sin60° - 2/√3) ?

A. -1/2√3
B. -1/2
C. 1/√3
D. (1-2√3)/2

Question 1153

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 1154

If Cot θ = 24/7, then Sin θ = ?

A. 24/25
B. 8/25
C. 7/25
D. 9/25

Question 1155

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 1156

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 1157

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 1158

If 3a+4b3c+4d = 3a-4b3c-4d, then

A. ab = cd
B. ad = bc
C. ac = bd
D. a = b = c ≠ d

Question 1159

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 1160

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 1161

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 1162

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 1163

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 1164

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 1165

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 1166

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 1167

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 1168

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 1169

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 1170

∆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 1171

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 1172

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 1173

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 1174

If x + 1/x = √13, then 3x(x2-1) equal to

A. 3√13
B. √13/3
C. 1
D. 3

Question 1175

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 1176

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

A. 4
B. 5
C. 0
D. 1

Question 1177

cos3A is equal to

A. cos3A - 3sin2cosA
B. cos3A + 4sin2cosA
C. cos3A + 3sin2cosA
D. cos3A - 4sin2cosA

Question 1178

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 1179

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

A. cosec4A - sin4A
B. cos4A - sin4A
C. cos4A - tan4A
D. cosec4A - tan4A

Question 1180

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 1181

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

A. 437.88
B. 4.3788
C. 0.43788
D. 0.043788

Question 1182

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 1183

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 1184

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

A. 169
B. 37
C. 73
D. 48

Question 1185

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 1186

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 1187

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 1188

Sec 45% + Tan 30% =

A. (√6 + 1)/√3
B. (1 + √3)/2
C. (√3 + 2)/√3
D. 5/√3

Question 1189

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 1190

43% of 616.6 + 37% of 217 =?

A. 345.428
B. 354.428
C. 344.428
D. 364.428

Question 1191

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

A. 0
B. 2 cos2 A
C. cos2A
D. 1

Question 1192

If  C+1C = 3, then what is the value of C3+1C3 = ?

A. 0
B. 3√3
C. 1/√3
D. 6√3

Question 1193

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 1194

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 1195

On dividing 111a2b2c2 by 37a2, we get ______.

A. 2c2
B. 2b2
C. 3
D. 3b2c2

Question 1196

What is the value of 128 + 7232

A. 3.5
B. 7
C. 4.5
D. 9

Question 1197

What is the value of Tan 60 + Cosec 60?

A. 5/3
B. 2/√3
C. 5/√3
D. 2/3

Question 1198

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 1199

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 1200

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 1201

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 1202

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 1203

Tan 45° + Cosec 60° =

A. (1 + 2√2)/2
B. (√3 + 2)/√6
C. 5/√3
D. (3 + 2√3)/3

Question 1204

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

A. 1
B. 2
C. 3
D. 4

Question 1205

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 1206

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 1207

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 1208

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 1209

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 1210

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 1211

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 1212

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 1213

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 1214

97 x 97 = ?

A. 9391
B. 9409
C. 9049
D. 9309

Question 1215

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 1216

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 1217

tanAcosec2A is equal to

A. (1 + tan2A)cotA
B. (1 -­ tan2A)cotA
C. √[(1 + tan2A)cotA]
D. √[(1 -­ tan2A)cotA]

Question 1218

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

A. 2
B. 4
C. 6
D. 3

Question 1219

Derivative of sinx by first principle?

A. -sinx
B. -cosx
C. cosx
D. sinx

Question 1220

The value of cos (1110°) is

A. √3/2
B. 1/2
C. 1/√2
D. 1

Question 1221

What is the square root of 5041?

A. 79
B. 81
C. 71
D. 69

Question 1222

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 1223

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 1224

What is the value of cos 4π/3?

A. -1/2
B. √3/2
C. - 1/√2
D. √3/2

Question 1225

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 1226

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 1227

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

A. cotA
B. cosecA
C. tanA
D. secA

Question 1228

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 1229

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 1230

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 1231

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 1232

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

A. -2
B. -2/√3
C. √3/2
D. √2

Question 1233

If a - b = 1 and ab = 6, then what is the value of a3- b3?

A. 21
B. 23
C. 19
D. 25

Question 1234

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 1235

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

A. 154
B. 64
C. 90
D. 26

Question 1236

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 1237

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 1238

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

A. -9
B. -69
C. -10.5
D. -63

Question 1239

Compute of 69696 x 9999 =

A. 696980304
B. 666890304
C. 696809304
D. 696890304

Question 1240

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 1241

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 1242

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

A. cosC + cosD
B. cosC ­- cosD
C. sinC ­- sinD
D. sinC + sinD

Question 1243

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 1244

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 1245

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 1246

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 1247

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 1248

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 1249

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 1250

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 1251

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 1252

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 1253

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 1254

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 1255

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 1256

What is the slope of the line 2x - 5y = 12?

A. 2/5
B. 5/2
C. -2/5
D. -5/2

Question 1257

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

A. -9
B. 81
C. 9
D. -81

Question 1258

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 1259

If cotA/√(1 + cot2A) = x, then the value of x is

A. sinA
B. cosecA
C. secA
D. cosA

Question 1260

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 1261

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 1262

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

A. sinA
B. secA
C. tanA
D. cosA

Question 1263

If x = y + 2 then x3 -  y3 -  z3 is

A. 0
B. 3xyz
C. -3xyz
D. 1

Question 1264

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 1265

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 1266

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 1267

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

A. -2
B. -1
C. 0
D. 2

Question 1268

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 1269

What is the value of [(cos32θ + 3 cos 2θ)÷(cos6θ – sin6θ)]?

A. 0
B. 1
C. 2
D. 4

Question 1270

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 1271

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

A. 1
B. 2
C. 3
D. 0

Question 1272

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 1273

0.196 + 1.96 + 19.6 + 196 = ?

A. 217.756
B. 216.856
C. 216.756
D. 217.676

Question 1274

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 1275

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 1276

Value of (cos 53° - sin 37°) is

A. 2 sin 37 ̊
B. 2 cos 53 ̊
C. 0
D. 1

Question 1277

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 1278

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

A. 12
B. 16
C. 18
D. 14

Question 1279

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

A. 13
B. 14
C. 7
D. 26

Question 1280

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 1281

The value of 1/64 is equal to square of

A. 0.125
B. 0.135
C. 0.145
D. 0.225

Question 1282

What is the value of cot 5π/3?

A. 1/√3
B. -1/√3
C. √3
D. -√3

Question 1283

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 1284

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 1285

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

A. 10
B. 12
C. 15
D. 18

Question 1286

√(1 + tan2A)/tanA is equal to

A. secA
B. sinA
C. cosecA
D. cosA

Question 1287

If 3x2 = 102 - 52, find the value of x?

A. 7
B. 5
C. 9
D. 11

Question 1288

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 1289

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 1290

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 1291

Determine the value of z in the equation: z = 20+20+20+20+...∞

A. 4
B. 5
C. 20
D. 25

Question 1292

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 1293

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 1294

If a + b = 10 and ab = 24, then what is the value of a3 + b3?

A. 280
B. 152
C. 140
D. 72

Question 1295

On dividing 256a2b2c2 by 64a2, we get

A. 2cxc
B. 2bxb
C. 4 bxb.cxc
D. 4

Question 1296

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 1297

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 1298

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 1299

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

A. (43 - 37)
B. (43 + 37)
C. (37 + 37)
D. 10

Question 1300

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 1301

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 1302

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

A. 0
B. 1
C. 1/4
D. 2

Question 1303

Simplify  413 + 215 + 414 = ?

A. 10 47/60
B. 11 45/73
C. 11 47/36
D. 10 35/48

Question 1304

What is the value of 26 + 152?

A. 17
B. 19
C. 15
D. 21

Question 1305

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 1306

What is the value of Cot 60 - Sec 30?

A. -1/3
B. -1/√3
C. 1/√3
D. 1/3

Question 1307

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 1308

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 1309

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 1310

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 1311

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 1312

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 1313

2 ­- (cosA + sinA)2 is equal to

A. (cosecA -­ sinA)2
B. cosA ­- sinA
C. cosecA ­- sinA
D. (cosA -­ sinA)2

Question 1314

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 1315

If 9x = 24311, then what is the value of x?

A. 5/11
B. 5/22
C. 5/7
D. 5/33

Question 1316

If Sec θ = 13/12, then Cot θ = ?

A. 12/5
B. 13/5
C. 5/13
D. 5/12

Question 1317

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 1318

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 1319

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

A. 1 + sinA
B. 1 ­- sinA
C. 1 -­ secA
D. 1 + secA

Question 1320

If P=9, Q=17 then the value of p2-q2-13

A. 4
B. 1/4
C. 3
D. 1/3

Question 1321

tan2Asin2A is equal to

A. tan2A - sin2A
B. tan2A + sin2A
C. cot2A - sin2A
D. cot2A + sin2A

Question 1322

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 1323

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 1324

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 1325

If cosθ + sinθ = m, secθ + cosecθ = n, what is m/n?

A. 1
B. sinθ cosθ
C. secθ cosecθ
D. cotθ tanθ

Question 1326

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 1327

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 1328

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

A. 11
B. 10
C. 12
D. -10

Question 1329

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 1330

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 1331

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 1332

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 1333

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 1334

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 1335

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 1336

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

A. 1 – cos2A
B. 2sin2A
C. sec2A
D. 0

Question 1337

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

A. cotA
B. tanA
C. sinA
D. cosA

Question 1338

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 1339

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 1340

What is the value of sin 330°?

A. 2
B. 2/√3
C. √2
D. -1/2

Question 1341

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 1342

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 1343

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 1344

∆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 1345

5.16 x 3.2 =

A. 15.502
B. 16.512
C. 17.772
D. 17.52

Question 1346

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 1347

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 1348

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 1349

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 1350

If cos 2π/3c = x, then the value of x is

A. -1/2
B. 1/2
C. -√3/2
D. √3/2

Question 1351

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

A. -1/√3
B. -√3
C. -1
D. -1/2

Question 1352

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 1353

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 1354

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

A. 9
B. 18
C. 27
D. 1

Question 1355

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 1356

19 x 23 = 437. Then 190 x 0.023 = ?

A. 43.7
B. 4.37
C. 0.0437
D. 0.437

Question 1357

Simplyfiy : 314÷114-12212-14+16

A. 78
B. 88
C. 98
D. 108

Question 1358

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 1359

If a - b = -7 and a2+ b2= 85, then find ab.

A. 18
B. -30
C. -44
D. 60

Question 1360

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

A. 2
B. 0
C. 1
D. 1/n

Question 1361

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 1362

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 1363

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 1364

If Sin x = 4/5, then Cosec x + Cot x =

A. 31/12
B. 35/12
C. 2
D. 1/2

Question 1365

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 1366

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 1367

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

A. 96
B. -30
C. 42
D. -18

Question 1368

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 1369

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 1370

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 1371

If 2x+4-2x+2=3, then the value of x?

A. 0
B. 2
C. -1
D. -2

Question 1372

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 1373

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 1374

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 1375

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

A. 29
B. 39
C. 19
D. 9

Question 1376

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

A. 5
B. -6
C. 7
D. -9

Question 1377

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 1378

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 1379

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 1380

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 1381

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 1382

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 1383

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 1384

Find the unit place in 194102+294103

A. 0
B. 6
C. 8
D. 2

Question 1385

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 1386

Simplify (b2x 3a2z4 ) × (b2x 4a4z3 )/(a3b2z4 )

A. b2x7a3z3
B. b3x7a3 z3
C. b2x5a3 z3
D. b2x7a3z2

Question 1387

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

A. 6
B. 10
C. 6√10
D. √10

Question 1388

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 1389

Coefficient of x in (x + 9)(8 - 5x) is

A. 37
B. -53
C. -37
D. 53

Question 1390

If sec 300° = x, then value of x is

A. ­√2
B. 1/√3
C. 2
D. ­1

Question 1391

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 1392

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

A. +- 1
B. +-2
C. +-3
D. +-4

Question 1393

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 1394

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 1395

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 1396

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 1397

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 1398

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 1399

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 1400

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 1401

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 1402

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 1403

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 1404

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 1405

If sin (3x ­ 20°) = cos (3y + 20°), then find the value of (x + y).

A. 90°
B. 60°
C. 120°
D. 30°

Question 1406

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

A. √3/2
B. 1/2
C. -√3/2
D. -1/2

Question 1407

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 1408

Solve : 12 - [26 - {2 + 5 x (6 - 3)}]

A. 2
B. 3
C. 7
D. 8

Question 1409

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 1410

9876-?+5431=5553

A. 9754
B. 9765
C. 8754
D. 9854

Question 1411

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

A. 1
B. -1
C. 4
D. 2√5

Question 1412

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 1413

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 1414

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 1415

∆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 1416

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 1417

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 1418

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

A. 72°
B. 108°
C. 54°
D. 36°

Question 1419

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 1420

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 1421

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 1422

1422 ÷ 1260.25 = ?

A. 586
B. 578
C. 568
D. 566

Question 1423

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 1424

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

A. 0
B. 2
C. 1
D. 3

Question 1425

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

A. 61
B. 41
C. 81
D. 51

Question 1426

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 1427

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

A. 30
B. 64
C. 98
D. 15

Question 1428

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 1429

What is the value of 36+729381+643

A. 5/12
B. 5/9
C. 4/9
D. 4/15

Question 1430

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 1431

For x = 462+3, what is the value of x+22x-22+x+23x-23

A. 1
B. √2
C. √3
D. 2

Question 1432

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 1433

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 1434

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

A. tan2A cot2A
B. sinA cosA
C. secA cosecA
D. sec2A cosec2A

Question 1435

What is the value of sec 4π/3?

A. 2
B. -2
C. 2/√3
D. -2/√3

Question 1436

If 3x - 10 = -(2x + 5), then the numerical value of (x - 4)3 is

A. 27
B. 125
C. -125
D. -27

Question 1437

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 1438

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 1439

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 1440

If 5x = 30-y = 6z, then what is the value of (xy + yz + zx)/xyz?

A. 0
B. 1
C. 2
D. 3

Question 1441

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 1442

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 1443

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

A. 2sec2A
B. 2cosecA
C. 2cosec2A
D. 2secA

Question 1444

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 1445

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 1446

If 3x -­ 7 = 5x ­- 1, then the numerical value of (x ­- 4)2 is

A. 1
B. 49
C. -1
D. -49

Question 1447

cosA/(1 -­ sin A) is equal to

A. (secA -­ tanA)
B. (secA + tanA)
C. √[(secA + tanA)]
D. √[(secA -­ tanA)]

Question 1448

1/(secA + tanA) is equal to

A. cosecA - cotA
B. sinA - cosA
C. secA - tanA
D. sinA + cosA

Question 1449

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 1450

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 1451

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 1452

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

A. 2x2 + 5xy + 2y2
B. 2x2 + 3xy - 2y2
C. x2 + 4xy + y2
D. x2+ 4xy - y2

Question 1453

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

A. 5
B. 17
C. 7
D. 0

Question 1454

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 1455

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

A. sec A
B. sec (A/2)
C. cot A
D. cot2 A

Question 1456

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 1457

If 9x2 + 16y2 = 60 and 3x + 4y = 6, then the value of xy is

A. -1
B. 1
C. -2
D. 2

Question 1458

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

A. 14
B. 13
C. 12
D. 11

Question 1459

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 1460

The value of cos0 deg is

A. 0
B. infinite
C. not defined
D. 1

Question 1461

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 1462

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

A. 0
B. 1
C. -1
D. 2

Question 1463

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 1464

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 1465

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 1466

What is the value of 13313 + 729 - 5123

A. 15
B. 20
C. 30
D. 23

Question 1467

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

A. 0.0493
B. 4.93
C. 0.493
D. 49.3

Question 1468

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

A. sinC ­-  sinD
B. cosC + cosD
C. cosC -­ cosD
D. sinC + sinD

Question 1469

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 1470

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

A. 0
B. 1
C. 2
D. 3

Question 1471

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 1472

Find the value of 532+108

A. 732
B. 1732
C. 2732
D. 3732

Question 1473

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

A. 1.5
B. 1.25
C. 1
D. 2

Question 1474

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 1475

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

A. √3
B. 2√3
C. √(3/2)
D. 3/√2

Question 1476

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 1477

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 1478

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 1479

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 1480

tan(A/2) is equal to

A. tanA/(1 + secA)
B. 1/(cosecA + cotA)
C. tanA/(1 + cosecA)
D. 1/(secA + cotA)