Simplification MCQs : This section focuses on the "Simplification". These Multiple Choice Questions (MCQs) should be practiced to improve the Simplification skills required for various interviews (campus interview, walk-in interview, company interview), placement, entrance exam and other competitive examinations.
Question 1
What is the simplified value of (sec4 A – tan2 A) – (tan4 A + sec2 A)?
A. -1
B. 1/2
C. 1
D. 0
Question 2
If a - b = 3 and ab =28, then a3 - b3 is
A. 279
B. 387
C. 513
D. 91
Question 3
The perimeter of two similar triangles is 36 units and 48 units. Find the ratio of their corresponding areas.
A. 1 : 3
B. 3 : 4
C. 4 : 9
D. 9 : 16
Question 4
If cot A = [sin B/(1 – cos B)], then what is the value of cot 2A?
A. cot(B/2)
B. cot 2B
C. cot B
D. tan B
Question 5
If a2+b2c2 = b2+c2a2 = c2+a2b2 = 1k k≠0 then k =
A. 2
B. 1
C. 0
D. 1/2
Question 6
If xy = 48 and x2 + y2 = 100, then (x + y) is
A. 12
B. 16
C. 18
D. 14
Question 7
A bag contains coins of denominations Rs.1, Rs.5 and Rs.10. Assuming there are equal number of Rs.1, Rs.5 and Rs.10, what will be the total number of coins in the bag be if the total money is Rs. 368?
A. 69
B. 96
C. 56
D. 65
Question 8
What is the value of tan 6° tan 36° tan 84° tan 54° tan 45°?
A. 1/2
B. 1/√2
C. 1
D. 1/3
Question 9
What is the value of equation a3+b3+c3-3abc if a2+b2+c2=ab+bc+ca+4 and a+b+c = 4.
A. 0
B. 1
C. 16
D. 256
Question 10
What is the value of 128 + 7232
A. 3.5
B. 7
C. 4.5
D. 9
Question 11
The value of 2.33+0.0272.33-0.69+0.09
A. 2
B. 2.27
C. 2.33
D. 2.6
Question 12
If 4x2= 152- 92, then value of x is
A. 9
B. 6
C. 3
D. 12
Question 13
If x + y = 13 and x2 + y2 = 89, then find xy is
A. 80
B. 169
C. 258
D. 40
Question 14
If a--b = 4 and ab = 45, find the value of a3 - b3
A. 604
B. 370
C. 253
D. 199
Question 15
Compute 4923 / 547 - 10
A. 1
B. -1
C. 1641/179
D. 1614/179
Question 16
Simplify 50 + 18 - 8
A. 8√2
B. 7√2
C. 6√2
D. 5√2
Question 17
If a and b are the roots of the equation Px2 – Qx + R = 0, then what is the value of (1/a2) + (1/b2) + (a/b) + (b/a)?
A. Q2-2P2R+PPR2
B. Q2-2PRR+PPR2
C. Q2-2R2P+RP2R2
D. Q2-2PR2R+2PP2R2
Question 18
If 2x + 3y3x - 4y = 117, then the value of x/y is __
A. 65/19
B. 68/19
C. 67/19
D. 64/19
Question 19
25 - 1/2{5 + 4 - (3 + 2 - 1 + 3)} = ?
A. 21
B. 23
C. 22
D. 24
Question 20
Solve : (x + 2y) (2x - y)
A. 2x2 + 5xy + 2y2
B. 2x2 + 3xy - 2y2
C. x2 + 4xy + y2
D. x2+ 4xy - y2
Question 21
112 × 54 =
A. 68947
B. 69874
C. 70000
D. 76000
Question 22
The average temperature of Monday to Wednesday was 37 C and of Tuesday to Thursday was 34 C. If the temperature on Thursday was 4/5 th of that of Monday, the temperature on Thursday was ?
A. 35 c
B. 36 c
C. 34 c
D. 32 c
Question 23
Simplify (b5x2a3z4)*(b3x2a4z5) / (a2b3z2)
A. b5x4a5z5
B. b5x4a5z7
C. b5x4a4z7
D. b4x4a5z7
Question 24
9876-?+5431=5553
A. 9754
B. 9765
C. 8754
D. 9854
Question 25
If a : b = c : d = 1 : 6, then what is the value of a2+c2b2+d2?
A. 1/600
B. 1/60
C. 1/36
D. 1/360
Question 26
Find the common factor of (3757+4357) and (3737+4337) ?
A. (43 - 37)
B. (43 + 37)
C. (37 + 37)
D. 10
Question 27
The points A(x,2), B(2,1) and C(6,3) are collinear. Find x?
A. 4
B. -2
C. -4
D. 2
Question 28
What is the value of cot210°?
A. 1/√3
B. -1/√3
C. √3
D. -√3
Question 29
40.36 - (9.347 - x ) - 29.02 = 3.68. Find x.
A. -56.353
B. 1.687
C. -17.007
D. 82.407
Question 30
If a + b + c + d = 4, then the value of 1(1-a)(1-b)(1-c) + 1(1-b)(1-c)(1-d) + 1(1-c)(1-d)(1-a) + 1(1-d)(1-a)(1-b)
A. 0
B. 1
C. 4
D. 1+ abcd
Question 31
If Cos θ = 5/13, then Cosec θ = ?
A. 5/12
B. 12/5
C. 13/5
D. 13/12
Question 32
An owner of a Dry fruits shop sold small packets of mixed nuts for Rs. 150 each and large packets for Rs. 250 each. One day he sold 5000 packets, for a total of Rs. 10.50 lakh. How many small packets were sold ?
A. 2000
B. 3000
C. 2500
D. 3500
Question 33
If cosαcosβ=m and cosαsinβ=n, then the value of m2+n2 cos2β is
A. n2
B. m2
C. mn
D. 1
Question 34
What is the reflection of the point (4, 7) in the line y = -1?
A. (-6 , 7)
B. (-4 , -9)
C. (4 , -9)
D. (-6 , -7)
Question 35
What is the value of x3-1x3+8 when 8x-8x-16=0 ?
A. 6
B. 8
C. 16
D. 22
Question 36
An angle is four times its complementary angle. What is the measure of the angle?
A. 72°
B. 108°
C. 54°
D. 36°
Question 37
If (6x - 5) = (4x + 7), then the numerical value of (x + 1)3 is
A. 216
B. 125
C. 64
D. 343
Question 38
What should be added to 8(3x - 4y) to obtain 18x - 18y?
A. 6x - 14y
B. 14y + 6x
C. 14y - 6x
D. 6xy
Question 39
Mr. Ankit is on tour to Siachin and he has Rs. 360 for his expenditure. If he exceeds his tour by 4 days, he must trim down his daily expenditure by Rs.3. Forhow many days is Mr. Ankit is on tour?
A. 20
B. 22
C. 24
D. 26
Question 40
What is the value of Cot 60°- Sec 45°?
A. (√2 - √3)/√6
B. (√3 - 3√2)/3
C. (1 - 2√2)/2
D. (1 - √3)/2
Question 41
If tan2A / (secA - 1)2 = x, then the value of x is
A. (1+cosecA) / (1-cosecA)
B. (1+cosA)(1-cosA)
C. (1+cosA) / (1-cosA)
D. (1+cosecA)(1-cosecA)
Question 42
If 22x - 40 = 207 + 3x, then x = ?
A. 14
B. 13
C. 12
D. 11
Question 43
If a - b = 4 and ab = -3, then what is the value of a3- b3?
A. 21
B. 28
C. 23
D. -20
Question 44
If (x + y)2 = xy + 1 and x3 – y3 = 1, then what is the value of x – y?
A. 1
B. 0
C. -1
D. 2
Question 45
What is the value of 1+aa1/2+a-1/2-a1/2+a-1/21+a+a-1/2 ?
A. √a
B. 1/√a
C. 0
D. √a+1
Question 46
If x - 2y = 2 and 3x + y = 20, then the value of (x,y) is
A. (6, 2)
B. (4, 1)
C. (3, 2)
D. (5, 5)
Question 47
When 2x + 2x = 3, then x3 + 1x + 2 value is
A. 2/7
B. 7/8
C. 7/2
D. 8/7
Question 48
(0.2 x 0.2 x 0.2)(0.06 x 0.06 x 0.06) / (0.12 x 0.12 x 0.12) = ?
A. 0.008
B. 0.001
C. 0.002
D. 0.006
Question 49
ΔDEF is right angled at E. If m∠F = 30 deg, then find the value of (sinD - 1/3).
A. -1/2√3
B. (3√3-2)/6
C. (√2-√3)/√6
D. (2√2-1)/√2
Question 50
ΔABC and ΔDEF are two similar triangles and the perimeter of ΔABC and ΔDEF are 30 cm and 18 cm respectively. If length of DE = 36 cm, then length of AB is
A. 60 cm
B. 40 cm
C. 45 cm
D. 50 cm
Question 51
Find the value of p if -3x - 11, x + p and 5x + 7 are in arithmetic progression.
A. 9
B. 2
C. -9
D. -2
Question 52
If x = 93 , y = 93 , z = 94 then the value of x2 - y2 + 10xz + 10yz is
A. 104784
B. 147840
C. 174840
D. 184740
Question 53
If 1/6 of x - 7/2 of 3/7 equals - 7/4, then the value of x is
A. -1.5
B. 3
C. -2.5
D. 6
Question 54
If Sin θ = 20/29, then what is the value of Cos θ?
A. 29/21
B. 21/29
C. 21/20
D. 20/29
Question 55
If sin - 5π/3 = x, then the value of x is
A. -√3/2
B. √3/2
C. -2
D. -2/√3
Question 56
If secA = x, then the value of x is
A. √(1 - cot2A)
B. √(1 - tan2A)
C. √(1 + cot2A)
D. √(1 + tan2A)
Question 57
Tan 45° + Cosec 60° =
A. (1 + 2√2)/2
B. (√3 + 2)/√6
C. 5/√3
D. (3 + 2√3)/3
Question 58
In a circle with centre O, AB is a diameter and CD is a chord which is equal to the radius OC. AC and BD are extended in such a way that they intersect each other at a point P, exterior to the circle. The measure of ∠APB is
A. 30°
B. 45°
C. 60°
D. 90°
Question 59
Find the value of 'y' if y84 = 225
A. 10
B. 12
C. 15
D. 18
Question 60
In ΔABC measure of angle B is 90 deg. If cotA = 7/24, and AB = 1.4cm, then what is the length (in cm) of side AC?
A. 5
B. 4.8
C. 4
D. 5.6
Question 61
What is the value of 99992 x 100008?
A. 9999999936
B. 9999899936
C. 9999999836
D. 9999999926
Question 62
What is the simplified value of cosec 2A + cot 2A?
A. sec A
B. sec (A/2)
C. cot A
D. cot2 A
Question 63
If cot π/3c - tan π/4c = x, then the value of x is
A. √3+2
B. (1-√3)/√3
C. (1-√2)/√2
D. (√3+4)/2√3
Question 64
If 4x = √5+ 2, then the value of x - 1/16x is
A. 1
B. -1
C. 4
D. 2√5
Question 65
If one more cobbler is hired the output of a shoe making unit will increase from 50 pairs of shoes to 55 pairs per day, but then the shoe making unit will have to reduce the price of a pair of shoes from Rs 3200 to Rs 3000 per pair to sell the additional output, the marginal revenue product of the last cobbler is
A. Rs 1000
B. Rs 5000
C. Rs 4000
D. Rs 200
Question 66
What is the value of (cos 45 - 1/3) ?
A. 2-√3
B. 2/√3
C. (3-√2)/3√2
D. 1/2√3
Question 67
If 9x+2 = 240 + 9x, the value of (8x)x is
A. 1
B. -1
C. 0
D. 2
Question 68
Expand and simplify (x + 4)2 + (x - 2)2
A. 2(x2 + 2x + 10)
B. 2(x2 + 2x - 10)
C. 2(x2 - 2x + 10)
D. 2(x2 - 2x - 10)
Question 69
Rs.7750 is divided among X, Y and Z such that 3 times of X's share is equal to 5 times of Y's share which is equal to 2 times of Z's share. What is the share (in Rs) of Z?
A. 4250
B. 3750
C. 3875
D. 4475
Question 70
10+10(9) =
A. 180
B. 110
C. 100
D. 19
Question 71
Slope of the line AB is -4/3. Co-ordinates of points A and B are (x, -5) and (-5, 3) respectively. What is the value of x?
A. -1
B. 2
C. -2
D. 1
Question 72
If x+y+z = 0, then what is the value of x23z+y33xz+z23x ?
A. 0
B. xz
C. y
D. 3y
Question 73
If a rod of length 208 45 is cut into equal pieces of length 23 15 then the total number of rods obtained is
A. 5
B. 8
C. 9
D. 7
Question 74
If a + b + c = 0 , then the value of a3 + b3+ c3 is
A. abc
B. 2abc
C. 3abc
D. 0
Question 75
If P = 99, then the value of P(P2+ 3P + 3) is
A. 9999
B. 999999
C. 99999
D. 9999999
Question 76
If 14/3 + (1/2)(x - 7/3) = -2x/3, then the value of x is?
A. -3
B. 3
C. -6
D. 6
Question 77
A man can cover a certain distance in 3 hours 36 minutes if he walks at the rate of 5 Km/hr. If he covers the same distance on cycle at the rate of 24 Km/hr, then the time taken by him in minutes is
A. 40
B. 45
C. 50
D. 55
Question 78
Which of the following value of 'x' satisfies the equation 814x+4 = 2432x+8?
A. 3
B. 4
C. 5
D. 6
Question 79
What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(-4, 0) and C(3, -4)?
A. ( 0, 3)
B. ( 0, -3)
C. ( 0, -5)
D. ( 0, 5)
Question 80
What is the equation of the line if its slope is 1/4 and y-intercept is -3?
A. x - 4y = 12
B. x + 4y = 12
C. x - 4y = -12
D. x + 4y = -12
Question 81
If a(a + b + c) = 45, b(a + b + c) = 75 and c(a + b + c) = 105, then what is the value of (a2 + b2 + c2 )?
A. 75
B. 83
C. 217
D. 225
Question 82
A man has Rs.480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
A. 45
B. 60
C. 75
D. 90
Question 83
A T.V was sold at a profit of 5% If it had been sold at a profit of 10% , the profit would have been Rs. 1000 more. What is its cost price ?
A. Rs.20000
B. Rs.5000
C. Rs.10000
D. Rs.15000
Question 84
What is the value of 0.55 x 4.5/0.81 ?
A. 3.555
B. 55/18
C. 3.05
D. 55/81
Question 85
In ΔPQR measure of angle Q is 90°. If tanP = 4/3, and PQ = 1.5cm, then what is the length (in cm) of side PR?
A. 2
B. 2.5
C. 3
D. 4.8
Question 86
x, y and z are prime numbers and x + y + z = 38. What is the maximum value of x?
A. 19
B. 23
C. 31
D. 29
Question 87
If cos2x + cos4x = 1, then tan2x + tan4x =
A. 0
B. 1
C. 2tanx
D. tanx
Question 88
ΔABC is right angled at B. If m∠C = 60°, then find the value of (cotA - 1/2).
A. -1/√3
B. (3-√2)/3√2
C. (2√3-1)/2
D. (√2-√3)/√6
Question 89
ΔABC is right angled at B. If cotA = 7/24, then what is the value of cosecC ?
A. 7/25
B. 25/7
C. 24/7
D. 7/24
Question 90
If tanA - cotA = x, then value of x is?
A. (1 + 2cos2A)/(sinA cosA)
B. (sinA cosA)/(1 - 2cos2A)
C. (sinA cosA)/(1 + 2cos2A)
D. (1 - 2cos2A)/(sinA cosA)
Question 91
A triangular prism has 9 edges. How many vertices does it have?
A. 8
B. 6
C. 12
D. 10
Question 92
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
A. 160
B. 175
C. 180
D. 195
Question 93
If (8x - 4) = (3x + 6), then the numerical value of (x + 1)3 is
A. 3
B. 9
C. 27
D. 81
Question 94
If 16% of an electricity bill is deducted, Rs 1806 is still to be paid. How much was the bill?
A. Rs 1557
B. Rs 2186
C. Rs 1593
D. Rs 2150
Question 95
What is the value of (-7776)25
A. 16
B. 36
C. 64
D. 21
Question 96
If 493/29 = 17, then 4.93/0.0017 = ?
A. 290
B. 0.29
C. 2.9
D. 2900
Question 97
P(3,1) and R(-7,5) are vertices of a rhombus PQRS. What is the equation of diagonal QS?
A. 5x - 2y = 16
B. 5x - 2y = -16
C. 5x + 2y = -16
D. 5x + 2y = 16
Question 98
If 14.35 - (1.956 - x ) - 83.92 = 3.858 then what is the value of x?
A. -92.456
B. 75.384
C. 71.472
D. 104.084
Question 99
Two fractions are such that their product is 2/5 and sum is 1/15. What are the two fractions.
A. 4/3, -3/10
B. 2/7, -7/5
C. 4/7, -7/10
D. 2/3, -3/5
Question 100
Simplyfiy : 314÷114-12212-14+16
A. 78
B. 88
C. 98
D. 108
Question 101
The highest score in an inning was 3/11 of the total and the next highest was 3/11 of the reminder . If the score differ by 9, the total score was :
A. 110
B. 121
C. 132
D. 143
Question 102
What is the simplified value of (cos4 A – sin4 A)?
A. 0
B. 2 cos2 A
C. cos2A
D. 1
Question 103
If a + b + c = 9, ab + bc + ca = 26, a3 + b3 = 91, b3 + c3 = 72 and c3 + a3 = 35, then what is the value of abc?
A. 48
B. 24
C. 36
D. 42
Question 104
If sin x + cos x = √2 sin x, then the value of tan x is
A. √2 - 1
B. √2 + 1
C. 1
D. √2
Question 105
A tower stands on the top of a building which is 40 metres high. The angle of depression of a point situated on the ground from the top and bottom of the tower are found to be 60 and 45 deg respectively. What is the height (in metres) of tower?
A. 20√3
B. 30(√3 + 1)
C. 40(√3 – 1)
D. 50(√3 – 1)
Question 106
If p and q are the roots of the equation x2 –15x + r = 0 and p –q = 1, then what is the value of r ?
A. 55
B. 56
C. 60
D. 64
Question 107
The value of sec217°-1tan273°-sin17°sec73°
A. 1
B. 0
C. -1
D. 2
Question 108
If in a triangle ABC, Sin A = Cos B then the value of Cos C is
A. √3/2
B. 0
C. 1
D. 1/√2
Question 109
In ΔABC, D and E are points on side AB and AC respectively. DE is parallel to BC. If lengths of AD, DB and DE are 8 cm, 6 cm and 7.2 cm respectively, find length of BC?
A. 12.6 cm
B. 9.3 cm
C. 8.1 cm
D. 5.4 cm
Question 110
If angles of measure (5y + 62°) and (22° + y) are supplementary , then value of y is
A. 16°
B. 32°
C. 8°
D. 1°
Question 111
Which of the following fractions is largest?
A. 3/4
B. 4/5
C. 5/6
D. 7/8
Question 112
There are 90 coins, comprising of 5 and 10 paisa coins. The value of all the coins is Rs. 7. How many 5 paisa coins are there?
A. 50
B. 45
C. 40
D. 35
Question 113
If M = 0.1 + (0.1)2 + (0.01)2 and N = 0.3 + (0.03)2 + (0.003)2, then what is the value of M + N?
A. 0.411009
B. 0.413131
C. 0.313131
D. 0.131313
Question 114
9997 x 10003 = ?
A. 9999991
B. 99999911
C. 99999991
D. 9999911
Question 115
If 3x - 8(2 - x) = -19, then the value of x is
A. -3/11
B. -33/11
C. -3/5
D. -33/5
Question 116
6 times a fraction is greater than 7 times its reciprocal by 11. What is the fraction?
A. 5/3
B. 7/3
C. 5/4
D. 4/5
Question 117
If secA + tanA = a, then the value of cosA is
A. a2+12a
B. 2aa2+1
C. a2-12a
D. 2aa2-1
Question 118
What is the value of 2sec2A?
A. secA/(cosecA - 1) + secA/(cosecA +1)
B. cosecA/(secA -1) + cosecA/(secA +1)
C. cosecA/(cosecA - 1) + cosecA/(cosecA +1)
D. secA/(secA - 1) + secA/(secA +1)
Question 119
Determine the value of 'x' in x = 11+2+12+3+13+2
A. -1
B. 0
C. 1
D. 2
Question 120
What is value of P+QP-Q if PQ=7 ?
A. 1/3
B. 2/3
C. 4/3
D. 5/3
Question 121
If Tan θ = 4/3, then what is the value of Sin θ?
A. 1.25
B. 0.8
C. 4/3
D. 3/4
Question 122
If x – 3 + [1/(x – 3)] = 4, what is the value of [(x – 3)3+ [1/(x – 3)3]?
A. 14
B. 18
C. 52
D. 76
Question 123
If 4x + 5y = 14 and x - 5y = 16 then the value of x and y are
A. 10 and -6/5
B. 6 and 2
C. 10 and 6/5
D. 6 and -2
Question 124
sin(A+B) - sin(A-B) is equal to
A. 2sinAcosB
B. 2cosAcosB
C. 2cosAsinB
D. 2sinAsinB
Question 125
At what point does the line 2x - 3y = 6 cuts the Y axis?
A. (0, 2)
B. (-2, 0)
C. (2, 0)
D. (0, -2)
Question 126
An aeroplane flying horizontally at a height of 3 Km. above the ground is observed at a certain point on earth to subtend an angle of 60°. After 15 sec flight, its angle of elevation is changed to 30°. The speed of the aeroplane (taking √3 = 1.732) is
A. 230.63 m/sec
B. 230.93 m/sec
C. 235.85 m/sec
D. 236.25 m/sec
Question 127
Determine the value of a+1b-1 when ab = 343.
A. 9
B. 64
C. 125
D. 216
Question 128
If (6 - 18x) - (x - 7) = 8, then the value of x is ______.
A. -5/19
B. -2/13
C. 2/13
D. 5/19
Question 129
If cos3A = X, then value of X?
A. 4cos3A - 3cosA
B. 4cos3A + 3cosA
C. 3cosA - 4cos3A
D. cosA + 4cos3A
Question 130
If x3 – 4x2 + 19 = 6(x – 1), then what is the value of [x2 + (1/x – 4)]?
A. 3
B. 5
C. 6
D. 8
Question 131
If sin = 2/3, find the value of secθ and cotθ
A. √5/2, 2/√5
B. 2/√5, 3/5
C. 3√5/5, √5/2
D. 3/5, 3√5/5
Question 132
What is the equation of a line having a slope -1/3 and y-intercept equal to 6?
A. x + 3y = 18
B. x - 3y = 6
C. x + 3y = -18
D. x - 3y = -6
Question 133
David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
A. 19
B. 28
C. 30
D. 37
Question 134
The value of 3x9n+1+9x32n-19x32n-6x9n-1 is equal to
A. 335
B. 325
C. 315
D. 3
Question 135
If (1 + secA)/tanA = x, then x is
A. cot(A/2)
B. tan(A/2)
C. cosec(A/2)
D. sec(A/2)
Question 136
If sec2A cosec2A = x, then x is
A. sec2A + cosec2A + 2
B. tan2A + cot2A - 2
C. tan2A + cot2A + 2
D. sec2A + cosec2A - 2
Question 137
What is the value of (4a2 + 8b + 14c + 2)/2 ?
A. 2a2 + 4b + 7c + 1
B. a2 + 4b + 7c + 1
C. 2a2 + 4b + 7c + 2
D. a2 + 4b + 7c + 2
Question 138
In ΔDEF measure of angle E is 90 deg. If sinD = 15/17, and DE = 4cm, then what is the length (in cm) of side EF?
A. 8.5
B. 7.5
C. 5
D. 6
Question 139
Simplify: b-[b-(a+b)-{b-(b-a-b)}+2a]
A. 2b
B. 1
C. 0
D. 3b
Question 140
What is the value of Cot 45° + Cosec 60°?
A. (√6 + 1)/√3
B. (1 + √3)/2
C. 5/√3
D. (√3 + 2)/√3
Question 141
If θ is positive acute angle and 4sin2θ = 3, then the value of tan θ - cot θ/2 is
A. 1
B. 0
C. √3
D. 1/√3
Question 142
The point Q(a,b) is first reflected in y-axis to Q1 and Q1 is reflected in xaxis to (-5,3). The coordinates of point Q are
A. (-5,3)
B. (5,-3)
C. (-5,-3)
D. (5,3)
Question 143
Reflection of the point (-3,6) in the x-axis is
A. (3,6)
B. (6,-3)
C. (-3,-6)
D. (-6,3)
Question 144
What is the x – intercept of the linear equation 18x + 25y – 900 = 0?
A. 18
B. 25
C. 50
D. 450
Question 145
If sum of the areas of the circumcircle and the incircle of an equilateral triangle is 770 cm2, then what is the area (in cm2) of the triangle?
A. 125√3
B. 147√3
C. 156√3
D. 169√3
Question 146
What is (x-y)3+y-23+z-x33x-yy-zz-x =?
A. 1
B. 0
C. 1/3
D. 3
Question 147
Expand : S + 23
A. S3+3S2+12S+8
B. S3+3S2+6S+8
C. S3+6S2+12S+8
D. S3+6S2+6S+8
Question 148
Two labourers A and B are paid a total of Rs. 1120 per day. If A is paid 180 percent of what is paid to B, how much (in Rs) is B paid?
A. 400
B. 720
C. 500
D. 620
Question 149
The value of 1/64 is equal to square of
A. 0.125
B. 0.135
C. 0.145
D. 0.225
Question 150
If 3a+4b3c+4d = 3a-4b3c-4d, then
A. ab = cd
B. ad = bc
C. ac = bd
D. a = b = c ≠ d
Question 151
What is the value of tan 4π/3?
A. 1/2
B. √3
C. √3/2
D. 1/√2
Question 152
Find the value of 200 x 20 x 2 x 0.2 x 0.02 x 0.002 = ?
A. 0.064
B. 0.64
C. 64
D. 640
Question 153
M is the largest 4 digit number, which when divided by 4, 5, 6 and 7 leaves remainder as 2, 3, 4, and 5 respectively. What will be the remainder when M is divided by 9?
A. 2
B. 1
C. 3
D. 6
Question 154
If x+1x ≠0 and x3+1x3 = 0, then the value of x+1x4 is :
A. 9
B. 12
C. 15
D. 16
Question 155
The point R(a,b) is first reflected in origin to R1 and R1 is reflected in X-axis to (-5,1). The co-ordinates of point R are?
A. (5,-1)
B. (-1,5)
C. (1,-5)
D. (5,1)
Question 156
What is the y – intercept of the linear equation 59x + 14y – 112 = 0?
A. 8
B. 14
C. 28
D. 59
Question 157
The point R(a,b) is first reflected in origin to R1 and R1 is reflected in x-axis to (-3,4). The co-ordinates of point R are
A. (3,4)
B. (-3,-4)
C. (-3,4)
D. (3,-4)
Question 158
If x2 – 16x – 59 = 0, then what is the value of (x – 6)2 + [1/(x – 6)2]?
A. 14
B. 18
C. 16
D. 20
Question 159
What is the value of sin (630 + A) + cos A?
A. √3/2
B. 1/2
C. 0
D. 2/√3
Question 160
A = (x8 – 1)/(x4 + 1) and B = (y4 – 1)/(y2 + 1). If x = 2 and y = 9, then what is the value ofA2 + 2AB + AB2?
A. 96475
B. 98625
C. 92425
D. 89125
Question 161
Expanded and simplification of (x + 3)(x - 1) will be equal to
A. x2+ 2x - 3
B. x2 + 3x + 2
C. x2 - 2x + 3
D. x2 + 3x - 2
Question 162
Find co-ordinates of the mid point of the segment joining points C (3,-5) and D (-7,3).
A. (-2, -1)
B. (5, -4)
C. (-5, 4)
D. (2, 1)
Question 163
The average number of visitors of a library in the first 4 days of a week was 58. The average for the 2nd, 3rd, 4th and 5th days was 60.If the number of visitors on the 1st and 5th days were in the ratio 8 : 9. Then what is the number of visitors on the 5th day of the library ?
A. 54
B. 64
C. 68
D. 72
Question 164
What is the value of tan4A + tan2A?
A. sec4A - sec2A
B. sec4A + sec2A
C. cosec4A - sec2A
D. sec4A + cosec2A
Question 165
Two parallel chords on the same side of the centre of a circle are 5 cm apart. If the chords are 20 and 28 cm long, what is the radius of the circle?
A. 14.69 cm
B. 15.69 cm
C. 18.65 cm
D. 16.42 cm
Question 166
If Cos θ = 35/37 , then what is the value of Cot θ?
A. 12/35
B. 35/12
C. 37/12
D. 12/37
Question 167
If cosAcotA/(1 - sinA) = x, then the value of x is
A. 1 - cosecA
B. 1 + cosecA
C. 1 + secA
D. 1 - secA
Question 168
If a + b = 4 and ab = -5, then what is the value of a3 + b3?
A. 34
B. 36
C. 124
D. 126
Question 169
If y = √3 - √2, then find the value of 1y3 - y3.
A. 11
B. 11√2
C. 22
D. 22√2
Question 170
If sinP = 2/3, find the value of secP and cotP.
A. √5/2, 2/√5
B. 2/√5, 3/5
C. 3√5/5, √5/2
D. 3/5, 3√5/5
Question 171
Coefficient of x2 in (x + 7)(5 - 3x)(3x - 6) is
A. 96
B. -30
C. 42
D. -18
Question 172
If a:b = 3:8, find the value of (5a 3b)/(2a + b).
A. 9/14
B. 14/9
C. -9/14
D. -14/9
Question 173
If 2x+14x = 1, then the value of x2+164x2 is
A. 0
B. 1
C. 1/4
D. 2
Question 174
If Cot θ = 24/7, then Sin θ = ?
A. 24/25
B. 8/25
C. 7/25
D. 9/25
Question 175
If cosec π/4 - sin π/3 = x, then the value of x is
A. 4/√3
B. (2√2-√3)/2
C. (1-√3)/√3
D. √3+2
Question 176
Simplify 486b3x2a4z3/27a3b2z
A. 18bx2az2
B. 18bx2a2z
C. 36ba2z
D. 36bxaz
Question 177
What is the value of 299996 x 300004?
A. 89999999984
B. 89999699984
C. 89999999884
D. 89999999974
Question 178
What is the value of (cot30°+ 2/√3) ?
A. 5/√3
B. (1+2√3)/2
C. 5/6
D. 2/√3
Question 179
What is the value of {(sin 4x + sin 4y) [(tan 2x – 2y)]}/(sin 4x – sin 4y)?
A. tan 2 (2x + 2y)
B. tan2
C. cot (x – y)
D. tan (2x + 2y)
Question 180
If a = √2 + 1 and b = √2 - 1, then the value of 1a+1+1b+1 will be
A. 0
B. 1
C. 2
D. -1
Question 181
If Sec θ = 5/3, then what is the value of Cosec θ?
A. 0.8
B. 1.25
C. 4/3
D. 3/4
Question 182
What is the simplified value of cosec Acot A + tan A2 ?
A. 2cos 2A
B. 1 – sin2 A
C. sec2A
D. secA tanA
Question 183
A fraction is greater than its reciprocal by (72)/(77). What is the fraction?
A. 7/11
B. 11/7
C. 4/7
D. 7/4
Question 184
If x1/4 + x-1/4 = 2, then what is the value of x81 + (1/x81)?
A. -2
B. 0
C. 1
D. 2
Question 185
In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 130 marks, the no of questions he attempts correctly is :
A. 35
B. 38
C. 40
D. 42
Question 186
If 3.5x = 0.07y, then find the result of [y-x / y+x]
A. 51/49
B. 49/53
C. 49/51
D. 53/57
Question 187
If Sinx = 4/5, then Secx/Sinx = ?
A. 23/12
B. 25/4
C. 4/5
D. 25/12
Question 188
Simplify: (213 x 213 + 187 x 187)
A. 80338
B. 80438
C. 60338
D. 60438
Question 189
If the value of √30 is approximately 5.477, then what is the approximate value of 56 ?
A. 0.853
B. 0.891
C. 0.913
D. 0.937
Question 190
Given: 2x - 4 ≤ 2 - x/3 and 2(2x + 5) > 3x - 5, then x can take which of the following values?
A. -14
B. 3
C. 4
D. 14
Question 191
ΔDEF is right angled at E. If m∠D = 45°, then find the value of (tanF + 1/3).
A. 4/3
B. 3√3/2
C. (√2+1)/√2
D. (3√2+1)/3
Question 192
If the roots of the equation a(b – c)x2 + b(c – a)x + c(a – b) = 0 are equal, then which of the following is true?
A. b = ( a + c)/ ac
B. 2/ b = (1/ a) + (1/ c)
C. 2 b = (1/ a) + (1/ c)
D. abc = ab + bc + ca
Question 193
If x + 1x = -2, then the value of x631 + 1x632?
A. -2
B. -1
C. 0
D. 2
Question 194
What is the value of Sec 30° + Tan 60°?
A. 5/√3
B. (√6 + 1)/√3
C. (√3 + 2)/√3
D. (1 + √3)/2
Question 195
N is the smallest three digit prime number. When N is divided by 13, then what will be the remainder?
A. 8
B. 9
C. 7
D. 10
Question 196
If x = 313- 3-13, then 3x2 + 9x is equal to
A. 5
B. 6
C. 7
D. 8
Question 197
If P = 22 + 62 + 102 + 142 + ... 942 and Q = 12 + 52 + 92 + ... 812, then what is the value of P – Q?
A. 24645
B. 26075
C. 29317
D. 31515
Question 198
What is the value of Tan 45° - 1/√3 Sec 60°?
A. (1 - 2√3)/2
B. (√2 - √3)/√6
C. (3 - 2√3)/3
D. (1 - 2√2)/2
Question 199
If 3√7 + √343 = 19.21, then find the value of √252 + 20√7.
A. 39.4
B. 49.9
C. 56.8
D. 92.3
Question 200
Compute : 4082 / 157 - 23
A. -3
B. 3
C. 2041/67
D. 2014/67
Question 201
On dividing a number by 38, we get 70 as quotient and 12 as remainder. What is the number?
A. 2648
B. 2636
C. 2684
D. 2672
Question 202
If Cosec θ = 25/7 , then what is the value of Cot θ?
A. 24/25
B. 7/24
C. 7/25
D. 24/7
Question 203
What is the value of 1xp-q+1+1xq-p+1?
A. 0
B. 1
C. x
D. cant determine
Question 204
2sin[(C+D)/2].cos[(C-D)/2] is equal to
A. sinC - sinD
B. cosC + cosD
C. cosC - cosD
D. sinC + sinD
Question 205
A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:
A. 22
B. 23
C. 24
D. 26
Question 206
If -5x3+2 = x-6, then find the value of x?
A. 1
B. 2
C. 3
D. 4
Question 207
What is the value of 1/√2 Cot 30° + 1/√3 Cosec 60°?
A. (3√3 + 2√2)/3√2
B. (3√3 - 2√2)/3√2
C. (3√3 + 2√2)/√2
D. (3√3 - 2√2)/√2
Question 208
If (1 - sinA)/(1 + sinA) = x, then x is
A. (cosecA - cotA)2
B. secA - tanA
C. (secA - tanA)2
D. cosecA - cotA
Question 209
Find the value of 'a' for which x+3x+a24 is a perfect square.
A. √3
B. 2√3
C. 3√3
D. 4√3
Question 210
The value of ds+t÷ds÷dt
A. 0
B. d
C. 1
D. ds+t
Question 211
If Tan A = 15/8 and Tan B = 7/24, then Tan (A - B) = ?
A. 304/297
B. 304/425
C. 416/87
D. 87/416
Question 212
Determine the value of y-1y2 when y4+1y4=34
A. 1
B. 2
C. 3
D. 4
Question 213
If 9x - [5(2x + 1)/2] = 9/2, then the value of x is?
A. 7/4
B. -7/4
C. 4/7
D. -4/7
Question 214
If sinC + sinD =X, then the value of X is?
A. 2cos[(C+D)/2]sin[(C-D)/2]
B. 2sin[(C+D)/2]cos[(C-D)/2]
C. 2cos[(C+D)/2]cos[(C-D)/2]
D. 2sin[(C+D)/2]sin[(D-C)/2]
Question 215
Common factor of 12a4b6, 18a6c2, 36a2b2 is
A. 36a2
B. 108b2
C. 6a2b2
D. 6a2
Question 216
If 2x - 5y = 5 and 2x - y = 9, then x - y is ______.
A. 2
B. 4
C. 6
D. 3
Question 217
If 3x2 - ax + 6 = ax2 + 2x + 2 has only one (repeated) solution, then the positive integral solution of a is
A. 4
B. 5
C. 2
D. 3
Question 218
If 1aa2+1 = 3, then the value of a6+1a3 is
A. 9
B. 18
C. 27
D. 1
Question 219
There are 10 dozen apples, 15 dozen mangoes and 20 dozen oranges for selling. If 1/2, 1/3 and 1/4 of them are sold respectively. How many of the total fruits are remaining?
A. 420
B. 380
C. 180
D. 360
Question 220
If 3x-y=27, 3x+y=243 then find the x value
A. 2
B. 8
C. 4
D. 1
Question 221
What is the simplified value of sin2(90–θ)–[sin(90–θ)sinθ/tanθ]?
A. 1
B. cosec θ
C. 0
D. cos θ
Question 222
A spherical lead ball of radius 6 cm is melted and small lead balls of radius 3 mm are made. The total number of possible small lead balls is
A. 4250
B. 4000
C. 8005
D. 8000
Question 223
Calculate the value of 0.77777 + 0.7777 + 0.777 + 0.77 + 0.7 + 0.07.
A. 3.86274
B. 3.80247
C. 3.85274
D. 3.87247
Question 224
The rate of discount on an article whose marked price is Rs. 170 and selling price is Rs. 130?
A. 24.26%
B. 22.45%
C. 23.53%
D. 23.60%
Question 225
x, y and z are real numbers. If x3 + y3 + z3 = 13, x + y + z = 1 and xyz = 1, then what is the value of xy + yz + zx?
A. -1
B. 1
C. 3
D. -3
Question 226
If cos 45° - sec 30° = x, then value of x is
A. (1+√2)/2
B. (2√2√3)/2
C. (√32√2)/√6
D. 4/√3
Question 227
A fraction, when taken away from 1/3 gives 1/12. The fraction is
A. 5/12
B. 1/4
C. 3/4
D. 1/9
Question 228
CAlculate : 72-6-45÷5-72-2×2÷2+2
A. -16/18
B. -14/7
C. -12/7
D. -12/18
Question 229
If ab+c=bc+a=Cb+athen which one of the following statements is correct?
A. Each fraction is equal to 1 or -1
B. Each fraction is equal to 1/2 or 1
C. Each fraction is equal to 1/2 or -1
D. Each fraction is equal to 1.2 only
Question 230
If (x – 2)2 + (y + 3)2 + (z – 15)2 = 0, then what is the value of x + y + z – 5?
A. 5
B. 9
C. 15
D. 20
Question 231
If x+1/x = 2, then the value of x7+2/x6 is equal to?
A. 0
B. 1
C. 2
D. 3
Question 232
Solve the following equation to find x: (x − 2)2 − 36 = 0 : xεN
A. 4
B. 8
C. -4
D. -8
Question 233
What is the value of (cos45° + 1/3) ?
A. 2+√3
B. (2√2+1)/√2
C. (3+√2)/3√2
D. 5/√3
Question 234
If 3n = 2187, then the value of n is:
A. 13
B. 14
C. 15
D. 16
Question 235
The Simplified form of (b3x2a4z3)*(b4x3a3z2)/(a2b4z3) is
A. b2x4a6z
B. b3x2a4z3
C. b3x5a5z2
D. bazx
Question 236
(secA - tanA)/(cosecA + cotA) is equal to
A. (secA - cotA) / (cosecA + tanA)
B. (secA - cosA) / (cosecA + sinA)
C. (cosecA - cotA) / (secA + tanA)
D. (secA + cosA) / (cosecA - sinA)
Question 237
If Sin θ = 12/13, then what is the value of Cot θ?
A. 13/12
B. 5/13
C. 5/12
D. 13/5
Question 238
217 x 217 + 183 x 183 = ?
A. 84521
B. 87487
C. 80578
D. 78458
Question 239
If sin θ + sin 5θ = sin 3θ and 0 < θ < (π/2), then what is the value of θ (in degrees)?
A. 30
B. 45
C. 60
D. 75
Question 240
If (7x - 13) (12x + 3) = 14, then the value of x is ______ .
A. -6
B. 6
C. -2/5
D. 2/5
Question 241
If x = 1 - q and y = 2q + 1, then for what value of q, x is equal to y ?
A. 0
B. 1
C. -1
D. -2
Question 242
Simplify : 213 - 112 of 35 + 125 ÷ 213
A. 1/10
B. 3/10
C. 11/10
D. 1
Question 243
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
A. 20
B. 80
C. 100
D. 120
Question 244
The factors of x2 + 8x + 12 are
A. (x+6)(x+2)
B. (x-6)(x+2)
C. (x-4)(x-4)
D. (x+6)(x-2)
Question 245
If x = 3+13, then the value of x-12642x-1x-233 is
A. √3/6
B. 2√3/6
C. 5/6
D. 2/3
Question 246
The value of tan(-405°)
A. 1
B. -1
C. 2
D. 0
Question 247
If XY = a+23 and YX = 13, then find the value of X2 + Y2X2 - Y2.
A. 1
B. 2
C. 3
D. 4
Question 248
If sin P + cosec P = 2, then the value of sin7P + cosec7P is
A. 1
B. 2
C. 3
D. 0
Question 249
If (x/5) + (5/x) = – 2, then what is the value of x3?
A. –125
B. 5
C. 1/125
D. 625
Question 250
The simplest value of 38-212+20318-227+45 is
A. 3/2
B. 2/3
C. 1/3
D. 2
Question 251
If xy = -18 and x2+ y2= 85, then find the value of (x + y).
A. 8
B. 10
C. 9
D. 7
Question 252
Find the value of 532+108
A. 732
B. 1732
C. 2732
D. 3732
Question 253
If 17/3 + [3(2x - 5/3)]/2 = 1/6, then what is the value of x?
A. 1
B. 3
C. -3
D. -1
Question 254
If a – (1/a) = b, b – (1/b) = c and c – (1/c) = a, then what is the value of (1/ab) + (1/bc) + (1/ca)?
A. – 3
B. – 6
C. – 1
D. – 9
Question 255
Factorise 24x2 - 54x - 15
A. 3(2x + 5)(4x - 1)
B. 3(2x - 5)(4x + 1)
C. 2(3x - 5)(4x + 1)
D. 4(2x - 5)(3x + 1)
Question 256
2cos[(C+D)/2]sin[(C-D)/2] is equal to
A. sinC + sinD
B. sinC - sinD
C. cosC - cosD
D. cosC + cosD
Question 257
Value of (4a2+ 12ab + 9b2)/(2a + 3b) is
A. 2a - 3b
B. 2a + 3b
C. 2a
D. 3b
Question 258
2sin[(C+D)/2].sin[(D-C)/2] is equal to
A. cosC + cosD
B. cosC - cosD
C. sinC - sinD
D. sinC + sinD
Question 259
If 3 tan θ = cot θ where 0 < θ < π/2, then what is the value of θ ?
A. π/6
B. π/4
C. π/2
D. 1
Question 260
If x + y + z = 0, then what is the value of (3y2 + x2 + z2 )/(2y2 – xz)?
A. 2
B. 1
C. 3/2
D. 5/3
Question 261
What is the slope of the line perpendicular to the line passing through the points (8,2) and (3,1)?
A. 5
B. 3/5
C. 5/3
D. 1/5
Question 262
In ∆ABC, ∠B=35°, ∠C=65° and the bisector of ∠BAC meets BC in D. Then ADB is
A. 40°
B. 75°
C. 90°
D. 105°
Question 263
What is the value of ( 1/√3 + cot60) ?
A. 3√3/2
B. 7/2√3
C. (4+√3)/2√3
D. 2/√3
Question 264
5 + 2 x 10 =
A. 70
B. 20
C. 25
D. 52
Question 265
If √[(1 + cosA)/2] = x, then find the value of x.
A. sin(A/2)
B. tan(A/2)
C. cot(A/2)
D. cos(A/2)
Question 266
A tank is 2/5 full. If 16 litres of water is added to the tank, it becomes 6/7 full. The capacity of the tank is:
A. 28 litres
B. 32 litres
C. 35 litres
D. 42 litres
Question 267
What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)?(55.01+16.0003)×22.01÷10.998 =?
A. 190
B. 130
C. 110
D. 142
Question 268
What is the value of cos 11π/6?
A. -1/√2
B. -√3/2
C. 2/√3
D. √3/2
Question 269
What is the value of cosecA/√(cosec2A - 1)?
A. sinA
B. secA
C. tanA
D. cosA
Question 270
If sec (4x - 50°) = cosec(50° - x), Then the value of x is
A. 45°
B. 90°
C. 30°
D. 60°
Question 271
θ is a positive acute angle and sinθ cosθ = 0, then the value of secθ + cosecθ is
A. 2
B. √2
C. 2√2
D. 3√2
Question 272
[15% of 300% of 560] × 2 ÷ 5 =
A. 100
B. 90
C. 85
D. 105
Question 273
If x = 313- 3-13, then 3x3 + 9x value is
A. 8
B. 9
C. 27
D. 16
Question 274
The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
A. Rs. 1200
B. Rs. 2400
C. Rs. 4800
D. Cannot be determined
Question 275
What is the value of 143 + 163 + 183 + ... + 303?
A. 134576
B. 120212
C. 115624
D. 111672
Question 276
0.196 + 1.96 + 19.6 + 196 = ?
A. 217.756
B. 216.856
C. 216.756
D. 217.676
Question 277
0 is the circumference of a triangle ∆ABC. The point A and the chord BC are on the opposite side of O. If ∠BOC=150° then the value of ∠BAC is
A. 65°
B. 60°
C. 70°
D. 75°
Question 278
If 8x/3 + [7(5 - 2x/3)]/2 = 1/2 , then what is the value of x?
A. -17
B. 51
C. -51
D. 17
Question 279
If tan2A + cot2A + 2 = x, then the value of x is
A. tan2Acosec2A
B. secAcosecA
C. sec2Acosec2A
D. tanAcosecA
Question 280
If 2x/3 - [5(4x/5 - 4/3)]/2 = 1/3, then what is the value of x?
A. 9/4
B. 4/9
C. -9/4
D. -4/9
Question 281
What is the value of √2 Sec 45 - Tan 30?
A. (2√3 - 1)/3
B. (√3 - 1)/√3
C. (2√3 - 1)/√3
D. (√3 - 1)/3
Question 282
If SinX-CosX=1, where 'X' is an acute angle, the value of SinX+CosX is
A. 0
B. 1
C. 1/2
D. 2
Question 283
What is the value of 13313 + 729 - 5123
A. 15
B. 20
C. 30
D. 23
Question 284
If √(cosec2A - 1) = x, then the value of x is
A. tanA
B. sinA
C. cosA
D. cotA
Question 285
If x + y = 12 and x2 + y2 = 94, then xy is
A. 25
B. 50
C. 144
D. 238
Question 286
Factors of 48x3- 8x2- 93x- 45 are
A. (4x + 3)(4x - 3)(3x - 5)
B. (4x - 3)(4x - 3)(3x- 5)
C. (4x + 3)(4x + 3)(3x - 5)
D. (4x - 3)(4x + 3)(3x + 5)
Question 287
What is the unit digit of 15+25+35+...+205 ?
A. 0
B. 5
C. 2
D. 4
Question 288
If a2+1a2 = 38, then find the value of a-1a?
A. 2
B. 4
C. 6
D. 8
Question 289
If cosec θ + cot θ= 2, then cosec θ= ?
A. 1.5
B. 1.25
C. 1
D. 2
Question 290
Square of (7 - 4x) is
A. 16x2 - 28x + 49
B. 49 - 28x - 16x2
C. 49 - 56x - 16x2
D. 16x2 - 56x + 49
Question 291
If a - b = 6 and ab =16, then a3 - b3 is
A. 504
B. 702
C. 728
D. 511
Question 292
If x3 + y3 + z3 = 3(1 + xyz), P = y + z – x, Q = z + x – y and R = x + y – z, then what is the value of P3 + Q3 + R3 – 3PQR?
A. 9
B. 8
C. 12
D. 6
Question 293
What is the value of cos 4π/3?
A. -1/2
B. √3/2
C. - 1/√2
D. √3/2
Question 294
(secA - 1)/(secA + 1) is equal to?
A. (1 - sinA)/(1 + sinA)
B. (1 + cosA)/(1 - cosA)
C. (1 + sinA)/(1 - sinA)
D. (1 - cosA)/(1 + cosA)
Question 295
If x2+ x = 19, then what is the value of (x + 5)2+ [1/(x + 5)2]?
A. 77
B. 79
C. 81
D. 83
Question 296
If a2b+c=b2C+a=a2a+b=1 then 11+a+11+b+11+c is
A. 1
B. 2
C. 3
D. 4
Question 297
What is the value of (32 cos6x – 48 cos4x + 18 cos2x – 1)/[4 sin x cos x sin (60 – x) cos (60 – x) sin (60 + x) cos (60 + x)]?
A. 4 tan 6x
B. 4 cot 6x
C. 8 cot 6x
D. 8 tan 6x
Question 298
If a - b = 2 and ab = 8, then what is the value of a3 - b3?
A. 65
B. 34
C. 43
D. 56
Question 299
What is the value of sin(11π/6)?
A. 2/√3
B. -2/√3
C. -1/2
D. 1/2
Question 300
What is the value of [2 sin (45 + θ) sin (45 – θ)]/cos 2θ?
A. 0
B. tan 2θ
C. cot 2θ
D. 1
Question 301
What is the value of cosec 5π/3?
A. √2
B. -2/√3
C. -√2
D. 1/√3
Question 302
The value of x for which the expressions 5x + 17 and 17x - 5 become equal is _____.
A. 11/6
B. -11/6
C. 6/11
D. -6/11
Question 303
If sinC - sinD = x, then value of x is
A. 2sin[(C+D)/2]cos[(C-D)/2]
B. 2cos[(C+D)/2]cos[(C-D)/2]
C. 2cos[(C+D)/2]sin[(C-D)/2]
D. 2sin[(C+D)/2]sin[(D-C)/2]
Question 304
In ∆UVW measure of angle V is 900. If cosecU = 13/12, and UV = 2.5 cm, then what is the length (in cm) of side VW?
A. 6.5
B. 6
C. 4
D. 5.6
Question 305
The point P(a,b) is first reflected in origin to P1 and P1 is reflected in y-axis to (6,-5). The co-ordinates of point P are
A. (-6,-5)
B. (6,5)
C. (6,-5)
D. (-6,5)
Question 306
Δ ABC is right angled at B. If m∠A = 60°, then what is the value of sec C.sin A?
A. 2/√3
B. √3/2
C. 2/3
D. 1
Question 307
The two lines 4x+3y=0 and 7x+5y=0 will ______ in their graphical representation.
A. be parallel to each other
B. intersect each other at one point only
C. intersect each other at three points only
D. coincide each other
Question 308
What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)? √580×∛510+ 49.999 x 3.999=?
A. 384
B. 392
C. 410
D. 372
Question 309
The value of 2.31 x 0.34 = ?
A. 1.7854
B. 0.7854
C. 0.7845
D. 0.7584
Question 310
If 1/√(1 - sin2A) = x, then the value of x is
A. tanA
B. cosecA
C. secA
D. cosA
Question 311
Sin6A + Cos6A - 1 is equal to
A. -3Sin2ACos2A
B. 1 - 3 SinACosA
C. 1 + 3Sin2ACos2A
D. 0
Question 312
If xy = 22 and x2+ y2= 100, then what will be the value of (x + y)?
A. 12
B. 144
C. 72
D. 6
Question 313
The inradius of a equilateral triangle is 10 cm. What is the circum-radius (in cm) of the same triangle?
A. 5
B. 10√3
C. 20
D. 20√3
Question 314
What is the value of [12/(√5 + √3)] + [18/(√5 – √3)]?
A. 15(√5 – √3)
B. 3(5√5 + √3)
C. 15(√5 + √3)
D. 3(3√5 + √3
Question 315
The value of Cot17°Cot73°Cos222° + 1Cot17°Sec268° is
A. 0
B. 1
C. 2
D. √3
Question 316
Simplify : 69 X 69 X 69 -65 X 65 X 669 X 69 + 69 X 65 + 65 X 65
A. 1
B. 4
C. 0.216
D. 0.164
Question 317
If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (c/a) + (a/c), then what is the value of xyz – x2 – y2 – z2?
A. – 4
B. 2
C. – 1
D. – 6
Question 318
What is the value of [(sin 7x – sin 5x)÷(cos 7x + cos 5x)] – [(cos 6x – cos 4x)÷(sin 6x + sin 4x)]?
A. 1
B. 2 tan x
C. tan 2 x
D. tan (3 x/2)
Question 319
If pq(p+q) = 1, then the value of 1p3q3-p3-q3 is equal to
A. 1
B. 2
C. 3
D. 4
Question 320
cos3A is equal to
A. cos3A - 3sin2cosA
B. cos3A + 4sin2cosA
C. cos3A + 3sin2cosA
D. cos3A - 4sin2cosA
Question 321
If (9 - 3x) - (17x - 10) = -1, then the value of x is
A. 1
B. -1
C. 9/10
D. -0.9
Question 322
If l + m + n = 9 and l2+m2+n2 = 31, then the value of lm + mn + nl will be
A. 22
B. 50
C. 25
D. -25
Question 323
If tan θ + sec θ = (x – 2)/(x + 2), then what is the value of cos θ?
A. (x2 – 1)/(x2 + 1)
B. (2x2 – 4)/(2x2 + 4)
C. (x2 – 4)/(x2 + 4)
D. (x2 – 2)/(x2 + 2)
Question 324
Δ DEF is right angled at E. If m∠D = 45°, then what is the value of cosecF X cotD?
A. 1/√2
B. 2
C. 1/2
D. √2
Question 325
What is the value of cot 11π/6?
A. -√3
B. -1
C. √3
D. -1/2
Question 326
If a + b + c = 11 and ab + bc + ca = 17, then what is the value of a3 + b3 + c3 – 3abc?
A. 121
B. 168
C. 300
D. 770
Question 327
The zeros of the cubic polynomial 2x3-x2-2x+1 are a, b and c respectively. Find a+b+c :
A. -1
B. 2
C. 1
D. none
Question 328
If x2+1x2 = 2, then the value of x - 1x is
A. -2
B. 0
C. 1
D. -1
Question 329
The costs of daily ticket of local train is Rs. 50 and Monthly Pass costs is Rs. 1125. If I buy the Monthly Pass and travel for 30 days in a month then I save?
A. 10 percent
B. 25 percent
C. 14 percent
D. 15 percent
Question 330
If sec θ (cos θ + sin θ) = √2, then what is the value of (2 sin θ)/(cos θ – sin θ)?
A. 3√2
B. 3/√2
C. 1/√2
D. √2
Question 331
If P = 7 + 4√3 and PQ = 1, then what is the value of (1/P2) + (1/Q2)?
A. 148
B. 189
C. 194
D. 204
Question 332
Solve the following : 80÷[48−56−(60−36÷12×4)]=?
A. 5
B. 8
C. 4
D. 2
Question 333
What is the value of √[(1 - cosA)/(1 + cosA)]?
A. cosecA - cotA
B. cosecA + cotA
C. secA - cotA
D. secA + cotA
Question 334
If (4a +7b) (4c-7d) = (4a -7b) (4c +7d, then which one of the following is correct ?
A. a/b = c/d
B. a/d = c/b
C. a/b = d/c
D. none
Question 335
If 2cos2A - 1 = x, then the value of x is
A. cosec4A - sin4A
B. cos4A - sin4A
C. cos4A - tan4A
D. cosec4A - tan4A
Question 336
In ∆ABC if the median AD=1/2 BC, then ∠BAC is
A. 90°
B. 45°
C. 60°
D. 75°
Question 337
Water boils at 212°F or 100°C and melts at 32°F or 0°C . If the temparature of the particular day is 35°C , it is equal to :
A. 85°F
B. 95°F
C. 96°F
D. 97°F
Question 338
Reflection of the point (4,6) in the origin is
A. (4,6)
B. (-4,-6)
C. (-4,6)
D. (4,-6)
Question 339
Find the value of x3 - y3, if x - y = 4 and xy = 12.
A. 198
B. 208
C. 218
D. 228
Question 340
ΔABC is right angled at B. If m ∠A = 60°, then what is the value of 1/√3 Cosec C?
A. 2/√3
B. 2/3
C. √2/√3
D. √2/3
Question 341
If x = 2+32-3, then what is the value of x2+x-9 ?
A. 0
B. 3√2
C. 3√3
D. 5√3
Question 342
If A = 0.216 + 0.0080.36+0.04-0.12 & B = 0.729-0.0270.81+0.09+0.27, then what is the value of A2+B22 ?
A. 0.8
B. 1
C. 1.4
D. 2.2
Question 343
If Sec θ = 13/12, then Cot θ = ?
A. 12/5
B. 13/5
C. 5/13
D. 5/12
Question 344
For what value of k, the expression x6– 18x3 + k will be a perfect square?
A. -9
B. 81
C. 9
D. -81
Question 345
Which of the following is not a quadratic equation?
A. 2x(x + 4) -11 = x(x - 3) + 6
B. 4x(x + 4) -11 = 5x(x - 3) + 5
C. x(x + 2) -15 = x(x - 5) + 11
D. 2x2 + 8x - 11 = 0
Question 346
The average revenues of 13 consecutive years of a company is Rs 70 lakhs. If the average of first 7 years is Rs 65 lakhs and that of last 7 years is Rs 77 lakhs, find the revenue for the 7th year.
A. Rs 86 lakhs
B. Rs 84 lakhs
C. Rs 82 lakhs
D. Rs 80 lakhs
Question 347
Derivative of sinx by first principle?
A. -sinx
B. -cosx
C. cosx
D. sinx
Question 348
Sec 45% + Tan 30% =
A. (√6 + 1)/√3
B. (1 + √3)/2
C. (√3 + 2)/√3
D. 5/√3
Question 349
What is the value of (1 + cotA)2 + (1 - cotA)2?
A. 2cosec2A
B. 2sec2A
C. 1 - 2cosec2A
D. 1 - 2sec2A
Question 350
What will be the roots of the quadratic equation x2 - 25x + 156 = 0?
A. 12, 13
B. 25, 1
C. 9, 16
D. 31, 6
Question 351
If x3 – y3 = 81 and x – y = 3, then what is the value of x2 + y2?
A. 18
B. 21
C. 27
D. 36
Question 352
What is the equation of the line whose y-intercept is 3/4 and making an angle of 45° with the positive x-axis?
A. 4x - 4y = 3
B. 4x - 4y = -3
C. 3x - 3y = 4
D. 3x - 3y = -4
Question 353
Compute : (50 + 0.5 x 20) / 0.7
A. 8.571
B. 85.1
C. 85.71
D. 72.85
Question 354
2660 of 17 of 12 of 19.5 of 12 = ?
A. 1
B. 10
C. 0.1
D. 100
Question 355
In an acute-angled triangle ABC is Sin(B+A+C)=32 and tan(C+A-B)=1, then C is equal to
A. 37.5°
B. 67.5°
C. 52.5°
D. 72.5°
Question 356
If sum of the roots of a quadratic equation is -7 and product of the roots is 12. Find the quadratic equation.
A. x2 + 7x + 12 = 0
B. x2 - 7x + 12 = 0
C. x2 - 7x - 12 = 0
D. x2 + 7x - 12 = 0
Question 357
If the value 5 = 2.236,then calculate the value of 405 - 1280-125
A. 2.236
B. 4.472
C. 1.118
D. 8.994
Question 358
If Cosecθ + Cotθ = 2, then Cotθ = ?
A. 0
B. 0.5
C. 1
D. 0.75
Question 359
In an isosceles trapezium _____.
A. Diagonals are congruent
B. Opposite sides are parallel
C. Diagonals are bisectors of each other
D. Diagonals bisect opposite angles
Question 360
If a sum of money deposited in a bank at simple interest is doubled in 6 years, then after 12 years, the amount will be
A. 5/2times the original amount
B. 3times the original amount
C. 7/2times the original amount
D. 4times the original amount
Question 361
What is the simplified value of Sec ACot A + Tan A2 ?
A. 1 – cos2A
B. 2sin2A
C. sec2A
D. 0
Question 362
If α and β are roots of the equation 3x2 – 13x + 14 = 0, then what is the value of (α/β) + (β/α)?
A. 65/28
B. 53/14
C. 9
D. 85/42
Question 363
If ax= by= cz and b2= ac, then what is 1x+1z equal to ?
A. 1/y
B. -1/y
C. 2/y
D. -2/y
Question 364
If cos -225° = x, then the value of x is
A. 1/2
B. √3/2
C. -2/√3
D. -1/√2
Question 365
18800÷470÷20=?
A. 1
B. 2
C. 3
D. 4
Question 366
Δ DEF is right angled at E. If m∠F = 45°, then what is the value of 2 Sin F x Cot F?
A. √2
B. 2
C. 1/√2
D. 1/2
Question 367
Reflection of the point (1,4) in the xaxis is
A. (1,4)
B. (1,-4)
C. (-1,4)
D. (-1,-4)
Question 368
If p = 99, then the value of p(p2+3p+3) will be
A. 999999
B. 1000000
C. 1000001
D. 999998
Question 369
If cos 135° = x, then the value of x is
A. -1/√2
B. -√3/2
C. -1/2
D. 2
Question 370
If a2+b2+c2=14 and a+b+c=6, then the value of ab+bc+ca is,
A. 11
B. 12
C. 13
D. 14
Question 371
If a+1b=1 and b+1c=1 , then the value of c+1a is
A. 0
B. 1
C. -1
D. 2
Question 372
What is the value of sec 330°?
A. 2
B. -2/√3
C. -2
D. 2/√3
Question 373
What should be added to 3(x - 2y) to obtain 2(3x + y) - 5(2x + 3)?
A. 8y - 7x - 15
B. 8y - 7x + 15
C. 8y + 7x + 15
D. 8y + 7x - 15
Question 374
If 1 + (1/2) + (1/3) + ... + (1/20) = k, then what is the value of (1/4) + (1/6) + (1/8) + ... + (1/40)?
A. k/2
B. 2k
C. (k – 1)/2
D. (k + 1)/2
Question 375
78 books, 114 crayons and 141 notebooks were distributed to school children equally. It was found that 6 were left undistributed in each. What was the total number of children?
A. 9
B. 8
C. 13
D. 12
Question 376
If one root of the equation Ax2 +Bx + C = 0 is two and a half times the others, then which of the following is TRUE?
A. 7B2 = 3 CA
B. 7B2 = 4 CA
C. 7B2 = 36 CA
D. 10B2 = 49 CA
Question 377
If sin 3θ sec 2θ = 1, then what is the value of [3 tan2(5θ/2) – 1]?
A. 0
B. 1
C. 2
D. 3
Question 378
If x - y = 6 and xy = 40, then find x2 + y2 ?
A. 116
B. 80
C. 89
D. 146
Question 379
Hemavathi gets 3 marks for each right sum and loses 2 marks for each wrong sum. He attempts 35 sums and obtains 60 marks. The number of sums attempted correctly is ?
A. 23
B. 24
C. 25
D. 26
Question 380
If x + 1x = c + 1c, then the value of x =
A. C, 1/C
B. C, C2
C. C, 2C
D. 0,1
Question 381
If 7x - (3/2) * (4x - 9) = 6.5, then the value of x is?
A. 7
B. 20
C. -7
D. -20
Question 382
If a+1b = 1 and b+1c = 1 then c+1a = ?
A. 0
B. 2
C. 1
D. 3
Question 383
If a + b = 8 and ab = 15, then what is the value of a3 + b3?
A. 98
B. 152
C. 124
D. 260
Question 384
When a number is increased by 28, it becomes 107% of itself. What is the number?
A. 336
B. 420
C. 400
D. 252
Question 385
The standard deviation of the set {10, 11, 9, 11, 9} is
A. 1/√5
B. 2/√5
C. 3/√5
D. 0
Question 386
If sinA = x, then x is equal to
A. √(1 - cos2A)
B. √(1 - sin2A)
C. √(1 + cos2A)
D. √(1 + sin2A)
Question 387
A telephone bill costs Rs.13 for 19 minutes. What is the cost in rupees for 15 minutes 50 seconds?(rounded to one decimal)
A. 10.8
B. 10.7
C. 10.6
D. 10.9
Question 388
45 - [38 - {60 / 3 - (6 - 9 / 3)/ 3}]= ?
A. 24
B. 25
C. 26
D. 21
Question 389
If θ>0, be an acute angle, then the value of it in degrees satisfying cos2θ-3cosθ+2sin2θ=1 is
A. 90°
B. 30°
C. 45°
D. 60°
Question 390
The simplified form of (x + 3)2 + (x - 1)2 is
A. (x2 + 2x + 5)
B. 2(x2 + 2x + 5)
C. (x2 - 2x + 5)
D. 2(x2 - 2x + 5)
Question 391
Coefficient of x2 in (x + 9)(6 - 4x)(4x - 7) is
A. 216
B. -4
C. -92
D. 108
Question 392
If angles M and N measure 60 deg and 30 deg respectively, (sinM) x (cotN) = ?
A. 1/2
B. √3/2
C. 3/2
D. 0
Question 393
What value of 'p' will satisfy the equation p540 = 240p ?
A. 6
B. 10
C. 6√10
D. √10
Question 394
If 2x + 3y – 5z = 18, 3x + 2y + z = 29 and x + y + 3z = 17, then what is the value of xy + yz + zx?
A. 32
B. 52
C. 64
D. 46
Question 395
43% of 616.6 + 37% of 217 =?
A. 345.428
B. 354.428
C. 344.428
D. 364.428
Question 396
If a3- b3= 91 and a - b = 1, then what is the value of ab?
A. 27
B. 6
C. 9
D. 30
Question 397
In ΔABC, D and E are points on side AB and AC respectively. DE is parallel to BC. If lengths of AD, DB and DE are 9 cm, 6 cm and 5.4 cm respectively find length of BC?
A. 3.6 cm
B. 4.8 cm
C. 11.2 cm
D. 9 cm
Question 398
Compute : 28854 / 458 / 9
A. 70
B. 567
C. 7
D. 576
Question 399
The value of -261+(-380)-(-521)+821-(-121)
A. 833
B. 825
C. 822
D. 800
Question 400
If 2x+4-2x+2=3, then the value of x?
A. 0
B. 2
C. -1
D. -2
Question 401
Expand and simplify (3x + 2)2*(4x - 3) - (2x3 - 9x2 + 12x - 24)
A. 34x3 + 30x2 - 32x - 12
B. 34x3 + 30x2 - 32x + 12
C. 34x3 - 30x2 - 32x + 12
D. 34x3 - 30x2 + 32x - 12
Question 402
For what value of C, the system of equation 6x + 2y = 2 & 3x + y = C will be coincident?
A. 4
B. 0
C. 2
D. 1
Question 403
If secA/√(sec2A - 1) = x, then value of x is
A. tanA
B. cosecA
C. sinA
D. cosA
Question 404
If x + y + z = 22 and xy + yz + zx = 35, then what is the value of (x – y)2 + (y – z)2 + (z – x)2?
A. 793
B. 681
C. 758
D. 715
Question 405
The 3rd and 8th term of an arithmetic progression are -13 and 2 respectively. What is the 14th term?
A. 23
B. 17
C. 20
D. 26
Question 406
(798+579)2- (798-579)2798 x 579 =
A. 2
B. 6
C. 4
D. 8
Question 407
An angle is thrice its complementary angle. What is the measure of the angle?
A. 22.5°
B. 135°
C. 45°
D. 67.5°
Question 408
Find the products : 0.5 x 0.05 x 0.005 x 500
A. 0.0625
B. 0.00625
C. 0.06255
D. 0.625
Question 409
4 + 16 x -12 x 24 - 13 - 3 ÷ 20 - 4 = ?
A. 4
B. 6
C. 5
D. 3
Question 410
Slope of the line AB is -2/3. Co-ordinates of points A and B are (x , -3) and (5 , 2) respectively. What is the value of x?
A. 4
B. -14
C. 12.5
D. -4
Question 411
D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:5 and area of ΔADE is 8 cm sq, what is the area (in sq cm) of quadrilateral BDEC?
A. 98
B. 94
C. 90
D. 86
Question 412
If sin π/6 + sec π/6 = x, then x is
A. (2√2-1)/2
B. 5/√3
C. (√6-1)/√2
D. (√3+4)/2√3
Question 413
If A/3 = B/2 = C/5, then what is the value of ratio (C + A)2 : (A + B)2 : (B + C)2?
A. 9 : 4 : 25
B. 25 : 4 : 9
C. 64 : 25 : 49
D. 49 : 25 : 64
Question 414
If Cot θ = 24/7, then what is the value of Sec θ?
A. 7/25
B. 25/24
C. 8/25
D. 9/25
Question 415
What is the value of [1 – tan (90 – θ) + sec (90 – θ)]/[tan (90 – θ) + sec (90 – θ) + 1]?
A. cot (θ/2)
B. tan (θ/2)
C. sin θ
D. cos θ
Question 416
What is the value of [tan2 (90 – θ) – sin2 (90 – θ)] cosec2 (90 – θ) cot2 (90 – θ)?
A. 0
B. 1
C. -1
D. 2
Question 417
If the expression px3 – qx2 – 7x – 6 is completely divisible by x2 – x – 6, then what is the value of p and q respectively?
A. 0, 1
B. 1, 0
C. 2, 1
D. 1, 2
Question 418
Two numbers are such that the sum of twice the first number and thrice the second number is 36 and the sum of thrice the first number and twice the second number is 39. Find the difference between the numbers?
A. 15
B. 3
C. 9
D. 6
Question 419
1$ = Rs.67.89. Money changer adds a margin of RS. 1.11. What will be the cost of $150?
A. RS. 10,183
B. RS. 10,350
C. RS. 10,330
D. RS. 10,450
Question 420
What is the simplified value of [2/(cot A – tan A)]?
A. sin A cos A
B. tan 2A
C. sin2 A
D. cos2 A
Question 421
What is the value of cos2A/(1 + sinA)?
A. 1 + sinA
B. 1 - sinA
C. 1 - secA
D. 1 + secA
Question 422
If a=x13y13+x-13y-13 then a3-3ay-x is equal to
A. y^2x
B. x^2y
C. a^2x
D. a^2y
Question 423
What is the simplified value of 22433+393-11253?
A. 593
B. 493
C. 793
D. 1193
Question 424
If sinA + sin2A =1 then what is the value of cos2A + cos4A
A. 1/2
B. 1
C. 2
D. 3
Question 425
If α and β are the roots of equation x2 – 2x + 4 = 0, then what is the equation whose roots are α3/β2 and β3/α2?
A. x2 – 4 x + 8 = 0
B. x2 – 32 x + 4 = 0
C. x2 – 2 x + 4 = 0
D. x2 – 16 x + 4 = 0
Question 426
If x = 999, y = 1000, z = 1001, then the value of x3+y3+z3-3xyzx-y+z is
A. 1000
B. 9000
C. 1
D. 9
Question 427
What is the value of 26 + 152?
A. 17
B. 19
C. 15
D. 21
Question 428
Which of the following equations has real and distinct roots?
A. 3x2 - 6x + 2 = 0
B. 3x2 - 6x + 3 = 0
C. x2 - 8x + 16 = 0
D. 4x2 - 8x + 4 = 0
Question 429
If sinA/(1 + cosA) = x, then x is
A. cosecA + cotA
B. secA - cotA
C. secA + cotA
D. cosecA - cotA
Question 430
Find k, if the line 2x- 3y = 11 is perpendicular to the line 3x + ky = -4?
A. -2
B. 1
C. -1
D. 2
Question 431
The value of (0.00000729/0.00000027) is
A. 0.27
B. 0.027
C. 2.7
D. 27
Question 432
If aq-r+br-p-cp-q, then find the value of (pa + qp + rc) is
A. 0
B. 1
C. 2
D. -1
Question 433
56/32 simplified value?
A. 1.705
B. 1.45
C. 1.75
D. 7.5
Question 434
If the two lines px + 6y+3=0 and 2x + qy+3=0 have infinite solutions then find the value of p and q respectively.
A. 2,6
B. 6,2
C. 2,2
D. 6,6
Question 435
What is the value of sin (–π/3) + cos(–π/6)?
A. 0
B. 1
C. 2
D. 3
Question 436
At what point does the line 3x + 2y = -12 intercept the Y-axis?
A. (0,6)
B. (0,-6)
C. (-4,0)
D. (4,0)
Question 437
5 sin(x)+ 12 cos(x) + r is always greater than or equal to zero. What is the smallest value satisfied by 'r' ?
A. -13
B. 11
C. 13
D. -11
Question 438
What is the equation of the line perpendicular to the line 5x + 3y = 6 and having Y-intercept -3?
A. 3x - 5y = 15
B. 3x + 5y = 15
C. 3x - 5y = -15
D. 3x + 5y = -15
Question 439
If sin(A/2) = x, then the value of x is
A. √[(1 + cosA)/2]
B. √[(1 - cosA)/2]
C. √[(1 - sinA)/2]
D. √[(1 + sinA)/2]
Question 440
What is the value of [cos (90 + A)÷sec (270 – A)] + [sin (270 + A)÷cosec (630 – A)]?
A. 3 sec A
B. tan A sec A
C. 0
D. 1
Question 441
Δ LMN is right angled at M. If m∠N = 60 deg., then Tan L =______.
A. 1/2
B. 1/√3
C. 1/√2
D. 2
Question 442
What is the value of ( 1/2 - cot45) ?
A. (2√2-√3)/2
B. 3/2
C. (3√3-1)/3
D. -1/2
Question 443
What is the value of [(sin 59° cos 31° + cos 59° sin 31° )÷(cos 20° cos 25° – sin 20° sin 25° )]?
A. 1/√2
B. 2√2
C. √3
D. √2
Question 444
What is the value of (3/5 + 7/9)?
A. 62/45
B. 31/28
C. 5/7
D. 1/7
Question 445
If Sin θ = 20/29 , then what is the value of Sec Sin θ ?
A. 29/21
B. 29/20
C. 21/20
D. 21/29
Question 446
The value of cosec260 + sec260 cot260 + tan230 will be
A. 5
B. 5 1/2
C. 5 1/3
D. 5 2/3
Question 447
If 5 - 5x < 4 - x and 2 - x < 6 - 4x, then x can take which of the following values?
A. 1
B. 2
C. -1
D. -2
Question 448
What is the reflection of the point (3,-5) in the origin?
A. (-3, -5)
B. (5,-3)
C. (-5,-3)
D. (-3, 5)
Question 449
Vishnu spends Rs. 5000 in buying 12 tables and some chairs. The cost of one table is Rs. 50 and that of one chair is Rs. 40. What is the ratio of the numbers of tables purchased?
A. 5 :2
B. 55 : 6
C. 5 : 1
D. 55 : 4
Question 450
What is the reflection of the point (-1 , 5) in the line x = 1?
A. (3 , -5)
B. (-3 , -5)
C. (3 , 5)
D. (-3 , 5)
Question 451
If (x – 2) and (x + 3) are the factors of the equation x2 + k1x + k2 = 0, then what are the values of k1 and k2?
A. k1 = 6, k2 = – 1
B. k 1 = 1, k 2 = – 6
C. k 1 = 1, k2 = 6
D. k1 = – 6, k2 = 1
Question 452
Reflection of the point (2,7) in the yaxis is
A. (2,7)
B. (-2,-7)
C. (-7,2)
D. (7,2)
Question 453
If 5x - 4 ≤ 2 - x and 4x + 5 > 2x - 5, then x can take which of the following values?
A. 3
B. 6
C. -7
D. -1
Question 454
Which of the following is correct?
A. (3x + 4y)(4x - 3y) = 12x2 + 7xy - 12y2
B. (3x + 4y)(4x - 3y) = 12x2 + 251xy - 12y2
C. (3x + 4y)(4x - 3y) = 12x2 - 7xy + 12y2
D. (3x + 4y)(4x - 3y) = 12x2 - 251xy + 12y2
Question 455
Sum of twice a fraction and its reciprocal is 17/6. What is the fraction?
A. 4/3
B. 5/4
C. 3/4
D. 4/5
Question 456
1.004 - 0.4 is equal to
A. 0.604
B. 0.006
C. 0.64
D. 1
Question 457
If x=8+215, then what is the value of x+1x?
A. 2√15
B. 3√5
C. (3√5+√3)/2
D. 3√2+3
Question 458
The orthocentre of an obtuseangled triangle lies
A. inside the triangle
B. outside the triangle
C. on one side of a triangle
D. none of these
Question 459
If x + y = 5, x3 + y3 = 35, then what is the positive difference between x and y?
A. 0
B. 1
C. 5
D. 6
Question 460
Find the value of 64344?
A. 1
B. 2
C. 3
D. 4
Question 461
If (x + y + z) = 12, xy + yz + zx = 44 and xyz = 48, then what is the value of x3 + y3+ z3?
A. 104
B. 144
C. 196
D. 288
Question 462
In ΔPQR, S and T are points on side PQ and PR respectively. ST is parallel to QR. If S divides PQ in the ratio 4:1 and length of QR is 15 cm,what is the length of ST?
A. 3 cm
B. 5 cm
C. 12 cm
D. 10 cm
Question 463
The sum of two numbers is 7 and the sum their squares is 23, their product is equal to:
A. 10
B. 11
C. 12
D. 13
Question 464
The angle of elevation of the top of a tower, vertically erected in the middle of a paddy field, from two points on a horizontal line through the foot of the tower are given to be α and β (α>β). The height of the tower is h unit. A possible distance (in the same unit) between the points is
A. h(cotβ-cotα)cos(α+β)
B. h(cotα - cotβ)
C. h(tanβ - tanα)tanα tanβ
D. h(cotα+cotβ)
Question 465
What is the value of (1/√2) Cot 45° + (1/√3) Cosec 60°?
A. (√6 + 1)/√3
B. √3
C. (1 + 3√2)/√3
D. (3 + 2√2)/3√2
Question 466
If a+b=2c then the value of aa-c+cb-c is equal to (where a≠b≠c)
A. -1
B. 1
C. 0
D. 1/2
Question 467
If Sinx = 4/5, then Sec2x - 1 = ?
A. 16/25
B. 25/9
C. 9/16
D. 16/9
Question 468
A crate of egg holds one rotten egg out of every 25 egg in it. If 5 out of 8 rotten eggs are unusable and there are total 10 unusable eggs in the crate,then calculate the number of eggs in the crate.
A. 380
B. 400
C. 420
D. 440
Question 469
If x = a + 1/a, y = a - 1/a, then the value of x4+y4-2x2y2
A. 4
B. 8
C. 16
D. 64
Question 470
∆PQR is right angled at Q. If m∠R = 45°, then find the value of (cosecP - √3/2)
A. (3√3-1)/3
B. 2/√3
C. (2-√3)/√3
D. (2√2-√3)/2
Question 471
What is the value of (cot60 + 1/√3) ?
A. 4/√3
B. (2√2+√3)/2
C. 2/√3
D. (2√2+1)/√2
Question 472
If (x+1/x) = 5, then the value of 5xx2+5x+1?
A. 1/3
B. 1/4
C. 1/2
D. 1/5
Question 473
The angle of elevation of the top of a tower from two horizontal points (in opposite sides) at distances of 25 meter and 64 meter from the base of tower are x and 90° - x respectively . The height of the tower will be
A. 39 m
B. 89 m
C. 1.6 m
D. 40 m
Question 474
You have 20 big and 16 small diaries and want to make gift packs containing both in each pack. What is the maximum number of gift packs you can make without any left over?
A. 5
B. 4
C. 3
D. 2
Question 475
The expenses of a person increase by Rs. 50000 for every month in February and March. If his expenses in January was Rs. 50000, calculate his average expenditure (in Rs.) from January to March.
A. 100000
B. 150000
C. 75000
D. 50000
Question 476
tan3A is equal to
A. 3tanA - tan3A(1 - 3tan2A)
B. 3tanA + tan3A(1 - 3tan2A)
C. 3tanA - tan3A(1 + 3tan2A)
D. 3tanA + tan3A(1 + 3tan2A)
Question 477
If x – 4y = 0 and x + 2y = 24, then what is the value of (2x + 3y)/(2x – 3y)?
A. 9/5
B. 11/5
C. 13/7
D. 9/7
Question 478
Find the value of 27a3 + 1a3, if 9a2 + 1a2 = 43
A. 240
B. 280
C. 320
D. 360
Question 479
If 5x - (1/2)(2x -7) = 5.5, then what is the value of x?
A. 3/2
B. 1/2
C. -1/2
D. -3/2
Question 480
For which value of ‘g’ the linear graph of 6x + 12y +9 = 0 and 2x + gy + 3 = 0 has infinite number of solutions?
A. 3
B. 4
C. 6
D. 9
Question 481
If 2x + 3(5-2x) > 2 - 3x < 2x - x/3, then x can take which of the following values?
A. 0
B. -2
C. -4
D. 2
Question 482
97 x 97 = ?
A. 9391
B. 9409
C. 9049
D. 9309
Question 483
If x - y = -9 and xy = -20, then find x2 + y2 ?
A. 61
B. 41
C. 81
D. 51
Question 484
If tan θ + cot θ = x, then what is the value of tan4θ + cot4θ?
A. (x3 – 3)2 + 2
B. (x4 – 2x) + 4
C. x2 (x2 – 4) + 2
D. x
Question 485
If 1/√(1+tan2A) = x, then value of x is
A. cosA
B. sinA
C. cosecA
D. secA
Question 486
If x = 5 + 15 - 1 & y = 5 - 15 + 1 , then find the value of x2 - y2.
A. √5
B. 2√5
C. 3√5
D. 4√5
Question 487
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to ___ ?
A. 3.7
B. 2.7
C. 3.6
D. 2.9
Question 488
A, B and C are three points on a circle with centre O. The tangent at C meets BA produced at T. If ∠ATC = 30° and ∠ACT = 48°,then what is the value of ∠AOB ?
A. 78°
B. 96°
C. 102°
D. 108°
Question 489
If x = a cosθ+ b sinθ and y = b cosθ- a sinθ, then x2 + y2 is equal to
A. ab
B. a2+b2
C. a2-b2
D. 1
Question 490
In a party there are male and female members. If 15 female quit then the number of females will become double the number of males. If 45 males quit no. of female becomes five times the number of males. Find the number of females ?
A. 175
B. 145
C. 165
D. 135
Question 491
A, B and C can finish a job working alone in 72, 24 and 36 days respectively. In how many days they can finish the job if they worked together?
A. 12
B. 9
C. 15
D. 18
Question 492
In a circle, two arcs of unequal length subtend angles in the ratio 5:3. If the smaller angle is 45° then the measure of other angle in degrees.
A. 75°
B. 72°
C. 60°
D. 78°
Question 493
Find the unit place in 194102+294103
A. 0
B. 6
C. 8
D. 2
Question 494
3cosA is equal to
A. 4cos3A + 3cosA
B. 4cos3A - 3cosA
C. 3cos3A + 3cosA
D. 3cos3A - 3cosA
Question 495
If 2x + 3y = 0 and 3x - 4y = 34, then x - y = ______
A. 10
B. -10
C. 2
D. -2
Question 496
Point A (4 , 2) divides segment BC in the ratio 2:5. Co-ordinates of B are (2 , 6) and C are (7 , y). What is the value of y?
A. 8
B. -8
C. 6
D. -6
Question 497
What is the value of [sin (90 – A) + cos (180 – 2A)]/[cos (90 – 2A) + sin (180 – A)]?
A. sin (A/2) cos A
B. cot (A/2)
C. tan (A/2)
D. sin A cos (A/2)
Question 498
If x tan 60° + cos 45° = sec 45° then the value of x2 + 1 is
A. 6/7
B. 7/6
C. 5/6
D. 6/5
Question 499
If a3 + 3a2 + 9a = 1, then what is the value of a3 + (3/a)?
A. 31
B. 26
C. 28
D. 24
Question 500
What is the value of 1sin490-θ+1cos290-θ - 1 ?
A. tan2θ sec2θ
B. sec4θ
C. tan4θ
D. tan2θ sin2θ
Question 501
Factors of x2 + 7x + 10 are
A. (x-5)(x-2)
B. (x+5)(x+2)
C. (x-5)(x+2)
D. (x-4)(x+2)
Question 502
23 x 31 = 713. How much is 0.0713 / 3.1?
A. 0.23
B. 0.0023
C. 2.3
D. 0.023
Question 503
If cot A = n/(n + 1) and cot B = 1/(2n + 1), then what is the value of cot (A + B)?
A. -1
B. 0
C. 1
D. 2
Question 504
Solve the following : -1/4 { -45 - (-96) / (-32)} = ?
A. 12
B. 10.5
C. -12
D. -10.5
Question 505
A factory produced 18,58,509 cassettes in the month of January, 7623 more cassettes in the month of February and owing to short supply of electricity produced 25,838 less cassettes in March than in February. Find the total production in all?
A. 55,57,312
B. 59,83,245
C. 55,64,935
D. 56,08,988
Question 506
If cos -4π/3 = x, then the value of x is
A. √3/2
B. 1/2
C. -√3/2
D. -1/2
Question 507
If 9 * 6 = 45, 7 * 4 = 33, and 6 * 4 = 20, then what is the value of 5 * 3?
A. 24
B. 16
C. 13
D. 10
Question 508
What is the value of tan 1° tan 2° tan 3°....... tan 89°?
A. 0
B. 1
C. 2
D. infinity
Question 509
If x varies as y and x = 8 when y = 15 then the value of x when y = 10 is:
A. 5
B. 15/8
C. 8/15
D. 16/3
Question 510
If P = 7 + 4√3 and PQ = 1, then what is the value of 1/P2 + 1/Q2?
A. 196
B. 194
C. 206
D. 182
Question 511
Rehman walks at 8 km/hr and Roma cycles at 13 km/hr towards each other. What was the distance between them when they started if they meet after 36 minutes?
A. 12.6 kms
B. 18.9 kms
C. 15.8 kms
D. 9.5 kms
Question 512
If x + y = 3, then what is the value of x3 + y3 + 9xy?
A. 15
B. 81
C. 27
D. 9
Question 513
If 1/(tanA + cotA) = x, then value of x is
A. cosAsinA
B. cos2Asin2A
C. cosecAsecA
D. cosec2Asec2A
Question 514
If a = √2 + 1, b = √2 - 1 then the value of 1a+1+1b+1 ?
A. 0
B. 1
C. 2
D. 3
Question 515
If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3 is equal to :
A. 22
B. 23
C. 24
D. 25
Question 516
If x2+5x+6 = 0, then the value of 2xx2-7x+6 is
A. 1/6
B. 1/3
C. -1/6
D. -1/3
Question 517
If a-1a=7,then a2+1a2=?
A. 54
B. 51
C. 53
D. 52
Question 518
What is the value of (tan60 - 1/3) ?
A. 3-√2
B. (2√2-√3)/2
C. -1/2√3
D. (3√3-1)/3
Question 519
What is the reflection of the point (5, -2) in the line x = -1?
A. (-7 , -2)
B. (5 , 0)
C. (7 , -2)
D. (5 , 2)
Question 520
If 3x^2 + ax + 4 is perectly divisible by x - 5, then the value of a is :
A. -5
B. -15.8
C. -12
D. -15.6
Question 521
AB is the diameter of a circle with center O and P be a point on its circumference. If ∡POA = 120°, then the value of ∡PBO is
A. 30°
B. 60°
C. 50°
D. 40°
Question 522
If 123 x 356 = 43788, then 1.23 x 0.356 = ?
A. 437.88
B. 4.3788
C. 0.43788
D. 0.043788
Question 523
What is the area of the sector whose central angle is 90° and radius of the circle is 14 cm?
A. 308 sq cm
B. 77 sq cm
C. 154 sq cm
D. 231 sq cm
Question 524
If sinθ+cosecθ=2, the value of sinnθ+cosecnθ is
A. 2
B. 0
C. 1
D. 1/n
Question 525
If x - 1/x = 1 then what is the value of 1x1x-1-1x+1+1x2+1-1x2-1?
A. ±√5
B. 2/5
C. ±2/√5
D. ±√5/2
Question 526
If cos 45° - sec 60° = x, then the value of x is
A. (√3-4)/2√3
B. 1
C. (1-2√2)/√2
D. (√3+√2)/2
Question 527
What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)? 499.99 + 1999 ÷ 39.99 × 50.01=?
A. 3200
B. 2700
C. 3000
D. 2500
Question 528
In a triangle PQR, ∠Q = 90°. If PQ = 12 cm and QR = 5 cm, then what is the radius (in cm) of the circum circle of the triangle?
A. 5
B. 6
C. 6.5
D. 6√2
Question 529
ΔXYZ is right angled at Y. If m∠Z = 60°, then Cosec X =
A. 2
B. 1/2
C. 1/√2
D. 1/√3
Question 530
For triangle PQR, find equation of altitude PS if co-ordinates of P, Q and R are (1,2), (2,-1) and (0,5) respectively?
A. x - 3y = -7
B. x - 3y = -5
C. x + 3y = 4
D. x + 3y = 7
Question 531
Reciprocal of 235?
A. 235
B. 532
C. 513
D. 335
Question 532
23 x 19 = 437. How much is 0.0437 / 1.9 = ?
A. 0.0023
B. 0.23
C. 0.023
D. 2.3
Question 533
If C + 1C = 3, then what is the value of C-37+1C7?
A. 2
B. 0
C. 3
D. 1
Question 534
If 3a – (3/a) – 3 = 0, then what is the value of a3 – (1/a3) + 2?
A. 0
B. 2
C. 4
D. 6
Question 535
If a = 1/a-5, then the value of a + 1/a = ?
A. √29
B. √-29
C. - √29
D. √27
Question 536
Profit of Rs 144000 has to be divided among three partners Akram, Bipin and Chintan in the ratio 3:2:7. How much Rs. Chintan get?
A. 84000
B. 24000
C. 36000
D. 42000
Question 537
Calculate the value of √3√3 + 3, if √3 = 1.732
A. 0.366
B. 0.566
C. 0.356
D. 0.346
Question 538
The ratio of the curved surface area and total surface area of a right circular cylinder is 2 : 5. If the total surface area is 3080 cm2, then what is the volume (in cm3) of the cylinder?
A. 4312√6
B. 3822√6
C. 4522√6
D. 4642√6
Question 539
What is the value of x4+y4 when the value of x3+y3=8 and x+y=2 ?
A. 2
B. 8
C. 16
D. 32
Question 540
If 2x- 3(4-2x) < 4x - 5 < 4x + 2x/3, then x can take which of the following values?
A. 2
B. 8
C. 0
D. -8
Question 541
A 1.6 m tall observer is 45 meters away from a tower. The angle of elevation from his eye to the top of the tower is 30°, then the height of the tower in meters is
A. 25.98
B. 26.58
C. 27.58
D. 27.98
Question 542
Δ DEF is right angled at E. If m∠D = 45%., then Cosec F =
A. 1/2
B. 1/√2
C. √2
D. 1/√3
Question 543
If sin -330° = x, then the value of x is
A. √3/2
B. 1/2
C. -2/√3
D. √2
Question 544
0.296 + 2.96 + 29.6 + 296 = ?
A. 327.856
B. 328.756
C. 328.856
D. 327.756
Question 545
The sum of 6xy(2x - 4z) , 3yz(2x - 3z) and 4xz(3y - 2y2) is
A. 12x2y - 6xyz - 9yz2 + 8xy2z
B. 12x2y - 6xyz + 9yz2 - 8xy2z
C. 12x2y - 6xyz - 9yz2 - 8xy2z
D. 12x2y + 6xyz - 9yz2 - 8xy2z
Question 546
If 1/2 is added to a number and the sum is multipled by 3, the result is 21. Then the number is
A. 6.5
B. 5.5
C. 4.5
D. -6.5
Question 547
A hydrogen filled balloon ascending at the rate of 18 kmph was drifted by wind. Its angle of elevation at 10th and 15th minutes were found to be 60° and 45° respectively. The wind speed (in whole numbers) during the last five minutes, approximately, is equal to
A. 7 km/hr
B. 11 km/ hr
C. 26 km/hr.
D. 33 km/hr
Question 548
If x – y – √18 = –1 and x + y – 3√2 = 1, then what is the value of 12xy(x2 – y2)?
A. 0
B. 1
C. 512√2
D. 612√2
Question 549
If 1+121+141+161+181-131-151-17 = 1+ 1x, then what is the value of x?
A. 6
B. 8
C. 5
D. 7
Question 550
What is the slope of the line, perpendicular to the line 3x - 6y = 4?
A. -2
B. 2
C. 2/3
D. -2/3
Question 551
If x = 2 +√3, y = 2 – √3 and z = 1, then what is the value of (x/yz) + (y/xz) + (z/xy) + 2 [(1/x) + (1/y) + (1/z)]?
A. 25
B. 22
C. 17
D. 43
Question 552
A bag contains 25 paise, 50 paise and 1 Rs coins. There are 220 coinsinall and the total amount in the bag is Rs. 160. If there arethrice as many 1 Rs. coins as there are 25 paise coins, then what is the number of 50 paise coins?
A. 60
B. 40
C. 120
D. 80
Question 553
The average weight of Sudesh, Jyothi and Ritu is 89 kg. If the average weight of Sudesh and Jyothi be 98 kg and that of Jyothi and Ritu be 83 kg, then the weight of Jyothi is
A. 58
B. 56
C. 95
D. 66
Question 554
Calculate the value of 55-5, if the value of √5 = 2.236.
A. 0.809
B. 0.89
C. 0.089
D. 0.807
Question 555
If √(1 - cos2A)/cosA = x, then the value of x is
A. cotA
B. cosecA
C. tanA
D. secA
Question 556
If (1/x) + (1/y) + (1/z) = 0 and x + y + z = 9, then what is the value of x3 + y3 + z3 – 3xyz?
A. 81
B. 361
C. 729
D. 6561
Question 557
If a - b = 2 and ab = 15, then what is the value of a3- b3?
A. 152
B. 112
C. 108
D. 98
Question 558
If 3x + 5y + 7z = 49 and 9x + 8y + 21z = 126, then what is the value of y?
A. 4
B. 2
C. 3
D. 5
Question 559
What is the value of 4600+540+1280+250+36 ?
A. 69
B. 68
C. 70
D. 72
Question 560
If x+1x:x-1x=5:3 then the value of x is
A. +- 1
B. +-2
C. +-3
D. +-4
Question 561
In ΔPQR, S and T are points on side PQ and PR respectively. ST is parallel to QR. If S divides PQ in the ratio 4:3 and length of QR is 4.9 cm, find ST?
A. 5.6 cm
B. 7.2 cm
C. 2.8 cm
D. 3.6 cm
Question 562
In ΔABC measure of angle B is 90 deg. If cosA = 5/13, and AB = 10 cm, then what is the length (in cm) of side BC?
A. 26
B. 24
C. 25
D. 5
Question 563
Compute of 69696 x 9999 =
A. 696980304
B. 666890304
C. 696809304
D. 696890304
Question 564
If tanθ = 815, then 1-sinθ1+sinθ is
A. 1/5
B. 2/5
C. 3/5
D. 0
Question 565
If cosθ = x2-y2x2+y2, then the value of cotθ is
A. 2xyx2-y2
B. 2xyx2+y2
C. x2+y22xy
D. x2-y22xy
Question 566
p3 + q3 + r3 – 3pqr = 4. If a = q + r, b = r + p and c = p + q, then what is the value of a3 + b3 + c3 – 3abc?
A. 4
B. 8
C. 2
D. 12
Question 567
If x+19x=4, then 9x2+19x2 is
A. 140
B. 142
C. 144
D. 146
Question 568
Simplify 81x2 - 49y29x + 7y
A. 9x++7y
B. 9x-7y
C. 9x
D. 7y
Question 569
What is the value of [2 cot × (p – A)/2]/[1 + tan2× (2p – A)/2]?
A. 2 sin2 A/2
B. cos A
C. sin A
D. 2 cos2 A/2
Question 570
The sum of a number and 4 times its reciprocal is 5. What is the number?
A. 4
B. 5
C. 6
D. 7
Question 571
What is the simplified value of cosec6A – cot6A – 3 cosec2A cot2A?
A. -2
B. -1
C. 0
D. 1
Question 572
Calculate the angle subtended by the chord at the point on the major arc if the radius and the chord of the circle are equal in length.
A. 30°
B. 120°
C. 200°
D. 300°
Question 573
When 721+722+723+724 is divided by 25 the remainder is:
A. 5
B. 17
C. 7
D. 0
Question 574
If cosA = x, then x is
A. √(1 - cos2A)
B. √(1 + sin2A)
C. √(1 + cos2A)
D. √(1 - sin2A)
Question 575
If [a + (1/a)]2 – 2[a – (1/a)] = 12, then which of the following is a value of 'a'?
A. – 8 + √3
B. – 8 – √3
C. – 8 + √5
D. None of these
Question 576
The price of 4.5 m of cloth is Rs.60.75. Find the cost per meter.
A. 15.5
B. 13.5
C. 14.75
D. 13.75
Question 577
Given 17 x 29 = 493, then 170 x 0.029 = ?
A. 0.0493
B. 4.93
C. 0.493
D. 49.3
Question 578
If a + b = 1, then a4 + b4 - a3 - b3 - 2a2b2 + ab is equal to
A. 1
B. 2
C. 4
D. 0
Question 579
What is the value of 1.23+0.83+0.73-2.0161.351.22+0.82+0.72-0.96-0.84-0.56 =
A. 1/4
B. 1/2
C. 1
D. 2
Question 580
If a+b=3 then the value of a3+b3+9ab-27 is
A. 24
B. 25
C. 0
D. 27
Question 581
If tan A = 1/2 and tan B = 1/3, then what is the value of tan (2A + B)?
A. 1
B. 3
C. 5
D. 9
Question 582
If a + b = 8 and a2 + b2 = 34, then value of ab is
A. 30
B. 64
C. 98
D. 15
Question 583
What will be the value of r2+p2+s2-rp-ps-rs when r = 4, p = 2, s = 8?
A. 8
B. 18
C. 28
D. 38
Question 584
If a + b = 10 and ab- 13 = -ba - 11, then what is the value of 3ab + 4a2 + 5b2 ?
A. 450
B. 300
C. 600
D. 750
Question 585
If cot(A/2) = x, then the value of x is
A. √[(1 + cosA)/(1 - cosA)]
B. cosecA - cotA
C. √[(1 - cosA)/2]
D. √[(1 + cosA)/2]
Question 586
What is the value of tan 300°?
A. -1/2
B. -1/√2
C. -√3
D. -√3/2
Question 587
A line passing through the origin perpendicularly cuts the line 2x + 3y = 6 at point M. Find M?
A. (6/11, 9/11)
B. (6/7, 9/7)
C. (6/11, -9/11)
D. (-6/7, 9/7)
Question 588
If [7(5x/3 - 3/2)]/2 + 3/2 = 1/4, then what is the value of x?
A. 35/24
B. 24/35
C. -24/35
D. -35/24
Question 589
Find the degree of the polynomial 8x4 + 2x2y3 + 4
A. 4
B. 5
C. 0
D. 1
Question 590
If each median of an equilateral triangle has a length of 12cm. Then what will be the value of in-radius (in cm) of the equilateral triangle?
A. 3
B. 4
C. 5
D. 6
Question 591
(1155) +(18 − 6) × 9 =?
A. 113
B. 115
C. 100
D. 110
Question 592
If the mean of m observations out of n observations is n and the mean of remaining observations is m, then what is the mean of all n observations?
A. 2m –m^2/n
B. 2m –m/n
C. 2m
D. 2m –m
Question 593
One of the roots of the equation x2 - 4x + k = 0 is x = 3. The other root is
A. x = -1
B. x = -4
C. x = 1
D. x = 4
Question 594
Find the value of 777777?
A. 73164
B. 7164
C. 76364
D. 7764
Question 595
Compute : 1112 / 139 - 5
A. 557/67
B. -3
C. 556/67
D. 3
Question 596
If x4 + (1/x4) = 34, then what is the value of x3 – (1/x3)?
A. 0
B. 6
C. 8
D. 14
Question 597
If A = 30°, B = 60° and C = 135°, then what is the value of sin3A + cos3B + tan3C – 3sin A cos B tan C?
A. 0
B. 1
C. 8
D. 9
Question 598
What is the value of [tan (90 – A) + cot (90 – A)]2/[2 sec2(90 – 2A)]?
A. 0
B. 1
C. 2
D. – 1
Question 599
What is the value of [1 – sin (90 – 2A)] / [1 + sin (90 + 2A)]?
A. sinA cosA
B. cot2A
C. tan2A
D. sin2A cosA
Question 600
If 1/(1 + cosA) + 1/(1 - cosA) = x , then value of x is
A. 2sec2A
B. 2cosecA
C. 2cosec2A
D. 2secA
Question 601
2 sec2A is equal to
A. (1 - tanA)2 - (1 + tanA)2
B. √[(1 - tanA)2 + (1 + tanA)2 ]
C. √[(1 - tanA)2 - (1 + tanA)2]
D. (1 - tanA)2 + (1 + tanA)2
Question 602
If 2x + 6y = 3xy and 10x - 3y = 4xy, find x, y.
A. 3, 2
B. 2, 3
C. 4, 6
D. 6, 4
Question 603
If a – b = 11 and ab = 24, then value of a2 + b2 is
A. 169
B. 37
C. 73
D. 48
Question 604
If x + y = 10 and x2 + y2 = 68, then find xy
A. 21
B. 24
C. 25
D. 16
Question 605
What is the value of √[(1 + sinA)/(1 - sinA)]?
A. secA - tanA
B. cosecA + tanA
C. secA + tanA
D. cosecA - tanA
Question 606
If a - b = 3, a2+b2=29, find the value of ab.
A. 10
B. 12
C. 15
D. 18
Question 607
What is the value of 7293×16+676+169
A. 75
B. 64
C. 35
D. 60
Question 608
If x = 11, the value of x5 - 12x4 + 12x3 - 12x2 + 12x - 1 is
A. 11
B. 10
C. 12
D. -10
Question 609
The two roots of a quadratic equation are given as x = 1/7 and x = -1/8 . The equation can be written as:
A. (7x − 1)(8x − 1) = 0
B. (7x − 1)(8x + 1) = 0
C. (7x + 1)(8x − 1) = 0
D. (7x + 1)(8x + 1) = 0
Question 610
Divya and Kriti have total 46 candies. If Divya has 10 candies more than kriti, then find the total number of candies Divya have?
A. 20
B. 24
C. 28
D. 32
Question 611
If (sinA + CosA)/(sin A - cos A) = 5/4, the value of (tan2A + 1)/(tan2A - 1) = ?
A. 41/40
B. 12/13
C. 40/41
D. -31/49
Question 612
If P + 1P+2 = 1, then the value of P+23+1P+23-3 ?
A. 12
B. 16
C. 18
D. 15
Question 613
If sinA + sin2A = 1 then what is the value of cos2A + cos4A ?
A. 1
B. 2
C. 1/2
D. 1/4
Question 614
D and E are the points on the sides AB and AC respectively of a ΔABC and AD = 8 cm, DB = 12 cm, AE= 6 cm and EC = 9 cm, then BC is equal to:
A. 2/5 DE
B. 5/2 DE
C. 3/2 DE
D. 2/3 DE
Question 615
What is the simplified value of (cosec A – sin A)(sec A – cos A)(tan A + cot A)?
A. -1
B. 0
C. 1
D. 2
Question 616
ΔDEF is right angled at E. If cosD = 8/17, then what is the value of secF ?
A. 17/8
B. 8/17
C. 17/15
D. 15/17
Question 617
A and B are positive integers. If A + B + AB = 65, then what is the difference between A and B (A, B ≤ 15)?
A. 3
B. 4
C. 5
D. 6
Question 618
What is the reflection of the point (5, -2) in the line y = -1?
A. (-7 , -2)
B. (-5 , 0)
C. (5 , 0)
D. (-7 , 2)
Question 619
Simplify : 132 - 142 + 172 - 250 = ?
A. 196
B. 169
C. 121
D. 144
Question 620
If x/2 - [4(15/2 - x/3)]/3 = -x/18, then what is the value of x?
A. -10
B. 9/8
C. 10
D. -9/8
Question 621
If sinθ x cosθ = 1⁄2 . The value of sinθ - cosθ is where 0°< θ< 90°
A. 0
B. √2
C. 2
D. 1
Question 622
When [x + (1/x)] = 5, then what is the value of [x – (1/x)]?
A. 11
B. ± √22
C. 21
D. ± √21
Question 623
tan(A/2) is equal to
A. tanA/(1 + secA)
B. 1/(cosecA + cotA)
C. tanA/(1 + cosecA)
D. 1/(secA + cotA)
Question 624
The slope of the line passing through the points (7,-2) and (x,1) is -3/10. Find x.
A. 4
B. 2
C. -4
D. -3
Question 625
If cos 27° = x, the value of tan 63° is
A. x1-x2
B. x1+x2
C. 1-x2x
D. 1+x2x
Question 626
If x1x2x3 = 4(4 + x1 + x2 + x3 ), then what is the value of [1/(2 + x1 )] + [1/(2 + x2 )] + [1/(2 + x3 )]?
A. 1
B. 1/2
C. 2
D. 1/3
Question 627
If 4(2x + 3) > 5 - x and 5x - 3(2x - 7) > 3x - 1, then x can take which of the following values?
A. 6
B. -1
C. 5
D. -6
Question 628
If x = at2 and y = 2at then
A. x2 = 4ay
B. y2 = 4ax
C. x2 + y 2 = a2
D. x 2 - y2 = a 2
Question 629
What is the value of {[sin (x + y) – 2 sin x + sin (x – y)]/[cos (x – y) + cos (x + y) – 2 cos x]} × [(sin 10x – sin 8x)/(cos 10x + cos 8x)]?
A. 0
B. tan2x
C. 1
D. 2 tan x
Question 630
If cosecA + cotA = x, then value of x is
A. 1/(cosecA - cotA)
B. 1/(secA - tanA)
C. 1/(secA - cosA)
D. 1/(sinA - cosA)
Question 631
The two roots of an quadratic equation are given as x = 1/2 and x = -1/3. The equation can be written as
A. (2x - 1)(3x - 1) = 0
B. (2x + 1)(3x - 1) = 0
C. (2x - 1)(3x + 1) = 0
D. (2x + 1)(3x + 1) = 0
Question 632
If 27x + 27[x–(1/3)] = 972, then what is the value of x?
A. 2
B. 3
C. 4
D. 5
Question 633
The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a distance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 60°. The height of the tower in meters is
A. √3
B. 5√3
C. 10√3
D. 20√3
Question 634
If a/(a+b) = 15/21, what is (a+b)/(a-b) is equal to?
A. 13/9
B. 23/11
C. 14/5
D. 21/9
Question 635
If 4(4x + 5) > 2x - 1 > 4x - 3, then the value of x is
A. 2
B. 3
C. -2
D. 0
Question 636
The value of cos220°+cos270° is
A. 0
B. 1
C. 1/2
D. 13
Question 637
If sec2θ+tan2θ=3, then sec4θ-tan4θ =
A. 1/√3
B. 1
C. √3
D. 0
Question 638
What is the value of (1+cosA)/(1-cosA)?
A. (cosecA - cotA)2
B. (cosecA + cotA)2
C. (secA + cotA)2
D. (secA - cotA)2
Question 639
If xy = 56 and x2+ y2= 113, then what will be the value of (x + y)?
A. 29
B. 21
C. 36
D. 15
Question 640
If 13x2 = 172 - 92, find the value of x?
A. 16
B. 12
C. 8
D. 4
Question 641
Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 4 cm, then what is the area (in cm2) of an equilateral triangle with side equal to the bigger diagonal of the rhombus?
A. 6
B. 9√3
C. 12
D. 12√3
Question 642
The number of solutions of the pair of linear equations x + 2y - 8 = 0 and 2x + 4y = 16 is
A. 0
B. 1
C. Infinitely many
D. 2
Question 643
Simplify 4(x-1) -3x
A. 7x - 4
B. 7x + 4
C. x + 4
D. x - 4
Question 644
In each of the following questions two equations I and II are given. Solve both the equations and give answer: I. x2+2x-195=0II. y2+30y+225=0
A. x = y or relation can’t be established between x and y
B. x > y
C. x < y
D. x ≥ y
Question 645
[63 - (-3){-2 - 8 - 3}] / 3{6 + (-2) (-1)} = ?
A. 0
B. 3
C. 1
D. 2
Question 646
If Cot θ = 21/20, then what is the value of Sec θ?
A. 29/21
B. 21/29
C. 29/20
D. 20/29
Question 647
64/12 in simplest form?
A. 19/6
B. 32/4
C. 16/3
D. None of the above
Question 648
If (4x - 5) = (3x - 1), then the numerical value of (x + 4)2
A. 16
B. 64
C. 32
D. 8
Question 649
If a+bab=21 , then the value of (a-b) is
A. 1
B. 0
C. -1
D. 2
Question 650
1422 ÷ 1260.25 = ?
A. 586
B. 578
C. 568
D. 566
Question 651
The line passing through the point (5,a) and point (4,3) is perpendicular to the line x - 6y = 8. What is the value of 'a'?
A. -3
B. -2
C. 4
D. 5
Question 652
If 56 × 75 × 60 × 84 × 210 = 2p × 3q × 5r × 7s, then what is the value of [(p + q)/s] + r?
A. 6
B. 8
C. 12
D. 10
Question 653
If the sum of the digits of any integer between 100 and 1000 is subtracted from the same integer , the resulting number is always divisibleby
A. 2
B. 5
C. 6
D. 9
Question 654
One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
A. Rs. 30,000
B. Rs. 50,000
C. Rs. 60,000
D. Rs. 90,000
Question 655
If 2/3(6x/5 - 1/4) + 1/3 = 9x/5, then what is the value of x?
A. 1/6
B. -1/6
C. 1/5
D. -1/5
Question 656
If a1-2a+b1-2b+c1-2c = 12, then 11-2a+11-2b+11-2c value is
A. 1
B. 2
C. 3
D. 4
Question 657
The value of 8(sin6θ + cos6θ) - 12(sin4θ + cos4θ) is equal to
A. 20
B. -20
C. 4
D. -4
Question 658
What is the value of sin 75°+ sin 15°?
A. √3
B. 2√3
C. √(3/2)
D. 3/√2
Question 659
What is the value of 4cos90-A sin390+A - 4sin90+A cos390-Acos180+8A2 ?
A. 1
B. -1
C. 0
D. 2
Question 660
If x and y are natural numbers such that x + y = 2017, then what is the value of (– 1)x+ (– 1)y?
A. 2
B. – 2
C. 0
D. 1
Question 661
What is the value of (cosec45 + √3/2) ?
A. 5/6
B. (4+√3)/2√3
C. (2√2+√3)/2
D. 3√3/2
Question 662
If cosec4A - cosec2A = x, then value of x is?
A. tan4A + tan2A
B. cot4A + cot2A
C. cot4A - cot2A
D. tan4A - tan2A
Question 663
If (x - 2) (x - p) = x2 - ax + 6, then the value of (a - p) is
A. 0
B. 1
C. 2
D. 3
Question 664
What is the value of cosec 11π/6?
A. -2/√3
B. √2
C. -2
D. -√2
Question 665
In the first 10 overs of a cricket game, the run rate was only 3.2. The run rate in the remaining 40 overs to reach the target of 282 runs is
A. 6.4
B. 6.3
C. 6.25
D. 6.5
Question 666
cosA/(1 - sin A) is equal to
A. (secA - tanA)
B. (secA + tanA)
C. √[(secA + tanA)]
D. √[(secA - tanA)]
Question 667
2sinAsinB is equal to
A. sin(A+B) + sin(A-B)
B. cos(A-B) - cos(A+B)
C. sin(A+B) - sin(A-B)
D. cos(A+B) + cos(A-B)
Question 668
Expand and simplify (x + 5)2 + (x - 3)2
A. 2(x2 + 2x - 17)
B. 2(x2 - 2x + 17)
C. 2(x2 - 2x - 17)
D. 2(x2 + 2x + 17)
Question 669
The diagonal of a square equals the side of an equilateral triangle. If the area of the square is 12 sq cm, what is the area of the equilateral triangle?
A. 12√3 sq cm
B. 6√3 sq cm
C. 12√2 sq cm
D. 24 sq cm
Question 670
3x2-14x+16=05y2-16y+12=0
A. x > y
B. x < y
C. x=y or relation cannot be established between x and y
D. x ≥ y
Question 671
50.003% of 99.8÷49.988 = ?
A. 2
B. 0
C. 1
D. 50
Question 672
Simplify the equation 0.733+0.2730.732+0.272-0.73×0.27
A. 1
B. 0.4087
C. 0.73
D. 0.27
Question 673
If x = 1.1, then what is the value of 4x2 -4x + 1 ?
A. 1.21
B. 1.331
C. 2.21
D. 1.2
Question 674
If 4x + 3y = 11 and 3x + 2y = 8, then (x,y) is
A. 2, 0
B. 1, 6
C. 2, 1
D. 5, 6
Question 675
What is the simplified value of (sin A – cosec A)(sec A – cos A) (tan A + cot A)?
A. 1
B. -1
C. 0
D. 2
Question 676
If tan π/3c + cosec π/6c = x, then x is
A. (1-√2)/√2
B. (√3+4)/2√3
C. √3+2
D. (2√2-1)/2
Question 677
Calculate the sum of squares from 1 to 9.
A. 284
B. 285
C. 385
D. 380
Question 678
If ab+ba=1, then the value of a3+b3 is
A. 1
B. 0
C. -1
D. 2
Question 679
78 of 448 + 67 of 3374 = ?
A. 3084
B. 3184
C. 3584
D. None of these
Question 680
If Tan A = 15/8 and Tan B = 7/24, then Cos(A - B) = ?
A. 297/425
B. 304/425
C. 87/425
D. 416/425
Question 681
The quadratic equation 1+a2x2+2abx+b2-c2=0 has only one root. What is the value of c21+a2 ?
A. a2
B. b2
C. c2
D. ab
Question 682
What is the sum of a3+b3+c3-3abc, when the value of a=4, b=2 and c=-6?
A. 0
B. 2
C. 4
D. 6
Question 683
If a3 + b3 = 19 and ab = -6 , then what is the value of a + b?
A. 5
B. 7
C. 1
D. -5
Question 684
What is the square root of 5041?
A. 79
B. 81
C. 71
D. 69
Question 685
If (1 + cosA)/(1 - cosA) = x, then x is
A. cot2A/(secA - 1)2
B. cot2A/(secA + 1)2
C. tan2A/(secA + 1)2
D. tan2A/(secA - 1)2
Question 686
If 3sinθ+4cosθ=5 (0<θ<90°) then the value of sinθ is
A. 1/5
B. 2/5
C. 3/5
D. 4/5
Question 687
Which of the following points lies on the line 3x - 4y = -13?
A. (5,7)
B. (-5,7)
C. (5,-7)
D. (-5,-7)
Question 688
Along a yard 225 metres long, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees
A. 8
B. 9
C. 10
D. 11
Question 689
A box weighs 8.5 kg when full of sand and weighs 5.5 kg when it is half filled with sand . Weight of the empty box is
A. 5 kg
B. 6 kg
C. 2.5 kg
D. 4.5 kg
Question 690
If X + Y = 19 and X - Y = 7, then XY = ?
A. 13
B. 48
C. 78
D. 72
Question 691
2*[0.3(1.3 + 3.7)] of 0.8 = ?
A. 1.92
B. -0.72
C. 2.16
D. -2.4
Question 692
If 2cosec2A = x, then the value of x is
A. 1/(1 - cosecA) - 1/(1 + cosecA)
B. 1/(1 + sinA) + 1/(1 - tanA)
C. 1/(1 + cosA) + 1/(1 - cosA)
D. 1/(1 - tanA) - 1/(1 + sinA)
Question 693
If the selling price is Rs 1680 after getting a discount of 16%, what was the marked price?
A. Rs 2000
B. Rs 1948.8
C. Rs 1411.2
D. Rs 1448
Question 694
What is the value of 7293 + 441 - 3433 ?
A. 48
B. 23
C. 7
D. 41
Question 695
Reduce 3596 / 4292 to lowest terms.
A. 29/37
B. 17/43
C. 31/37
D. 19/23
Question 696
If (x + y)/z = 2, then what is the value of [y/(y – z)] + [x/(x – z)]?
A. 0
B. 1
C. 2
D. – 1
Question 697
If Sec θ = 13/12, then what is the value of Sin θ?
A. 5/13
B. 12/5
C. 12/13
D. 5/12
Question 698
If x + y = 10 and xy = 4, then what is the value of x4 + y4?
A. 8464
B. 8432
C. 7478
D. 6218
Question 699
What is the x-intercept of line joining (4, 2) and (6, 3)?
A. 0
B. 1
C. 2
D. 3
Question 700
What is the slope of the line 4x - 8y = 3?
A. -1/2
B. 2
C. 1/2
D. -2
Question 701
The line passing through (-2,5) and (6,b) is perpendicular to the line 20x + 5y = 3. Find b?
A. -7
B. 4
C. 7
D. -4
Question 702
Product of 9b2, 3a2 and 4ab is
A. 108a2b2
B. 108a3b3
C. 108a3b2
D. 108a4b4
Question 703
If a3+ b3 = 19 and a + b = 1, then what is the value of ab?
A. 5
B. -6
C. 7
D. -9
Question 704
The price of 2 oranges, 3 bananas and 4 apples is Rs. 15. The price of 3 oranges, 2 bananas and 1 apple is Rs. 10. What will be price of 4 oranges, 4 bananas and 4 apples ?
A. Rs. 10
B. Rs. 15
C. Rs. 20
D. Rs. 25
Question 705
If x = √2+1, then the value of x4-1/x4
A. 8√2
B. 18√2
C. 6√2
D. 24√2
Question 706
ΔUVW is right angled at V. If secU = 5/3, then what is the value of tanW ?
A. 3/4
B. 5/3
C. 4/5
D. 4/3
Question 707
If (1/4 of x) - (4/5 of 6/7) equals - 9/7, then value of x is
A. -12
B. -2.4
C. -3.6
D. -14
Question 708
Find the common factor of 3757+ 4357 and 3737+ 4337
A. (43 - 37)
B. (43 + 37)
C. 37
D. 10
Question 709
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
A. 10
B. 35
C. 62.5
D. Cannot be determined
Question 710
If (4x - 3) - (2x + 1) = 4, then the value of x is
A. 0
B. 1
C. 2
D. 3
Question 711
If a+1/a = 3, then a3+1a3?
A. 12
B. 18
C. 9
D. 6
Question 712
Find the greatest number that will divide 390, 495 and 300 without leaving a remainder
A. 5
B. 15
C. 25
D. 35
Question 713
The length of a chord which is at a distance of 12 cm from the centre of a circle of radius 13 cm is
A. 10 cm
B. 5 cm
C. 6 cm
D. 12 cm
Question 714
If sec2A + cosec2A = X, then the value of X is
A. tan2A cot2A
B. sinA cosA
C. secA cosecA
D. sec2A cosec2A
Question 715
What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(4, 0) and C(-2, 2)?
A. (1 , -1)
B. (-1 , 1)
C. (2 , -2)
D. (-2 , 2)
Question 716
The sum of two positive integers is 80 & difference between them is 20. Then what is difference of squares of those numbers ?
A. 1400
B. 1600
C. 1800
D. 2000
Question 717
If X + 2Y = 27 and X - 2Y = -1, find the value of Y.
A. 13
B. 14
C. 7
D. 26
Question 718
What is the perimeter of the sector whose central angle is 60° and radius of the circle is 21 cm?
A. 128 cm
B. 96 cm
C. 64 cm
D. 32 cm
Question 719
What is the value of |3(1) - 6|?
A. 3
B. 0
C. -3
D. 4
Question 720
If x2 + (1/x2) = 31/9 and x > 0, then what is the value of x3 + (1/x3)?
A. 70/9
B. 154/27
C. 349/27
D. 349/7
Question 721
If (cotAcotB - 1) / (cotB + cotA) = x, then the value of x is
A. cot(A - B)
B. tan(A + B)
C. cot(A + B)
D. tan(A - B)
Question 722
In ∆XYZ measure of angle Y is 90 deg. If cosecX = 13/12, and XY = 1cm, then what is the length ( in cm ) of side YZ?
A. 2.6
B. 1.5
C. 2.4
D. 2
Question 723
What is the value of Tan 45° + 4/√3 Sec 60°?
A. (√3 + 8)/√3
B. (√3 + 8)/3
C. (√3 - 8)/√3
D. (√3 - 8)/3
Question 724
If X = 423 + 32 then find the value of ( X + 1X ).
A. 103 + 15212
B. (103 - 52)12
C. -103 - 33212
D. (103+332)12
Question 725
What is the simplified value of 12-13 ?
A. 5√3
B. 5/√3
C. 3√5
D. 3/√5
Question 726
ΔPQR is right angled at Q. If m∠R = 45°, then find the value of (tanP - 1/2).
A. (2-√3)/√3
B. (2√3-√6)/2√2
C. 1/2
D. (√6-6)/3√3
Question 727
If x - y = 7 and xy = 32, then value of (x2 + y2) is
A. 49
B. 64
C. 113
D. 15
Question 728
The cost of 15 kg of groundnuts and 4 kg of cashews is Rs.7,000. The cost of 10 kg of cashews is equal to 25 kg of groundnuts. Find the cost of groundnut per kg.
A. Rs.320
B. Rs.700
C. Rs.540
D. Rs.280
Question 729
If 3x + 4y – 2z + 9 = 17, 7x + 2y + 11z + 8 = 23 and 5x + 9y + 6z – 4 = 18, then what is the value of x + y + z – 34?
A. – 28
B. – 14
C. – 31
D. – 45
Question 730
If a - b = 3 and a^2 + b^2 = 29, find the value of ab.
A. 10
B. 12
C. 15
D. 18
Question 731
If x, y, z are the three factors of a3 -7a - 6, then value of x+y+z will be
A. 3a
B. 3
C. 6
D. a
Question 732
What is the value of 12 + 3(-2 x 3) - (18 / 6) ?
A. -5
B. 9
C. -9
D. 5
Question 733
5 + 2 x 10/2 = ?
A. 15
B. 35
C. 10
D. 20
Question 734
If 1/(cosecA cotA) = x, then the value of x is
A. cosecA + cotA
B. cosecA - cotA
C. cosec2A + cot2A
D. √[cosec2A + cot2A]
Question 735
2 - (cosA + sinA)2 is equal to
A. (cosecA - sinA)2
B. cosA - sinA
C. cosecA - sinA
D. (cosA - sinA)2
Question 736
At what point does the line 3x + 2y = 12 cuts the Y-axis?
A. (0, 6)
B. (0, -6)
C. (6, 0)
D. (-6, 0)
Question 737
1747 + 13212 - ? = 1123
A. 16
B. 17
C. 18
D. 19
Question 738
Simplify 0.1x0.1x0.1 + 0.3x0.3x0.30.3x0.3 - 0.3x0.1 + 0.1x0.1
A. 0.09
B. 0.03
C. 0.05
D. 0.04
Question 739
If M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) and N = (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), then what is the value of M/N?
A. 207/560
B. 339/1120
C. 113/350
D. 69/175
Question 740
If tanθ = 43, then the value of 3sinθ+2cosθ3sinθ-2cosθ ?
A. 1/2
B. 3/2
C. 3
D. -3
Question 741
If Sin 31° = xy, then the value of Sec 31° - Sin 59° is
A. x2yy2-x2
B. -x2yy2-x2
C. -y2y2-x2
D. x
Question 742
What is the value of sin 46 cos 44+ cos 46 sin 44?
A. 2
B. sin 2
C. 1
D. 0
Question 743
If x + y = 12 and xy = 32, then what is the value of x2 + y2 ?
A. 24
B. 144
C. 128
D. 80
Question 744
If the value of 3-1.732, then calculate the value of 243-12108-147
A. 1.732
B. -1.464
C. 3.464
D. -1.732
Question 745
P(4,2) and R(-2,0) are vertices of a rhombus PQRS. What is the equation of diagonal QS.
A. x - 3y = -2
B. 3x + y = 4
C. 3x + y = -4
D. x - 3y = 2
Question 746
If xy+yz+zx = 1, then the value of (1+y2)(x+y)(y+z) ?
A. 2
B. 3
C. 4
D. 1
Question 747
What is the equation of the line passing through the point (1,3) and making an angle of -45° with the positive x-axis?
A. x + y = 4
B. x + y = 2
C. x - y = 4
D. x - y = 2
Question 748
Find equation of the perpendicular bisector of segment joining the points (2,6) and (4,0)?
A. x + 3y = 6
B. x + 3y = -6
C. x - 3y = -6
D. x - 3y = 6
Question 749
If x +y = √3 and x - y = √2, then the value of 8xy (x2 + y2) is
A. 6
B. √6
C. 5
D. √5
Question 750
If xy = -30 and x2 + y2 = 61, then find the value of (x + y).
A. 2
B. 3
C. 1
D. 4
Question 751
Determine the value of a/b + b/a when a + b = 8 and ab = 4.
A. 4
B. 8
C. 12
D. 14
Question 752
If sin -240° = x, then the value of x is
A. 2/√3
B. √2
C. 2
D. √3/2
Question 753
If ( x - 5)2 + (y - 2)2 + (z - 9)2 = 0 , then value of (x + y - z) is
A. 16
B. -1
C. -2
D. 12
Question 754
If tan2A - sin2A = x, then value of x is
A. tan2A sin2A
B. cot2A cosec2A
C. tanA sinA
D. cotA cosecA
Question 755
If x + 1x = 3, then x18 + x12 + x6 + 1 value is
A. 0
B. 1
C. 2
D. 3
Question 756
If 'Q ' means ' +', 'J ' means ' X',T ' ' means '- ' and 'K ' means '÷ ', then what is the value of18K3Q7J ?
A. 15
B. 10
C. 18
D. 12
Question 757
Find length of the arc whose central angle is 45° and radius of the circle is 28 cm?
A. 11 cm
B. 33 cm
C. 44 cm
D. 22 cm
Question 758
On dividing 221a2b2 by 13b2, we get _____.
A. 17a2
B. 17b2
C. 13a2b2
D. 13
Question 759
Find the value of 0.0112 - 0.0012 of 0.14 + 0.25 × 0.20.02 × 0.01
A. 257
B. 25.7
C. 2.57
D. 0.0257
Question 760
If cosec 240° = x, then the value of x is
A. √2
B. 2
C. -2/√3
D. -√2
Question 761
Simplify 11.9983 = ?
A. 1727.136
B. 1331.136
C. 1685.136
D. 1700.136
Question 762
If x + 3 ≤ 4x + 4 and 3(4 - x) - 4 ≥ 2x - 2, then x can take which of the following values?
A. 1
B. 3
C. -1
D. -3
Question 763
The solution set of 4x - 3y = 47 and 3x + y = 32 is
A. {(15, 3)}
B. {(4, 12)}
C. {(11, -1)}
D. {(12, 3)}
Question 764
If a + b = 9 and a2+ b2= 61, then ab is
A. 20
B. 10
C. 81
D. 142
Question 765
If x + [1/(4x)] = 5/2, then what is the value of (64x6+ 1)/8x3?
A. 110
B. 115
C. 125
D. 140
Question 766
Point A divides segment BC in the ratio 4:1. Co-ordinates of B are (6 , 1) and C are (7/2 , 6). What are the co-ordinates of point A?
A. (4 , 3)
B. (4 , 5)
C. (2 , 5)
D. (3 , 5)
Question 767
What is the value of sec 5π/4?
A. 1/√3
B. -√2
C. √3
D. 1
Question 768
Simplify : -21973 × -1253 ÷ 275123
A. 492/7
B. 520/3
C. 554/7
D. 571/5
Question 769
6.651 - (148.6 - x ) - 57.22 = 6.098. Find x.
A. 205.267
B. 90.827
C. -91.933
D. 218.569
Question 770
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter were to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?
A. 10 m
B. 14 m
C. 12 m
D. 8 m
Question 771
The total of 324 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is :
A. 50
B. 100
C. 150
D. 200
Question 772
If πsinθ= 1, πcosθ= 1, then (3tan 23θ+1) is
A. 1
B. √3
C. 2
D. 1/√3
Question 773
Find the value of 1006×994?
A. 999932
B. 999964
C. 1000032
D. 1000064
Question 774
In a farm, in addition to 48 hens there are 42 sheep and 11 oxen with some shepherds. If the total number of feet be 224 more than the number of heads, find the number of shepherd.
A. 11
B. 13
C. 15
D. 17
Question 775
8 x {5 - (-2) x (-3)} = ?
A. 8
B. -168
C. 88
D. -8
Question 776
Factorise x2 + 3x - 18
A. (x+18)(x-1)
B. (x-1)(x+18)
C. (x+6)(x-3)
D. (x-6)(x+3)
Question 777
Solve the following : 27 - [38 - {46 - (15 - 13 - 2)}]
A. 31
B. 35
C. 30
D. 29
Question 778
What is the simplified value of 1-sin A1+sin A ?
A. tan A
B. sec A
C. sec A + tan A
D. sec A – tan A
Question 779
If 2x+13x = 5, the value of 5x6x2+20x+1 is
A. 1/4
B. 1/6
C. 1/5
D. 1/7
Question 780
What is the value of sinAtanA/(1 - cosA)?
A. 1 - secA
B. 1 + secA
C. 1 + cotA
D. 1 - cotA
Question 781
If √3 = 1.732, then the value of 9+233?
A. 7.169
B. 7.196
C. 5.198
D. 7.296
Question 782
If a - b = -6 and a2 + b2 = 44, then ab is
A. -4
B. 8
C. 4
D. -8
Question 783
What is the value of tan 7π/4?
A. √3
B. -1/2
C. √3/2
D. -1
Question 784
If 3P/5 = 7Q/2 = 7R/5, then what is the ratio of p, Q and R respectively?
A. 3 : 2 : 5
B. 3 : 35 : 14
C. 5 : 7 : 5
D. 35 : 6 : 15
Question 785
If a + b = 4 and ab = 3, then what is the value of a3 + b3?
A. 21
B. 17
C. 28
D. 31
Question 786
The cost of one dozen bananas is Rs.5. The cost of one dozen oranges is Rs.75. What will the cost of one and a quarter dozen bananas and three-fourth dozen oranges?
A. Rs. 109.25
B. Rs. 87.25
C. Rs. 71.75
D. Rs. 62.50
Question 787
What is the value of Cot 45° - (1/√3)Cosec 60°?
A. 1/√3
B. 1/2
C. 1/√2
D. 1/3
Question 788
If xy (x + y) = m, then the value of x3 + y3 + 3m is:
A. m3xy
B. m3x+y3
C. m3x3y3
D. mx3y3
Question 789
Simplify 437bxaz / 23ab.
A. 17xzb
B. 9xz
C. 19xz
D. 19ab
Question 790
If 5x - 40 = 3x, then the numerical value of 2x - 11 is
A. 29
B. 39
C. 19
D. 9
Question 791
Which of the following numbers is completely divisible by 99?
A. 57717
B. 57627
C. 55162
D. 56982
Question 792
XYZ is a right angled triangle and ∠Y = 90°. If XY = 2.5 cm and YZ = 6 cm then the circumradius of ∆XYZ is
A. 6.5 cm
B. 3.25 cm
C. 3 cm
D. 2.5 cm
Question 793
What is the equation of the line which has 3/2 and -4/7 as x and y intercept respectively?
A. 8x - 21y = -12
B. 8x + 21y = 14
C. 8x - 21y = 12
D. 8x + 21y = -14
Question 794
What is the equation of line whose slope is -1/2 and passes through the intersection of the lines x - y = -1 and 3x - 2y = 0?
A. x + 2y = 8
B. 3x + y = 7
C. x + 2y = -8
D. 3x + y = -7
Question 795
If x = 1/(√2+1) then the value of x2 + 2x - 1 is
A. 2√2
B. 4
C. 0
D. 2
Question 796
What is the value of cosec -7π/6?
A. -2
B. 2
C. 2/√3
D. -2/√3
Question 797
If (-1/2) * ( x - 5) + 3 = -5/2, then what is the value of x?
A. 16
B. 4
C. -6
D. -4
Question 798
In ΔUVW measure of angle V is 90 deg. If sinU = 24/25, and UV = 0.7cm, then what is the length (in cm) of side VW?
A. 2.5
B. 3
C. 2.4
D. 4
Question 799
Triangle DEF is right angled at E. If cot D = 5/12, then what is the value of sin F?
A. 5/12
B. 13/5
C. 5/13
D. 13/12
Question 800
If a(x + y) = b(x - y) = 2ab, then the value of 2(x2 + y2)
A. 2(a2 - b2)
B. 2(a2 + b2)
C. 4(a2 - b2)
D. 4(a2 + b2)
Question 801
If a+1a2 = 3, then the value of a3+1a3 is
A. 0
B. a
C. 1/a
D. 1
Question 802
∆DEF is right angled at E. If cosD = 5/13, then what is the value of tanF?
A. 5/13
B. 5/12
C. 13/5
D. 13/12
Question 803
If x/3 - [5(7x/5 - 4/3)]/2 = -x/6, then what is the value of x?
A. 10/9
B. -10/9
C. -9/10
D. 9/10
Question 804
The simplest form of 3774/2958 is
A. 43/19
B. 37/29
C. 31/13
D. 31/23
Question 805
If 4(2x - 4) - 2 > 3x - 1 ≥ 4x - 7, then x can take which of the following values?
A. 7
B. 6
C. 2
D. 0
Question 806
If 5/2 - (6/5)(x - 15/2) = -x/5, then what is the value of x?
A. -23/2
B. 13/2
C. -13/2
D. 23/2
Question 807
What is the value of [(cos 7A + cos 5A)÷(sin 7A – sin 5A)]?
A. tan A
B. tan 4 A
C. cot 4 A
D. cot A
Question 808
Solve this inequality 3b - 7 < 32?
A. b = 13
B. b < 13
C. b > = 13
D. b < = 13
Question 809
If u : v = v : w, then what is the value of u4 : v4?
A. u2 : wv
B. u2 : w2
C. u2 v : w3
D. u : w
Question 810
∆XYZ is right angled at Y. If m ∠Z = 60. What is the length (in cm) of YZ, if ZX = 9√3 cm?
A. 3√3
B. 3√3/2
C. 9√3/2
D. √3
Question 811
If (tanA - tanB)/(1 + tanAtanB) = x, then the value of x is
A. tan(A - B)
B. tan(A + B)
C. cot(A - B)
D. cot(A + B)
Question 812
If (23)2= 4x then 3x is equal to
A. 3
B. 6
C. 9
D. 27
Question 813
If cosec θ + sinθ = 5/2 then the value of cosecθ - sinθ is
A. -3/2
B. 3/2
C. −√3/2
D. √3/2
Question 814
ΔPQR is right angled at Q. If m∠P = 45°, then find the value of (cosecR + 1/3).
A. (√3+2)/2√3
B. (√3+2)/2
C. (3√2+1)/3
D. (2+2√3)/√3
Question 815
If x - y = -8 and xy = 45, then (x2 + y2) is
A. 154
B. 64
C. 90
D. 26
Question 816
If x/y = 4/9, then what is the value of (7x2 – 19xy + 11y2)/y2 ?
A. 59/81
B. 100/27
C. 319/81
D. 913/81
Question 817
If x+1x=5, then the value of x1+x+x2 is
A. 1/5
B. 1/6
C. 5
D. 6
Question 818
What is the square root of 9409?
A. 83
B. 87
C. 89
D. 97
Question 819
1/(tanA + cotA) is equal to
A. (cosecA + sinA)(secA - cosA)
B. √[(cosecA - sinA)(secA - cosA)]
C. √[(cosecA + sinA)(secA - cosA)]
D. (cosecA - sinA)(secA - cosA)
Question 820
Out of the 60 students of a class, 29 took Mathematics, 32 took Biology and 8 took none of the two subjects. How many students took both Mathematics and Biology?
A. 8
B. 9
C. 7
D. 6
Question 821
The value of sinθ+sin∅cosθ+cos∅ + cosθ-cos∅sinθ-sin∅ is
A. 1
B. 2
C. 1/2
D. 0
Question 822
What is the equation of a line which has 3 as x-intercept and -5 as y-intercept?
A. 3x - 5y = 15
B. 5x - 3y = 15
C. 5x + 3y = 15
D. 3x + 5y = 15
Question 823
A and B together have Rs. 6300. If 5/19 of A's amount is equal to 2/5 of B's amount. The amount of 'B' is
A. Rs. 2500
B. Rs. 3800
C. Rs.2300
D. Rs. 4000
Question 824
What is the value of tan3A?
A. (3tanA - tan3A)/(1 - 3tan2A)
B. (3tanA + tan3A)/(1 + 3tan2A)
C. (3tanA - tan3A)/(1 + 3tan2A)
D. (3tanA + tan3A)/(1- 3tan2A)
Question 825
If x = 1 + √2 + √3 , then the value of 2x4 - 8x3 - 5x2 + 26x - 28 is
A. 2√2
B. 3√3
C. 5√5
D. 6√6
Question 826
Reflection of the point (3,-6) in the y-axis is
A. (3,6)
B. (3,-6)
C. (-3,-6)
D. (-3,6)
Question 827
The value of 122 + 345 - 3 / 1116 x 372 is
A. 466
B. 469
C. 446
D. 460
Question 828
If 5x + 1/x = 10, then x2 + 125x2 is equal to
A. 215
B. 335
C. 315
D. 235
Question 829
A man has only 20-paise and 25-paise coins in a bag. If he has 50 coins in all totaling to Rs.10.25, then the number of 20-paise coins is
A. 42
B. 45
C. 38
D. 36
Question 830
-70 + 28 / (7 - 3) = ?
A. -9
B. -69
C. -10.5
D. -63
Question 831
What is the value of tanπ4+A×tan3π4+A ?
A. 1
B. 0
C. cot A/2
D. – 1
Question 832
If tanθ = 724 then find the value of p such that tanθ - secθsinθ = -p28
A. 25
B. 75
C. 50
D. 100
Question 833
The slopes of two lines are 1 and √3. What is the angle between these two lines?
A. 15°
B. 30°
C. 45°
D. 60°
Question 834
If x – (1/x) = 3, then what is the value of (2x4 + 3x3 + 13x2 – 3x + 2) / (3x4 + 3)?
A. 1/3
B. 2/3
C. 4/3
D. 5/3
Question 835
On dividing 111a2b2c2 by 37a2, we get ______.
A. 2c2
B. 2b2
C. 3
D. 3b2c2
Question 836
What is the reflection of the point (4 , -3) in the line y = 1?
A. (4, -5)
B. (4, 5)
C. (-4, -5)
D. (-4, 5)
Question 837
A 12 m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle?
A. 12/π+4
B. 6/π+4
C. 3/π+4
D. 6/π+2√2
Question 838
The value of 16 - [5 - 2{14 of 2 - (8 ÷ 4 x 2 - 1 + 3}] is
A. -12
B. -9
C. -10
D. -14
Question 839
If 3x + [1/(5x)] = 7, then what is the value of 5x/(15x2+ 15x + 1)?
A. 1/5
B. 1/10
C. 2/5
D. 10
Question 840
Which of the following equations has the sum of its roots as 11?
A. x2 - 11x + 18 = 0
B. x2 - 7x + 10 = 0
C. x2 + 2x - 26 = 0
D. x2 + 5x - 6 = 0
Question 841
What is the value of 13×7+17×11+111×15+...+1899×903 ?
A. 21/509
B. 18/403
C. 25/301
D. 29/31
Question 842
If √(1 - sin2A) = x, then the value of x is
A. tanA
B. cosA
C. cosecA
D. secA
Question 843
ΔPQR is right angled at Q. If tanP = 24/7, then what is the value of cosR ?
A. 25/7
B. 24/25
C. 24/7
D. 7/24
Question 844
Reflection of the point (4,-5) in the y-axis is
A. (4,5)
B. (-4,-5)
C. (4,-5)
D. (-4,5)
Question 845
Sumit and Amit undertook a work for Rs 7200. Sumit alone can do the work in 5 days and Amit alone can do the work in 4 days. If they work together,then what will be the difference (in Rs.) in the amount they receive?
A. 800
B. 1600
C. 1200
D. 1400
Question 846
The distance between the points (11,5) and (k,0) is 13. Find k.
A. k = 1 or 23
B. k = -1 or 23
C. k = 1 or -23
D. k = -1 or -23
Question 847
What is the value of tan 7π/6?
A. 1/√3
B. -1/√3
C. √3
D. -√3
Question 848
What is the sum of the first 12 terms of an arithmetic progression if the 3rd term is -13 and the 6th term is -4?
A. 67
B. 45
C. -30
D. -48
Question 849
What is the total number of points in the plane of triangle ABC which is equidistant from the vertices of the triangle?
A. 0
B. 1
C. 2
D. 3
Question 850
What is the value of (√3 - sec60) ?
A. √3-2
B. (1-√6)/√2
C. (2√3-√6)/2√2
D. (1-3√2)/3
Question 851
If a3 + b3 = 28 and a + b = 4, then what is the value of ab?
A. -3
B. 2
C. 8
D. 3
Question 852
If cosC + cosD = x, then value of x is
A. 2cos[(C+D)/2]cos[(C-D)/2]
B. 2sin[(C+D)/2]sin[(C-D)/2]
C. 2cos[(C+D)/2]sin[(C-D)/2]
D. 2sin[(C+D)/2]cos[(C-D)/2]
Question 853
72 ÷ 52 × 3272 ÷ 52 of 32 ÷ 5.25
A. 3/5
B. 3/6
C. 3/7
D. 3/8
Question 854
∆LMN is right angled at M. If m ∠N = 45°. What is the length (in cm) of MN, if NL = 6√2 cm?
A. 3
B. 4
C. 2
D. 6
Question 855
If x2+1x2 = 98, then x3+1x3 = ?
A. 970
B. 1030
C. -970
D. -1030
Question 856
If secA - tanA = x, then the value of x is
A. √[(1 + sinA)/(1 - sinA)]
B. √[(1-sinA)/(1+sinA)]
C. (1-sinA)/(1+sinA)
D. (1 + sinA)/(1 - sinA)
Question 857
If (tanA + tanB)/(1 tanAtanB) = x, then the value of x is
A. tan(A + B)
B. tan(A - B)
C. cot(A + B)
D. cot(A - B)
Question 858
If a2+b2=80 and ab = 32, then calculate the value of a-b/a+b.
A. 0.337
B. 0.339
C. 0.333
D. 0.335
Question 859
If secA + tanA = x, then find the value of x.
A. √[(1 - sinA)/(1 + sinA)]
B. (1 + sinA)/(1 - sinA)
C. (1 - sinA)/(1 + sinA)
D. √[(1 + sinA)/(1 - sinA)]
Question 860
What is the value of tan -240°?
A. -√3
B. 1/√3
C. -1/√3
D. √3
Question 861
If 3+12=x+3y, then the x+y is
A. 2
B. 4
C. 6
D. 8
Question 862
23x12+49x15312+50 = ?
A. 0.5
B. 1
C. 2
D. 3
Question 863
If a+1b= b+1c = c+1a (a , b, c are not equal) then the value of abc =
A. + 1
B. - 1
C. +1 & -1
D. None of the options
Question 864
If a3+1a3 = 2, then the value of a2+1a?
A. 1
B. 2
C. 3
D. 4
Question 865
If 3x - 7 = 5x - 1, then the numerical value of (x - 4)2 is
A. 1
B. 49
C. -1
D. -49
Question 866
If cosec2 θ = 625/576, then what is the value of [(sin θ – cos θ)/(sin θ + cos θ)]?
A. 1
B. 31/17
C. 17/31
D. 14/25
Question 867
If a + b = 11 and a2+ b2= 61, then value of ab is
A. 12
B. 96
C. 24
D. 30
Question 868
What is the value of 96+21624?
A. 8
B. 4
C. 5
D. 10
Question 869
The difference between two numbers is 1146. When we divide the larger number by smaller we get 4 as quotient and 6 as remainder. Find the larger number
A. 1526
B. 1431
C. 1485
D. 1234
Question 870
If α and βare the zeros of the polynomial 5x2 - 7x + 2 then the sum of their reciprocals is
A. 5/2
B. 7/5
C. 2/5
D. 7/2
Question 871
What is the value of Sin 30° - Cosec 45°?
A. (2√6 - 1)/√3
B. (1 - 2√3)/2
C. (√2 - √3)/√6
D. (1 - 2√2)/2
Question 872
The areas of two similar triangles ΔABC and ΔPQR are 121 sq cms and 64 sq cms respectively. If PQ = 12 cm, what is the length (in cm) of AB?
A. 7.25
B. 6.25
C. 16.5
D. 5.25
Question 873
If ax + by = 1 and bx + ay = 2aba2+b2 then x2+y2a2+b2 is equal to
A. 1
B. 2
C. 0.5
D. 0
Question 874
If cos 2π/3c = x, then the value of x is
A. -1/2
B. 1/2
C. -√3/2
D. √3/2
Question 875
If a3 + b3 = 35 and ab = 6, then what is the value of a + b?
A. 5
B. 8
C. 2
D. -8
Question 876
P is a point outside the circle at distance of 6.5 cm from centre O of the circle. PR be a secant such that it intersects the circle at Q and R. If PQ = 4.5 cm and QR = 3.5 cm, then what is the radius (in cm) of the circle?
A. 1.5
B. 2
C. 2.5
D. 3
Question 877
What is the value of √[(1 - sinA)/(1 + sinA)]?
A. cosA/(1 - sinA)
B. cosecA/(1 + sinA)
C. cosA/(1 + sinA)
D. cosecA/(1 - sinA)
Question 878
If √20 + √125 = 15.65, then what is the value of √45 + √5?
A. 6.98
B. 8.94
C. 9.98
D. 11.27
Question 879
Coefficient of x2 in 6x3 + 4x2 + 2x + 3 is
A. 4
B. 6
C. 3
D. 2
Question 880
For real a, b and c if a2 + b2 + c2 = ab + bc + ca, then find the value of a+b+c2.
A. 9a2
B. 81a2
C. 27a2
D. 243a2
Question 881
A bag contain equal number of 1 rupee, 50 paisa and 25 paisa coins. If the total amount is Rs 105, then how many coins of each type are there?
A. 15
B. 45
C. 60
D. 80
Question 882
If 2x -3(x + 2) < 5 - 2x < -x + 2, then find the value of x.
A. 2
B. 0
C. 10
D. 12
Question 883
If a.sin 45°.cos 45°.tan60° = tan 245° cos60° then find the value of a ?
A. 13
B. 3
C. 1
D. 32
Question 884
Simplify 413 + 215 + 414 = ?
A. 10 47/60
B. 11 45/73
C. 11 47/36
D. 10 35/48
Question 885
Cost of 4 pens, 6 note books and 9 files is Rs 305. Cost of 3 pens, 4 notebooks and 2 files is Rs 145. What is the cost (in Rs) of 5 pens, 8 notebooks and 16 files?
A. 415
B. 465
C. 440
D. Cannot be determined
Question 886
A complete factorisation of x4 + 64 is
A. (x2 + 8)2
B. (x2 + 8)(x2 - 8)
C. (x2 - 4x + 8)(x2 -4x - 8)
D. (x2 + 4x + 8)(x2 - 4x + 8)
Question 887
If sec -5π/4 = x, then the value of x is
A. -1/√3
B. -√2
C. -1
D. √3
Question 888
If ab = 21 and a+b2a-b2 = 254,then the value of a2+b2+3ab
A. 115
B. 121
C. 125
D. 127
Question 889
If C+1C = 3, then what is the value of C3+1C3 = ?
A. 0
B. 3√3
C. 1/√3
D. 6√3
Question 890
If Cos θ = 15/17 , then what is the value of Cosec θ?
A. 17/8
B. 8/17
C. 8/15
D. 17/15
Question 891
If 51.97 (81.18 - x ) - 59.39 = 5.268, then value of x will be
A. - 24.912
B. - 68.492
C. 93.868
D. 197.808
Question 892
If sin3A = x, then value of x is
A. 3sinA + 4sin3A
B. 4sin3A - 3sinA
C. 4sin3A + sinA
D. 3sinA - 4sin3A
Question 893
What is the equation of the line if its slope is 2/5 and y-intercept is 6?
A. 2x + 5y = 6
B. 2x + 5y = 30
C. 2x - 5y = 6
D. 2x + 5y = -30
Question 894
If x = 222, y = 223, z = 225 then the value of x3 + y3 + z3 - 3xyz is
A. 4590
B. 4690
C. 4950
D. 4960
Question 895
Find the value of 491321973
A. 17/13
B. 13/17
C. 13/7
D. 17/7
Question 896
If sec 300° = x, then value of x is
A. √2
B. 1/√3
C. 2
D. 1
Question 897
If a3+ b3 = 341 and ab = 30, then what is the value of a + b?
A. 1
B. 9
C. 7
D. 11
Question 898
If price of oranges is increased by 30%, then a person can buy 12 oranges less for Rs 208. What is the original price (in Rs) of an orange?
A. 2
B. 4
C. 8
D. 3
Question 899
Coefficient of x in (x + 8)(6 - 3x) is
A. 18
B. 30
C. -18
D. -30
Question 900
Which of the following is a Pythagorean triplet?
A. 8, 15, 17
B. 17, 21, 29
C. 7, 9, 11
D. 2, 3, 5
Question 901
How many times the keys of a typewriter have to be pressed in order to write numbers from 121 to 1346?
A. 3675
B. 4018
C. 4021
D. 4025
Question 902
If p/q = (x+3)/(x-3), then what is the value of p2+q2p2-q2 ?
A. x+9
B. x2+96x
C. x2+186x
D. 0
Question 903
If sin (3x 20°) = cos (3y + 20°), then find the value of (x + y).
A. 90°
B. 60°
C. 120°
D. 30°
Question 904
If 3x= 4y= 12, then z is equal to
A. xy
B. x + y
C. xy/x+Y
D. 4x +3y
Question 905
The value of (sec245 - cot245) - (sin230 + sin260) is
A. 1
B. 2√3
C. 0
D. 1/√2
Question 906
The point P (a,b) is first reflected in origin to P1 and P1 is reflected in Yaxis to (4,3). The co-ordinates of point P are
A. (4,3)
B. (-4,3)
C. (-3,4)
D. (3,-4)
Question 907
Simplify : (-4.6)x(-4.6)/(-4.6+0.6)
A. -5.29
B. -0.529
C. -4.06
D. 5.01
Question 908
If Tan θ = 7/24, then what is the value of Sec θ?
A. 24/25
B. 24/7
C. 25/7
D. 25/24
Question 909
What is the reflection of the point (2, 3) in the line y = 4?
A. (2, 5)
B. (2, -5)
C. (-2, -5)
D. (-2, 5)
Question 910
What is the value of sin 330°?
A. 2
B. 2/√3
C. √2
D. -1/2
Question 911
What is the value of sin 5π/3?
A. √3/2
B. 2/√3
C. 1/√3
D. -2/√3
Question 912
Solve the following: (−18)[36÷7−(−2)]÷{}(−4)19−(−3)×(−5)={}?
A. -4.5
B. 4.5
C. -2.5
D. 2.5
Question 913
Square root of 0.9 is equal to
A. 0.03
B. 0.3
C. 0.9487
D. 0.9463
Question 914
If α + β = 90° and α:β = 2:1, then the ratio of cosα to cosβ is
A. 1:√3
B. 1:3
C. 1:√2
D. 1:2
Question 915
Which of the following is TRUE?
A. 1123>1294>15
B. 1294>1123>15
C. 15>1123>1294
D. 15>1294>1123
Question 916
tanAcosec2A is equal to
A. (1 + tan2A)cotA
B. (1 - tan2A)cotA
C. √[(1 + tan2A)cotA]
D. √[(1 - tan2A)cotA]
Question 917
The value of cos0 deg is
A. 0
B. infinite
C. not defined
D. 1
Question 918
[sinA/(1 + cosA)] + [(1 + cosA)/sinA] is equal to
A. 2secA
B. 2cosecA
C. 2tanA
D. 2cotA
Question 919
If 3x - 10 = -(2x + 5), then the numerical value of (x - 4)3 is
A. 27
B. 125
C. -125
D. -27
Question 920
If 2 cos θ = 2 – sin θ, then what is the value of cos θ?
A. 1 or 3/5
B. 1 or –1/2
C. –1 or–1/2
D. –1 or 3/5
Question 921
Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?
A. 4/5
B. 9/4
C. 4/9
D. 5/4
Question 922
PQR is an equilateral triangle whose side is 10 cm. What is the value (in cm) of the inradius of triangle PQR?
A. 5/√3
B. 10√3
C. 10/√3
D. 5√2
Question 923
What is the simplified value of (1– sin A cos A)(sin A + cos A)?
A. sin2A – cos2A
B. sin3A + cos3A
C. 0
D. 1
Question 924
What is the area (in sq cm) of a regular hexagon of side 9 cm?
A. 50√3
B. 300√3
C. 243√3/2
D. 200√3
Question 925
If cosA/(1 - sinA) = x, then the value of x is
A. secA - tanA
B. cosecA + tanA
C. secA + tanA
D. cosecA - tanA
Question 926
If (cosecA - 1)/(cosecA + 1) = x, then the value of x is
A. (sinA/(1 + cosA))2
B. cosA/(1 + sinA)
C. (cosA/(1 + sinA))2
D. sinA/(1 + cosA)
Question 927
Find the unit place digit in 192102 + 193103
A. 0
B. 1
C. 3
D. 5
Question 928
If x - y = 7 and x + y = 13, then x2 - y2 is
A. 91
B. -30
C. 30
D. -91
Question 929
If tan(A/2) = x, then the value of x is
A. sinA/(1 - cosA)
B. sinA/(1 + cosA)
C. √[sinA/(1 + cosA)]
D. √[sinA/(1 - cosA)]
Question 930
tan2Asin2A is equal to
A. tan2A - sin2A
B. tan2A + sin2A
C. cot2A - sin2A
D. cot2A + sin2A
Question 931
If x = 1 + √2 + √3, then the value of x2-2x-4=0
A. √6
B. 2√3
C. 3√2
D. 2√6
Question 932
A man spends in 8 months as much as he earns in 6 months. He saves Rs. 6000 in a year. His average monthly income is
A. Rs. 2400
B. Rs. 2000
C. Rs. 2150
D. Rs. 1800
Question 933
The solution set of 4x - 3y = 10 and 3x + y = 14 is
A. {(5, 3)}
B. {(4, 2)}
C. {(11, 1)}
D. {(2, 3)}
Question 934
If (6x - 1) - (8x - 5) = 7, then the value of x is _______ .
A. -3/2
B. 3/2
C. 11/2
D. -11/2
Question 935
If the zeroes of the polynomial x2 - ax + b are 3 and 4, then 'a' and 'b' are respectively equal to
A. 4, 3
B. 12, 7
C. 3, 4
D. 7, 12
Question 936
Find the value of x if 1-x24 = 1318
A. 155
B. 157
C. 159
D. 161
Question 937
What is the value of sin225°+ sin265°?
A. 0
B. 1
C. 2
D. 4
Question 938
If x2-3x+1=0, then x+1x is (x≠0)
A. 1
B. 0
C. 3
D. 2
Question 939
If cosec 45° - sin 30° = x, then x is
A. 5/√3
B. (√6-1)/√2
C. √3+2
D. (2√2-1)/2
Question 940
What is the value of (cos30° + 1/2) ?
A. (√3+1)/√3
B. (√2+1)/√2
C. (√3+1)/2
D. (2√3+1)/√3
Question 941
What is the area (in square units) of the figure enclosed by the x-axis, the y-axis and the line x + 2y = 6 ?
A. 3
B. 6
C. 9
D. 12
Question 942
If tanA + tanB = X, then the value of X is
A. (tanA - tanB)/(1 + tanAtanB)
B. (tanA + tanB)/(1 - tanAtanB)
C. (tanA + tanB)/(1 + tanAtanB)
D. (tanA - tanB)/(1 - tanAtanB)
Question 943
What is the value of cosec 120°
A. 2/√3
B. 2
C. -2/√3
D. -2
Question 944
If tanα = 2 - 1, then the value of tanα - cotα = ?
A. -2
B. √2 + 1
C. 1
D. 2√2
Question 945
If a - b = 2 and ab = 24, then what is the value of a3- b3?
A. 280
B. 124
C. 140
D. 152
Question 946
If x + (1/x) = 2, then what is the value of x21 + (1/x1331)?
A. 0
B. 1
C. 2
D. 3
Question 947
If A and B are the roots of the equation Ax2 – A2x + AB = 0, then what is the value of A and B respectively?
A. 1, 0
B. 1, 1
C. 0, 2
D. 0, 1
Question 948
P + Q = 2(P-Q). If Q = 10, what is the value of P?
A. 10
B. 40
C. 20
D. 30
Question 949
Mayur can complete a work in 27 hours. If he is joined by Jayantika who is 100% more efficient, in what time will they together finish the work?
A. 6 hours
B. 3 hours
C. 9 hours
D. 10 hours
Question 950
Find the value of 6813+6413314
A. 5
B. 6
C. 36
D. 216
Question 951
If cosec 135° = x, then the value of x is
A. √2
B. 2
C. -√2
D. 1/√3
Question 952
ΔXYZ is right angled at Y. If m∠X = 30 deg, then find the value of (sinZ + √3).
A. 4/√3
B. 5/√3
C. 4/3
D. 3√3/2
Question 953
A circle is inscribed in a square. If the length of the diagonal of the square is 14√2 cm, what is the area of the circle?
A. 308 sq cm
B. 462 sq cm
C. 154 sq cm
D. 616 sq cm
Question 954
In ΔPQR measure of angle Q is 90°. If cosP = 5/13, and PQ = 2.5cm, then what is the length (in cm) of side PR?
A. 6
B. 6.5
C. 4
D. 5.6
Question 955
What is the simplified value of 0.042+0.212-0.00840.043+0.213
A. 0.5
B. 2
C. 10.25
D. 10.3
Question 956
If Cos θ = 35/37, then what is the value of Cosec θ?
A. 37/12
B. 33/12
C. 35/12
D. 12/35
Question 957
If 1/√(cosec2A - 1) = x, then value of x is
A. cotA
B. tanA
C. sinA
D. cosA
Question 958
AB is a diameter of a circle. C is a point on the tangent drawn at A . If AB = 8 cm and AC = 6 cm , then the length of BC is
A. 10 cm
B. 14 cm
C. 5 cm
D. 7 cm
Question 959
If the expression px3 – 2x2 – qx + 18 is completely divisible by (x2 – 9), then what is the ratio between p and q respectively?
A. 1:9
B. 1:3
C. 3:1
D. 9:1
Question 960
If a2+b2+c2=83 and a+b+c=15 then the value of ab+bc+ca is
A. 69
B. 70
C. 71
D. 72
Question 961
What is the value 32cos 39sin 51-sin239 + sin251
A. 1/2
B. 5/2
C. 0
D. Both 1/2 and 5/2
Question 962
Shaan got a total of Rs. 912 in the denomination of equal numbers of Rs. 1, Rs. 5 and Rs. 10 coins. How many coins do Shaan posses?
A. 16
B. 57
C. 171
D. 323
Question 963
If 2sec2x - tan2x = 5 and 0° ≤ x ≤ 90° , then x = ?
A. 60°
B. 90°
C. 30°
D. 45°
Question 964
If cosθ + sinθ = m, secθ + cosecθ = n, what is m/n?
A. 1
B. sinθ cosθ
C. secθ cosecθ
D. cotθ tanθ
Question 965
If (x/a) + (y/b) = 3 and (x/b) – (y/a) = 9, then what is the value of x/y?
A. ( b + 3 a)/( a – 3 b)
B. ( a + 3 b)/( b – 3 a)
C. (1 + 3 a)/( a + 3 b)
D. ( a + 3 b2)/( b – 3 a2)
Question 966
Geetha weighs 11.235 kg. Her sister weighs 1.4 times her weight. Find their combined weight?
A. 15.729 kg
B. 25.964 kg
C. 26.964 kg
D. 26.946 kg
Question 967
If 1p+1q = 1p+q, then the value of p3-q3
A. p-q
B. pq
C. 1
D. 0
Question 968
What is the value of Sin 60° + (1/2)Cosec 45°?
A. (√3 + 2)/2
B. (√3 + √2)/√2
C. (√3 + 2)/√2
D. (√3 + √2)/2
Question 969
Point P (-2, 5) is the midpoint of segment AB. Co-ordinates of A are (-5, y) and B are (x, 3). What is the value of x?
A. 1
B. -1
C. 2
D. -2
Question 970
What is the value of 2 - 2z + z22 + 2z - z2, when z+2z = 2 ?
A. 0
B. 2
C. 4
D. 8
Question 971
For triangle ABC, what would be the equation of median AD if co-ordinates of A, B and C are (-5,4), (-4,0) and (-2,2) respectively?
A. 3x - 2y = -11
B. 3x + 2y = 7
C. 3x + 2y = -7
D. 3x - 2y = 11
Question 972
Determine the value of a2+b2a3+b3 when a = 2+√3 and b = 2-√3.
A. 0.27
B. 0.42
C. 0.58
D. 0.93
Question 973
For triangle ABC, find equation of median AD if co-ordinates of points A, B and C are (2,4), (3,0) and (5,2) respectively?
A. 3x - 2y = 14
B. 3x - 2y = 2
C. 3x + 2y = 14
D. 3x + 2y = 2
Question 974
Simplify 576b3x2a4z3/36a3b2z
A. 16bx2az2
B. 8bx2az2
C. 32ba2 z
D. 32bxa2
Question 975
If one root of the equation (1-m)x2 + 1 = 0 is double the other and 'I' is a real number, then which of the following is true?
A. m > 9/8
B. m> 8/9
C. m = 8/9
D. m <= 9/8
Question 976
What is the value of [(cos 3θ + 2cos 5θ + cos 7θ)÷(cos θ + 2cos 3θ + cos 5θ)] + sin 2θ tan 3θ?
A. cos 2θ
B. sin 2θ
C. tan 2θ
D. cot θ sin 2θ
Question 977
What is the value of 34+122 ?
A. 13
B. 15
C. 17
D. 19
Question 978
If x + √5 = 5 + √y, and x, y are positive integers, then the value of x+yx + y
A. 1
B. 2
C. √5
D. 5
Question 979
If cotA + cotB = x, then value of x is
A. (cotAcotB + 1)/(cotB - cotA)
B. (cotAcotB + 1)/(cotB + cotA)
C. (cotAcotB - 1)/(cotB + cotA)
D. (cotAcotB - 1)/(cotB - cotA)
Question 980
If x + 3y - 2z4 = 6, x + 232y + 3z = 33 and 17x + y +z + 2z =9, then what is the value of 46x+ 131y ?
A. 414
B. 364
C. 384
D. 464
Question 981
The difference of 18 and its reciprocal is equal to :
A. 1/8
B. 4/3
C. 15/16
D. 105/304
Question 982
What is the value of 36+729381+643
A. 5/12
B. 5/9
C. 4/9
D. 4/15
Question 983
If 11-13xx + 11-13yy + 11-13zz = 5 then what is the value of 1x + 1y + 1z = ?
A. 1
B. 13/11
C. 13/5
D. 4
Question 984
If x = (√2 + 1)/(√2 – 1), then what is the value of (x5 + x4 + x2 + x)/x3 ?
A. 5
B. 2
C. 2√3
D. 2√2
Question 985
∆XYZ is right angled at Y. If tanX = 24/7, then what is the value of cotZ ?
A. 25/7
B. 24/25
C. 7/24
D. 24/7
Question 986
Product of 6ab, 3b and 4a is
A. 72a2b2
B. 144ab
C. 72ab
D. 144a2b2
Question 987
What is the simplified value of sec6 A – tan6 A – 3 sec2 A tan2 A?
A. -1
B. 0
C. 1
D. sec A tan A
Question 988
The sum of 4x + 3y 7z, x y z and 2x 3y + 4z is
A. 3x - y - 4z
B. 3x - y + 4z
C. 3x + y - 4z
D. 3x + y + 4z
Question 989
If the equation 4x + 3y + 5 = 0 and 6x - ky - 7 = 0 have no solution, then the value of k is
A. -4.5
B. -8
C. 8
D. 4.5
Question 990
19 x 23 = 437. Then 190 x 0.023 = ?
A. 43.7
B. 4.37
C. 0.0437
D. 0.437
Question 991
The sum of the parallel sides of a trapezium is 12.4 cm. If the distance between the parallel sides is 3.5 cm, what is the area of this trapezium?
A. 43.4 sq cm
B. 86.8 sq cm
C. 130.2 sq cm
D. 21.7 sq cm
Question 992
If Cot θ = 21/20, then what is the value of Cosec θ?
A. 21/29
B. 29/21
C. 20/29
D. 29/20
Question 993
If (cotA - cosecA)2 = x, then the value of x is
A. (1 - cosA)/(1 + cosA)
B. (1 - sinA)/(1 + sinA)
C. (1 - secA)/(1 + secA)
D. (1 - cosecA)/(1 + cosecA)
Question 994
If a=101 then the value of a(a2-3a+3) is
A. 1000000
B. 1010101
C. 1000001
D. 999999
Question 995
If 10x/3 + 5/2(2 - x/3) = 7/2, then the value of x is?
A. 3/5
B. -5/3
C. 5/3
D. -3/5
Question 996
If [√(a2 + b2 + ab)] + [√(a2 + b2 – ab)] = 1, then what is the value of (1 – a2 )(1 – b2 )?
A. 1/4
B. 4/7
C. 5/4
D. 3/4
Question 997
The square root of 4096 is
A. 56
B. 68
C. 74
D. 64
Question 998
If α and β are the roots of the equation x2+ x – 1 = 0, then what is the equation whose roots are α5 and β5?
A. x2 + 7x – 1 = 0
B. x2 – 7x – 1 = 0
C. x2 – 11x – 1 = 0
D. x2 + 11x – 1 = 0
Question 999
The sum of 2xy(3x + 4y - 5z) and 5yz(2x - 3y) is
A. 6x2y - 8xy2 + 15y2z
B. 6x2y + 8xy2 - 15y2z
C. 6x2y + 8xy2 - 15y2z - 20xyz
D. 6x2y - 8xy2 + 15y2z + 20xyz
Question 1000
What is the reflection of the point (5, 2) in the line x = -3?
A. (-11 ,2)
B. (-11 ,-2)
C. (11 ,-2)
D. (11 ,2)
Question 1001
Solve the following : 3/4+{3/4 + 3/4 ÷ (3/4 + 3/4)} = ?
A. 0
B. 3/4
C. 1
D. 2
Question 1002
If (x + 1/x) = 3, then x8+1x8 is equal to
A. 2201
B. 2203
C. 2207
D. 2213
Question 1003
If √(1+tan2A) = x, then the value of x is
A. sinA
B. cosecA
C. secA
D. cosA
Question 1004
If 9x - 6(3 - x) = 12, then the value of x is
A. 2
B. 4
C. 6
D. 9
Question 1005
If 3x + 2y = 7 and 4x - y = 24, then x - y = ______.
A. 9
B. 1
C. -9
D. -1
Question 1006
What is the value of Sin 30- √2 Cos 30
A. (1 - √6)/√2
B. (1 - √6)/2
C. (3 - √6)/2
D. (3 - √6)/√2
Question 1007
If 5 sin2θ+ 4 cos2θ= 9/2 and 0 <θ<Π/2 then tanθ is equal to?
A. 1
B. 0
C. -1
D. 1/4
Question 1008
The value of x for which the expressions 15x + 4 and 13x - 2 become equal is ______
A. -1
B. 1
C. -3
D. 3
Question 1009
1/(secA + tanA) is equal to
A. cosecA - cotA
B. sinA - cosA
C. secA - tanA
D. sinA + cosA
Question 1010
If 12x = 192- 112, what is the value of x?
A. 20
B. 17
C. 13
D. 11
Question 1011
Two points P and Q are at the distance of x and y (where y > x) respectively from the base of a building and on a straight line. If the angles of elevation of the top of the building from points P and Q are complementary, then what is the height of the building?
A. xy
B. √( y/ x)
C. √( x/ y)
D. √( xy)
Question 1012
What is the value of (sinA - 2sin3A)/(2cos3A - cosA)?
A. cotA
B. cosecA
C. secA
D. tanA
Question 1013
If 2x+29x = 4, then the value of 27x3+127x3
A. 180
B. 198
C. 234
D. 252
Question 1014
In a farm, there are goats and peacocks. If the number of heads are 60 and the number of feet are 170, then the number of goats = ?
A. 18
B. 20
C. 23
D. 25
Question 1015
The value of (1 - √2) + (√2 - √3) + (√3 - √4) + ..... + (√15 - √16) is
A. 0
B. 1
C. -3
D. 4
Question 1016
The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
A. Rs. 3500
B. Rs. 3750
C. Rs. 3840
D. Rs. 3900
Question 1017
Δ XYZ is right angled at Y. If m∠Z = 60°, what is the length of YZ (in cm), if ZX = 3√3 cm?
A. 3√3/2
B. 3√3
C. 9
D. 6
Question 1018
If a - b = 1 and ab = 6, then what is the value of a3- b3?
A. 21
B. 23
C. 19
D. 25
Question 1019
If x2-2x+1=0, then the value of x4+1x4 is
A. 0
B. 1
C. 2
D. 3
Question 1020
If a4 + 1 = [a2 /b2 ] (4b2 – b4 – 1), then what is the value of a4 + b4?
A. 2
B. 16
C. 32
D. 64
Question 1021
What is the value of sin6θ + cos6θ + 3 sin2θ cos2θ –1?
A. 0
B. 1
C. 2
D. 4
Question 1022
∆ABC is right angled at B. If m∠A = 30°., then Sec C =?
A. 1/2
B. 1/√2
C. 2
D. 1/√3
Question 1023
Find the value of '?' in 512 × 125 ÷ 15625 = 3125 × 25?
A. 4
B. 3
C. 2
D. 1
Question 1024
What is the value of Cot 45°+ 1/3 Cosec 60°?
A. √3 + 2
B. (9 + 2√3)/9
C. √3
D. (2√2 + 3)/√6
Question 1025
What is the value of [(sin x + sin y) (sin x – sin y)]/[(cosx + cosy) (cosy – cosx)]?
A. 0
B. 1
C. – 1
D. 2
Question 1026
If √(1 + cot2A) = x, then the value of x is
A. secA
B. sinA
C. cosecA
D. cosA
Question 1027
If x(2x + 3) = 90 and 7y-1/2+ 2y-1/2= y1/2 (x and y are positive numbers), then what is the value of x2+ y2?
A. 45
B. 109
C. 117
D. 126
Question 1028
If (8 - 10x) - (13x - 2) = -9, then the value of x is
A. -19/23
B. 19/23
C. -1/23
D. 1/23
Question 1029
If a + b = 1 and ab = -6, then what is the value of a3+ b3?
A. 17
B. 15
C. 19
D. 13
Question 1030
For triangle PQR, what is the equation of altitude PS if coordinates of P, Q and R are (5,1), (0,4) and (2,3) respectively?
A. 7x + 2y = 33
B. 2x - 7y = 9
C. 2x - 7y = -3
D. 7x + 2y = -33
Question 1031
If 2x-12x = 5, then what is the value x2 + 116x2 - 2
A. 19/4
B. 23/4
C. 27/4
D. 31/4
Question 1032
The value of the expression 2(sin6θ+cos6θ) - 3(sin4θ+cos4θ) + 1 is
A. -1
B. 0
C. 1
D. 2
Question 1033
If 7x - 5y = 13 and 2x - y = 5, then (x - y) is
A. 3
B. 4
C. 5
D. 1
Question 1034
The value of cos (1110°) is
A. √3/2
B. 1/2
C. 1/√2
D. 1
Question 1035
What is the value of Tan 60 + Cosec 60?
A. 5/3
B. 2/√3
C. 5/√3
D. 2/3
Question 1036
If cosec 4π/3 = x, then the value of x is
A. √2
B. 2/√3
C. √2
D. -1/√3
Question 1037
The average of 100 observations was calculated as 35.It was found later, that one of the observation was misread as 83 instead of 53. The correct average is :
A. 32.7
B. 34.7
C. 35.7
D. 36.7
Question 1038
Reduce 2530/1430 to lowest terms.
A. 47/17
B. 23/13
C. 47/19
D. 29/17
Question 1039
Find x, if 5x-6+5x+6 = 6
A. -4
B. 0
C. 2
D. 4
Question 1040
If Cosec θ = 17/8, then Cot θ = ?
A. 17/8
B. 15/8
C. 8/15
D. 17/15
Question 1041
If Sec θ = 25/24 , then what is the value of Sin θ?
A. 24/25
B. 7/25
C. 24/7
D. 25/7
Question 1042
If (333 + 333 + 333) (233 + 233) = 6x, then what is the value of x?
A. 34
B. 35
C. 33
D. 33.5
Question 1043
199994 x 200006 = ?
A. 39999799964
B. 39999999864
C. 39999999954
D. 39999999964
Question 1044
Solve : 12 - [26 - {2 + 5 x (6 - 3)}]
A. 2
B. 3
C. 7
D. 8
Question 1045
The first and last terms of an arithmetic progression are 37 and 18. If the sum of the series is 114, then it has how many terms?
A. 13
B. 12
C. 14
D. 15
Question 1046
If 3x + 4y – 11 = 18 and 8x – 6y + 12 = 6, then what is the value of 5x – 3y – 9?
A. 18
B. – 9
C. – 27
D. – 18
Question 1047
A root of equation ax2 + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3√3. What is the value of (a2 + b2 + c2)/(a + b + c)?
A. 35/3
B. 37/3
C. – 105/11
D. – 105/13
Question 1048
If x+1x=5, then 6xx2+x+1 value is
A. 3
B. 2
C. 1
D. 0
Question 1049
Coefficient of x2 in (x + 9)(6 - 4x) is
A. 54
B. -4
C. 30
D. 4
Question 1050
If (x - 4) (x2 + 4x + 16) = x3 - P, then P is equal to
A. 27
B. 8
C. 64
D. 0
Question 1051
If (x – y) = 7, then what is the value of (x – 15)3 – (y – 8)3?
A. 0
B. 343
C. 392
D. 399
Question 1052
If a3 + b 3 = 35 and ab = 6, then what is the value of a + b?
A. 5
B. 8
C. 2
D. -8
Question 1053
If a+b=5 then the value of a-37+b-27 is
A. 27
B. 37
C. 1
D. 0
Question 1054
Calculate the value of 61681x61681-31681x3168130000
A. 93352
B. 94362
C. 93362
D. 95362
Question 1055
What is the value of √2 Sec 45° + (1/√3)Tan 30°?
A. (1 + √3)/2
B. (1 + 3√2)/√3
C. 7/3
D. (3 + 2√2)/3√2
Question 1056
What is the simplest form of (1 + cosA)(cosecA cotA)?
A. cosA
B. tanA
C. cotA
D. sinA
Question 1057
If cot 240° = x, then the value of x is
A. -1
B. -1/√3
C. 1/√3
D. √3
Question 1058
If 2(3x-2) < 6-3x and 6x + 2(6-x) > 2x-2, then x can take which of the following values?
A. -8
B. 5
C. 8
D. -5
Question 1059
If x = a + 1a, y = a - 1a ,(a>0), then the value of x4+y4-2x2y2 is
A. 16
B. 20
C. 10
D. 5
Question 1060
If a+b+c = 0, then (a^3 + b^3 + c^3)^2 = ?
A. 27abc
B. 9abc
C. 3abc
D. 9a^2b^2c^2
Question 1061
If 5(4 - x) - 4 > 5x -2 > 2x - 6, then the value of x is
A. -2
B. 2
C. -1
D. 3
Question 1062
If secθ = cosecq with 0° < θ , q < 90°, then the value of sin (θ + q) is
A. 1
B. 0
C. 2
D. 4
Question 1063
If 4x - 7y = 3 and 2x - y = 9, then x - y is.
A. 3
B. 4
C. 5
D. 6
Question 1064
If ab-1b=cb-1c=ac-1a, then ac+ba+cb
A. 1
B. 2
C. 3
D. 4
Question 1065
∆ABC is right angled at B. If m∠A = 45°, then find the value of (coseC + 1/√3).
A. (3√2+1)/3
B. (2+√3)/2
C. 5/√3
D. (√6+1)/√3
Question 1066
If x2+ y2+ z2= xy + yz + zx, then what is the value of (7x + 3y – 5z)/5x?
A. 0
B. 1
C. 5
D. 33/5
Question 1067
If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ?
A. 500
B. 1000
C. 1500
D. 2000
Question 1068
The sum of a fraction and 4 times its reciprocal is 13/3. What is the fraction?
A. 4/3
B. 3/4
C. 5/4
D. 4/5
Question 1069
Which of the following is correct?
A. (3x - 2y)2 = 9x2 - 12xy + 4y2
B. (3x - 2y)2 = 9x2 - 6xy + 4y2
C. (3x + 2y)2 = 9x2 - 12xy + 4y2
D. (3x + 2y)2 = 9x2 - 6xy + 4y2
Question 1070
38% of 7500 + ?% of 375 = 50% of 6000
A. 50
B. 40
C. 60
D. 45
Question 1071
If 9x2 + 16y2 = 60 and 3x + 4y = 6, then the value of xy is
A. -1
B. 1
C. -2
D. 2
Question 1072
If a = 299, b = 298, c = 297 then the value of 2a3 + 2b3 + 2c3 - 6abc is
A. 5154
B. 5267
C. 5364
D. 5456
Question 1073
Δ LMN is right angled at M. If m∠N = 60°, then Tan L =______.
A. 1/2
B. 1/√3
C. 1/√2
D. 2
Question 1074
α and β are the roots of quadratic equation. If α + β = 8 and α – β = 2√5, then which of the following equation will have roots α4 and β4?
A. x2 – 1522x + 14641 = 0
B. x2 + 1921x + 14641 = 0
C. x2– 1764x + 14641 = 0
D. x2+ 2520x + 14641 = 0
Question 1075
Which of the following quadratic equations has real roots?
A. 4x2 - 3x + 6 = 0
B. 2x2 + 7x + 6 = 0
C. x2 - 2x + 4 = 0
D. 3x2 - 4x + 3 = 0
Question 1076
If a-b=1 and a3-b3 = 61, then the value of ab will be
A. -20
B. 20
C. 30
D. 60
Question 1077
Simplify (533bxaz)/(41ab)
A. 17xzb
B. 19xz
C. 13xz
D. 31ab
Question 1078
If x = 6+26, then what is the value of x-1 + 1x-1 ?
A. 2√3
B. 3√2
C. 2√2
D. 3√3
Question 1079
Find the sum of interior angles of a dodecagon?
A. 1620°
B. 1800°
C. 1440°
D. 1260°
Question 1080
If (1 - cosA)/(1 + cosA) = x, then the value of x is
A. (cotA + cosecA)2
B. (cotA - cosecA)2
C. cotA - cosecA
D. cotA + cosecA
Question 1081
What is the value of sin (90° + 2A)[4 – cos2(90° – 2A)]?
A. 2(cos3 A – sin3 A)
B. 2(cos3 A + sin3 A)
C. 4(cos6 A+ sin6 A)
D. 4(cos6 A – sin6 A)
Question 1082
If 2x-y2+(3y-2z)2=0, then the ratio of x:y:z is
A. 1 : 3 : 2
B. 1 : 2 : 3
C. 3 : 1 : 2
D. 3 : 2 : 1
Question 1083
If √(1 - cos2A) = x, then the value of x is
A. cosecA
B. sinA
C. tanA
D. secA
Question 1084
If x2 + y2 + 6x + 5 = 4(x - y) then x - y is
A. 1
B. -1
C. 0
D. 4
Question 1085
Solve : 1000x - 5 = -6
A. 1/1000
B. -1/1000
C. -11/1000
D. 11/1000
Question 1086
A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook ?
A. 15
B. 20
C. 10
D. 8
Question 1087
The measures of the three angles of a triangle are in the ratio 1:2:3. What is the measure of the biggest angle?
A. 30°
B. 60°
C. 90°
D. 120°
Question 1088
ABCD is a parallelogram. Co-ordinates of A, B and C are (5,0), (-2,3) and (-1,4) respectively. What will be the equation of line AD?
A. y = 2x - 5
B. y = x + 5
C. y = 2x + 5
D. y = x - 5
Question 1089
Find the value of x if 0.08x + 0.04y = 10 and 0.2(x-1) + 0.4y = 24.8
A. 125
B. 150
C. 1.25
D. 12.5
Question 1090
What is the value of z2+1z2 when z = 5+26 ?
A. 49
B. 50
C. 98
D. 100
Question 1091
10 dozen apples, 15 dozen mangoes & 20 dozen oranges are kept for sale. 1/2, 1/3rd & 1/4th of each item respectively have been added. What is the total number of fruits kept for sale now?
A. 720
B. 600
C. 580
D. 820
Question 1092
If 31x + 31y = 403, then what is the average of x and y?
A. 3.5
B. 5
C. 6.5
D. 13
Question 1093
At what point does the line 2x + 5y = -6 cuts the X-axis?
A. (3, 0)
B. (0, 3)
C. (-3, 0)
D. (0, -3)
Question 1094
If sec (3x – 20°) = cosec (3y + 20°), then what is the value of tan (x + y)?
A. 1
B. √3
C. 1/√3
D. 2√3
Question 1095
If √[(1 - cosA)/2] = x, then the value of x is
A. cos(A/2)
B. tan(A/2)
C. sin(A/2)
D. cot(A/2)
Question 1096
What is the value of {sin (90 – x) cos [π – (x – y)]} + {cos (90 – x) sin [π – (y – x)]}?
A. -cos y
B. -sin y
C. cos x
D. tan y
Question 1097
Two equal circles intersect such that each passes through the centre of the other. If the length of the common chord of the circles is 10√3 cm, then what is the diameter of the circle?
A. 10 cm
B. 15 cm
C. 20 cm
D. 30 cm
Question 1098
The value of cos(1110) is
A. √3/2
B. 1/2
C. 1/√2
D. 1
Question 1099
For triangle PQR, find equation of altitude PS if co-ordinates of P, Q and R are (6,2), (0,3) and (-4,5) respectively?
A. 2x - y = 14
B. 2x + y = 10
C. 2x - y = 10
D. 2x + y = 14
Question 1100
If 11+11+11+1x = 58, then what is the value of x?
A. 2
B. 3
C. 1
D. 4
Question 1101
cot2A + cos2A is equal to
A. (cosecA - sinA)2(cosecA + sinA)
B. (cosecA + sinA)(cosecA - sinA)
C. (secA + sinA)(secA - sinA)
D. (secA - sinA)2(secA + sinA)
Question 1102
If A = (-14 + 4) and B = 4 - 14, then AB =
A. 0
B. -100
C. 100
D. -1
Question 1103
On dividing 8a2b2c2 by 4a2, we get
A. 2b2
B. 2c2
C. 2b2c2
D. 2
Question 1104
If a + b = 8 and ab =15, then a3 + b3 is
A. 224
B. 244
C. 152
D. 128
Question 1105
If secθ + tanθ = 4, then secθ - tanθ = ?
A. 1
B. 0.25
C. 0.5
D. 0.75
Question 1106
ABC is a right angled triangle. ∠BAC = 90 deg and ∠ACB = 60 deg. What is the ratio of the circum radius of the triangle to the side AB?
A. 1 : 2
B. 1 : √3
C. 2 : √3
D. 2 : 3
Question 1107
If √(1 + cot2A)/cotA = x, then the value of x is
A. sinA
B. cosecA
C. secA
D. cosA
Question 1108
5 bottles cost as much as 2 bags. The cost of 15 bottles and 4 bags is Rs 2,000. What is the price (in Rs.) of a single bag?
A. 200
B. 215
C. 240
D. 250
Question 1109
Value of (cos 53° - sin 37°) is
A. 2 sin 37 ̊
B. 2 cos 53 ̊
C. 0
D. 1
Question 1110
If a = 2 , b = 3 then the value of 27a3 - 54a2b + 36ab2 - 8b3 is
A. 1562
B. 1616
C. 1676
D. 1728
Question 1111
The value of x for which the expressions 15 7x and 15x + 7 become equal is _____.
A. -4/11
B. 11/4
C. -11/4
D. 4/11
Question 1112
If (1 + sinA)/cosA + cosA/(1 + sinA) = x, then the value of x is
A. 2cosecA
B. 2cosec2A
C. 2sec2A
D. 2secA
Question 1113
What is the simplified value of sec4θ – sec2θ tan2θ?
A. cosec2θ
B. Cot2θ
C. sec2 θ
D. secθ tan θ
Question 1114
If (1/cos θ) – (1/cot θ) = 1/P, then what is the value of cos θ?
A. (P + 1)/(P – 1)
B. (P2+ 1)/2P
C. 2(P2+ 1)/P
D. 2P/(P2+ 1)
Question 1115
What is the value of cos (90 – B) sin (C – A) + sin (90 + A) cos (B + C) – sin (90 – C) cos (A + B)?
A. 1
B. sin ( A + B – C)
C. cos ( B + C – A)
D. 0
Question 1116
Calculate the value of 61681 x 61681 - 31681 x 3168130000?
A. 93352
B. 94362
C. 93362
D. 95362
Question 1117
The sum of a fraction and 3 times its reciprocal is 37/10. What is the fraction?
A. 5/2
B. 2/5
C. 5/4
D. 4/5
Question 1118
What is the equation of a line of slope 1/3 and y-intercept 5?
A. x - 3y = -15
B. x - 3y = 15
C. x + 3y = -15
D. x + 3y = 15
Question 1119
If secA + tanA = x, then the value of x is
A. cosA/(1 + sinA)
B. √[cosA/(1 - sinA)]
C. √[cosA/(1 + sinA)]
D. cosA/(1 - sinA)
Question 1120
For x > 0, what is the minimum value of x + x+22x?
A. 1
B. 2
C. 2.5
D. 1.5
Question 1121
An army lost 10% of its men in war, 10% of the remaining died due to disease and 10% of the rest were declared disabled. Thus the strength of the army was reduced to 7,29,000 active men. The original strength of the army was
A. 1500000
B. 1000000
C. 1200000
D. 1100000
Question 1122
A ship is full of cargo containers. It drops 2/3 of cargo containers at the first port and takes 60 more, at the second port it drops two third of the new total and takes eleven more. On arriving at the third port it is found that it have 48 cargo containers. Find the number of cargo containers in the ship at the starting?
A. 189
B. 159
C. 161
D. 153
Question 1123
A tetrahedron has 4 vertices. How many edges does it have?
A. 8
B. 12
C. 6
D. 10
Question 1124
If a = 73, b = 74 and c = 75, then what is the value of a3 + b3 + c3 – 3abc?
A. 365
B. 444
C. 666
D. 999
Question 1125
If tanA - tanB = X, then the value of X is
A. (tanA + tanB)/(1 - tanAtanB)
B. (tanA + tanB)/(1 + tanAtanB)
C. (tanA - tanB)/(1- tanAtanB)
D. (tanA - tanB)/(1 + tanAtanB)
Question 1126
Point P is the midpoint of seg AB. Co-ordinates of P are (-1,1) and A are (4,3). What are the co-ordinates of point B?
A. (6, 1)
B. (-6, 1)
C. (6, -1)
D. (-6, -1)
Question 1127
Square of (3x – 5xy) is
A. 9x2 - 30x2y + 25x2y2
B. 9x2 - 15x2y + 25x2y2
C. 25x2 - 15x2y + 9x2y2
D. 25x2 - 30x2y + 9x2y2
Question 1128
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
A. 20
B. 80
C. 100
D. 200
Question 1129
ΔDEF is right angled at E. If secD = 25/7, then what is the value of cosecF ?
A. 7/25
B. 24/7
C. 25/7
D. 7/24
Question 1130
Coefficient of x in (x + 9)(8 - 5x) is
A. 37
B. -53
C. -37
D. 53
Question 1131
If a + b = 10 and ab = 24, then what is the value of a3 + b3?
A. 280
B. 152
C. 140
D. 72
Question 1132
What is the value of (sin60° - 2/√3) ?
A. -1/2√3
B. -1/2
C. 1/√3
D. (1-2√3)/2
Question 1133
If Tan θ = 7/24, then what is the value of Cosec θ?
A. 25/24
B. 25/7
C. 24/7
D. 24/25
Question 1134
ΔPQR is right angled at Q. If cosP = 5/13, then what is the value of cosecR ?
A. 13/5
B. 5/12
C. 5/13
D. 13/12
Question 1135
sinA/(1 + cos A) is equal to
A. (cosecA - cotA)
B. (cosecA + cotA)
C. √[(cosecA - cotA)]
D. √[(cosecA + cotA)]
Question 1136
If √x - √y = 1 , √x + √y = 17 then √xy = ?
A. √72
B. 72
C. 32
D. 24
Question 1137
What is the equation of the line which passes through the points (3,2) and (5,3)?
A. 5x - 2y = -19
B. 5x - 2y = 19
C. 5x + 2y = 31
D. 5x + 2y = -31
Question 1138
What is the value of (1/√3 + sin45 ) ?
A. √3+2
B. (√2+√3)/√6
C. (1+√6)/√3
D. (4+√3)/2
Question 1139
If α and β are the roots of equation x2 – x + 1 = 0, then which equation will have roots α3 and β3?
A. x2 + 2x + 1 = 0
B. x2 – 2x – 1 = 0
C. x2 + 3x – 1 = 0
D. x2 – 3x + 1 = 0
Question 1140
If P2+1P2 = 47, then the value of P + 1P is
A. 5
B. 6
C. 7
D. 8
Question 1141
What is the value of [(cos32θ + 3 cos 2θ)÷(cos6θ – sin6θ)]?
A. 0
B. 1
C. 2
D. 4
Question 1142
If (4x - 3) = (3x + 8), then the numerical value of(x + 1)3 is
A. 1331
B. 1000
C. 1728
D. 729
Question 1143
What is the value of (cosec30 - 1/√3)?
A. (2√3-1)/√3
B. (√3-4)/2√3
C. -1/√3
D. 2/√3
Question 1144
What is the value of xy if x - y = 3 and x2+y2=15?
A. 1
B. 3
C. 5
D. 7
Question 1145
If √(sec2A - 1)/secA = x, then the value of x is
A. cosecA
B. cosA
C. sinA
D. tanA
Question 1146
If the value of √42 is approximately 6.480, then what is the approximate value of √(6/7)?
A. 0.925
B. 0.935
C. 0.945
D. 0.955
Question 1147
If 310 × 272 = 92 × 3n then the value of n is
A. 10
B. 12
C. 15
D. 20
Question 1148
The pair of linear equations 3x + y = 1 and px + 2y = 5 has no finite solution if
A. p>=6
B. p = 6
C. 0 < p < 6
D. p = 0
Question 1149
∆PQR is right angled at Q. If sinP = 12/13, then what is the value of tanR?
A. 5/13
B. 13/5
C. 13/12
D. 5/12
Question 1150
Anuj runs 1 2/3 laps of 7 laps race, find the remaining laps to be run.
A. 16/3
B. 14/3
C. 11/3
D. 10/3
Question 1151
If 2x + 3 = 9 then find the value of 3x + 2
A. 12
B. 16
C. 13
D. 11
Question 1152
By how much is three-fifth of 350 greater than four-seventh of 210 ?
A. 90
B. 100
C. 110
D. 120
Question 1153
If x = cosecθ - sinθ and y = secθ - cosθ, then the relation between x and y is
A. x2+ y2+ 3 =1
B. x2y2 (x2+ y2+3)=1
C. x2 (x2+ y2 - 5)=1
D. y2 (x2+ y2 - 5)=1
Question 1154
If cosx.cosy + sinx.siny = -1 then cosx + cosy is
A. -2
B. 1
C. 0
D. 2
Question 1155
What is the difference between the total sale of English newspapers and the total sale of Hindi newspapers in all the localities together.
A. 7500
B. 5600
C. 6500
D. 5700
Question 1156
What is the value of [sin (90– 10θ) – cos (p – 6θ)]/ [cos (p/2 – 10θ) – sin (p – 6θ)]?
A. tan 2θ
B. cot 2θ
C. cot θ
D. cot 3θ
Question 1157
Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
A. 1/7
B. 1/8
C. 1/9
D. 7/8
Question 1158
√(1 + tan2A)/tanA is equal to
A. secA
B. sinA
C. cosecA
D. cosA
Question 1159
If 60/75 is equivalent to 4/x, then the value of x is
A. 5
B. 4
C. 15
D. 18
Question 1160
Coefficient of x in (x + 11)(3 - 5x) is _____.
A. 33
B. -5
C. 3
D. -52
Question 1161
What is the simplified value of 31253 + 4253 + 36753
A. 18253
B. 5253
C. 9√125
D. 1253
Question 1162
A sum of Rs. 1360 has been divided among A, B and C such that A gets 2/3 of what B gets and B gets 1/4 of what C gets. B's share is:
A. Rs. 120
B. Rs. 160
C. Rs. 240
D. Rs. 300
Question 1163
If cos -300° = x, then the value of x is
A. 1/2
B. -1/√2
C. -1/2
D. √3/2
Question 1164
If a + b = 10 and ab = 21, then the value of (a - b)2 is
A. 15
B. 16
C. 17
D. 18
Question 1165
If cos 21° = x/y, then cosec 21° - cos 69° is equal to
A. x2yy2-x2
B. y2xy2-x2
C. y2xx2-y2
D. x2yx2-y2
Question 1166
If tan2θ + cot2θ = 2, then what is the value of 2sec θ cosec θ?
A. 0
B. 1
C. 2
D. 4
Question 1167
If 3x2 = 102 - 52, find the value of x?
A. 7
B. 5
C. 9
D. 11
Question 1168
Given w = -2, x = 3, y = 0 & z = -1/2. Find the value of (z/w) + x.
A. 13/4
B. -13/4
C. 3.2
D. 3.5
Question 1169
If cotA = x, then the value of x is
A. √(sec2A + 1)
B. √(cosec2A + 1)
C. √(sec2A - 1)
D. √(cosec2A - 1)
Question 1170
What is the value of sec 30° + cot 30°?
A. (√6-1)/√2
B. √3+2
C. 5/√3
D. (√3-2√2)/√6
Question 1171
What are the components of X6 - X4 - X5 - X4 + X2 - 4?
A. (X - 1)
B. (X + 2)
C. Both 1 and 2
D. Neither 1 nor 2
Question 1172
If cot(A/2) = x, then the value of x is
A. cosecA - cotA
B. cosecA + cotA
C. secA + cotA
D. secA - cotA
Question 1173
If x + 1/x = √13, then 3x(x2-1) equal to
A. 3√13
B. √13/3
C. 1
D. 3
Question 1174
If x = 1 – y and x2 = 2 – y2, then what is the value of xy?
A. 1
B. 2
C. -1/2
D. -1
Question 1175
If P=9, Q=17 then the value of p2-q2-13
A. 4
B. 1/4
C. 3
D. 1/3
Question 1176
What are the coordinates of the centroid of a triangle, whose vertices are A(2,5), B(4,4) and C(7,3)?
A. (4,-3)
B. (-1,0)
C. (-3,-3)
D. (3,-2)
Question 1177
Δ PQR is right angled at Q. If m√R = 30°, then what is the value of Cot P?
A. 1/2
B. 1/√2
C. 1/√3
D. 2
Question 1178
Reflection of the point (2,5) in the x axis is
A. (2,5)
B. (-2,5)
C. (2,-5)
D. (-2,-5)
Question 1179
What is the simplified value of 18 - 12 ?
A. 5/√2
B. 5√2
C. 2√5
D. 2/√5
Question 1180
If 23x + 23y = 184, then what is the average of x and y?
A. 2
B. 4
C. 3
D. 2.5
Question 1181
If cot -4π/3 = x, then the value of x is
A. -1
B. -1/√3
C. √3
D. 1
Question 1182
If (x – 2)2 + (y + 3)2 + (z – 15)2 = 0, then what is the value of x + y + z – 5?
A. 5
B. 9
C. 15
D. 20
Question 1183
If x+y+z = 1, 1/x + 1/y + 1/z = 1 and xyz = -1, then x3+y3+z3 is equal to
A. -1
B. 1
C. -2
D. 2
Question 1184
If cos -11π/6 = x, then the value of x is
A. -√3/2
B. 1/2
C. -2
D. √3/2
Question 1185
The distance between the points (7,7) and (k,-5) is 13. Find k?
A. -2
B. 4
C. -4
D. 2
Question 1186
What is the value of cosec 3π/4?
A. -√2
B. √2
C. 2/√3
D. -2/√3
Question 1187
When x2+ax+b is divided by (x-1), the remainder is 15 and when x2+bx+a is divided by (x+1), the remainder is -1, then the value of a2+b2 is
A. 10
B. 20
C. 8
D. 16
Question 1188
If cosθ1-sinθ+cosθ1+sinθ = 4, then the value of θ (0°<θ<90°)?
A. 60°
B. 45°
C. 30°
D. 35°
Question 1189
What is the value of the expression a3 - 5 + 2816a, when a = 2?
A. 2
B. 5
C. 7
D. 8
Question 1190
ΔPQR is right angled at Q. If secP = 13/5, then what is the value of sinR ?
A. 5/13
B. 5/12
C. 13/5
D. 13/12
Question 1191
The co-ordinates of the centroid of a triangle ABC are (3,-2). What are the co-ordinates of vertex C if co-ordinates of A and B are (-2,5) and (6,-2) respectively?
A. (-5,-9)
B. (5,-9)
C. (5,9)
D. (-5,9)
Question 1192
What is the value of a2 + b2a3 - b3, when a + b = 8 and a - b = 2?
A. 0.313
B. 0.347
C. 0.368
D. 0.381
Question 1193
If tan -5π/3 = x, then the value of x is
A. √3
B. 1
C. -1/2
D. √3/2
Question 1194
What is the value of 5.6x0.36+0.42x3.20.8 x 2.1 ?
A. 2
B. 1
C. 3
D. 3/2
Question 1195
What is the value of cot 5π/3?
A. 1/√3
B. -1/√3
C. √3
D. -√3
Question 1196
The least value of tan2x + cot2x is
A. 3
B. 2
C. 0
D. 1
Question 1197
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
A. 30 birds
B. 60 birds
C. 72 birds
D. 90 birds
Question 1198
Δ XYZ is right angled at Y. If m∠Z = 60°, then what is the value of (1/√2) Sec X?
A. 2/√3
B. 1/√6
C. 1/√3
D. 2/√6
Question 1199
Which of the following pair of numbers is the solution of the equation 3x+2+ 3–x= 10 ?
A. 0, 2
B. 0, -2
C. 1, -1
D. 1, 2
Question 1200
If 1/3(12x/5 - 1/2) + 6/5 = 7/6, then what is the value of x?
A. 1/6
B. -1/6
C. 1/5
D. -1/5
Question 1201
If 2cosAsinB = x, then the value of x is?
A. sin(A+B) + sin(A-B)
B. cos(A+B) + cos(A-B)
C. sin(A+B) - sin(A-B)
D. cos(A-B) - cos(A+B)
Question 1202
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed :
A. 30 birds
B. 60 birds
C. 72 birds
D. 90 birds
Question 1203
If 1 = 2, 3 = 6, 4 = 8, and + = -, what would be the value of 41 + 34 + 13 = ?
A. -88
B. 88
C. 12
D. -12
Question 1204
If m n = 2 , mn = 15 , (m , n > 0) then the value of m2-n2m3-n3
A. 1856
B. 1658
C. 1586
D. 1568
Question 1205
Which of the following is not a quadratic equation?
A. 3x(x + 5) 11 = 2x(x - 2) + 6
B. 4x(x + 3) + 7 = 4x(x - 11) + 9
C. x(x + 2) 15 = x(2x - 5) + 11
D. 4x - 6x + 9 = 0
Question 1206
If 9x = 24311, then what is the value of x?
A. 5/11
B. 5/22
C. 5/7
D. 5/33
Question 1207
If cos 240° = x, then value of x is
A. -1/√2
B. -√3/2
C. 1/2
D. -1/2
Question 1208
Determine the value of z in the equation: z = 20+20+20+20+...∞
A. 4
B. 5
C. 20
D. 25
Question 1209
If x2 – 4x + 1 = 0, then what is the value of x9 + x7 – 194x5 – 194x3?
A. 4
B. – 4
C. 1
D. – 1
Question 1210
If a + b = 10 and ab = 24, then the value of a3 + b3 is
A. 280
B. 370
C. 520
D. 730
Question 1211
A 8 cm long perpendicular is drawn from the centre of a circle to a 12 cm long chord. The diameter of the circle is
A. 10 cm
B. 12 cm
C. 16 cm
D. 20 cm
Question 1212
What is the value of Cot 60 - Sec 30?
A. -1/3
B. -1/√3
C. 1/√3
D. 1/3
Question 1213
Point P is the midpoint of segment AB. Co-ordinates of P are (5, -1) and A are (2, -4). What are the co-ordinates of point B?
A. (6, 4)
B. (8, 2)
C. (1,-2)
D. (-6, -2)
Question 1214
The slope of the line passing through the points (2,-1) and (x,5) is -1. Find x?
A. 4
B. -4
C. 8
D. -8
Question 1215
The first and last terms of an arithmetic progression are 25 and 52. What is the sum of the series if it has 12 terms?
A. -162
B. -110
C. 162
D. 110
Question 1216
What is the equation of the line whose y-intercept is 4 and making an angle of 45° with the positive x-axis?
A. x + y = -4
B. x - y = 4
C. x + y = 4
D. x - y = -4
Question 1217
What is the value of 23+5252-23 ?
A. 9
B. 49
C. 561
D. 571
Question 1218
What is the slope of the line 2x - 5y = 12?
A. 2/5
B. 5/2
C. -2/5
D. -5/2
Question 1219
If X + Y + Z = 9 then the value of (X - 4)3 + (Y - 2)3 + (Z - 3)3 - 3 (X - 4) (Y - Z) (Z - 3) is
A. 6
B. 9
C. 0
D. 1
Question 1220
A line passing through the origin perpendicularly cuts the line 3x - 2y = 6 at point M. Find M?
A. (18/13, 12/13)
B. (18/13, -12/13)
C. (-18/13, -12/13)
D. (-18/13, 12/13)
Question 1221
If sin - 4π/3 = x, then the value of x is
A. -2
B. -2/√3
C. √3/2
D. √2
Question 1222
Solve the following 7 x {4 + (-2) x (-3)} = ?
A. 14
B. -42
C. -14
D. 70
Question 1223
If 5x - 5(3x - 2) < 4x - 1 < 2 + 2x, then x can take which of the following values?
A. 2
B. 1
C. -1
D. -2
Question 1224
Simplify (b2x 3a2z4 ) × (b2x 4a4z3 )/(a3b2z4 )
A. b2x7a3z3
B. b3x7a3 z3
C. b2x5a3 z3
D. b2x7a3z2
Question 1225
What is the simplified value of (sec A + cos A)(sec A – cos A)?
A. 2 tan2A
B. 2 sin2 A
C. sin2 A tan2 A
D. sin2A + tan2 A
Question 1226
If (5/9 of x) - (2/5 of 9/4) equals -4/5 then find x.
A. 0.18
B. 0.12
C. 2
D. 0.54
Question 1227
If a = 3+23-2, b = 3-23+2 then a2+b2-ab ?
A. 97
B. (2√3) + 2
C. (4√6) + 1
D. 98
Question 1228
If x2 + (1/x2) = 1, then what is the value of x48 + x42 + x36 + x30 + x24 + x18 + x12 + x6 + 1?
A. -9
B. 0
C. 1
D. 9
Question 1229
Determine the value of “s” for which the equation 5x + 35 = 60x + s has infinite number of solutions.
A. 420
B. 440
C. 460
D. 480
Question 1230
In a slip test, K got the 15th rank and he was 44th from the bottom of the list of passed students. 4 students did not take up the slip test and 3 students were failed. What is the total strenght of the class ?
A. 63
B. 62
C. 64
D. 65
Question 1231
If x = (√5) + 1 and y = (√5) – 1, then what is the value of (x2/y2) + (y2/x2) + 4[(x/y) + (y/x)] + 6?
A. 31
B. 23√5
C. 27√5
D. 25
Question 1232
Simplify x5 ÷ x43 ÷ x
A. x3
B. x2
C. X
D. 1/X
Question 1233
If ab+ba = -1, then the value of a2b-b2a is
A. 1
B. -1
C. 0
D. 2
Question 1234
PQ is a tangent to the circle at T. If TR = TS where R and S are points on the circle and ∠RST = 65°, the ∠PTS =
A. 65°
B. 130°
C. 115°
D. 55°
Question 1235
If Cosec θ = 17/8, then what is the value of Cos θ?
A. 15/8
B. 15/17
C. 8/15
D. 17/15
Question 1236
If [4(2x/5 - 3/2)]/3 + 7/5 = 37/5, then what is the value of x?
A. -15
B. 7/5
C. 15
D. -7/5
Question 1237
If u+v = 10 and uv = 16, then find the value of u2-v2uv
A. 0
B. 15/8
C. 15/4
D. 15/2
Question 1238
If x3+ 2x2– 5x + k is divisible by x + 1, then what is the value of k?
A. -6
B. -1
C. 0
D. 6
Question 1239
If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what is the value of (a + c)/b?
A. 9/5
B. 11/7
C. 7/11
D. 7/4
Question 1240
What is the value of sec 4π/3?
A. 2
B. -2
C. 2/√3
D. -2/√3
Question 1241
If n + n2 + n4 + n8 = 45, then find the value of 'n' which will satisfy the equation.
A. 16
B. 24
C. 36
D. 48
Question 1242
Which of the following quadratic equations has equal roots?
A. x2 - 14x - 49 = 0
B. x2 + 7x + 49 = 0
C. x2 - 7x - 49 = 0
D. x2 + 14x + 49 = 0
Question 1243
If -3/2 + (2/3)(3x + 9) = x/2, then what is the value of x?
A. -9
B. 11
C. 9
D. -3
Question 1244
If 2x - 6 ≤ x - 3 and 1+3x < 4x + 4, then x can take which of the following values?
A. 4
B. -4
C. -6
D. 2
Question 1245
If cot(A/2) = x, then x is equal to
A. tanA/(1 + secA)
B. 1/(secA + cotA)
C. tanA/(1 + cosecA)
D. 1/(cosecA - cotA)
Question 1246
If 5 3x < 4 x and 5(2 x) > 2 2x, then x can take which of the following values?
A. 0
B. 1
C. 3
D. -1
Question 1247
What are the co-ordinates of the mid point of the segment joining points C(0,-3) and D(8,5)?
A. (4, 1)
B. (-4, 1)
C. (4, -1)
D. (-4, -1)
Question 1248
If 7x + 6y = 5xy and 10x - 4y = 4xy, then value of x and y is
A. 3, 2
B. 2, 3
C. 4, 2
D. 5, 6
Question 1249
What are the roots of the quadratic equation: x2 + 3x - 154 = 0
A. 11, 14
B. 11, -14
C. 14, -11
D. 14, -22
Question 1250
The points A(3,-2), B(1,4) and C(-2,x) are collinear. What is the value of x?
A. 13
B. -2
C. 5
D. 3
Question 1251
If √(sec2A 1) = x, then the value of x is
A. cotA
B. tanA
C. cosecA
D. cosA
Question 1252
What is the value of (cos 40° – cos 140°)/(sin 80° + sin 20°)?
A. 2√3
B. 2/√3
C. 1/√3
D. √3
Question 1253
Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?
A. 256
B. 432
C. 512
D. 640
Question 1254
The square root of 6084 is
A. 82
B. 78
C. 74
D. 76
Question 1255
Consider a regular hexagon ABCDEF. Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is 30 deg, and the angle of elevation to the top of the tower at C is 45 deg. What is the ratio of the height of towers at B and C?
A. 1:√3
B. 1:3
C. 1:2
D. 1:2√3
Question 1256
If (x/y)a-4 = (y/x)2a-5, then what is the relation between x and y?
A. x > y
B. Cannot be determined
C. x < y
D. x = y
Question 1257
If 3x+22x+1 = a2x+1+bx+2 be an identity, then the value of b
A. 0
B. -1
C. 2
D. 3
Question 1258
An angle is greater than its complementary angle by 30°. Find the measure of the angle?
A. 30°
B. 90°
C. 60°
D. 120°
Question 1259
If x-1x = 10, then find the value of x4+1x2
A. 98
B. 100
C. 102
D. 106
Question 1260
If 4(x+y) = 256 and (256)(x-y) = 4, then what is the value of x and y?
A. 17/8, 15/8
B. 17/4, 15/4
C. 9/17, 15/17
D. 8/17, 8/15
Question 1261
If cot2A - cos2A = x, then value of x is
A. tan2Asec2A
B. cotAcosA
C. cot2Acos2A
D. tanAsecA
Question 1262
ΔXYZ is right angled at Y. If m∠Z = 45°, then find the value of (cosecX - 2/√3).
A. (2-√3)/2√3
B. (1-√6)/√2
C. (√6-2)/√3
D. -1/√3
Question 1263
If x - y = -6 and x + y = 16, then x2- y2 is?
A. 96
B. -96
C. 22
D. -22
Question 1264
A tailor has 37.5 metres of cloth and he has to make 8 pieces out of a metre of cloth. How many pieces can he make out of half of the cloth he has ?
A. 300
B. 150
C. 175
D. 200
Question 1265
If 2secA - (1 + sinA)/cosA = x, then the value of x is
A. cosecA/(1+sinA)
B. cosA/(1+sinA)
C. cosA(1+sinA)
D. cosecA(1+sinA)
Question 1266
If (36 - 16x) - (4x - 8) = 4, then the value of x is
A. 4
B. 2
C. 6
D. 3
Question 1267
If 2x+2x=3, then the value of x3+1x3+2 is
A. 3/4
B. 4/5
C. 5/8
D. 7/8
Question 1268
If a + b = 3 and ab = -4, then what is the value of a3 + b3?
A. 36
B. 63
C. 12
D. -15
Question 1269
Point P is the midpoint of segment AB. Co-ordinates of P are (5,-4) and A are (7,0). What will be the co-ordinates of point B?
A. (3, -8)
B. (-3, -8)
C. (3, 8)
D. (-3, 8)
Question 1270
ΔDEF is right angled at E. If cosecD = 5/4, then what is the value of cosecF?
A. 5/3
B. 3/4
C. 4/5
D. 4/3
Question 1271
If 2x + (9/x) = 9, then what is the minimum value of x2+1x2 = ?
A. 95/36
B. 97/36
C. 87/25
D. 623/27
Question 1272
If secA/(secA - 1) + secA/(secA + 1) = x, then x is
A. 2cosec2A
B. 2sec2A
C. 2cosecA
D. 2secA
Question 1273
If Sin x = 4/5, then Cosec x + Cot x =
A. 31/12
B. 35/12
C. 2
D. 1/2
Question 1274
If Tan θ = 9/40, then Sec θ = ?
A. 40/41
B. 9/41
C. 41/40
D. 41/9
Question 1275
∆XYZ is right angled at Y. If tanX = 15/8, then what is the value of sinZ ?
A. 15/17
B. 17/8
C. 17/15
D. 8/17
Question 1276
What is the equation of the line passing through the point (-1,3) and having x-intercept of 4 units?
A. 3x - 5y = 12
B. 3x + 5y = 12
C. 3x + 5y = -12
D. 3x - 5y = -12
Question 1277
If a - b = 10 and ab =-21, then what is the value of a3-b3 ?
A. 316
B. 370
C. 185
D. 158
Question 1278
If 4x + 1x = 5, (x≠0), then the value of 5x4x2+10x+1 is
A. 1/2
B. 1/3
C. 2/3
D. 3
Question 1279
Find k, if the line 4x - y = 1 is perpendicular to the line 5x - ky = 2?
A. 20
B. -20
C. 4
D. -4
Question 1280
How many 18' s are there in 3712?
A. 300
B. 400
C. 500
D. 600
Question 1281
The point Q(a,b) is first reflected in yaxis to Q1 and Q1 is reflected in xaxis to (6,2). The coordinates of point Q are
A. (-6,2)
B. (2,-6)
C. (6,-2)
D. (-2,6)
Question 1282
If 2x + 5 > 2 + 3x and 2x - 3 ≤ 4x - 5, then x can take which of the following values?
A. -2
B. 2
C. -4
D. 4
Question 1283
What is the value of (4a2 - 9b2 )/(2a + 3b) is
A. 2a - 3b
B. 2a + 3b
C. 2a
D. 3b
Question 1284
If 5x + 6(3-2x) = 4, then what is the value of x?
A. 1
B. 2
C. 3
D. 4
Question 1285
Compute 33800/520/5
A. 31
B. 325
C. 13
D. 352
Question 1286
What is the slope of the line parallel to the line passing through the points (-4,-6) and (2,-3)?
A. -1/2
B. -2
C. 2
D. 1/2
Question 1287
If √5 = 2.236, then √5/2 is
A. 1.851
B. 1.118
C. 2.236
D. 1.782
Question 1288
Which of the following quadratic equations has real roots?
A. 4x2 - 9x + 6 = 0
B. 3x2 - 2x + 6 = 0
C. 2x2 - 7x + 6 = 0
D. x2 - 2x + 2 = 0
Question 1289
The point R(a,b) is first reflected in origin to R1 and R1 is reflected in xaxis to (-4,2). The co-ordinates of point R are
A. (4,-2)
B. (-4,2)
C. (4,2)
D. (-4,-2)
Question 1290
The simplest form of 3565/1495 is
A. 31/13
B. 43/19
C. 23/13
D. 31/23
Question 1291
Δ ABC is right angled at B. If m∠A = 60°, then what is the value of 2 Sec C x 1/2 Sin A?
A. 1/2
B. 1/3
C. 1
D. 1/√2
Question 1292
In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group ?
A. 6
B. 10
C. 8
D. 12
Question 1293
What is the equation of the line which intercepts xaxis and yaxis at 3/4 and 2/3 respectively?
A. 8x + 9y = 6
B. 9x + 8y = 12
C. 8x - 9y = 6
D. 9x + 8y = -12
Question 1294
If cot 60° + cosec 60° = x, then the value of x is
A. (1-2√2)/√2
B. (√3-4)/2√3
C. 1
D. √3
Question 1295
Find the value of 6732.8 + 673.28 + 67.328 + 6.7328 + 0.67328 ?
A. 74808.1408
B. 7480.78408
C. 74808.2408
D. 7480.81408
Question 1296
On dividing 256a2b2c2 by 64a2, we get
A. 2cxc
B. 2bxb
C. 4 bxb.cxc
D. 4
Question 1297
What are the coordinates of the mid point of the segment joining points C(5,-2) and D(-1,8).
A. (-2, 3)
B. (2, 3)
C. (2, -3)
D. (-2, -3)
Question 1298
Arrange them in ascending order 64, 33 and 43
A. 33 < 64 > 43
B. 33 > 64 > 43
C. 33 > 43 > 64
D. 33 < 64 < 43
Question 1299
If cot2A = x, then x is
A. 2cotA/(cot2A - 1)
B. (cot2A - 1)/2cotA
C. (cot2A + 1)/2cotA
D. 2cotA/(1 - cot2A)
Question 1300
A sphere of radius 5 cm is melted to form a cone with base of same radius. The height (in cm) of the cone is
A. 5
B. 10
C. 20
D. 22
Question 1301
If A = (1/0.4) + (1/0.04) + (1/0.004) + ... upto 8 terms, then what is the value of A?
A. 27272727.5
B. 25252525.5
C. 27777777.5
D. 25555555.5
Question 1302
Which of the following quadratic equations has real roots?
A. 3x2 - 5x + 2 = 0
B. 3x2 - 4x + 2 = 0
C. 4x2 - 3x + 2 = 0
D. 5x2 - 2x + 2 = 0
Question 1303
What is the distance between the points (4,-8) and (-2,0)?
A. 100 units
B. 5 units
C. 25 units
D. 10 units
Question 1304
What is the value of (cosecA - cotA) / (secA + tanA)?
A. (secA + tanA)/(cosecA - cotA)
B. √[(secA - tanA)/(cosecA + cotA)]
C. (secA - tanA)/(cosecA + cotA)
D. √[(secA + tanA)/(cosecA - cotA)]
Question 1305
What is the value of ( 1/3 + cosec30)?
A. (√6+1)/√3
B. 7/3
C. (4+√3)/2
D. (√3+1)/2
Question 1306
If x=2+3, then the value of x2-x+1x2+x+1 is
A. 2/3
B. 3/4
C. 4/5
D. 3/5
Question 1307
The value of x13+x-13x23-1+x-23
A. x-1+x23
B. x+x-13
C. x13+x-1
D. x+x-1
Question 1308
125 - 73 + 48 - 137 + 99 = ?
A. 237
B. 62
C. -37
D. 52
Question 1309
Solve this inequality 3p - 16 < 20?
A. p >= 12
B. p <= 11/3
C. p < 12
D. p > 11/3
Question 1310
If 7x - [3(2x - 3)]/2 = 1/2, then what is the value of x?
A. -1
B. 1
C. 3
D. -3
Question 1311
A bag has Rs 30.8 in the form of 1 rupee, 50 paise and 10 paise coins in the ratio of 6:3:2. What is the number of 50 paise coins?
A. 8
B. 24
C. 12
D. 4
Question 1312
What is the value of cos [(180 – θ)/2] cos [(180 – 9θ)/2] + sin [(180 – 3θ)/2] sin [(180 – 13θ)/2]?
A. sin 2θ sin 4θ
B. cos 2θ cos 6θ
C. sin 2θ sin 6θ
D. cos 2θ cos 4θ
Question 1313
If (1 + cosA)/2 = x, then the value of x is
A. sin(A/2)
B. √sin(A/2)
C. √cos(A/2)
D. cos2(A/2)
Question 1314
Given a - b = 2, a3 - b3=26 then (a + b)2 is
A. 9
B. 4
C. 16
D. 12
Question 1315
On dividing 24a2b2 by 6b2, we will get
A. 4b
B. 4ab
C. 4
D. 4a2
Question 1316
If tan(A/2) = x, then the value of x is
A. √[(1 + cosA)/(1 - cosA)]
B. (1 - cosA)/(1 + cosA)
C. (1 + cosA)/(1 - cosA)
D. √[(1 - cosA)/(1 + cosA)]
Question 1317
If x2 – 12x + 33 = 0, then what is the value of (x – 4)2 + [1/(x – 4)2]?
A. 16
B. 14
C. 18
D. 20
Question 1318
If A + B = 90 deg and Cos B = 1/3, then the value of Sin A is
A. 1/2
B. 1/4
C. 1/3
D. 2/3
Question 1319
(1 + sec 20° + cot 70°)(1 - cosec 20° + tan70°) is equal to
A. 0
B. 1
C. 2
D. 3
Question 1320
Twenty times a positive integer is less than its square by 96. What is the integer ?
A. 42
B. 36
C. 48
D. 24
Question 1321
What is the value of sin -300°?
A. 1
B. √3/2
C. 1/2
D. √3/2
Question 1322
What is the simplified value of 0.072+0.292-0.02030.073+0.293
A. 0.6
B. 0.06
C. 1/0.6
D. 1/0.06
Question 1323
If a2sec2x - b2tan2x = c2 then the value of sec2x + tan2x is equal to (assume b2 ≠ a2 )
A. b2-a2+2c2b2+a2
B. b2+a2-2c2b2-a2
C. b2-a2-2c2b2+a2
D. b2-a2b2+a2+2c2
Question 1324
What is the value of [(tan 5θ + tan 3θ)/4 cos 4θ (tan 5θ – tan 3θ)]?
A. sin 2θ
B. cos 2θ
C. tan 4θ
D. cot 2θ
Question 1325
Which of the following is correct?
A. (4x + 5y)(5x - 4y) = 20x2 + 9xy - 20y2
B. (4x + 5y)(5x - 4y) = 20x2 + 41xy - 20y2
C. (4x + 5y)(5x - 4y) = 20x2 - 9xy + 20y2
D. (4x + 5y)(5x - 4y) = 20x2 - 41xy + 20y2
Question 1326
If 5x/2 - [7(6x - 3/2)]/4 = 5/8, then what is the value of x?
A. 1/4
B. -1/4
C. 4
D. -4
Question 1327
If a-1a=1, then a2 + 1a2 ?
A. 1
B. 3
C. 2
D. 4
Question 1328
For triangle ABC, find equation of median AD if coordinates of points A, B and C are (2,4), (3,0) and (5,2) respectively?
A. 3x - 2y = 14
B. 3x - 2y = 2
C. 3x + 2y = 14
D. 3x + 2y = 2
Question 1329
Determine the value of ‘r’ for which the equation 13x + 5 = rx + 18 has no solution.
A. 0
B. 5
C. 13
D. 18
Question 1330
The value of x for which the expressions 7x + 13 and 13x - 7 become equal is _____
A. -10/3
B. 3/10
C. -3/10
D. 10/3
Question 1331
What is the value of 3.6×1.62+0.48×3.61.8×0.8+10.8×0.3-2.16 ?
A. 2.4
B. 2
C. 4
D. 3
Question 1332
If 2x+ 4(x - 3) < -2 - x < 2x - 1, then find the value of x.
A. -1
B. 1
C. 2
D. -2
Question 1333
If tan 45° + cosec 30° = x, then find the value of x.
A. √3
B. (1-2√2)/√2
C. (√3-4)/2√3
D. 3
Question 1334
If 5x = 30-y = 6z, then what is the value of (xy + yz + zx)/xyz?
A. 0
B. 1
C. 2
D. 3
Question 1335
If (4a-3)2=0, then the value of 64a3+12a+13 is
A. 0
B. 11
C. 22
D. 33
Question 1336
If -3[1-(x/2)] + 5x/3 = 1/6, then what is the value of x?
A. 2
B. -1
C. 1
D. -2
Question 1337
If x3 = 62 - 32, then the value of x is
A. 9
B. 6
C. 3
D. 1
Question 1338
√[(1 sinA)/(1 + sinA)] is equal to?
A. secA - tanA
B. cosecA - cotA
C. secA + tanA
D. cosecA + cotA
Question 1339
What is the smplified value of Sin2A/1+Cos2A ?
A. tan A
B. cot A
C. sin A
D. cos A
Question 1340
The two roots of an quadratic equation are given as x = 2/3 and x = -1/2. The equation can be written as
A. (2x - 1) (3x + 2) = 0
B. (2x + 1) (3x + 2) = 0
C. (2x + 1) (3x - 2) = 0
D. (2x - 1) (3x - 2) = 0
Question 1341
Ifab=45andbc=1516, then c2-a2c2+a2 is :
A. 7/5
B. 7/25
C. 7/125
D. 7
Question 1342
Find the roots of the quadratic equation 27x2 + 57x - 14 = 0
A. 2/9, 7/3
B. 2/9, -7/3
C. 9/2, -3/7
D. -9/2, 3/7
Question 1343
If x=aCosθCosΦ, y = aCosθSinΦ and z= aSinθ, then the value of x2+ y2 + z2 is
A. 2a2
B. 0
C. 4a2
D. a2
Question 1344
Triangle PQR is inscribed in a circle such that P, Q and R lie on the circumference. If PQ is the diameter of the circle and ∠PQR = 40°, then what is the value (in degrees) of ∠QPR?
A. 40
B. 45
C. 50
D. 55
Question 1345
If 1 + secA = x, then the value of x is
A. sinAtanA/(1 + cosA)
B. √[sinAtanA/(1 - cosA)]
C. sinAtanA/(1 - cosA)
D. √[sinAtanA/(1 + cosA)]
Question 1346
Determine the value of 'a' which satisfies the equation 9a + 40a = 41a
A. 1
B. 2
C. 3
D. 4
Question 1347
If a + b = 5 and ab = 6, then what is the value of a3 + b3?
A. 32
B. 38
C. 35
D. 34
Question 1348
If a + b + c = 13, a2+b2+c2=69 then find the ab + bc + ca :
A. 10
B. 30
C. 50
D. 70
Question 1349
What is the value of tan150°?
A. -√3
B. 1/√3
C. √3
D. -1/√3
Question 1350
What is the value of 13 x 4932?
A. 4369
B. 4459
C. 4549
D. 4639
Question 1351
The distance between the points (2, 7) and (k, -5) is 13. What is the value of k?
A. -7
B. 7
C. 6
D. -6
Question 1352
If θ is positive acute angle and 7cos2Ɵ + 3sin2Ɵ = 4, then the value of θ is
A. 60°
B. 30°
C. 45°
D. 90°
Question 1353
If 5 sec θ – 3 tan θ = 5, then what is the value of 5 tan θ – 3 sec θ?
A. 1
B. 2
C. 3
D. 4
Question 1354
What is the value of sec2θ + 1sec2θ - 1 x 12cotθ - tanθ ?
A. 0
B. 1
C. cosec θ
D. sec θ
Question 1355
What is the value of sin (B – C) cos (A – D) + sin (A – B) cos (C – D) + sin (C – A) cos (B – D)?
A. 3/2
B. – 3
C. 1
D. 0
Question 1356
The number whose square is equal to the difference of the squares of 37 and 23 is:-
A. 45.09
B. 28.98
C. 47.09
D. 28
Question 1357
A class consists of both boys and girls along with a teacher. After a class, the teacher drinks 9 litres of water, a boy drinks 7 litres of water and a girl drinks 4 litres of water. If after a class 42 litres of water was consumed, find the number of girls in the class ?
A. 8
B. 6
C. 5
D. 3
Question 1358
If a - b = 5 and a2 + b2 = 97, ab = ?
A. 48
B. 32
C. 36
D. 72
Question 1359
The value of tan 315° cot ( -405° ) is equal to
A. -1
B. 1
C. 0
D. 2
Question 1360
cot3A is equal to
A. 3cotA - cot3A(1 - 3cot2A)
B. 3cotA + cot3A(1 - 3cot2A)
C. 3cotA - cot3A(1 + 3cot2A)
D. 3cotA + cot3A(1 + 3cot2A)
Question 1361
If (5x – y)/(5x + y) = 3/7, then what is the value of (4x2 + y2 – 4xy)/(9x2 + 16y2 + 24xy) ?
A. 0
B. 3/7
C. 18/49
D. 1/6
Question 1362
In an examination, a student scores 4 marks for every correct answer and loses I mark for every wrong answer. If he attempts in all 60 questions and secures 130 marks, the number of questions he attempts correctly, is:
A. 35
B. 38
C. 40
D. 42
Question 1363
If the difference between the roots of the equation Ax2 – Bx + C = 0 is 4, then which of the following is TRUE?
A. B2 – 16A2 = 4AC + 4B2
B. B2 – 10A2 = 4AC + 6A2
C. B2 – 8A2 = 4AC + 10A2
D. B2 – 16A2 = 4AC + 8B2
Question 1364
Which of the following is correct?
A. (4x - 5y)2 = 16x2 - 20xy + 25y2
B. (4x - 5y)2 = 16x2 + 40xy - 25y2
C. (4x - 5y)2 = 16x2 - 40xy + 25y2
D. (4x - 5y)2 = 16x2 - 20xy - 25y2
Question 1365
If x , y, and z are real numbers such that (x - 3)2 + (y - 4)2 + (z - 5)2 = 0 then (x+y+z) is equal to
A. -12
B. 0
C. 8
D. 12
Question 1366
ΔABC is right angled at B. If m∠A = 45 deg, then find the value of (tanC + √3/2).
A. 4/√3
B. (2+√3)/2
C. (√2+2)/2√2
D. (2+√3)/3
Question 1367
∆ABC is right angled at B. If m∠A = 30°, then find the value of (sinC + 1/3).
A. 4/3
B. (√3+1)/2
C. (√3+2)/√3
D. (3√3+2)/6
Question 1368
If 3.352 - (9.759 - x ) - 19.64 = 7.052, then what is the value of x?
A. -6.181
B. 13.581
C. 33.099
D. 39.803
Question 1369
If x = x2+11 2 - 2, then x3 + 5x2 + 12x is
A. 0
B. 3
C. 7
D. 11
Question 1370
Simplify (2/7 + 3/5) / (2/5 + 2/7)
A. 31/24
B. 24/31
C. 26/25
D. 12/13
Question 1371
If tan4θ + tan2θ = 1 then the value of cos4θ + cos2θ is
A. 2
B. 0
C. 1
D. -1
Question 1372
ax + 3y = 6 has slope -2/3. What is the value of a?
A. -2
B. 2
C. 3
D. -3
Question 1373
Common factor of 24b6c8d2, 18a6c2d4, 12a4b4 is
A. 72a2b2c2d2
B. 72a6b6c8d4
C. 6a2b2
D. 6
Question 1374
The value of (0.3)2/100=?
A. 0.09
B. 0.0009
C. 0.009
D. 0.9
Question 1375
In ΔUVW measure of angle V is 90 deg. If cosecU = 13/12, and UV = 2.5cm, then what is the length (in cm) of side VW?
A. 6.5
B. 6
C. 4
D. 5.6
Question 1376
What is the value of (sin60° + 2/√3) ?
A. (2√3+1)/√3
B. 7/2√3
C. 3
D. 2+√3
Question 1377
What is the value of (cot45 - √2) ?
A. (√3-1)/2√3
B. (√3-1)/2
C. 1-√2
D. 1-√3
Question 1378
If 2+aa + 2+bb + 2+cc = 4, then the value of ab+bc+caabc is
A. 2
B. 1
C. 0
D. 1/2
Question 1379
You purchased two pieces of cloth measring 1.2 m and 1.3 m each at Rs. 330 and Rs. 270 per meter respectively and gave Rs. 1000 at the payment counter. How much cash will you get back?
A. Rs. 253
B. Rs. 604
C. Rs. 649
D. Rs. 235
Question 1380
If cot 135° = x, then the value of x is
A. -1/√3
B. -√3
C. -1
D. -1/2
Question 1381
If p/q = r/s = t/u = √5, then what is the value of [(3p2 + 4r2 + 5t2)/(3q2 + 4s2 + 5u2)]?
A. 1/5
B. 5
C. 25
D. 60
Question 1382
If a + b + c = 27, then what is the value of (a – 7)3 + (b – 9)3 + (c – 11)3 – 3(a – 7)(b – 9)(c – 11)?
A. 0
B. 9
C. 27
D. 3
Question 1383
In the given figure, AB is a diameter of the circle with center O and XY is the tangent at a point C. If ACX = 35 deg, then what is the value (in deg) of CAB?
A. 45
B. 35
C. 55
D. 65
Question 1384
What is the value of (tan60 + 1/3) ?
A. (2√2+1)/2
B. (√3+1)/√3
C. (3√3+1)/3
D. (3+√2)/3√2
Question 1385
If a - b = -7 and a2+ b2= 85, then find ab.
A. 18
B. -30
C. -44
D. 60
Question 1386
Which of the following conditions is TRUE for the two line segments AB and CD to be congruent?
A. AB=CD
B. AB>CD
C. AB
Question 1387
For which value of ‘g’ the linear graph of 6x + 12y +9 = 0 and 2x + gy + 3 =0 has infinite number of solutions?
A. 3
B. 4
C. 6
D. 9
Question 1388
If x2+y2+z2-8x+6y-4z+29 = 0, then find the value of z(x+y).
A. 1
B. 2
C. 3
D. 4
Question 1389
If 3x+7=x2+p=7x+5, what is the value of P ?
A. 17/2
B. 25/3
C. 33/4
D. 41/5
Question 1390
For the inequation x^2–7x + 12 > 0, which one of the following is correct ?
A. 3 < x < 4
B. –∞ < x < 3 only
C. 4 < x < ∞ only
D. –∞ < x < 3 or 4 < x < ∞
Question 1391
If 2x - 3 = 3x - 5, then the numerical value of (x - 3)2 is
A. 5
B. 1
C. -5
D. -1
Question 1392
The value of aa-b+bb-a is
A. a+b/a-b
B. -1
C. 2ab
D. 1
Question 1393
What is the value of sin 300°?
A. -1/2
B. 2
C. 2/√3
D. -√3/2
Question 1394
What is the value of (1/2) Sec 30° + √2 Tan 60°?
A. (1 + 3√2)/√3
B. (√3 + 2)/√3
C. √3 + 2
D. (√3 + 2)/2
Question 1395
What is the value of S = 11x3x5 + 11x4 + 13x5x7 + 14x7 + 15x7x9 + 17x10 + ... upto 20 terms. Then what is the value of S?
A. 6179/15275
B. 6070/14973
C. 7191/15174
D. 5183/16423
Question 1396
What is the value of [sin (y – z) + sin (y + z) + 2 sin y]/[sin (x – z) + sin (x + z) + 2 sin x]?
A. cos x sin y
B. (sin y)/(sin x)
C. sin z
D. sin x tan y
Question 1397
If 5+x+5-x5+x-5-x = 3,then what is the value of x ?
A. 5/2
B. 25/3
C. 4
D. 3
Question 1398
If tan2A - tan2B = x, then the value of x is
A. (sin2A - sin2B)/(cos2A cos2B)
B. (sin2A sin2B)/(cos2A - cos2B)
C. (sin2A + sin2B)/(cos2A cos2B)
D. (sin2A sin2B)/(cos2A + cos2B)
Question 1399
What should be added to 5(2x-y) to obtain 4(2x - 3y) + 5(x + 4y)?
A. 3x - 13y
B. 3x + 13y
C. 13x - 3y
D. 13x + 3y
Question 1400
What is the value of ( 1/3 - cosec30°) ?
A. (√6-1)/√3
B. -1/2
C. -5/3
D. 3/2
Question 1401
The value of 14 ÷ 5 of 2 - 3 x 47 - 2 is
A. 44
B. 40
C. 1/10
D. 14/19
Question 1402
What is the value of Sin 30° + Cos 30°?
A. (√6 + 1)/√3
B. (√3 + 2)/√3
C. (1 + √3)/2
D. 5/√3
Question 1403
What is the equation of the line passing through the point (0,4) and making an angle of 45° with the positive xaxis?
A. x + y = 4
B. x - y = - 4
C. x + y = -4
D. x - y = 4
Question 1404
In ∆DEF measure of angle E is 90°. If secD = 25/7, and DE = 1.4cm, then what is the length (in cm) of side DF?
A. 5
B. 4.8
C. 4
D. 5.6
Question 1405
Given that tan(θ + 15°) = √3. Then the value of θ is?
A. 15°
B. 75°
C. 45°
D. 65°
Question 1406
What is the reflection of the point (-1 , 3) in the line x = -4?
A. (-7 ,-3)
B. (-7 ,3)
C. (7 ,-3)
D. (7 ,3)
Question 1407
If cotA/√(1 + cot2A) = x, then the value of x is
A. sinA
B. cosecA
C. secA
D. cosA
Question 1408
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ?
A. 52.5
B. 62.5
C. 72.5
D. 82.5
Question 1409
The value of sec2θ + 2tanθcotθ - tan2θ is
A. 0
B. 1
C. 2
D. 3
Question 1410
What is the value of cosec -150°?
A. -2
B. 2/√3
C. 2
D. -2/√3
Question 1411
What is the value of sec -2π/3 ?
A. -2
B. 2
C. 2/√3
D. -2/√3
Question 1412
If [2(4x/5 - 3/4)]/3 - 5/3 = -1/6, then the value of x is?
A. 4/15
B. -15/4
C. -4/15
D. 15/4
Question 1413
If x = y + 2 then x3 - y3 - z3 is
A. 0
B. 3xyz
C. -3xyz
D. 1
Question 1414
What is the slope of the line perpendicular to the line passing through the points (-2, 3) and (2, 0)?
A. 4/3
B. 3/4
C. -3/4
D. -4/3
Question 1415
What is the value of Sin 30° + 2 Cos 30° ?
A. (2√2 + 3)/√6
B. (9 + 2√3)/9
C. (1 + 2√3)/2
D. (2√6 + 1)/√3
Question 1416
Find the value of 62532+18
A. 1635
B. 2635
C. 3635
D. 4635
Question 1417
In a school there are 1500 students, 44% of them are girls. Monthly fee of each boy is 540 and fee of each girl is 25% less than that of a boy. The sum of fees of boys & girl is
A. Rs. 720600
B. Rs. 720800
C. Rs. 720900
D. Rs. 721000
Question 1418
If θ is acute angle and sin(θ+18°)= 1/2, then the value of θ in circular measure is
A. Π/12 radians
B. Π/15 radians
C. 2Π/5 radians
D. 3Π/13 radians
Question 1419
If a + b + c = 7/12, 3a – 4b + 5c = 3/4 and 7a – 11b – 13c = – 7/12, then what is the value of a + c?
A. 1/2
B. 5/12
C. 3/4
D. 1/4
Question 1420
If x = 4aba+b, then what is the value of x+2ax-2a+x+2bx-2b ?
A. 0
B. 2
C. 4
D. 1
Question 1421
What is the equation of the line if its slope is 4/3 and it passes through the point (-7 , 2)?
A. 4x - 3y = -22
B. 4x + 3y = -34
C. 4x + 3y = -22
D. 4x - 3y = -34
Question 1422
ΔABC is right angled at B. If m∠A = 45°, then find the value of (cosecC + 1/√3).
A. (3√2+1)/3
B. (2+√3)/2
C. 5/√3
D. (√6+1)/√3
Question 1423
What is the equation of the line passing through the point (2,-3) and making an angle of -45°with the positive X-axis?
A. x - y = -5
B. x - y = -1
C. x + y = -5
D. x + y = -1
Question 1424
If the simple interest on Rs. 1 for 1 month is 1 paisa, then the rate percent per annum will be
A. 10%
B. 8%
C. 12%
D. 6%
Question 1425
If 2560.256 = 25.6x, then what will be the value of x?
A. 2.56
B. 25.6
C. 0.256
D. 0.0256
Question 1426
If 3√2 + √18 + √50 = 15.55, then what is the value of √32 + √72?
A. 13.22
B. 10.83
C. 14.13
D. 16.54
Question 1427
The value of Sin 60 is
A. √1/2
B. √3/2
C. 1/√2
D. 1/2
Question 1428
The value of 2 Tan53°Cot37°-Cot80°Tan10° ?
A. 3
B. 2
C. 1
D. 0
Question 1429
What is the value of 2+2+2+2.......
A. 1
B. 2
C. 3
D. 4
Question 1430
If cotθ = 4, then the value of 5sinθ+3cosθ5sinθ-3cosθ is
A. 1/9
B. 1/3
C. 3
D. 9
Question 1431
If secA - tanA = x, then the value of x is
A. 1/(sec2A - tan2A)
B. 1/(sec2A + tan2A)
C. 1/√[(sec2A - tan2A)]
D. 1/(secA + tanA)
Question 1432
The value of sinθ1+cosθ + sinθ1-cosθ
A. 2sinθ
B. 2cosθ
C. 2secθ
D. 2cosecθ
Question 1433
If a+b=5 and ab=3, then the value of (a2+b2) is
A. 17
B. 18
C. 19
D. 20
Question 1434
Find the unit digit in the given product (4211)102 x (361)52.
A. 3
B. 1
C. 4
D. 7
Question 1435
Δ DEF is right angled at E. If m∠F = 45, then what is the value of Sin F x Tan F?
A. √2
B. 1/√3
C. 1/√2
D. 2/√3
Question 1436
What is the slope of the line, parallel to the line 3x - 6y = 4?
A. -1/2
B. 1/2
C. 2
D. -2
Question 1437
In ΔXYZ measure of angle Y is 90 deg. If cot X = 5/12, and XY = 2.5 cm, then what is the length (in cm) of side XZ?
A. 6
B. 4
C. 5.6
D. 6.5
Question 1438
Find the value of sin230 cos245 + 4 tan230 + 1/2sin290 - 2 cos290 + 1/24
A. 3
B. 4
C. 2
D. 1
Question 1439
If 3 dozen guavas cost Rs. 90, how many guavas can be bought for Rs. 240?
A. 98
B. 96
C. 102
D. 90
Question 1440
The value of(1(p-n)(n-q)+1(n-q)(q-p)+1(q-p)(p-n)) is
A. 1
B. 0
C. p+q+n
D. 2np+q
Question 1441
What is the value of a-b when a2+b2-6a-6b+18 = 0 ?
A. 0
B. 3
C. 6
D. 9
Question 1442
If the angle of elevation of the sun decreases from 45° to 30°, then the length of the shadow of a pillar increases by 60m. The height of the pillar is
A. 60(√3+1) m
B. 30(√3-1) m
C. 30(√3+1) m
D. 60(√3-1) m
Question 1443
If x + 1/x = 6, then value of x2 + 1/x2 is
A. 23
B. 16
C. 34
D. 32
Question 1444
tan(A/2) is equal to
A. cosecA + cotA
B. secA - cotA
C. cosecA - cotA
D. secA + cotA
Question 1445
If (x2/yz) + (y2/zx) + (z2/xy) = 3, then what is the value of (x + y + z)3?
A. 0
B. 1
C. 2
D. 3
Question 1446
If a2b+c=b2c+a=c2a+b=1 then the value of 21+a+21+b+21+c
A. 0
B. 1
C. 2
D. 3
Question 1447
A secret can be told to only 3 persons in 3 minutes. Each person in turn tells 3 other persons in the next 3 minutes and the processes continues accordingly. In 30 minutes how many persons can be told this secret in this way ?
A. 88572
B. 77854
C. 99584
D. 55654
Question 1448
∆XYZ is right angled at Y. If CosecX = 17/15, then what is the value of CotZ?
A. 17/15
B. 8/17
C. 17/8
D. 15/8
Question 1449
If (x+a) is the H.C.F of 2x2+5x-12 and x2+x-12 then find the value of a.
A. -3
B. -2
C. 4
D. 5
Question 1450
What is the value of 643 × 121289 - 169 ?
A. 12
B. 11
C. 1/11
D. 1/12
Question 1451
If 1/√(1 + cot2A) = x, then value of x is
A. sinA
B. cosecA
C. cosA
D. secA
Question 1452
Coefficient of x2 in 4x3 - 2x2 + 2x - 3 are
A. 6
B. -2
C. 3
D. -3
Question 1453
In a Rhombus ABCD, measure of angle CAB is 35°, what is the measure of angle ABC?
A. 70°
B. 40°
C. 50°
D. 110°
Question 1454
If cosπ/4c - tanπ/4c = x, then x is
A. (√3+4)/2√3
B. (2√2-1)/2
C. (1-√2)/√2
D. 5/√3
Question 1455
The length of a median of an equilateral triangle is 12√3 cms. Then the area of the triangle is
A. 144 sq. cms
B. 288√3 sq. cms
C. 144√3 sq. cms
D. 288sq.cms
Question 1456
If tanA = x, then x is
A. √(cosec2A + 1)
B. √(sec2A + 1)
C. √(cosec2A - 1)
D. √(sec2A - 1)
Question 1457
If a + b + c = 9 and ab + bc + ca = 18, then what is the value of a3 + b3 + c3 – 3abc?
A. 189
B. 243
C. 361
D. 486
Question 1458
The coordinates of the point that divides the line segment joining the points (-5, 5) and (7,-3) internally in the ratio 3 : 1 are given by
A. (-2, 3)
B. (4, -1)
C. (5/2, 0)
D. (1, 1)
Question 1459
sec2Acosec2A is equal to
A. sec2A - cosec2A
B. √[sec2A + cosec2A]
C. sec2A + cosec2A
D. √[sec2A - cosec2A]
Question 1460
If xa+b+1=xa-b+a-ba+b, then x is equal to
A. 2a-b
B. a+b
C. a-b
D. 2a+b
Question 1461
What is the reflection of the point (6, -1) in the line y = 2?
A. (-2 , -1)
B. (-6 , 5)
C. (-2 , 1)
D. (6 , 5)
Question 1462
What is the value of (4/3) cot2 (p/6) + 3 cos2 (150) – 4 cosec2 45 + 8 sin (p/2)?
A. 25/4
B. 1
C. – 7/2
D. 13/2
Question 1463
5.16 x 3.2 =
A. 15.502
B. 16.512
C. 17.772
D. 17.52
Question 1464
For x = 462+3, what is the value of x+22x-22+x+23x-23
A. 1
B. √2
C. √3
D. 2
Question 1465
If y = 2x - 1x + 3, find x when y = 1
A. 4
B. -4
C. 3/2
D. 4/3
Question 1466
If x3-2x=3x, then the value of x2+1x2 will be
A. 3 1/9
B. 3 2/9
C. 2 1/9
D. 2 4/9
Question 1467
If sinθ + cosθ = 1, then the sinθ cosθ is equal to
A. 0
B. 1
C. 1/2
D. -1/2
Question 1468
In a rectangle _____.
A. Consecutive angles are congruent as well as supplementary
B. Diagonals are perpendicular to each other
C. Diagonals bisect opposite angles
D. Diagonals are not equal
Question 1469
If a - b = -1 and ab = 6, then what is the value of a3- b3?
A. 33
B. -19
C. 18
D. 35
Question 1470
If θ is acute angle and tan θ – cot θ = 0, then what is the value of tan26θ + cot100θ?
A. -2
B. 0
C. 1
D. 2
Question 1471
Find the value of y(y4 - y2 - y) when y = 5.
A. 2900
B. 2975
C. 2925
D. 2995
Question 1472
If sinθ+cosθsinθ-cosθ=3, then the value of sin4θ-cos4θ is
A. 4/3
B. 3/4
C. 5/3
D. 3/5