Simplification MCQs : This section focuses on the "Simplification". These Multiple Choice Questions (MCQs) should be practiced to improve the Simplification skills required for various interviews (campus interview, walk-in interview, company interview), placement, entrance exam and other competitive examinations.
Question 1
If a - b = 3, a2+b2=29, find the value of ab.
A. 10
B. 12
C. 15
D. 18
Question 2
If 2x+13x = 5, the value of 5x6x2+20x+1 is
A. 1/4
B. 1/6
C. 1/5
D. 1/7
Question 3
What is the value of the expression a3 - 5 + 2816a, when a = 2?
A. 2
B. 5
C. 7
D. 8
Question 4
What is the x-intercept of line joining (4, 2) and (6, 3)?
A. 0
B. 1
C. 2
D. 3
Question 5
If a=x13y13+x-13y-13 then a3-3ay-x is equal to
A. y^2x
B. x^2y
C. a^2x
D. a^2y
Question 6
What is the value of S = 11x3x5 + 11x4 + 13x5x7 + 14x7 + 15x7x9 + 17x10 + ... upto 20 terms. Then what is the value of S?
A. 6179/15275
B. 6070/14973
C. 7191/15174
D. 5183/16423
Question 7
If xy = -18 and x2+ y2= 85, then find the value of (x + y).
A. 8
B. 10
C. 9
D. 7
Question 8
If A and B are the roots of the equation Ax2 – A2x + AB = 0, then what is the value of A and B respectively?
A. 1, 0
B. 1, 1
C. 0, 2
D. 0, 1
Question 9
If a3 + 3a2 + 9a = 1, then what is the value of a3 + (3/a)?
A. 31
B. 26
C. 28
D. 24
Question 10
The first and last terms of an arithmetic progression are 37 and 18. If the sum of the series is 114, then it has how many terms?
A. 13
B. 12
C. 14
D. 15
Question 11
The ratio of the curved surface area and total surface area of a right circular cylinder is 2 : 5. If the total surface area is 3080 cm2, then what is the volume (in cm3) of the cylinder?
A. 4312√6
B. 3822√6
C. 4522√6
D. 4642√6
Question 12
If Tan θ = 7/24, then what is the value of Cosec θ?
A. 25/24
B. 25/7
C. 24/7
D. 24/25
Question 13
If (x - 2) (x - p) = x2 - ax + 6, then the value of (a - p) is
A. 0
B. 1
C. 2
D. 3
Question 14
If Sinx = 4/5, then Sec2x - 1 = ?
A. 16/25
B. 25/9
C. 9/16
D. 16/9
Question 15
The value of ds+t÷ds÷dt
A. 0
B. d
C. 1
D. ds+t
Question 16
If 9 * 6 = 45, 7 * 4 = 33, and 6 * 4 = 20, then what is the value of 5 * 3?
A. 24
B. 16
C. 13
D. 10
Question 17
What is the value of [(cos 3θ + 2cos 5θ + cos 7θ)÷(cos θ + 2cos 3θ + cos 5θ)] + sin 2θ tan 3θ?
A. cos 2θ
B. sin 2θ
C. tan 2θ
D. cot θ sin 2θ
Question 18
The 3rd and 8th term of an arithmetic progression are -13 and 2 respectively. What is the 14th term?
A. 23
B. 17
C. 20
D. 26
Question 19
If sinθ x cosθ = 1⁄2 . The value of sinθ - cosθ is where 0°< θ< 90°
A. 0
B. √2
C. 2
D. 1
Question 20
If cotθ = 4, then the value of 5sinθ+3cosθ5sinθ-3cosθ is
A. 1/9
B. 1/3
C. 3
D. 9
Question 21
If tan -5π/3 = x, then the value of x is
A. √3
B. 1
C. -1/2
D. √3/2
Question 22
If (x+1/x) = 5, then the value of 5xx2+5x+1?
A. 1/3
B. 1/4
C. 1/2
D. 1/5
Question 23
Simplify 50 + 18 - 8
A. 8√2
B. 7√2
C. 6√2
D. 5√2
Question 24
If x = 2+32-3, then what is the value of x2+x-9 ?
A. 0
B. 3√2
C. 3√3
D. 5√3
Question 25
In a school there are 1500 students, 44% of them are girls. Monthly fee of each boy is 540 and fee of each girl is 25% less than that of a boy. The sum of fees of boys & girl is
A. Rs. 720600
B. Rs. 720800
C. Rs. 720900
D. Rs. 721000
Question 26
(1155) +(18 − 6) × 9 =?
A. 113
B. 115
C. 100
D. 110
Question 27
What is the simplified value of (cosec A – sin A)(sec A – cos A)(tan A + cot A)?
A. -1
B. 0
C. 1
D. 2
Question 28
If 2secA - (1 + sinA)/cosA = x, then the value of x is
A. cosecA/(1+sinA)
B. cosA/(1+sinA)
C. cosA(1+sinA)
D. cosecA(1+sinA)
Question 29
If tan2A - sin2A = x, then value of x is
A. tan2A sin2A
B. cot2A cosec2A
C. tanA sinA
D. cotA cosecA
Question 30
If a = 299, b = 298, c = 297 then the value of 2a3 + 2b3 + 2c3 - 6abc is
A. 5154
B. 5267
C. 5364
D. 5456
Question 31
If x2 + (1/x2) = 31/9 and x > 0, then what is the value of x3 + (1/x3)?
A. 70/9
B. 154/27
C. 349/27
D. 349/7
Question 32
If a + b = 10 and ab = 21, then the value of (a - b)2 is
A. 15
B. 16
C. 17
D. 18
Question 33
If [4(2x/5 - 3/2)]/3 + 7/5 = 37/5, then what is the value of x?
A. -15
B. 7/5
C. 15
D. -7/5
Question 34
Which of the following equations has real and distinct roots?
A. 3x2 - 6x + 2 = 0
B. 3x2 - 6x + 3 = 0
C. x2 - 8x + 16 = 0
D. 4x2 - 8x + 4 = 0
Question 35
David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
A. 19
B. 28
C. 30
D. 37
Question 36
If sinA + sin2A =1 then what is the value of cos2A + cos4A
A. 1/2
B. 1
C. 2
D. 3
Question 37
The average number of visitors of a library in the first 4 days of a week was 58. The average for the 2nd, 3rd, 4th and 5th days was 60.If the number of visitors on the 1st and 5th days were in the ratio 8 : 9. Then what is the number of visitors on the 5th day of the library ?
A. 54
B. 64
C. 68
D. 72
Question 38
If a-b=1 and a3-b3 = 61, then the value of ab will be
A. -20
B. 20
C. 30
D. 60
Question 39
If x2+5x+6 = 0, then the value of 2xx2-7x+6 is
A. 1/6
B. 1/3
C. -1/6
D. -1/3
Question 40
The factors of x2 + 8x + 12 are
A. (x+6)(x+2)
B. (x-6)(x+2)
C. (x-4)(x-4)
D. (x+6)(x-2)
Question 41
The angle of elevation of the top of a tower from two horizontal points (in opposite sides) at distances of 25 meter and 64 meter from the base of tower are x and 90° - x respectively . The height of the tower will be
A. 39 m
B. 89 m
C. 1.6 m
D. 40 m
Question 42
Determine the value of a+1b-1 when ab = 343.
A. 9
B. 64
C. 125
D. 216
Question 43
If a-1a=7,then a2+1a2=?
A. 54
B. 51
C. 53
D. 52
Question 44
If tanA = x, then x is
A. √(cosec2A + 1)
B. √(sec2A + 1)
C. √(cosec2A - 1)
D. √(sec2A - 1)
Question 45
Anuj runs 1 2/3 laps of 7 laps race, find the remaining laps to be run.
A. 16/3
B. 14/3
C. 11/3
D. 10/3
Question 46
Simplify 11.9983 = ?
A. 1727.136
B. 1331.136
C. 1685.136
D. 1700.136
Question 47
If (1 + sinA)/cosA + cosA/(1 + sinA) = x, then the value of x is
A. 2cosecA
B. 2cosec2A
C. 2sec2A
D. 2secA
Question 48
At what point does the line 3x + 2y = -12 intercept the Y-axis?
A. (0,6)
B. (0,-6)
C. (-4,0)
D. (4,0)
Question 49
If x + 1x = c + 1c, then the value of x =
A. C, 1/C
B. C, C2
C. C, 2C
D. 0,1
Question 50
When 2x + 2x = 3, then x3 + 1x + 2 value is
A. 2/7
B. 7/8
C. 7/2
D. 8/7
Question 51
What is the value of 2+2+2+2.......
A. 1
B. 2
C. 3
D. 4
Question 52
The costs of daily ticket of local train is Rs. 50 and Monthly Pass costs is Rs. 1125. If I buy the Monthly Pass and travel for 30 days in a month then I save?
A. 10 percent
B. 25 percent
C. 14 percent
D. 15 percent
Question 53
2 sec2A is equal to
A. (1 - tanA)2 - (1 + tanA)2
B. √[(1 - tanA)2 + (1 + tanA)2 ]
C. √[(1 - tanA)2 - (1 + tanA)2]
D. (1 - tanA)2 + (1 + tanA)2
Question 54
If [√(a2 + b2 + ab)] + [√(a2 + b2 – ab)] = 1, then what is the value of (1 – a2 )(1 – b2 )?
A. 1/4
B. 4/7
C. 5/4
D. 3/4
Question 55
The value of 2 Tan53°Cot37°-Cot80°Tan10° ?
A. 3
B. 2
C. 1
D. 0
Question 56
What is the value of [1 – tan (90 – θ) + sec (90 – θ)]/[tan (90 – θ) + sec (90 – θ) + 1]?
A. cot (θ/2)
B. tan (θ/2)
C. sin θ
D. cos θ
Question 57
If 9x+2 = 240 + 9x, the value of (8x)x is
A. 1
B. -1
C. 0
D. 2
Question 58
If m n = 2 , mn = 15 , (m , n > 0) then the value of m2-n2m3-n3
A. 1856
B. 1658
C. 1586
D. 1568
Question 59
If 3 tan θ = cot θ where 0 < θ < π/2, then what is the value of θ ?
A. π/6
B. π/4
C. π/2
D. 1
Question 60
If √(sec2A - 1)/secA = x, then the value of x is
A. cosecA
B. cosA
C. sinA
D. tanA
Question 61
If y = 2x - 1x + 3, find x when y = 1
A. 4
B. -4
C. 3/2
D. 4/3
Question 62
Simplify 81x2 - 49y29x + 7y
A. 9x++7y
B. 9x-7y
C. 9x
D. 7y
Question 63
If x2+ y2+ z2= xy + yz + zx, then what is the value of (7x + 3y – 5z)/5x?
A. 0
B. 1
C. 5
D. 33/5
Question 64
If ab+ba = -1, then the value of a2b-b2a is
A. 1
B. -1
C. 0
D. 2
Question 65
The point P(a,b) is first reflected in origin to P1 and P1 is reflected in y-axis to (6,-5). The co-ordinates of point P are
A. (-6,-5)
B. (6,5)
C. (6,-5)
D. (-6,5)
Question 66
If cosec 45° - sin 30° = x, then x is
A. 5/√3
B. (√6-1)/√2
C. √3+2
D. (2√2-1)/2
Question 67
The simplest value of 38-212+20318-227+45 is
A. 3/2
B. 2/3
C. 1/3
D. 2
Question 68
If (7x - 13) (12x + 3) = 14, then the value of x is ______ .
A. -6
B. 6
C. -2/5
D. 2/5
Question 69
What is the value of cot210°?
A. 1/√3
B. -1/√3
C. √3
D. -√3
Question 70
If cosec 135° = x, then the value of x is
A. √2
B. 2
C. -√2
D. 1/√3
Question 71
In an acute-angled triangle ABC is Sin(B+A+C)=32 and tan(C+A-B)=1, then C is equal to
A. 37.5°
B. 67.5°
C. 52.5°
D. 72.5°
Question 72
If x + 1/x = 6, then value of x2 + 1/x2 is
A. 23
B. 16
C. 34
D. 32
Question 73
If (6 - 18x) - (x - 7) = 8, then the value of x is ______.
A. -5/19
B. -2/13
C. 2/13
D. 5/19
Question 74
If y = √3 - √2, then find the value of 1y3 - y3.
A. 11
B. 11√2
C. 22
D. 22√2
Question 75
∆ABC is right angled at B. If m∠A = 45°, then find the value of (coseC + 1/√3).
A. (3√2+1)/3
B. (2+√3)/2
C. 5/√3
D. (√6+1)/√3
Question 76
If α + β = 90° and α:β = 2:1, then the ratio of cosα to cosβ is
A. 1:√3
B. 1:3
C. 1:√2
D. 1:2
Question 77
A 12 m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle?
A. 12/π+4
B. 6/π+4
C. 3/π+4
D. 6/π+2√2
Question 78
What is the simplified value of 31253 + 4253 + 36753
A. 18253
B. 5253
C. 9√125
D. 1253
Question 79
The average weight of Sudesh, Jyothi and Ritu is 89 kg. If the average weight of Sudesh and Jyothi be 98 kg and that of Jyothi and Ritu be 83 kg, then the weight of Jyothi is
A. 58
B. 56
C. 95
D. 66
Question 80
If 11+11+11+1x = 58, then what is the value of x?
A. 2
B. 3
C. 1
D. 4
Question 81
10 dozen apples, 15 dozen mangoes & 20 dozen oranges are kept for sale. 1/2, 1/3rd & 1/4th of each item respectively have been added. What is the total number of fruits kept for sale now?
A. 720
B. 600
C. 580
D. 820
Question 82
The diagonal of a square equals the side of an equilateral triangle. If the area of the square is 12 sq cm, what is the area of the equilateral triangle?
A. 12√3 sq cm
B. 6√3 sq cm
C. 12√2 sq cm
D. 24 sq cm
Question 83
[sinA/(1 + cosA)] + [(1 + cosA)/sinA] is equal to
A. 2secA
B. 2cosecA
C. 2tanA
D. 2cotA
Question 84
What is the value of (cosec45 + √3/2) ?
A. 5/6
B. (4+√3)/2√3
C. (2√2+√3)/2
D. 3√3/2
Question 85
Determine the value of “s” for which the equation 5x + 35 = 60x + s has infinite number of solutions.
A. 420
B. 440
C. 460
D. 480
Question 86
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
A. 30 birds
B. 60 birds
C. 72 birds
D. 90 birds
Question 87
What is the value of sin (630 + A) + cos A?
A. √3/2
B. 1/2
C. 0
D. 2/√3
Question 88
If X + Y = 19 and X - Y = 7, then XY = ?
A. 13
B. 48
C. 78
D. 72
Question 89
If M = 0.1 + (0.1)2 + (0.01)2 and N = 0.3 + (0.03)2 + (0.003)2, then what is the value of M + N?
A. 0.411009
B. 0.413131
C. 0.313131
D. 0.131313
Question 90
If (x – 2) and (x + 3) are the factors of the equation x2 + k1x + k2 = 0, then what are the values of k1 and k2?
A. k1 = 6, k2 = – 1
B. k 1 = 1, k 2 = – 6
C. k 1 = 1, k2 = 6
D. k1 = – 6, k2 = 1
Question 91
If 2x-12x = 5, then what is the value x2 + 116x2 - 2
A. 19/4
B. 23/4
C. 27/4
D. 31/4
Question 92
Given that tan(θ + 15°) = √3. Then the value of θ is?
A. 15°
B. 75°
C. 45°
D. 65°
Question 93
0.296 + 2.96 + 29.6 + 296 = ?
A. 327.856
B. 328.756
C. 328.856
D. 327.756
Question 94
If x - y = 7 and x + y = 13, then x2 - y2 is
A. 91
B. -30
C. 30
D. -91
Question 95
If a and b are the roots of the equation Px2 – Qx + R = 0, then what is the value of (1/a2) + (1/b2) + (a/b) + (b/a)?
A. Q2-2P2R+PPR2
B. Q2-2PRR+PPR2
C. Q2-2R2P+RP2R2
D. Q2-2PR2R+2PP2R2
Question 96
If xy = -30 and x2 + y2 = 61, then find the value of (x + y).
A. 2
B. 3
C. 1
D. 4
Question 97
Δ DEF is right angled at E. If m∠F = 45°, then what is the value of 2 Sin F x Cot F?
A. √2
B. 2
C. 1/√2
D. 1/2
Question 98
The points A(x,2), B(2,1) and C(6,3) are collinear. Find x?
A. 4
B. -2
C. -4
D. 2
Question 99
What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(4, 0) and C(-2, 2)?
A. (1 , -1)
B. (-1 , 1)
C. (2 , -2)
D. (-2 , 2)
Question 100
If a+b=5 and ab=3, then the value of (a2+b2) is
A. 17
B. 18
C. 19
D. 20
Question 101
If 8x/3 + [7(5 - 2x/3)]/2 = 1/2 , then what is the value of x?
A. -17
B. 51
C. -51
D. 17
Question 102
What is the value of (4a2 - 9b2 )/(2a + 3b) is
A. 2a - 3b
B. 2a + 3b
C. 2a
D. 3b
Question 103
Calculate the value of 0.77777 + 0.7777 + 0.777 + 0.77 + 0.7 + 0.07.
A. 3.86274
B. 3.80247
C. 3.85274
D. 3.87247
Question 104
If xy+yz+zx = 1, then the value of (1+y2)(x+y)(y+z) ?
A. 2
B. 3
C. 4
D. 1
Question 105
ΔPQR is right angled at Q. If tanP = 24/7, then what is the value of cosR ?
A. 25/7
B. 24/25
C. 24/7
D. 7/24
Question 106
The standard deviation of the set {10, 11, 9, 11, 9} is
A. 1/√5
B. 2/√5
C. 3/√5
D. 0
Question 107
If (9 - 3x) - (17x - 10) = -1, then the value of x is
A. 1
B. -1
C. 9/10
D. -0.9
Question 108
If a3- b3= 91 and a - b = 1, then what is the value of ab?
A. 27
B. 6
C. 9
D. 30
Question 109
A spherical lead ball of radius 6 cm is melted and small lead balls of radius 3 mm are made. The total number of possible small lead balls is
A. 4250
B. 4000
C. 8005
D. 8000
Question 110
If Tan θ = 9/40, then Sec θ = ?
A. 40/41
B. 9/41
C. 41/40
D. 41/9
Question 111
If 7x - [3(2x - 3)]/2 = 1/2, then what is the value of x?
A. -1
B. 1
C. 3
D. -3
Question 112
If a = 2 , b = 3 then the value of 27a3 - 54a2b + 36ab2 - 8b3 is
A. 1562
B. 1616
C. 1676
D. 1728
Question 113
Δ LMN is right angled at M. If m∠N = 60°, then Tan L =______.
A. 1/2
B. 1/√3
C. 1/√2
D. 2
Question 114
If sinA = x, then x is equal to
A. √(1 - cos2A)
B. √(1 - sin2A)
C. √(1 + cos2A)
D. √(1 + sin2A)
Question 115
If sec2A cosec2A = x, then x is
A. sec2A + cosec2A + 2
B. tan2A + cot2A - 2
C. tan2A + cot2A + 2
D. sec2A + cosec2A - 2
Question 116
The value of (sec245 - cot245) - (sin230 + sin260) is
A. 1
B. 2√3
C. 0
D. 1/√2
Question 117
Common factor of 12a4b6, 18a6c2, 36a2b2 is
A. 36a2
B. 108b2
C. 6a2b2
D. 6a2
Question 118
If Cos θ = 15/17 , then what is the value of Cosec θ?
A. 17/8
B. 8/17
C. 8/15
D. 17/15
Question 119
If α and β are the roots of the equation x2+ x – 1 = 0, then what is the equation whose roots are α5 and β5?
A. x2 + 7x – 1 = 0
B. x2 – 7x – 1 = 0
C. x2 – 11x – 1 = 0
D. x2 + 11x – 1 = 0
Question 120
If 1/(cosecA cotA) = x, then the value of x is
A. cosecA + cotA
B. cosecA - cotA
C. cosec2A + cot2A
D. √[cosec2A + cot2A]
Question 121
Which of the following quadratic equations has equal roots?
A. x2 - 14x - 49 = 0
B. x2 + 7x + 49 = 0
C. x2 - 7x - 49 = 0
D. x2 + 14x + 49 = 0
Question 122
If ax + by = 1 and bx + ay = 2aba2+b2 then x2+y2a2+b2 is equal to
A. 1
B. 2
C. 0.5
D. 0
Question 123
If sinC + sinD =X, then the value of X is?
A. 2cos[(C+D)/2]sin[(C-D)/2]
B. 2sin[(C+D)/2]cos[(C-D)/2]
C. 2cos[(C+D)/2]cos[(C-D)/2]
D. 2sin[(C+D)/2]sin[(D-C)/2]
Question 124
If x tan 60° + cos 45° = sec 45° then the value of x2 + 1 is
A. 6/7
B. 7/6
C. 5/6
D. 6/5
Question 125
In the first 10 overs of a cricket game, the run rate was only 3.2. The run rate in the remaining 40 overs to reach the target of 282 runs is
A. 6.4
B. 6.3
C. 6.25
D. 6.5
Question 126
If 2sec2x - tan2x = 5 and 0° ≤ x ≤ 90° , then x = ?
A. 60°
B. 90°
C. 30°
D. 45°
Question 127
Expand and simplify (x + 5)2 + (x - 3)2
A. 2(x2 + 2x - 17)
B. 2(x2 - 2x + 17)
C. 2(x2 - 2x - 17)
D. 2(x2 + 2x + 17)
Question 128
ΔABC is right angled at B. If cotA = 7/24, then what is the value of cosecC ?
A. 7/25
B. 25/7
C. 24/7
D. 7/24
Question 129
If 310 × 272 = 92 × 3n then the value of n is
A. 10
B. 12
C. 15
D. 20
Question 130
What is the value of (cos 40° – cos 140°)/(sin 80° + sin 20°)?
A. 2√3
B. 2/√3
C. 1/√3
D. √3
Question 131
Find the common factor of 3757+ 4357 and 3737+ 4337
A. (43 - 37)
B. (43 + 37)
C. 37
D. 10
Question 132
Find the value of 777777?
A. 73164
B. 7164
C. 76364
D. 7764
Question 133
If x+1x ≠0 and x3+1x3 = 0, then the value of x+1x4 is :
A. 9
B. 12
C. 15
D. 16
Question 134
If a1-2a+b1-2b+c1-2c = 12, then 11-2a+11-2b+11-2c value is
A. 1
B. 2
C. 3
D. 4
Question 135
If (x+a) is the H.C.F of 2x2+5x-12 and x2+x-12 then find the value of a.
A. -3
B. -2
C. 4
D. 5
Question 136
What is the value of 12 + 3(-2 x 3) - (18 / 6) ?
A. -5
B. 9
C. -9
D. 5
Question 137
If x3 – 4x2 + 19 = 6(x – 1), then what is the value of [x2 + (1/x – 4)]?
A. 3
B. 5
C. 6
D. 8
Question 138
Which of the following conditions is TRUE for the two line segments AB and CD to be congruent?
A. AB=CD
B. AB>CD
C. AB
Question 139
If a - b = 2 and ab = 8, then what is the value of a3 - b3?
A. 65
B. 34
C. 43
D. 56
Question 140
If 2x + 3y3x - 4y = 117, then the value of x/y is __
A. 65/19
B. 68/19
C. 67/19
D. 64/19
Question 141
If P = 22 + 62 + 102 + 142 + ... 942 and Q = 12 + 52 + 92 + ... 812, then what is the value of P – Q?
A. 24645
B. 26075
C. 29317
D. 31515
Question 142
What is the reflection of the point (2, 3) in the line y = 4?
A. (2, 5)
B. (2, -5)
C. (-2, -5)
D. (-2, 5)
Question 143
The value of cos(1110) is
A. √3/2
B. 1/2
C. 1/√2
D. 1
Question 144
The sum of two numbers is 7 and the sum their squares is 23, their product is equal to:
A. 10
B. 11
C. 12
D. 13
Question 145
If tan π/3c + cosec π/6c = x, then x is
A. (1-√2)/√2
B. (√3+4)/2√3
C. √3+2
D. (2√2-1)/2
Question 146
The average temperature of Monday to Wednesday was 37 C and of Tuesday to Thursday was 34 C. If the temperature on Thursday was 4/5 th of that of Monday, the temperature on Thursday was ?
A. 35 c
B. 36 c
C. 34 c
D. 32 c
Question 147
What is the value of tan 6° tan 36° tan 84° tan 54° tan 45°?
A. 1/2
B. 1/√2
C. 1
D. 1/3
Question 148
What is the value of (cot30°+ 2/√3) ?
A. 5/√3
B. (1+2√3)/2
C. 5/6
D. 2/√3
Question 149
If sum of the areas of the circumcircle and the incircle of an equilateral triangle is 770 cm2, then what is the area (in cm2) of the triangle?
A. 125√3
B. 147√3
C. 156√3
D. 169√3
Question 150
Find length of the arc whose central angle is 45° and radius of the circle is 28 cm?
A. 11 cm
B. 33 cm
C. 44 cm
D. 22 cm
Question 151
What is the value of (sin60° + 2/√3) ?
A. (2√3+1)/√3
B. 7/2√3
C. 3
D. 2+√3
Question 152
If 2 cos θ = 2 – sin θ, then what is the value of cos θ?
A. 1 or 3/5
B. 1 or –1/2
C. –1 or–1/2
D. –1 or 3/5
Question 153
If 2x+ 4(x - 3) < -2 - x < 2x - 1, then find the value of x.
A. -1
B. 1
C. 2
D. -2
Question 154
If XY = a+23 and YX = 13, then find the value of X2 + Y2X2 - Y2.
A. 1
B. 2
C. 3
D. 4
Question 155
If 5 - 5x < 4 - x and 2 - x < 6 - 4x, then x can take which of the following values?
A. 1
B. 2
C. -1
D. -2
Question 156
If cot(A/2) = x, then the value of x is
A. cosecA - cotA
B. cosecA + cotA
C. secA + cotA
D. secA - cotA
Question 157
If 1/3(12x/5 - 1/2) + 6/5 = 7/6, then what is the value of x?
A. 1/6
B. -1/6
C. 1/5
D. -1/5
Question 158
In ΔABC, D and E are points on side AB and AC respectively. DE is parallel to BC. If lengths of AD, DB and DE are 8 cm, 6 cm and 7.2 cm respectively, find length of BC?
A. 12.6 cm
B. 9.3 cm
C. 8.1 cm
D. 5.4 cm
Question 159
If Sec θ = 25/24 , then what is the value of Sin θ?
A. 24/25
B. 7/25
C. 24/7
D. 25/7
Question 160
If the sum of the digits of any integer between 100 and 1000 is subtracted from the same integer , the resulting number is always divisibleby
A. 2
B. 5
C. 6
D. 9
Question 161
If x + y = 10 and x2 + y2 = 68, then find xy
A. 21
B. 24
C. 25
D. 16
Question 162
One of the roots of the equation x2 - 4x + k = 0 is x = 3. The other root is
A. x = -1
B. x = -4
C. x = 1
D. x = 4
Question 163
If a2+b2+c2=83 and a+b+c=15 then the value of ab+bc+ca is
A. 69
B. 70
C. 71
D. 72
Question 164
Find the value of 200 x 20 x 2 x 0.2 x 0.02 x 0.002 = ?
A. 0.064
B. 0.64
C. 64
D. 640
Question 165
If u+v = 10 and uv = 16, then find the value of u2-v2uv
A. 0
B. 15/8
C. 15/4
D. 15/2
Question 166
If 3x + 4y – 2z + 9 = 17, 7x + 2y + 11z + 8 = 23 and 5x + 9y + 6z – 4 = 18, then what is the value of x + y + z – 34?
A. – 28
B. – 14
C. – 31
D. – 45
Question 167
If a - b = -6 and a2 + b2 = 44, then ab is
A. -4
B. 8
C. 4
D. -8
Question 168
Find equation of the perpendicular bisector of segment joining the points (2,6) and (4,0)?
A. x + 3y = 6
B. x + 3y = -6
C. x - 3y = -6
D. x - 3y = 6
Question 169
A ship is full of cargo containers. It drops 2/3 of cargo containers at the first port and takes 60 more, at the second port it drops two third of the new total and takes eleven more. On arriving at the third port it is found that it have 48 cargo containers. Find the number of cargo containers in the ship at the starting?
A. 189
B. 159
C. 161
D. 153
Question 170
If 4x2= 152- 92, then value of x is
A. 9
B. 6
C. 3
D. 12
Question 171
If √[(1 - cosA)/2] = x, then the value of x is
A. cos(A/2)
B. tan(A/2)
C. sin(A/2)
D. cot(A/2)
Question 172
The value of x13+x-13x23-1+x-23
A. x-1+x23
B. x+x-13
C. x13+x-1
D. x+x-1
Question 173
ΔDEF is right angled at E. If cosD = 8/17, then what is the value of secF ?
A. 17/8
B. 8/17
C. 17/15
D. 15/17
Question 174
ΔUVW is right angled at V. If secU = 5/3, then what is the value of tanW ?
A. 3/4
B. 5/3
C. 4/5
D. 4/3
Question 175
If x = 1/(√2+1) then the value of x2 + 2x - 1 is
A. 2√2
B. 4
C. 0
D. 2
Question 176
If 5x - (1/2)(2x -7) = 5.5, then what is the value of x?
A. 3/2
B. 1/2
C. -1/2
D. -3/2
Question 177
What is the value of ( 1/3 - cosec30°) ?
A. (√6-1)/√3
B. -1/2
C. -5/3
D. 3/2
Question 178
If secA - tanA = x, then the value of x is
A. √[(1 + sinA)/(1 - sinA)]
B. √[(1-sinA)/(1+sinA)]
C. (1-sinA)/(1+sinA)
D. (1 + sinA)/(1 - sinA)
Question 179
What is the value of √[(1 + sinA)/(1 - sinA)]?
A. secA - tanA
B. cosecA + tanA
C. secA + tanA
D. cosecA - tanA
Question 180
What is the value of sin (B – C) cos (A – D) + sin (A – B) cos (C – D) + sin (C – A) cos (B – D)?
A. 3/2
B. – 3
C. 1
D. 0
Question 181
If a = 1/a-5, then the value of a + 1/a = ?
A. √29
B. √-29
C. - √29
D. √27
Question 182
If 5x + 6(3-2x) = 4, then what is the value of x?
A. 1
B. 2
C. 3
D. 4
Question 183
Two equal circles intersect such that each passes through the centre of the other. If the length of the common chord of the circles is 10√3 cm, then what is the diameter of the circle?
A. 10 cm
B. 15 cm
C. 20 cm
D. 30 cm
Question 184
The value of 122 + 345 - 3 / 1116 x 372 is
A. 466
B. 469
C. 446
D. 460
Question 185
What is the sum of the first 12 terms of an arithmetic progression if the 3rd term is -13 and the 6th term is -4?
A. 67
B. 45
C. -30
D. -48
Question 186
If (4a-3)2=0, then the value of 64a3+12a+13 is
A. 0
B. 11
C. 22
D. 33
Question 187
What is the value of √2 Sec 45 - Tan 30?
A. (2√3 - 1)/3
B. (√3 - 1)/√3
C. (2√3 - 1)/√3
D. (√3 - 1)/3
Question 188
What is the reflection of the point (-1 , 3) in the line x = -4?
A. (-7 ,-3)
B. (-7 ,3)
C. (7 ,-3)
D. (7 ,3)
Question 189
If x, y, z are the three factors of a3 -7a - 6, then value of x+y+z will be
A. 3a
B. 3
C. 6
D. a
Question 190
What is the value of cos 11π/6?
A. -1/√2
B. -√3/2
C. 2/√3
D. √3/2
Question 191
If x = cosecθ - sinθ and y = secθ - cosθ, then the relation between x and y is
A. x2+ y2+ 3 =1
B. x2y2 (x2+ y2+3)=1
C. x2 (x2+ y2 - 5)=1
D. y2 (x2+ y2 - 5)=1
Question 192
If x + 1x = 3, then x18 + x12 + x6 + 1 value is
A. 0
B. 1
C. 2
D. 3
Question 193
Triangle DEF is right angled at E. If cot D = 5/12, then what is the value of sin F?
A. 5/12
B. 13/5
C. 5/13
D. 13/12
Question 194
If x = 2 +√3, y = 2 – √3 and z = 1, then what is the value of (x/yz) + (y/xz) + (z/xy) + 2 [(1/x) + (1/y) + (1/z)]?
A. 25
B. 22
C. 17
D. 43
Question 195
199994 x 200006 = ?
A. 39999799964
B. 39999999864
C. 39999999954
D. 39999999964
Question 196
In ΔPQR, S and T are points on side PQ and PR respectively. ST is parallel to QR. If S divides PQ in the ratio 4:3 and length of QR is 4.9 cm, find ST?
A. 5.6 cm
B. 7.2 cm
C. 2.8 cm
D. 3.6 cm
Question 197
1 - [5 - {2 + (- 5 + 6 - 2) 2}] is equal to:
A. -4
B. 2
C. 0
D. 2
Question 198
Hemavathi gets 3 marks for each right sum and loses 2 marks for each wrong sum. He attempts 35 sums and obtains 60 marks. The number of sums attempted correctly is ?
A. 23
B. 24
C. 25
D. 26
Question 199
If u : v = v : w, then what is the value of u4 : v4?
A. u2 : wv
B. u2 : w2
C. u2 v : w3
D. u : w
Question 200
What is the equation of the line passing through the point (-1,3) and having x-intercept of 4 units?
A. 3x - 5y = 12
B. 3x + 5y = 12
C. 3x + 5y = -12
D. 3x - 5y = -12
Question 201
If 1/√(1 - sin2A) = x, then the value of x is
A. tanA
B. cosecA
C. secA
D. cosA
Question 202
If (4x - 3) = (3x + 8), then the numerical value of(x + 1)3 is
A. 1331
B. 1000
C. 1728
D. 729
Question 203
If α and β are roots of the equation 3x2 – 13x + 14 = 0, then what is the value of (α/β) + (β/α)?
A. 65/28
B. 53/14
C. 9
D. 85/42
Question 204
If a + b + c = 11 and ab + bc + ca = 17, then what is the value of a3 + b3 + c3 – 3abc?
A. 121
B. 168
C. 300
D. 770
Question 205
An army lost 10% of its men in war, 10% of the remaining died due to disease and 10% of the rest were declared disabled. Thus the strength of the army was reduced to 7,29,000 active men. The original strength of the army was
A. 1500000
B. 1000000
C. 1200000
D. 1100000
Question 206
If tan θ + sec θ = (x – 2)/(x + 2), then what is the value of cos θ?
A. (x2 – 1)/(x2 + 1)
B. (2x2 – 4)/(2x2 + 4)
C. (x2 – 4)/(x2 + 4)
D. (x2 – 2)/(x2 + 2)
Question 207
If a2sec2x - b2tan2x = c2 then the value of sec2x + tan2x is equal to (assume b2 ≠ a2 )
A. b2-a2+2c2b2+a2
B. b2+a2-2c2b2-a2
C. b2-a2-2c2b2+a2
D. b2-a2b2+a2+2c2
Question 208
If x + y = 12 and x2 + y2 = 94, then xy is
A. 25
B. 50
C. 144
D. 238
Question 209
If the roots of the equation a(b – c)x2 + b(c – a)x + c(a – b) = 0 are equal, then which of the following is true?
A. b = ( a + c)/ ac
B. 2/ b = (1/ a) + (1/ c)
C. 2 b = (1/ a) + (1/ c)
D. abc = ab + bc + ca
Question 210
What is the value of tanπ4+A×tan3π4+A ?
A. 1
B. 0
C. cot A/2
D. – 1
Question 211
If x1x2x3 = 4(4 + x1 + x2 + x3 ), then what is the value of [1/(2 + x1 )] + [1/(2 + x2 )] + [1/(2 + x3 )]?
A. 1
B. 1/2
C. 2
D. 1/3
Question 212
Simplify : 213 - 112 of 35 + 125 ÷ 213
A. 1/10
B. 3/10
C. 11/10
D. 1
Question 213
What is the value of a2 + b2a3 - b3, when a + b = 8 and a - b = 2?
A. 0.313
B. 0.347
C. 0.368
D. 0.381
Question 214
If tan2A + cot2A + 2 = x, then the value of x is
A. tan2Acosec2A
B. secAcosecA
C. sec2Acosec2A
D. tanAcosecA
Question 215
If xy = 56 and x2+ y2= 113, then what will be the value of (x + y)?
A. 29
B. 21
C. 36
D. 15
Question 216
If secA/(secA - 1) + secA/(secA + 1) = x, then x is
A. 2cosec2A
B. 2sec2A
C. 2cosecA
D. 2secA
Question 217
The sum of a fraction and 4 times its reciprocal is 13/3. What is the fraction?
A. 4/3
B. 3/4
C. 5/4
D. 4/5
Question 218
If the mean of m observations out of n observations is n and the mean of remaining observations is m, then what is the mean of all n observations?
A. 2m –m^2/n
B. 2m –m/n
C. 2m
D. 2m –m
Question 219
If x – (1/x) = 3, then what is the value of (2x4 + 3x3 + 13x2 – 3x + 2) / (3x4 + 3)?
A. 1/3
B. 2/3
C. 4/3
D. 5/3
Question 220
Given: 2x - 4 ≤ 2 - x/3 and 2(2x + 5) > 3x - 5, then x can take which of the following values?
A. -14
B. 3
C. 4
D. 14
Question 221
Rehman walks at 8 km/hr and Roma cycles at 13 km/hr towards each other. What was the distance between them when they started if they meet after 36 minutes?
A. 12.6 kms
B. 18.9 kms
C. 15.8 kms
D. 9.5 kms
Question 222
18800÷470÷20=?
A. 1
B. 2
C. 3
D. 4
Question 223
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to ___ ?
A. 3.7
B. 2.7
C. 3.6
D. 2.9
Question 224
If cosec2 θ = 625/576, then what is the value of [(sin θ – cos θ)/(sin θ + cos θ)]?
A. 1
B. 31/17
C. 17/31
D. 14/25
Question 225
The rate of discount on an article whose marked price is Rs. 170 and selling price is Rs. 130?
A. 24.26%
B. 22.45%
C. 23.53%
D. 23.60%
Question 226
What is the value of sec 330°?
A. 2
B. -2/√3
C. -2
D. 2/√3
Question 227
If x – y – √18 = –1 and x + y – 3√2 = 1, then what is the value of 12xy(x2 – y2)?
A. 0
B. 1
C. 512√2
D. 612√2
Question 228
The least number that must be subtracted from 63522 to make the result a perfect square is = ?
A. 18
B. 20
C. 24
D. 30
Question 229
What is the value of Sin 60° + (1/2)Cosec 45°?
A. (√3 + 2)/2
B. (√3 + √2)/√2
C. (√3 + 2)/√2
D. (√3 + √2)/2
Question 230
If 5/2 - (6/5)(x - 15/2) = -x/5, then what is the value of x?
A. -23/2
B. 13/2
C. -13/2
D. 23/2
Question 231
The square root of 6084 is
A. 82
B. 78
C. 74
D. 76
Question 232
If a + b = 3 and ab = -4, then what is the value of a3 + b3?
A. 36
B. 63
C. 12
D. -15
Question 233
If x - y = -6 and x + y = 16, then x2- y2 is?
A. 96
B. -96
C. 22
D. -22
Question 234
Which of the following fractions is largest?
A. 3/4
B. 4/5
C. 5/6
D. 7/8
Question 235
If one root of the equation (1-m)x2 + 1 = 0 is double the other and 'I' is a real number, then which of the following is true?
A. m > 9/8
B. m> 8/9
C. m = 8/9
D. m <= 9/8
Question 236
Find the sum of interior angles of a dodecagon?
A. 1620°
B. 1800°
C. 1440°
D. 1260°
Question 237
Determine the value of a2+b2a3+b3 when a = 2+√3 and b = 2-√3.
A. 0.27
B. 0.42
C. 0.58
D. 0.93
Question 238
If 4x + 3y = 11 and 3x + 2y = 8, then (x,y) is
A. 2, 0
B. 1, 6
C. 2, 1
D. 5, 6
Question 239
What is the value of cot 11π/6?
A. -√3
B. -1
C. √3
D. -1/2
Question 240
What is the value of 99992 x 100008?
A. 9999999936
B. 9999899936
C. 9999999836
D. 9999999926
Question 241
If x3 + y3 + z3 = 3(1 + xyz), P = y + z – x, Q = z + x – y and R = x + y – z, then what is the value of P3 + Q3 + R3 – 3PQR?
A. 9
B. 8
C. 12
D. 6
Question 242
If x = 313- 3-13, then 3x2 + 9x is equal to
A. 5
B. 6
C. 7
D. 8
Question 243
Solve the following : 27 - [38 - {46 - (15 - 13 - 2)}]
A. 31
B. 35
C. 30
D. 29
Question 244
An angle is greater than its complementary angle by 30°. Find the measure of the angle?
A. 30°
B. 90°
C. 60°
D. 120°
Question 245
If sinA + sin2A = 1 then what is the value of cos2A + cos4A ?
A. 1
B. 2
C. 1/2
D. 1/4
Question 246
What is the value of 299996 x 300004?
A. 89999999984
B. 89999699984
C. 89999999884
D. 89999999974
Question 247
What is the value of (tan60 - 1/3) ?
A. 3-√2
B. (2√2-√3)/2
C. -1/2√3
D. (3√3-1)/3
Question 248
If secA + tanA = a, then the value of cosA is
A. a2+12a
B. 2aa2+1
C. a2-12a
D. 2aa2-1
Question 249
Reflection of the point (4,6) in the origin is
A. (4,6)
B. (-4,-6)
C. (-4,6)
D. (4,-6)
Question 250
If (x + 1/x) = 3, then x8+1x8 is equal to
A. 2201
B. 2203
C. 2207
D. 2213
Question 251
What is the slope of the line perpendicular to the line passing through the points (8,2) and (3,1)?
A. 5
B. 3/5
C. 5/3
D. 1/5
Question 252
Two fractions are such that their product is 2/5 and sum is 1/15. What are the two fractions.
A. 4/3, -3/10
B. 2/7, -7/5
C. 4/7, -7/10
D. 2/3, -3/5
Question 253
Calculate the value of √3√3 + 3, if √3 = 1.732
A. 0.366
B. 0.566
C. 0.356
D. 0.346
Question 254
For triangle PQR, find equation of altitude PS if co-ordinates of P, Q and R are (6,2), (0,3) and (-4,5) respectively?
A. 2x - y = 14
B. 2x + y = 10
C. 2x - y = 10
D. 2x + y = 14
Question 255
One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
A. Rs. 30,000
B. Rs. 50,000
C. Rs. 60,000
D. Rs. 90,000
Question 256
The difference between two numbers is 1146. When we divide the larger number by smaller we get 4 as quotient and 6 as remainder. Find the larger number
A. 1526
B. 1431
C. 1485
D. 1234
Question 257
Compute : 1112 / 139 - 5
A. 557/67
B. -3
C. 556/67
D. 3
Question 258
The value of (1 - √2) + (√2 - √3) + (√3 - √4) + ..... + (√15 - √16) is
A. 0
B. 1
C. -3
D. 4
Question 259
If 5(4 - x) - 4 > 5x -2 > 2x - 6, then the value of x is
A. -2
B. 2
C. -1
D. 3
Question 260
If x +y = √3 and x - y = √2, then the value of 8xy (x2 + y2) is
A. 6
B. √6
C. 5
D. √5
Question 261
23 x 19 = 437. How much is 0.0437 / 1.9 = ?
A. 0.0023
B. 0.23
C. 0.023
D. 2.3
Question 262
Determine the value of a/b + b/a when a + b = 8 and ab = 4.
A. 4
B. 8
C. 12
D. 14
Question 263
If 3x+7=x2+p=7x+5, what is the value of P ?
A. 17/2
B. 25/3
C. 33/4
D. 41/5
Question 264
Water boils at 212°F or 100°C and melts at 32°F or 0°C . If the temparature of the particular day is 35°C , it is equal to :
A. 85°F
B. 95°F
C. 96°F
D. 97°F
Question 265
If a + b = 1, then a4 + b4 - a3 - b3 - 2a2b2 + ab is equal to
A. 1
B. 2
C. 4
D. 0
Question 266
Find the products : 0.5 x 0.05 x 0.005 x 500
A. 0.0625
B. 0.00625
C. 0.06255
D. 0.625
Question 267
If the equation 4x + 3y + 5 = 0 and 6x - ky - 7 = 0 have no solution, then the value of k is
A. -4.5
B. -8
C. 8
D. 4.5
Question 268
If x+y+z = 0, then what is the value of x23z+y33xz+z23x ?
A. 0
B. xz
C. y
D. 3y
Question 269
If a+b=2c then the value of aa-c+cb-c is equal to (where a≠b≠c)
A. -1
B. 1
C. 0
D. 1/2
Question 270
What is the value of (3/5 + 7/9)?
A. 62/45
B. 31/28
C. 5/7
D. 1/7
Question 271
In an isosceles trapezium _____.
A. Diagonals are congruent
B. Opposite sides are parallel
C. Diagonals are bisectors of each other
D. Diagonals bisect opposite angles
Question 272
ΔDEF is right angled at E. If m∠D = 45°, then find the value of (tanF + 1/3).
A. 4/3
B. 3√3/2
C. (√2+1)/√2
D. (3√2+1)/3
Question 273
6.651 - (148.6 - x ) - 57.22 = 6.098. Find x.
A. 205.267
B. 90.827
C. -91.933
D. 218.569
Question 274
Solve : 1000x - 5 = -6
A. 1/1000
B. -1/1000
C. -11/1000
D. 11/1000
Question 275
In a circle, two arcs of unequal length subtend angles in the ratio 5:3. If the smaller angle is 45° then the measure of other angle in degrees.
A. 75°
B. 72°
C. 60°
D. 78°
Question 276
If x2-2x+1=0, then the value of x4+1x4 is
A. 0
B. 1
C. 2
D. 3
Question 277
Solve the following : 80÷[48−56−(60−36÷12×4)]=?
A. 5
B. 8
C. 4
D. 2
Question 278
ΔDEF is right angled at E. If m∠F = 30 deg, then find the value of (sinD - 1/3).
A. -1/2√3
B. (3√3-2)/6
C. (√2-√3)/√6
D. (2√2-1)/√2
Question 279
Compute 4923 / 547 - 10
A. 1
B. -1
C. 1641/179
D. 1614/179
Question 280
If 14/3 + (1/2)(x - 7/3) = -2x/3, then the value of x is?
A. -3
B. 3
C. -6
D. 6
Question 281
Find the value of 6732.8 + 673.28 + 67.328 + 6.7328 + 0.67328 ?
A. 74808.1408
B. 7480.78408
C. 74808.2408
D. 7480.81408
Question 282
What is the x – intercept of the linear equation 18x + 25y – 900 = 0?
A. 18
B. 25
C. 50
D. 450
Question 283
In ΔABC measure of angle B is 90 deg. If cotA = 7/24, and AB = 1.4cm, then what is the length (in cm) of side AC?
A. 5
B. 4.8
C. 4
D. 5.6
Question 284
If a2b+c=b2C+a=a2a+b=1 then 11+a+11+b+11+c is
A. 1
B. 2
C. 3
D. 4
Question 285
Solve the following : 3/4+{3/4 + 3/4 ÷ (3/4 + 3/4)} = ?
A. 0
B. 3/4
C. 1
D. 2
Question 286
Calculate the angle subtended by the chord at the point on the major arc if the radius and the chord of the circle are equal in length.
A. 30°
B. 120°
C. 200°
D. 300°
Question 287
∆DEF is right angled at E. If cosD = 5/13, then what is the value of tanF?
A. 5/13
B. 5/12
C. 13/5
D. 13/12
Question 288
23 x 31 = 713. How much is 0.0713 / 3.1?
A. 0.23
B. 0.0023
C. 2.3
D. 0.023
Question 289
If 4(x+y) = 256 and (256)(x-y) = 4, then what is the value of x and y?
A. 17/8, 15/8
B. 17/4, 15/4
C. 9/17, 15/17
D. 8/17, 8/15
Question 290
What are the co-ordinates of the mid point of the segment joining points C(0,-3) and D(8,5)?
A. (4, 1)
B. (-4, 1)
C. (4, -1)
D. (-4, -1)
Question 291
What is the value of Cot 45° - (1/√3)Cosec 60°?
A. 1/√3
B. 1/2
C. 1/√2
D. 1/3
Question 292
If a – (1/a) = b, b – (1/b) = c and c – (1/c) = a, then what is the value of (1/ab) + (1/bc) + (1/ca)?
A. – 3
B. – 6
C. – 1
D. – 9
Question 293
How many 18' s are there in 3712?
A. 300
B. 400
C. 500
D. 600
Question 294
If x + 3 ≤ 4x + 4 and 3(4 - x) - 4 ≥ 2x - 2, then x can take which of the following values?
A. 1
B. 3
C. -1
D. -3
Question 295
If (1/x) + (1/y) + (1/z) = 0 and x + y + z = 9, then what is the value of x3 + y3 + z3 – 3xyz?
A. 81
B. 361
C. 729
D. 6561
Question 296
If 3.352 - (9.759 - x ) - 19.64 = 7.052, then what is the value of x?
A. -6.181
B. 13.581
C. 33.099
D. 39.803
Question 297
What is the value of a-b when a2+b2-6a-6b+18 = 0 ?
A. 0
B. 3
C. 6
D. 9
Question 298
A hydrogen filled balloon ascending at the rate of 18 kmph was drifted by wind. Its angle of elevation at 10th and 15th minutes were found to be 60° and 45° respectively. The wind speed (in whole numbers) during the last five minutes, approximately, is equal to
A. 7 km/hr
B. 11 km/ hr
C. 26 km/hr.
D. 33 km/hr
Question 299
Compute : 4082 / 157 - 23
A. -3
B. 3
C. 2041/67
D. 2014/67
Question 300
If the expression px3 – qx2 – 7x – 6 is completely divisible by x2 – x – 6, then what is the value of p and q respectively?
A. 0, 1
B. 1, 0
C. 2, 1
D. 1, 2
Question 301
If p = 99, then the value of p(p2+3p+3) will be
A. 999999
B. 1000000
C. 1000001
D. 999998
Question 302
If x2 – 16x – 59 = 0, then what is the value of (x – 6)2 + [1/(x – 6)2]?
A. 14
B. 18
C. 16
D. 20
Question 303
What is the value of ( 1/3 + cosec30)?
A. (√6+1)/√3
B. 7/3
C. (4+√3)/2
D. (√3+1)/2
Question 304
(98764 + 89881 + 99763 + 66342) ÷ (1186 + ? + 1040 + 1870) = 55
A. 2254
B. 2354
C. 2368
D. 2404
Question 305
In ΔUVW measure of angle V is 90 deg. If cosecU = 13/12, and UV = 2.5cm, then what is the length (in cm) of side VW?
A. 6.5
B. 6
C. 4
D. 5.6
Question 306
Solve the following : -1/4 { -45 - (-96) / (-32)} = ?
A. 12
B. 10.5
C. -12
D. -10.5
Question 307
If cosAcotA/(1 - sinA) = x, then the value of x is
A. 1 - cosecA
B. 1 + cosecA
C. 1 + secA
D. 1 - secA
Question 308
If x + y + z = 22 and xy + yz + zx = 35, then what is the value of (x – y)2 + (y – z)2 + (z – x)2?
A. 793
B. 681
C. 758
D. 715
Question 309
If sin 3θ sec 2θ = 1, then what is the value of [3 tan2(5θ/2) – 1]?
A. 0
B. 1
C. 2
D. 3
Question 310
If (x + y + z) = 12, xy + yz + zx = 44 and xyz = 48, then what is the value of x3 + y3+ z3?
A. 104
B. 144
C. 196
D. 288
Question 311
Find k, if the line 4x - y = 1 is perpendicular to the line 5x - ky = 2?
A. 20
B. -20
C. 4
D. -4
Question 312
The highest score in an inning was 3/11 of the total and the next highest was 3/11 of the reminder . If the score differ by 9, the total score was :
A. 110
B. 121
C. 132
D. 143
Question 313
6 times a fraction is greater than 7 times its reciprocal by 11. What is the fraction?
A. 5/3
B. 7/3
C. 5/4
D. 4/5
Question 314
N is the smallest three digit prime number. When N is divided by 13, then what will be the remainder?
A. 8
B. 9
C. 7
D. 10
Question 315
An aeroplane flying horizontally at a height of 3 Km. above the ground is observed at a certain point on earth to subtend an angle of 60°. After 15 sec flight, its angle of elevation is changed to 30°. The speed of the aeroplane (taking √3 = 1.732) is
A. 230.63 m/sec
B. 230.93 m/sec
C. 235.85 m/sec
D. 236.25 m/sec
Question 316
The zeros of the cubic polynomial 2x3-x2-2x+1 are a, b and c respectively. Find a+b+c :
A. -1
B. 2
C. 1
D. none
Question 317
If a - b = 5 and a2 + b2 = 97, ab = ?
A. 48
B. 32
C. 36
D. 72
Question 318
What is the value of [(sin x + sin y) (sin x – sin y)]/[(cosx + cosy) (cosy – cosx)]?
A. 0
B. 1
C. – 1
D. 2
Question 319
Which of the following is not a quadratic equation?
A. 2x(x + 4) -11 = x(x - 3) + 6
B. 4x(x + 4) -11 = 5x(x - 3) + 5
C. x(x + 2) -15 = x(x - 5) + 11
D. 2x2 + 8x - 11 = 0
Question 320
What is the simplified value of cosec Acot A + tan A2 ?
A. 2cos 2A
B. 1 – sin2 A
C. sec2A
D. secA tanA
Question 321
Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?
A. 256
B. 432
C. 512
D. 640
Question 322
If α and β are the roots of equation x2 – x + 1 = 0, then which equation will have roots α3 and β3?
A. x2 + 2x + 1 = 0
B. x2 – 2x – 1 = 0
C. x2 + 3x – 1 = 0
D. x2 – 3x + 1 = 0
Question 323
Find the value of 64344?
A. 1
B. 2
C. 3
D. 4
Question 324
If [7(5x/3 - 3/2)]/2 + 3/2 = 1/4, then what is the value of x?
A. 35/24
B. 24/35
C. -24/35
D. -35/24
Question 325
Δ DEF is right angled at E. If m∠D = 45%., then Cosec F =
A. 1/2
B. 1/√2
C. √2
D. 1/√3
Question 326
A, B and C can finish a job working alone in 72, 24 and 36 days respectively. In how many days they can finish the job if they worked together?
A. 12
B. 9
C. 15
D. 18
Question 327
If θ is positive acute angle and 4sin2θ = 3, then the value of tan θ - cot θ/2 is
A. 1
B. 0
C. √3
D. 1/√3
Question 328
What will be the roots of the quadratic equation x2 - 25x + 156 = 0?
A. 12, 13
B. 25, 1
C. 9, 16
D. 31, 6
Question 329
ΔABC is right angled at B. If m∠C = 60°, then find the value of (cotA - 1/2).
A. -1/√3
B. (3-√2)/3√2
C. (2√3-1)/2
D. (√2-√3)/√6
Question 330
If 4(2x - 4) - 2 > 3x - 1 ≥ 4x - 7, then x can take which of the following values?
A. 7
B. 6
C. 2
D. 0
Question 331
Reflection of the point (4,-5) in the y-axis is
A. (4,5)
B. (-4,-5)
C. (4,-5)
D. (-4,5)
Question 332
Simplify 576b3x2a4z3/36a3b2z
A. 16bx2az2
B. 8bx2az2
C. 32ba2 z
D. 32bxa2
Question 333
P(4,2) and R(-2,0) are vertices of a rhombus PQRS. What is the equation of diagonal QS.
A. x - 3y = -2
B. 3x + y = 4
C. 3x + y = -4
D. x - 3y = 2
Question 334
If 1/√(1 + cot2A) = x, then value of x is
A. sinA
B. cosecA
C. cosA
D. secA
Question 335
What is the value of tan 4π/3?
A. 1/2
B. √3
C. √3/2
D. 1/√2
Question 336
Coefficient of x2 in (x + 9)(6 - 4x) is
A. 54
B. -4
C. 30
D. 4
Question 337
What is the value of z2+1z2 when z = 5+26 ?
A. 49
B. 50
C. 98
D. 100
Question 338
If sec θ (cos θ + sin θ) = √2, then what is the value of (2 sin θ)/(cos θ – sin θ)?
A. 3√2
B. 3/√2
C. 1/√2
D. √2
Question 339
Which of the following is a Pythagorean triplet?
A. 8, 15, 17
B. 17, 21, 29
C. 7, 9, 11
D. 2, 3, 5
Question 340
Given a - b = 2, a3 - b3=26 then (a + b)2 is
A. 9
B. 4
C. 16
D. 12
Question 341
The perimeter of two similar triangles is 36 units and 48 units. Find the ratio of their corresponding areas.
A. 1 : 3
B. 3 : 4
C. 4 : 9
D. 9 : 16
Question 342
If the two lines px + 6y+3=0 and 2x + qy+3=0 have infinite solutions then find the value of p and q respectively.
A. 2,6
B. 6,2
C. 2,2
D. 6,6
Question 343
The square root of 4096 is
A. 56
B. 68
C. 74
D. 64
Question 344
If P + 1P+2 = 1, then the value of P+23+1P+23-3 ?
A. 12
B. 16
C. 18
D. 15
Question 345
What is the value of [1 – sin (90 – 2A)] / [1 + sin (90 + 2A)]?
A. sinA cosA
B. cot2A
C. tan2A
D. sin2A cosA
Question 346
2sinAsinB is equal to
A. sin(A+B) + sin(A-B)
B. cos(A-B) - cos(A+B)
C. sin(A+B) - sin(A-B)
D. cos(A+B) + cos(A-B)
Question 347
If the selling price is Rs 1680 after getting a discount of 16%, what was the marked price?
A. Rs 2000
B. Rs 1948.8
C. Rs 1411.2
D. Rs 1448
Question 348
The two roots of an quadratic equation are given as x = 1/2 and x = -1/3. The equation can be written as
A. (2x - 1)(3x - 1) = 0
B. (2x + 1)(3x - 1) = 0
C. (2x - 1)(3x + 1) = 0
D. (2x + 1)(3x + 1) = 0
Question 349
If √3 = 1.732, then the value of 9+233?
A. 7.169
B. 7.196
C. 5.198
D. 7.296
Question 350
What are the coordinates of the mid point of the segment joining points C(5,-2) and D(-1,8).
A. (-2, 3)
B. (2, 3)
C. (2, -3)
D. (-2, -3)
Question 351
If √20 + √125 = 15.65, then what is the value of √45 + √5?
A. 6.98
B. 8.94
C. 9.98
D. 11.27
Question 352
∆XYZ is right angled at Y. If tanX = 15/8, then what is the value of sinZ ?
A. 15/17
B. 17/8
C. 17/15
D. 8/17
Question 353
112 × 54 =
A. 68947
B. 69874
C. 70000
D. 76000
Question 354
If Sin θ = 20/29, then what is the value of Cos θ?
A. 29/21
B. 21/29
C. 21/20
D. 20/29
Question 355
If M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) and N = (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), then what is the value of M/N?
A. 207/560
B. 339/1120
C. 113/350
D. 69/175
Question 356
If cosec 240° = x, then the value of x is
A. √2
B. 2
C. -2/√3
D. -√2
Question 357
If x/2 - [4(15/2 - x/3)]/3 = -x/18, then what is the value of x?
A. -10
B. 9/8
C. 10
D. -9/8
Question 358
Simplify : (-4.6)x(-4.6)/(-4.6+0.6)
A. -5.29
B. -0.529
C. -4.06
D. 5.01
Question 359
If x + [1/(4x)] = 5/2, then what is the value of (64x6+ 1)/8x3?
A. 110
B. 115
C. 125
D. 140
Question 360
If 2cosec2A = x, then the value of x is
A. 1/(1 - cosecA) - 1/(1 + cosecA)
B. 1/(1 + sinA) + 1/(1 - tanA)
C. 1/(1 + cosA) + 1/(1 - cosA)
D. 1/(1 - tanA) - 1/(1 + sinA)
Question 361
If a + b + c = 9 and ab + bc + ca = 18, then what is the value of a3 + b3 + c3 – 3abc?
A. 189
B. 243
C. 361
D. 486
Question 362
Point P is the midpoint of seg AB. Co-ordinates of P are (-1,1) and A are (4,3). What are the co-ordinates of point B?
A. (6, 1)
B. (-6, 1)
C. (6, -1)
D. (-6, -1)
Question 363
Find the value of 62532+18
A. 1635
B. 2635
C. 3635
D. 4635
Question 364
If tan2A - tan2B = x, then the value of x is
A. (sin2A - sin2B)/(cos2A cos2B)
B. (sin2A sin2B)/(cos2A - cos2B)
C. (sin2A + sin2B)/(cos2A cos2B)
D. (sin2A sin2B)/(cos2A + cos2B)
Question 365
Δ DEF is right angled at E. If m∠D = 45°, then what is the value of cosecF X cotD?
A. 1/√2
B. 2
C. 1/2
D. √2
Question 366
If a + b + c + d = 4, then the value of 1(1-a)(1-b)(1-c) + 1(1-b)(1-c)(1-d) + 1(1-c)(1-d)(1-a) + 1(1-d)(1-a)(1-b)
A. 0
B. 1
C. 4
D. 1+ abcd
Question 367
Solve this inequality 3p - 16 < 20?
A. p >= 12
B. p <= 11/3
C. p < 12
D. p > 11/3
Question 368
Which of the following is correct?
A. (4x + 5y)(5x - 4y) = 20x2 + 9xy - 20y2
B. (4x + 5y)(5x - 4y) = 20x2 + 41xy - 20y2
C. (4x + 5y)(5x - 4y) = 20x2 - 9xy + 20y2
D. (4x + 5y)(5x - 4y) = 20x2 - 41xy + 20y2
Question 369
Calculate the value of 61681x61681-31681x3168130000
A. 93352
B. 94362
C. 93362
D. 95362
Question 370
The quadratic equation 1+a2x2+2abx+b2-c2=0 has only one root. What is the value of c21+a2 ?
A. a2
B. b2
C. c2
D. ab
Question 371
If 51.97 (81.18 - x ) - 59.39 = 5.268, then value of x will be
A. - 24.912
B. - 68.492
C. 93.868
D. 197.808
Question 372
If cot(A/2) = x, then the value of x is
A. √[(1 + cosA)/(1 - cosA)]
B. cosecA - cotA
C. √[(1 - cosA)/2]
D. √[(1 + cosA)/2]
Question 373
A man has only 20-paise and 25-paise coins in a bag. If he has 50 coins in all totaling to Rs.10.25, then the number of 20-paise coins is
A. 42
B. 45
C. 38
D. 36
Question 374
If tan(A/2) = x, then the value of x is
A. sinA/(1 - cosA)
B. sinA/(1 + cosA)
C. √[sinA/(1 + cosA)]
D. √[sinA/(1 - cosA)]
Question 375
Rs.7750 is divided among X, Y and Z such that 3 times of X's share is equal to 5 times of Y's share which is equal to 2 times of Z's share. What is the share (in Rs) of Z?
A. 4250
B. 3750
C. 3875
D. 4475
Question 376
If cot -4π/3 = x, then the value of x is
A. -1
B. -1/√3
C. √3
D. 1
Question 377
Which of the following is TRUE?
A. 1123>1294>15
B. 1294>1123>15
C. 15>1123>1294
D. 15>1294>1123
Question 378
sec2Acosec2A is equal to
A. sec2A - cosec2A
B. √[sec2A + cosec2A]
C. sec2A + cosec2A
D. √[sec2A - cosec2A]
Question 379
M is the largest 4 digit number, which when divided by 4, 5, 6 and 7 leaves remainder as 2, 3, 4, and 5 respectively. What will be the remainder when M is divided by 9?
A. 2
B. 1
C. 3
D. 6
Question 380
The line passing through (-2,5) and (6,b) is perpendicular to the line 20x + 5y = 3. Find b?
A. -7
B. 4
C. 7
D. -4
Question 381
What is the value of √2 Sec 45° + (1/√3)Tan 30°?
A. (1 + √3)/2
B. (1 + 3√2)/√3
C. 7/3
D. (3 + 2√2)/3√2
Question 382
If 5x - 4 ≤ 2 - x and 4x + 5 > 2x - 5, then x can take which of the following values?
A. 3
B. 6
C. -7
D. -1
Question 383
Two points P and Q are at the distance of x and y (where y > x) respectively from the base of a building and on a straight line. If the angles of elevation of the top of the building from points P and Q are complementary, then what is the height of the building?
A. xy
B. √( y/ x)
C. √( x/ y)
D. √( xy)
Question 384
If x = 1 - q and y = 2q + 1, then for what value of q, x is equal to y ?
A. 0
B. 1
C. -1
D. -2
Question 385
If a = 3+23-2, b = 3-23+2 then a2+b2-ab ?
A. 97
B. (2√3) + 2
C. (4√6) + 1
D. 98
Question 386
If Sec θ = 5/3, then what is the value of Cosec θ?
A. 0.8
B. 1.25
C. 4/3
D. 3/4
Question 387
A, B and C are three points on a circle with centre O. The tangent at C meets BA produced at T. If ∠ATC = 30° and ∠ACT = 48°,then what is the value of ∠AOB ?
A. 78°
B. 96°
C. 102°
D. 108°
Question 388
If cot A = n/(n + 1) and cot B = 1/(2n + 1), then what is the value of cot (A + B)?
A. -1
B. 0
C. 1
D. 2
Question 389
If tan θ + cot θ = x, then what is the value of tan4θ + cot4θ?
A. (x3 – 3)2 + 2
B. (x4 – 2x) + 4
C. x2 (x2 – 4) + 2
D. x
Question 390
The two roots of an quadratic equation are given as x = 2/3 and x = -1/2. The equation can be written as
A. (2x - 1) (3x + 2) = 0
B. (2x + 1) (3x + 2) = 0
C. (2x + 1) (3x - 2) = 0
D. (2x - 1) (3x - 2) = 0
Question 391
What is the value of sin 46 cos 44+ cos 46 sin 44?
A. 2
B. sin 2
C. 1
D. 0
Question 392
The distance between the points (2, 7) and (k, -5) is 13. What is the value of k?
A. -7
B. 7
C. 6
D. -6
Question 393
What is the value of Sec 30° + Tan 60°?
A. 5/√3
B. (√6 + 1)/√3
C. (√3 + 2)/√3
D. (1 + √3)/2
Question 394
If πsinθ= 1, πcosθ= 1, then (3tan 23θ+1) is
A. 1
B. √3
C. 2
D. 1/√3
Question 395
What is the value of (cot60 + 1/√3) ?
A. 4/√3
B. (2√2+√3)/2
C. 2/√3
D. (2√2+1)/√2
Question 396
If a sum of money deposited in a bank at simple interest is doubled in 6 years, then after 12 years, the amount will be
A. 5/2times the original amount
B. 3times the original amount
C. 7/2times the original amount
D. 4times the original amount
Question 397
If 1 = 2, 3 = 6, 4 = 8, and + = -, what would be the value of 41 + 34 + 13 = ?
A. -88
B. 88
C. 12
D. -12
Question 398
For the inequation x^2–7x + 12 > 0, which one of the following is correct ?
A. 3 < x < 4
B. –∞ < x < 3 only
C. 4 < x < ∞ only
D. –∞ < x < 3 or 4 < x < ∞
Question 399
For real a, b and c if a2 + b2 + c2 = ab + bc + ca, then find the value of a+b+c2.
A. 9a2
B. 81a2
C. 27a2
D. 243a2
Question 400
Which of the following is correct?
A. (3x + 4y)(4x - 3y) = 12x2 + 7xy - 12y2
B. (3x + 4y)(4x - 3y) = 12x2 + 251xy - 12y2
C. (3x + 4y)(4x - 3y) = 12x2 - 7xy + 12y2
D. (3x + 4y)(4x - 3y) = 12x2 - 251xy + 12y2
Question 401
The sum of 4x + 3y 7z, x y z and 2x 3y + 4z is
A. 3x - y - 4z
B. 3x - y + 4z
C. 3x + y - 4z
D. 3x + y + 4z
Question 402
What is the value of 96+21624?
A. 8
B. 4
C. 5
D. 10
Question 403
What is the value of 1.23+0.83+0.73-2.0161.351.22+0.82+0.72-0.96-0.84-0.56 =
A. 1/4
B. 1/2
C. 1
D. 2
Question 404
If tanA + tanB = X, then the value of X is
A. (tanA - tanB)/(1 + tanAtanB)
B. (tanA + tanB)/(1 - tanAtanB)
C. (tanA + tanB)/(1 + tanAtanB)
D. (tanA - tanB)/(1 - tanAtanB)
Question 405
If A/3 = B/2 = C/5, then what is the value of ratio (C + A)2 : (A + B)2 : (B + C)2?
A. 9 : 4 : 25
B. 25 : 4 : 9
C. 64 : 25 : 49
D. 49 : 25 : 64
Question 406
If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3 is equal to :
A. 22
B. 23
C. 24
D. 25
Question 407
What will be the value of r2+p2+s2-rp-ps-rs when r = 4, p = 2, s = 8?
A. 8
B. 18
C. 28
D. 38
Question 408
Product of 9b2, 3a2 and 4ab is
A. 108a2b2
B. 108a3b3
C. 108a3b2
D. 108a4b4
Question 409
If cos 45° - sec 30° = x, then value of x is
A. (1+√2)/2
B. (2√2√3)/2
C. (√32√2)/√6
D. 4/√3
Question 410
What is the value of [(sin 59° cos 31° + cos 59° sin 31° )÷(cos 20° cos 25° – sin 20° sin 25° )]?
A. 1/√2
B. 2√2
C. √3
D. √2
Question 411
The points A(3,-2), B(1,4) and C(-2,x) are collinear. What is the value of x?
A. 13
B. -2
C. 5
D. 3
Question 412
Square of (3x – 5xy) is
A. 9x2 - 30x2y + 25x2y2
B. 9x2 - 15x2y + 25x2y2
C. 25x2 - 15x2y + 9x2y2
D. 25x2 - 30x2y + 9x2y2
Question 413
If 2x/3 - [5(4x/5 - 4/3)]/2 = 1/3, then what is the value of x?
A. 9/4
B. 4/9
C. -9/4
D. -4/9
Question 414
64/12 in simplest form?
A. 19/6
B. 32/4
C. 16/3
D. None of the above
Question 415
If (1 + secA)/tanA = x, then x is
A. cot(A/2)
B. tan(A/2)
C. cosec(A/2)
D. sec(A/2)
Question 416
If a - b = 6 and ab =16, then a3 - b3 is
A. 504
B. 702
C. 728
D. 511
Question 417
ΔPQR is right angled at Q. If cosP = 5/13, then what is the value of cosecR ?
A. 13/5
B. 5/12
C. 5/13
D. 13/12
Question 418
What is the value of Cot 60°- Sec 45°?
A. (√2 - √3)/√6
B. (√3 - 3√2)/3
C. (1 - 2√2)/2
D. (1 - √3)/2
Question 419
The value of tan(-405°)
A. 1
B. -1
C. 2
D. 0
Question 420
A sphere of radius 5 cm is melted to form a cone with base of same radius. The height (in cm) of the cone is
A. 5
B. 10
C. 20
D. 22
Question 421
If (4a +7b) (4c-7d) = (4a -7b) (4c +7d, then which one of the following is correct ?
A. a/b = c/d
B. a/d = c/b
C. a/b = d/c
D. none
Question 422
What is the value of tan 1° tan 2° tan 3°....... tan 89°?
A. 0
B. 1
C. 2
D. infinity
Question 423
Which of the following pair of numbers is the solution of the equation 3x+2+ 3–x= 10 ?
A. 0, 2
B. 0, -2
C. 1, -1
D. 1, 2
Question 424
56/32 simplified value?
A. 1.705
B. 1.45
C. 1.75
D. 7.5
Question 425
If 13x2 = 172 - 92, find the value of x?
A. 16
B. 12
C. 8
D. 4
Question 426
If cot2A - cos2A = x, then value of x is
A. tan2Asec2A
B. cotAcosA
C. cot2Acos2A
D. tanAsecA
Question 427
The least value of tan2x + cot2x is
A. 3
B. 2
C. 0
D. 1
Question 428
Find the value of x if 1-x24 = 1318
A. 155
B. 157
C. 159
D. 161
Question 429
If a + b + c = 27, then what is the value of (a – 7)3 + (b – 9)3 + (c – 11)3 – 3(a – 7)(b – 9)(c – 11)?
A. 0
B. 9
C. 27
D. 3
Question 430
9997 x 10003 = ?
A. 9999991
B. 99999911
C. 99999991
D. 9999911
Question 431
What is the simplified value of cosec6A – cot6A – 3 cosec2A cot2A?
A. -2
B. -1
C. 0
D. 1
Question 432
If C + 1C = 3, then what is the value of C-37+1C7?
A. 2
B. 0
C. 3
D. 1
Question 433
Profit of Rs 144000 has to be divided among three partners Akram, Bipin and Chintan in the ratio 3:2:7. How much Rs. Chintan get?
A. 84000
B. 24000
C. 36000
D. 42000
Question 434
If 3P/5 = 7Q/2 = 7R/5, then what is the ratio of p, Q and R respectively?
A. 3 : 2 : 5
B. 3 : 35 : 14
C. 5 : 7 : 5
D. 35 : 6 : 15
Question 435
If sin - 5π/3 = x, then the value of x is
A. -√3/2
B. √3/2
C. -2
D. -2/√3
Question 436
What is the value of tan 300°?
A. -1/2
B. -1/√2
C. -√3
D. -√3/2
Question 437
If a rod of length 208 45 is cut into equal pieces of length 23 15 then the total number of rods obtained is
A. 5
B. 8
C. 9
D. 7
Question 438
The simplest form of 3774/2958 is
A. 43/19
B. 37/29
C. 31/13
D. 31/23
Question 439
The angle of elevation of the top of a tower, vertically erected in the middle of a paddy field, from two points on a horizontal line through the foot of the tower are given to be α and β (α>β). The height of the tower is h unit. A possible distance (in the same unit) between the points is
A. h(cotβ-cotα)cos(α+β)
B. h(cotα - cotβ)
C. h(tanβ - tanα)tanα tanβ
D. h(cotα+cotβ)
Question 440
If secθ = cosecq with 0° < θ , q < 90°, then the value of sin (θ + q) is
A. 1
B. 0
C. 2
D. 4
Question 441
If 4x - 7y = 3 and 2x - y = 9, then x - y is.
A. 3
B. 4
C. 5
D. 6
Question 442
What is the value of (1/√3 + sin45 ) ?
A. √3+2
B. (√2+√3)/√6
C. (1+√6)/√3
D. (4+√3)/2
Question 443
What is the reflection of the point (5, -2) in the line y = -1?
A. (-7 , -2)
B. (-5 , 0)
C. (5 , 0)
D. (-7 , 2)
Question 444
Find the value of 27a3 + 1a3, if 9a2 + 1a2 = 43
A. 240
B. 280
C. 320
D. 360
Question 445
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter were to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?
A. 10 m
B. 14 m
C. 12 m
D. 8 m
Question 446
What is the area (in sq cm) of a regular hexagon of side 9 cm?
A. 50√3
B. 300√3
C. 243√3/2
D. 200√3
Question 447
For which value of ‘g’ the linear graph of 6x + 12y +9 = 0 and 2x + gy + 3 = 0 has infinite number of solutions?
A. 3
B. 4
C. 6
D. 9
Question 448
What is the equation of the line passing through the point (0,4) and making an angle of 45° with the positive xaxis?
A. x + y = 4
B. x - y = - 4
C. x + y = -4
D. x - y = 4
Question 449
ΔPQR is right angled at Q. If m∠P = 45°, then find the value of (cosecR + 1/3).
A. (√3+2)/2√3
B. (√3+2)/2
C. (3√2+1)/3
D. (2+2√3)/√3
Question 450
If tan4θ + tan2θ = 1 then the value of cos4θ + cos2θ is
A. 2
B. 0
C. 1
D. -1
Question 451
AB is a diameter of a circle. C is a point on the tangent drawn at A . If AB = 8 cm and AC = 6 cm , then the length of BC is
A. 10 cm
B. 14 cm
C. 5 cm
D. 7 cm
Question 452
If x + √5 = 5 + √y, and x, y are positive integers, then the value of x+yx + y
A. 1
B. 2
C. √5
D. 5
Question 453
What is the value of tan 7π/6?
A. 1/√3
B. -1/√3
C. √3
D. -√3
Question 454
If x - y = 6 and xy = 40, then find x2 + y2 ?
A. 116
B. 80
C. 89
D. 146
Question 455
If x , y, and z are real numbers such that (x - 3)2 + (y - 4)2 + (z - 5)2 = 0 then (x+y+z) is equal to
A. -12
B. 0
C. 8
D. 12
Question 456
The value of tan 315° cot ( -405° ) is equal to
A. -1
B. 1
C. 0
D. 2
Question 457
Find k, if the line 2x- 3y = 11 is perpendicular to the line 3x + ky = -4?
A. -2
B. 1
C. -1
D. 2
Question 458
If 1p+1q = 1p+q, then the value of p3-q3
A. p-q
B. pq
C. 1
D. 0
Question 459
Find the value of x if 0.08x + 0.04y = 10 and 0.2(x-1) + 0.4y = 24.8
A. 125
B. 150
C. 1.25
D. 12.5
Question 460
What is the unit digit of 15+25+35+...+205 ?
A. 0
B. 5
C. 2
D. 4
Question 461
If A = 0.216 + 0.0080.36+0.04-0.12 & B = 0.729-0.0270.81+0.09+0.27, then what is the value of A2+B22 ?
A. 0.8
B. 1
C. 1.4
D. 2.2
Question 462
What is the slope of the line parallel to the line passing through the points (-4,-6) and (2,-3)?
A. -1/2
B. -2
C. 2
D. 1/2
Question 463
Solve this inequality 3b - 7 < 32?
A. b = 13
B. b < 13
C. b > = 13
D. b < = 13
Question 464
θ is a positive acute angle and sinθ cosθ = 0, then the value of secθ + cosecθ is
A. 2
B. √2
C. 2√2
D. 3√2
Question 465
What is the value of [2 cot × (p – A)/2]/[1 + tan2× (2p – A)/2]?
A. 2 sin2 A/2
B. cos A
C. sin A
D. 2 cos2 A/2
Question 466
If θ is acute angle and sin(θ+18°)= 1/2, then the value of θ in circular measure is
A. Π/12 radians
B. Π/15 radians
C. 2Π/5 radians
D. 3Π/13 radians
Question 467
If √[(1 + cosA)/2] = x, then find the value of x.
A. sin(A/2)
B. tan(A/2)
C. cot(A/2)
D. cos(A/2)
Question 468
Factors of 48x3- 8x2- 93x- 45 are
A. (4x + 3)(4x - 3)(3x - 5)
B. (4x - 3)(4x - 3)(3x- 5)
C. (4x + 3)(4x + 3)(3x - 5)
D. (4x - 3)(4x + 3)(3x + 5)
Question 469
If cos 27° = x, the value of tan 63° is
A. x1-x2
B. x1+x2
C. 1-x2x
D. 1+x2x
Question 470
Reduce 2530/1430 to lowest terms.
A. 47/17
B. 23/13
C. 47/19
D. 29/17
Question 471
If √(cosec2A - 1) = x, then the value of x is
A. tanA
B. sinA
C. cosA
D. cotA
Question 472
Simplify (533bxaz)/(41ab)
A. 17xzb
B. 19xz
C. 13xz
D. 31ab
Question 473
If p/q = r/s = t/u = √5, then what is the value of [(3p2 + 4r2 + 5t2)/(3q2 + 4s2 + 5u2)]?
A. 1/5
B. 5
C. 25
D. 60
Question 474
If cosπ/4c - tanπ/4c = x, then x is
A. (√3+4)/2√3
B. (2√2-1)/2
C. (1-√2)/√2
D. 5/√3
Question 475
∆XYZ is right angled at Y. If tanX = 24/7, then what is the value of cotZ ?
A. 25/7
B. 24/25
C. 7/24
D. 24/7
Question 476
What is the value of [tan2 (90 – θ) – sin2 (90 – θ)] cosec2 (90 – θ) cot2 (90 – θ)?
A. 0
B. 1
C. -1
D. 2
Question 477
If a4 + 1 = [a2 /b2 ] (4b2 – b4 – 1), then what is the value of a4 + b4?
A. 2
B. 16
C. 32
D. 64
Question 478
If x3 – y3 = 81 and x – y = 3, then what is the value of x2 + y2?
A. 18
B. 21
C. 27
D. 36
Question 479
If tan2θ + cot2θ = 2, then what is the value of 2sec θ cosec θ?
A. 0
B. 1
C. 2
D. 4
Question 480
What is the simplified value of sin2(90–θ)–[sin(90–θ)sinθ/tanθ]?
A. 1
B. cosec θ
C. 0
D. cos θ
Question 481
Find the unit place digit in 192102 + 193103
A. 0
B. 1
C. 3
D. 5
Question 482
What is (x-y)3+y-23+z-x33x-yy-zz-x =?
A. 1
B. 0
C. 1/3
D. 3
Question 483
What is the value of √[(1 - cosA)/(1 + cosA)]?
A. cosecA - cotA
B. cosecA + cotA
C. secA - cotA
D. secA + cotA
Question 484
cot3A is equal to
A. 3cotA - cot3A(1 - 3cot2A)
B. 3cotA + cot3A(1 - 3cot2A)
C. 3cotA - cot3A(1 + 3cot2A)
D. 3cotA + cot3A(1 + 3cot2A)
Question 485
If ( x - 5)2 + (y - 2)2 + (z - 9)2 = 0 , then value of (x + y - z) is
A. 16
B. -1
C. -2
D. 12
Question 486
If (1 + cosA)/(1 - cosA) = x, then x is
A. cot2A/(secA - 1)2
B. cot2A/(secA + 1)2
C. tan2A/(secA + 1)2
D. tan2A/(secA - 1)2
Question 487
What is the equation of the line passing through the point (2,-3) and making an angle of -45°with the positive X-axis?
A. x - y = -5
B. x - y = -1
C. x + y = -5
D. x + y = -1
Question 488
What is the value of xy if x - y = 3 and x2+y2=15?
A. 1
B. 3
C. 5
D. 7
Question 489
Value of (4a2+ 12ab + 9b2)/(2a + 3b) is
A. 2a - 3b
B. 2a + 3b
C. 2a
D. 3b
Question 490
If ab = 21 and a+b2a-b2 = 254,then the value of a2+b2+3ab
A. 115
B. 121
C. 125
D. 127
Question 491
If x3 = 62 - 32, then the value of x is
A. 9
B. 6
C. 3
D. 1
Question 492
If sinP = 2/3, find the value of secP and cotP.
A. √5/2, 2/√5
B. 2/√5, 3/5
C. 3√5/5, √5/2
D. 3/5, 3√5/5
Question 493
If cosecA + cotA = x, then value of x is
A. 1/(cosecA - cotA)
B. 1/(secA - tanA)
C. 1/(secA - cosA)
D. 1/(sinA - cosA)
Question 494
The solution set of 4x - 3y = 47 and 3x + y = 32 is
A. {(15, 3)}
B. {(4, 12)}
C. {(11, -1)}
D. {(12, 3)}
Question 495
If sinθ + cosθ = 1, then the sinθ cosθ is equal to
A. 0
B. 1
C. 1/2
D. -1/2
Question 496
If a = 73, b = 74 and c = 75, then what is the value of a3 + b3 + c3 – 3abc?
A. 365
B. 444
C. 666
D. 999
Question 497
Determine the value of 'a' which satisfies the equation 9a + 40a = 41a
A. 1
B. 2
C. 3
D. 4
Question 498
If cosC + cosD = x, then value of x is
A. 2cos[(C+D)/2]cos[(C-D)/2]
B. 2sin[(C+D)/2]sin[(C-D)/2]
C. 2cos[(C+D)/2]sin[(C-D)/2]
D. 2sin[(C+D)/2]cos[(C-D)/2]
Question 499
If (-1/2) * ( x - 5) + 3 = -5/2, then what is the value of x?
A. 16
B. 4
C. -6
D. -4
Question 500
If (tanA - tanB)/(1 + tanAtanB) = x, then the value of x is
A. tan(A - B)
B. tan(A + B)
C. cot(A - B)
D. cot(A + B)
Question 501
Common factor of 24b6c8d2, 18a6c2d4, 12a4b4 is
A. 72a2b2c2d2
B. 72a6b6c8d4
C. 6a2b2
D. 6
Question 502
What is the slope of the line, perpendicular to the line 3x - 6y = 4?
A. -2
B. 2
C. 2/3
D. -2/3
Question 503
If 9x - 6(3 - x) = 12, then the value of x is
A. 2
B. 4
C. 6
D. 9
Question 504
The Simplified form of (b3x2a4z3)*(b4x3a3z2)/(a2b4z3) is
A. b2x4a6z
B. b3x2a4z3
C. b3x5a5z2
D. bazx
Question 505
Reflection of the point (1,4) in the xaxis is
A. (1,4)
B. (1,-4)
C. (-1,4)
D. (-1,-4)
Question 506
A crate of egg holds one rotten egg out of every 25 egg in it. If 5 out of 8 rotten eggs are unusable and there are total 10 unusable eggs in the crate,then calculate the number of eggs in the crate.
A. 380
B. 400
C. 420
D. 440
Question 507
What is the value of 143 + 163 + 183 + ... + 303?
A. 134576
B. 120212
C. 115624
D. 111672
Question 508
A tank is 2/5 full. If 16 litres of water is added to the tank, it becomes 6/7 full. The capacity of the tank is:
A. 28 litres
B. 32 litres
C. 35 litres
D. 42 litres
Question 509
If x2-3x+1=0, then x+1x is (x≠0)
A. 1
B. 0
C. 3
D. 2
Question 510
If 3x= 4y= 12, then z is equal to
A. xy
B. x + y
C. xy/x+Y
D. 4x +3y
Question 511
Simplify: b-[b-(a+b)-{b-(b-a-b)}+2a]
A. 2b
B. 1
C. 0
D. 3b
Question 512
ΔXYZ is right angled at Y. If m∠X = 30 deg, then find the value of (sinZ + √3).
A. 4/√3
B. 5/√3
C. 4/3
D. 3√3/2
Question 513
Find the value of 6813+6413314
A. 5
B. 6
C. 36
D. 216
Question 514
If a+1a2 = 3, then the value of a3+1a3 is
A. 0
B. a
C. 1/a
D. 1
Question 515
If angles of measure (5y + 62°) and (22° + y) are supplementary , then value of y is
A. 16°
B. 32°
C. 8°
D. 1°
Question 516
Sumit and Amit undertook a work for Rs 7200. Sumit alone can do the work in 5 days and Amit alone can do the work in 4 days. If they work together,then what will be the difference (in Rs.) in the amount they receive?
A. 800
B. 1600
C. 1200
D. 1400
Question 517
If the angle of elevation of the sun decreases from 45° to 30°, then the length of the shadow of a pillar increases by 60m. The height of the pillar is
A. 60(√3+1) m
B. 30(√3-1) m
C. 30(√3+1) m
D. 60(√3-1) m
Question 518
Coefficient of x2 in (x + 9)(6 - 4x)(4x - 7) is
A. 216
B. -4
C. -92
D. 108
Question 519
What is value of P+QP-Q if PQ=7 ?
A. 1/3
B. 2/3
C. 4/3
D. 5/3
Question 520
If x4 + (1/x4) = 34, then what is the value of x3 – (1/x3)?
A. 0
B. 6
C. 8
D. 14
Question 521
What is the value of 34+122 ?
A. 13
B. 15
C. 17
D. 19
Question 522
If √(1 - cos2A) = x, then the value of x is
A. cosecA
B. sinA
C. tanA
D. secA
Question 523
You have 20 big and 16 small diaries and want to make gift packs containing both in each pack. What is the maximum number of gift packs you can make without any left over?
A. 5
B. 4
C. 3
D. 2
Question 524
The number of solutions of the pair of linear equations x + 2y - 8 = 0 and 2x + 4y = 16 is
A. 0
B. 1
C. Infinitely many
D. 2
Question 525
If x = 93 , y = 93 , z = 94 then the value of x2 - y2 + 10xz + 10yz is
A. 104784
B. 147840
C. 174840
D. 184740
Question 526
∆ABC is right angled at B. If m∠A = 30°., then Sec C =?
A. 1/2
B. 1/√2
C. 2
D. 1/√3
Question 527
Compute 33800/520/5
A. 31
B. 325
C. 13
D. 352
Question 528
Vishnu spends Rs. 5000 in buying 12 tables and some chairs. The cost of one table is Rs. 50 and that of one chair is Rs. 40. What is the ratio of the numbers of tables purchased?
A. 5 :2
B. 55 : 6
C. 5 : 1
D. 55 : 4
Question 529
If cos -11π/6 = x, then the value of x is
A. -√3/2
B. 1/2
C. -2
D. √3/2
Question 530
The price of 4.5 m of cloth is Rs.60.75. Find the cost per meter.
A. 15.5
B. 13.5
C. 14.75
D. 13.75
Question 531
If sinC - sinD = x, then value of x is
A. 2sin[(C+D)/2]cos[(C-D)/2]
B. 2cos[(C+D)/2]cos[(C-D)/2]
C. 2cos[(C+D)/2]sin[(C-D)/2]
D. 2sin[(C+D)/2]sin[(D-C)/2]
Question 532
If x + y + z = 0, then what is the value of (3y2 + x2 + z2 )/(2y2 – xz)?
A. 2
B. 1
C. 3/2
D. 5/3
Question 533
Along a yard 225 metres long, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees
A. 8
B. 9
C. 10
D. 11
Question 534
Simplify the equation 0.733+0.2730.732+0.272-0.73×0.27
A. 1
B. 0.4087
C. 0.73
D. 0.27
Question 535
sinA/(1 + cos A) is equal to
A. (cosecA - cotA)
B. (cosecA + cotA)
C. √[(cosecA - cotA)]
D. √[(cosecA + cotA)]
Question 536
If cosθ = x2-y2x2+y2, then the value of cotθ is
A. 2xyx2-y2
B. 2xyx2+y2
C. x2+y22xy
D. x2-y22xy
Question 537
What is the value of [2 sin (45 + θ) sin (45 – θ)]/cos 2θ?
A. 0
B. tan 2θ
C. cot 2θ
D. 1
Question 538
If 1/2 is added to a number and the sum is multipled by 3, the result is 21. Then the number is
A. 6.5
B. 5.5
C. 4.5
D. -6.5
Question 539
If 2x + 3 = 9 then find the value of 3x + 2
A. 12
B. 16
C. 13
D. 11
Question 540
If cos3A = X, then value of X?
A. 4cos3A - 3cosA
B. 4cos3A + 3cosA
C. 3cosA - 4cos3A
D. cosA + 4cos3A
Question 541
What is the value of (sinA - 2sin3A)/(2cos3A - cosA)?
A. cotA
B. cosecA
C. secA
D. tanA
Question 542
ΔDEF is right angled at E. If secD = 25/7, then what is the value of cosecF ?
A. 7/25
B. 24/7
C. 25/7
D. 7/24
Question 543
What is the slope of the line, parallel to the line 3x - 6y = 4?
A. -1/2
B. 1/2
C. 2
D. -2
Question 544
78 books, 114 crayons and 141 notebooks were distributed to school children equally. It was found that 6 were left undistributed in each. What was the total number of children?
A. 9
B. 8
C. 13
D. 12
Question 545
If tanθ = 724 then find the value of p such that tanθ - secθsinθ = -p28
A. 25
B. 75
C. 50
D. 100
Question 546
Simplify : 132 - 142 + 172 - 250 = ?
A. 196
B. 169
C. 121
D. 144
Question 547
If a + b + c = 0 , then the value of a3 + b3+ c3 is
A. abc
B. 2abc
C. 3abc
D. 0
Question 548
What is the value of Sin 30° + 2 Cos 30° ?
A. (2√2 + 3)/√6
B. (9 + 2√3)/9
C. (1 + 2√3)/2
D. (2√6 + 1)/√3
Question 549
What is the simplified value of (sec4 A – tan2 A) – (tan4 A + sec2 A)?
A. -1
B. 1/2
C. 1
D. 0
Question 550
The point Q(a,b) is first reflected in y-axis to Q1 and Q1 is reflected in xaxis to (-5,3). The coordinates of point Q are
A. (-5,3)
B. (5,-3)
C. (-5,-3)
D. (5,3)
Question 551
What is the value of [(tan 5θ + tan 3θ)/4 cos 4θ (tan 5θ – tan 3θ)]?
A. sin 2θ
B. cos 2θ
C. tan 4θ
D. cot 2θ
Question 552
2cos[(C+D)/2]sin[(C-D)/2] is equal to
A. sinC + sinD
B. sinC - sinD
C. cosC - cosD
D. cosC + cosD
Question 553
Square root of 0.9 is equal to
A. 0.03
B. 0.3
C. 0.9487
D. 0.9463
Question 554
A man can cover a certain distance in 3 hours 36 minutes if he walks at the rate of 5 Km/hr. If he covers the same distance on cycle at the rate of 24 Km/hr, then the time taken by him in minutes is
A. 40
B. 45
C. 50
D. 55
Question 555
The cost of one dozen bananas is Rs.5. The cost of one dozen oranges is Rs.75. What will the cost of one and a quarter dozen bananas and three-fourth dozen oranges?
A. Rs. 109.25
B. Rs. 87.25
C. Rs. 71.75
D. Rs. 62.50
Question 556
If cot π/3c - tan π/4c = x, then the value of x is
A. √3+2
B. (1-√3)/√3
C. (1-√2)/√2
D. (√3+4)/2√3
Question 557
If cosx.cosy + sinx.siny = -1 then cosx + cosy is
A. -2
B. 1
C. 0
D. 2
Question 558
What is the value of cosec 120°
A. 2/√3
B. 2
C. -2/√3
D. -2
Question 559
If 3√7 + √343 = 19.21, then find the value of √252 + 20√7.
A. 39.4
B. 49.9
C. 56.8
D. 92.3
Question 560
If 2x - 3 = 3x - 5, then the numerical value of (x - 3)2 is
A. 5
B. 1
C. -5
D. -1
Question 561
3x2-14x+16=05y2-16y+12=0
A. x > y
B. x < y
C. x=y or relation cannot be established between x and y
D. x ≥ y
Question 562
If a(x + y) = b(x - y) = 2ab, then the value of 2(x2 + y2)
A. 2(a2 - b2)
B. 2(a2 + b2)
C. 4(a2 - b2)
D. 4(a2 + b2)
Question 563
For triangle PQR, find equation of altitude PS if co-ordinates of P, Q and R are (1,2), (2,-1) and (0,5) respectively?
A. x - 3y = -7
B. x - 3y = -5
C. x + 3y = 4
D. x + 3y = 7
Question 564
If 3x2 - ax + 6 = ax2 + 2x + 2 has only one (repeated) solution, then the positive integral solution of a is
A. 4
B. 5
C. 2
D. 3
Question 565
72 ÷ 52 × 3272 ÷ 52 of 32 ÷ 5.25
A. 3/5
B. 3/6
C. 3/7
D. 3/8
Question 566
What is the value of x4+y4 when the value of x3+y3=8 and x+y=2 ?
A. 2
B. 8
C. 16
D. 32
Question 567
If (x2/yz) + (y2/zx) + (z2/xy) = 3, then what is the value of (x + y + z)3?
A. 0
B. 1
C. 2
D. 3
Question 568
A tailor has 37.5 metres of cloth and he has to make 8 pieces out of a metre of cloth. How many pieces can he make out of half of the cloth he has ?
A. 300
B. 150
C. 175
D. 200
Question 569
∆PQR is right angled at Q. If m∠R = 45°, then find the value of (cosecP - √3/2)
A. (3√3-1)/3
B. 2/√3
C. (2-√3)/√3
D. (2√2-√3)/2
Question 570
What is the value of cosec -7π/6?
A. -2
B. 2
C. 2/√3
D. -2/√3
Question 571
If P2+1P2 = 47, then the value of P + 1P is
A. 5
B. 6
C. 7
D. 8
Question 572
What is the value of equation a3+b3+c3-3abc if a2+b2+c2=ab+bc+ca+4 and a+b+c = 4.
A. 0
B. 1
C. 16
D. 256
Question 573
The areas of two similar triangles ΔABC and ΔPQR are 121 sq cms and 64 sq cms respectively. If PQ = 12 cm, what is the length (in cm) of AB?
A. 7.25
B. 6.25
C. 16.5
D. 5.25
Question 574
8 x {5 - (-2) x (-3)} = ?
A. 8
B. -168
C. 88
D. -8
Question 575
A and B are positive integers. If A + B + AB = 65, then what is the difference between A and B (A, B ≤ 15)?
A. 3
B. 4
C. 5
D. 6
Question 576
In a rectangle _____.
A. Consecutive angles are congruent as well as supplementary
B. Diagonals are perpendicular to each other
C. Diagonals bisect opposite angles
D. Diagonals are not equal
Question 577
If x/y = 4/9, then what is the value of (7x2 – 19xy + 11y2)/y2 ?
A. 59/81
B. 100/27
C. 319/81
D. 913/81
Question 578
ΔXYZ is right angled at Y. If m∠Z = 45°, then find the value of (cosecX - 2/√3).
A. (2-√3)/2√3
B. (1-√6)/√2
C. (√6-2)/√3
D. -1/√3
Question 579
If √(1+tan2A) = x, then the value of x is
A. sinA
B. cosecA
C. secA
D. cosA
Question 580
PQR is an equilateral triangle whose side is 10 cm. What is the value (in cm) of the inradius of triangle PQR?
A. 5/√3
B. 10√3
C. 10/√3
D. 5√2
Question 581
What is the value of sec2θ + 1sec2θ - 1 x 12cotθ - tanθ ?
A. 0
B. 1
C. cosec θ
D. sec θ
Question 582
If x+1x=5, then 6xx2+x+1 value is
A. 3
B. 2
C. 1
D. 0
Question 583
What is the equation of a line having a slope -1/3 and y-intercept equal to 6?
A. x + 3y = 18
B. x - 3y = 6
C. x + 3y = -18
D. x - 3y = -6
Question 584
If (1 - sinA)/(1 + sinA) = x, then x is
A. (cosecA - cotA)2
B. secA - tanA
C. (secA - tanA)2
D. cosecA - cotA
Question 585
If cosec θ + sinθ = 5/2 then the value of cosecθ - sinθ is
A. -3/2
B. 3/2
C. −√3/2
D. √3/2
Question 586
If 23x + 23y = 184, then what is the average of x and y?
A. 2
B. 4
C. 3
D. 2.5
Question 587
What is the equation of the line perpendicular to the line 5x + 3y = 6 and having Y-intercept -3?
A. 3x - 5y = 15
B. 3x + 5y = 15
C. 3x - 5y = -15
D. 3x + 5y = -15
Question 588
Find the value of sin230 cos245 + 4 tan230 + 1/2sin290 - 2 cos290 + 1/24
A. 3
B. 4
C. 2
D. 1
Question 589
A and B together have Rs. 6300. If 5/19 of A's amount is equal to 2/5 of B's amount. The amount of 'B' is
A. Rs. 2500
B. Rs. 3800
C. Rs.2300
D. Rs. 4000
Question 590
What is the value of sin 300°?
A. -1/2
B. 2
C. 2/√3
D. -√3/2
Question 591
P + Q = 2(P-Q). If Q = 10, what is the value of P?
A. 10
B. 40
C. 20
D. 30
Question 592
If a + b = 11 and a2+ b2= 61, then value of ab is
A. 12
B. 96
C. 24
D. 30
Question 593
If tanθ = 815, then 1-sinθ1+sinθ is
A. 1/5
B. 2/5
C. 3/5
D. 0
Question 594
What is the value of sec 5π/4?
A. 1/√3
B. -√2
C. √3
D. 1
Question 595
What is the simplest form of (1 + cosA)(cosecA cotA)?
A. cosA
B. tanA
C. cotA
D. sinA
Question 596
What is the value of sin (–π/3) + cos(–π/6)?
A. 0
B. 1
C. 2
D. 3
Question 597
The number whose square is equal to the difference of the squares of 37 and 23 is:-
A. 45.09
B. 28.98
C. 47.09
D. 28
Question 598
The pair of linear equations 3x + y = 1 and px + 2y = 5 has no finite solution if
A. p>=6
B. p = 6
C. 0 < p < 6
D. p = 0
Question 599
If one root of the equation Ax2 +Bx + C = 0 is two and a half times the others, then which of the following is TRUE?
A. 7B2 = 3 CA
B. 7B2 = 4 CA
C. 7B2 = 36 CA
D. 10B2 = 49 CA
Question 600
What is the value of 7293×16+676+169
A. 75
B. 64
C. 35
D. 60
Question 601
50.003% of 99.8÷49.988 = ?
A. 2
B. 0
C. 1
D. 50
Question 602
If Sinx = 4/5, then Secx/Sinx = ?
A. 23/12
B. 25/4
C. 4/5
D. 25/12
Question 603
CAlculate : 72-6-45÷5-72-2×2÷2+2
A. -16/18
B. -14/7
C. -12/7
D. -12/18
Question 604
If a2+b2c2 = b2+c2a2 = c2+a2b2 = 1k k≠0 then k =
A. 2
B. 1
C. 0
D. 1/2
Question 605
Δ PQR is right angled at Q. If m√R = 30°, then what is the value of Cot P?
A. 1/2
B. 1/√2
C. 1/√3
D. 2
Question 606
If x - 1/x = 1 then what is the value of 1x1x-1-1x+1+1x2+1-1x2-1?
A. ±√5
B. 2/5
C. ±2/√5
D. ±√5/2
Question 607
If x - y = 7 and xy = 32, then value of (x2 + y2) is
A. 49
B. 64
C. 113
D. 15
Question 608
√[(1 sinA)/(1 + sinA)] is equal to?
A. secA - tanA
B. cosecA - cotA
C. secA + tanA
D. cosecA + cotA
Question 609
On dividing 221a2b2 by 13b2, we get _____.
A. 17a2
B. 17b2
C. 13a2b2
D. 13
Question 610
If 2x + 3(5-2x) > 2 - 3x < 2x - x/3, then x can take which of the following values?
A. 0
B. -2
C. -4
D. 2
Question 611
If in a triangle ABC, Sin A = Cos B then the value of Cos C is
A. √3/2
B. 0
C. 1
D. 1/√2
Question 612
If sec -5π/4 = x, then the value of x is
A. -1/√3
B. -√2
C. -1
D. √3
Question 613
If xy (x + y) = m, then the value of x3 + y3 + 3m is:
A. m3xy
B. m3x+y3
C. m3x3y3
D. mx3y3
Question 614
The value of 3x9n+1+9x32n-19x32n-6x9n-1 is equal to
A. 335
B. 325
C. 315
D. 3
Question 615
If a + b = 5 and ab = 6, then what is the value of a3 + b3?
A. 32
B. 38
C. 35
D. 34
Question 616
If √(sec2A 1) = x, then the value of x is
A. cotA
B. tanA
C. cosecA
D. cosA
Question 617
If a - b = 2 and ab = 15, then what is the value of a3- b3?
A. 152
B. 112
C. 108
D. 98
Question 618
ΔPQR is right angled at Q. If secP = 13/5, then what is the value of sinR ?
A. 5/13
B. 5/12
C. 13/5
D. 13/12
Question 619
If 'Q ' means ' +', 'J ' means ' X',T ' ' means '- ' and 'K ' means '÷ ', then what is the value of18K3Q7J ?
A. 15
B. 10
C. 18
D. 12
Question 620
Coefficient of x in (x + 8)(6 - 3x) is
A. 18
B. 30
C. -18
D. -30
Question 621
At what point does the line 2x - 3y = 6 cuts the Y axis?
A. (0, 2)
B. (-2, 0)
C. (2, 0)
D. (0, -2)
Question 622
If ab+c=bc+a=Cb+athen which one of the following statements is correct?
A. Each fraction is equal to 1 or -1
B. Each fraction is equal to 1/2 or 1
C. Each fraction is equal to 1/2 or -1
D. Each fraction is equal to 1.2 only
Question 623
The value of cosec260 + sec260 cot260 + tan230 will be
A. 5
B. 5 1/2
C. 5 1/3
D. 5 2/3
Question 624
The sum of a fraction and 3 times its reciprocal is 37/10. What is the fraction?
A. 5/2
B. 2/5
C. 5/4
D. 4/5
Question 625
What is the value of sin -300°?
A. 1
B. √3/2
C. 1/2
D. √3/2
Question 626
If 2(3x-2) < 6-3x and 6x + 2(6-x) > 2x-2, then x can take which of the following values?
A. -8
B. 5
C. 8
D. -5
Question 627
If 11-13xx + 11-13yy + 11-13zz = 5 then what is the value of 1x + 1y + 1z = ?
A. 1
B. 13/11
C. 13/5
D. 4
Question 628
0 is the circumference of a triangle ∆ABC. The point A and the chord BC are on the opposite side of O. If ∠BOC=150° then the value of ∠BAC is
A. 65°
B. 60°
C. 70°
D. 75°
Question 629
David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
A. 19th floor
B. 28th floor
C. 30th floor
D. 37th floor
Question 630
Find the value of p if -3x - 11, x + p and 5x + 7 are in arithmetic progression.
A. 9
B. 2
C. -9
D. -2
Question 631
A secret can be told to only 3 persons in 3 minutes. Each person in turn tells 3 other persons in the next 3 minutes and the processes continues accordingly. In 30 minutes how many persons can be told this secret in this way ?
A. 88572
B. 77854
C. 99584
D. 55654
Question 632
If Cosecθ + Cotθ = 2, then Cotθ = ?
A. 0
B. 0.5
C. 1
D. 0.75
Question 633
If a3+ b3 = 341 and ab = 30, then what is the value of a + b?
A. 1
B. 9
C. 7
D. 11
Question 634
If 3x-y=27, 3x+y=243 then find the x value
A. 2
B. 8
C. 4
D. 1
Question 635
If Tan θ = 7/24, then what is the value of Sec θ?
A. 24/25
B. 24/7
C. 25/7
D. 25/24
Question 636
If 1/6 of x - 7/2 of 3/7 equals - 7/4, then the value of x is
A. -1.5
B. 3
C. -2.5
D. 6
Question 637
If x2+1x2 = 98, then x3+1x3 = ?
A. 970
B. 1030
C. -970
D. -1030
Question 638
In ΔPQR measure of angle Q is 90°. If cosP = 5/13, and PQ = 2.5cm, then what is the length (in cm) of side PR?
A. 6
B. 6.5
C. 4
D. 5.6
Question 639
A class consists of both boys and girls along with a teacher. After a class, the teacher drinks 9 litres of water, a boy drinks 7 litres of water and a girl drinks 4 litres of water. If after a class 42 litres of water was consumed, find the number of girls in the class ?
A. 8
B. 6
C. 5
D. 3
Question 640
ABC is a right angled triangle. ∠BAC = 90 deg and ∠ACB = 60 deg. What is the ratio of the circum radius of the triangle to the side AB?
A. 1 : 2
B. 1 : √3
C. 2 : √3
D. 2 : 3
Question 641
If Cosec θ = 17/8, then Cot θ = ?
A. 17/8
B. 15/8
C. 8/15
D. 17/15
Question 642
The value of aa-b+bb-a is
A. a+b/a-b
B. -1
C. 2ab
D. 1
Question 643
x, y and z are real numbers. If x3 + y3 + z3 = 13, x + y + z = 1 and xyz = 1, then what is the value of xy + yz + zx?
A. -1
B. 1
C. 3
D. -3
Question 644
If sec (4x - 50°) = cosec(50° - x), Then the value of x is
A. 45°
B. 90°
C. 30°
D. 60°
Question 645
If (x - 4) (x2 + 4x + 16) = x3 - P, then P is equal to
A. 27
B. 8
C. 64
D. 0
Question 646
The value of sinθ1+cosθ + sinθ1-cosθ
A. 2sinθ
B. 2cosθ
C. 2secθ
D. 2cosecθ
Question 647
If a + b = 4 and ab = -5, then what is the value of a3 + b3?
A. 34
B. 36
C. 124
D. 126
Question 648
If a + b = 8 and ab =15, then a3 + b3 is
A. 224
B. 244
C. 152
D. 128
Question 649
If (cotA - cosecA)2 = x, then the value of x is
A. (1 - cosA)/(1 + cosA)
B. (1 - sinA)/(1 + sinA)
C. (1 - secA)/(1 + secA)
D. (1 - cosecA)/(1 + cosecA)
Question 650
23x12+49x15312+50 = ?
A. 0.5
B. 1
C. 2
D. 3
Question 651
1.004 - 0.4 is equal to
A. 0.604
B. 0.006
C. 0.64
D. 1
Question 652
If sum of the roots of a quadratic equation is -7 and product of the roots is 12. Find the quadratic equation.
A. x2 + 7x + 12 = 0
B. x2 - 7x + 12 = 0
C. x2 - 7x - 12 = 0
D. x2 + 7x - 12 = 0
Question 653
The point R(a,b) is first reflected in origin to R1 and R1 is reflected in X-axis to (-5,1). The co-ordinates of point R are?
A. (5,-1)
B. (-1,5)
C. (1,-5)
D. (5,1)
Question 654
What is the square root of 9409?
A. 83
B. 87
C. 89
D. 97
Question 655
If a(a + b + c) = 45, b(a + b + c) = 75 and c(a + b + c) = 105, then what is the value of (a2 + b2 + c2 )?
A. 75
B. 83
C. 217
D. 225
Question 656
Compute : (50 + 0.5 x 20) / 0.7
A. 8.571
B. 85.1
C. 85.71
D. 72.85
Question 657
In a Rhombus ABCD, measure of angle CAB is 35°, what is the measure of angle ABC?
A. 70°
B. 40°
C. 50°
D. 110°
Question 658
If a3 + b3 = 28 and a + b = 4, then what is the value of ab?
A. -3
B. 2
C. 8
D. 3
Question 659
If tanA - tanB = X, then the value of X is
A. (tanA + tanB)/(1 - tanAtanB)
B. (tanA + tanB)/(1 + tanAtanB)
C. (tanA - tanB)/(1- tanAtanB)
D. (tanA - tanB)/(1 + tanAtanB)
Question 660
If x = 1 – y and x2 = 2 – y2, then what is the value of xy?
A. 1
B. 2
C. -1/2
D. -1
Question 661
If 5 sec θ – 3 tan θ = 5, then what is the value of 5 tan θ – 3 sec θ?
A. 1
B. 2
C. 3
D. 4
Question 662
If 3x^2 + ax + 4 is perectly divisible by x - 5, then the value of a is :
A. -5
B. -15.8
C. -12
D. -15.6
Question 663
If x = 1 + √2 + √3 , then the value of 2x4 - 8x3 - 5x2 + 26x - 28 is
A. 2√2
B. 3√3
C. 5√5
D. 6√6
Question 664
If x+1x=5, then the value of x1+x+x2 is
A. 1/5
B. 1/6
C. 5
D. 6
Question 665
If x = 3+13, then the value of x-12642x-1x-233 is
A. √3/6
B. 2√3/6
C. 5/6
D. 2/3
Question 666
What is the distance between the points (4,-8) and (-2,0)?
A. 100 units
B. 5 units
C. 25 units
D. 10 units
Question 667
If Tan A = 15/8 and Tan B = 7/24, then Cos(A - B) = ?
A. 297/425
B. 304/425
C. 87/425
D. 416/425
Question 668
If 1 + secA = x, then the value of x is
A. sinAtanA/(1 + cosA)
B. √[sinAtanA/(1 - cosA)]
C. sinAtanA/(1 - cosA)
D. √[sinAtanA/(1 + cosA)]
Question 669
What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)? 499.99 + 1999 ÷ 39.99 × 50.01=?
A. 3200
B. 2700
C. 3000
D. 2500
Question 670
Find the value of 1006×994?
A. 999932
B. 999964
C. 1000032
D. 1000064
Question 671
If (1 + cosA)/2 = x, then the value of x is
A. sin(A/2)
B. √sin(A/2)
C. √cos(A/2)
D. cos2(A/2)
Question 672
Point P is the midpoint of segment AB. Co-ordinates of P are (5,-4) and A are (7,0). What will be the co-ordinates of point B?
A. (3, -8)
B. (-3, -8)
C. (3, 8)
D. (-3, 8)
Question 673
The value of Cot17°Cot73°Cos222° + 1Cot17°Sec268° is
A. 0
B. 1
C. 2
D. √3
Question 674
If xa+b+1=xa-b+a-ba+b, then x is equal to
A. 2a-b
B. a+b
C. a-b
D. 2a+b
Question 675
Solve the following 7 x {4 + (-2) x (-3)} = ?
A. 14
B. -42
C. -14
D. 70
Question 676
3cosA is equal to
A. 4cos3A + 3cosA
B. 4cos3A - 3cosA
C. 3cos3A + 3cosA
D. 3cos3A - 3cosA
Question 677
If cot 60° + cosec 60° = x, then the value of x is
A. (1-2√2)/√2
B. (√3-4)/2√3
C. 1
D. √3
Question 678
What is the simplified value of 1-sin A1+sin A ?
A. tan A
B. sec A
C. sec A + tan A
D. sec A – tan A
Question 679
Coefficient of x2 in 4x3 - 2x2 + 2x - 3 are
A. 6
B. -2
C. 3
D. -3
Question 680
If a - b = 3 and ab =28, then a3 - b3 is
A. 279
B. 387
C. 513
D. 91
Question 681
The measures of the three angles of a triangle are in the ratio 1:2:3. What is the measure of the biggest angle?
A. 30°
B. 60°
C. 90°
D. 120°
Question 682
If x = 313- 3-13, then 3x3 + 9x value is
A. 8
B. 9
C. 27
D. 16
Question 683
In ΔDEF measure of angle E is 90 deg. If sinD = 15/17, and DE = 4cm, then what is the length (in cm) of side EF?
A. 8.5
B. 7.5
C. 5
D. 6
Question 684
Coefficient of x2 in 6x3 + 4x2 + 2x + 3 is
A. 4
B. 6
C. 3
D. 2
Question 685
If cos2x + cos4x = 1, then tan2x + tan4x =
A. 0
B. 1
C. 2tanx
D. tanx
Question 686
What is the value of 13 x 4932?
A. 4369
B. 4459
C. 4549
D. 4639
Question 687
What is the value of [sin (90 – A) + cos (180 – 2A)]/[cos (90 – 2A) + sin (180 – A)]?
A. sin (A/2) cos A
B. cot (A/2)
C. tan (A/2)
D. sin A cos (A/2)
Question 688
If sin -240° = x, then the value of x is
A. 2/√3
B. √2
C. 2
D. √3/2
Question 689
[63 - (-3){-2 - 8 - 3}] / 3{6 + (-2) (-1)} = ?
A. 0
B. 3
C. 1
D. 2
Question 690
If secA + tanA = x, then find the value of x.
A. √[(1 - sinA)/(1 + sinA)]
B. (1 + sinA)/(1 - sinA)
C. (1 - sinA)/(1 + sinA)
D. √[(1 + sinA)/(1 - sinA)]
Question 691
The value of x for which the expressions 5x + 17 and 17x - 5 become equal is _____.
A. 11/6
B. -11/6
C. 6/11
D. -6/11
Question 692
If a = √2 + 1 and b = √2 - 1, then the value of 1a+1+1b+1 will be
A. 0
B. 1
C. 2
D. -1
Question 693
If √5 = 2.236, then √5/2 is
A. 1.851
B. 1.118
C. 2.236
D. 1.782
Question 694
If P = 7 + 4√3 and PQ = 1, then what is the value of 1/P2 + 1/Q2?
A. 196
B. 194
C. 206
D. 182
Question 695
If x = x2+11 2 - 2, then x3 + 5x2 + 12x is
A. 0
B. 3
C. 7
D. 11
Question 696
If 2x + (9/x) = 9, then what is the minimum value of x2+1x2 = ?
A. 95/36
B. 97/36
C. 87/25
D. 623/27
Question 697
The sum of a number and 4 times its reciprocal is 5. What is the number?
A. 4
B. 5
C. 6
D. 7
Question 698
If x+1/x = 2, then the value of x7+2/x6 is equal to?
A. 0
B. 1
C. 2
D. 3
Question 699
If the value of √42 is approximately 6.480, then what is the approximate value of √(6/7)?
A. 0.925
B. 0.935
C. 0.945
D. 0.955
Question 700
If (36 - 16x) - (4x - 8) = 4, then the value of x is
A. 4
B. 2
C. 6
D. 3
Question 701
If secA - tanA = x, then the value of x is
A. 1/(sec2A - tan2A)
B. 1/(sec2A + tan2A)
C. 1/√[(sec2A - tan2A)]
D. 1/(secA + tanA)
Question 702
Simplify : 69 X 69 X 69 -65 X 65 X 669 X 69 + 69 X 65 + 65 X 65
A. 1
B. 4
C. 0.216
D. 0.164
Question 703
x, y and z are prime numbers and x + y + z = 38. What is the maximum value of x?
A. 19
B. 23
C. 31
D. 29
Question 704
If the sum of two numbers is 22 and the sum of their squares is 404, then the product of two numbers is = ?
A. 40
B. 44
C. 80
D. 88
Question 705
D and E are the points on the sides AB and AC respectively of a ΔABC and AD = 8 cm, DB = 12 cm, AE= 6 cm and EC = 9 cm, then BC is equal to:
A. 2/5 DE
B. 5/2 DE
C. 3/2 DE
D. 2/3 DE
Question 706
The solution set of 4x - 3y = 10 and 3x + y = 14 is
A. {(5, 3)}
B. {(4, 2)}
C. {(11, 1)}
D. {(2, 3)}
Question 707
If x = (√2 + 1)/(√2 – 1), then what is the value of (x5 + x4 + x2 + x)/x3 ?
A. 5
B. 2
C. 2√3
D. 2√2
Question 708
What is the y – intercept of the linear equation 59x + 14y – 112 = 0?
A. 8
B. 14
C. 28
D. 59
Question 709
The simplest form of 3565/1495 is
A. 31/13
B. 43/19
C. 23/13
D. 31/23
Question 710
40.36 - (9.347 - x ) - 29.02 = 3.68. Find x.
A. -56.353
B. 1.687
C. -17.007
D. 82.407
Question 711
If 1/(tanA + cotA) = x, then value of x is
A. cosAsinA
B. cos2Asin2A
C. cosecAsecA
D. cosec2Asec2A
Question 712
In ΔPQR, S and T are points on side PQ and PR respectively. ST is parallel to QR. If S divides PQ in the ratio 4:1 and length of QR is 15 cm,what is the length of ST?
A. 3 cm
B. 5 cm
C. 12 cm
D. 10 cm
Question 713
If a3 + b3 = 35 and ab = 6, then what is the value of a + b?
A. 5
B. 8
C. 2
D. -8
Question 714
Two labourers A and B are paid a total of Rs. 1120 per day. If A is paid 180 percent of what is paid to B, how much (in Rs) is B paid?
A. 400
B. 720
C. 500
D. 620
Question 715
If 4(2x + 3) > 5 - x and 5x - 3(2x - 7) > 3x - 1, then x can take which of the following values?
A. 6
B. -1
C. 5
D. -6
Question 716
5 - [4 - {3 - (3 - 3 - 6)}] is equal to:
A. 10
B. 6
C. 4
D. 0
Question 717
If Cos θ = 35/37, then what is the value of Cosec θ?
A. 37/12
B. 33/12
C. 35/12
D. 12/35
Question 718
The length of a chord which is at a distance of 12 cm from the centre of a circle of radius 13 cm is
A. 10 cm
B. 5 cm
C. 6 cm
D. 12 cm
Question 719
If x+y+z = 1, 1/x + 1/y + 1/z = 1 and xyz = -1, then x3+y3+z3 is equal to
A. -1
B. 1
C. -2
D. 2
Question 720
What is the value of [cos (90 + A)÷sec (270 – A)] + [sin (270 + A)÷cosec (630 – A)]?
A. 3 sec A
B. tan A sec A
C. 0
D. 1
Question 721
If tanθ = 43, then the value of 3sinθ+2cosθ3sinθ-2cosθ ?
A. 1/2
B. 3/2
C. 3
D. -3
Question 722
10+10(9) =
A. 180
B. 110
C. 100
D. 19
Question 723
ΔABC and ΔDEF are two similar triangles and the perimeter of ΔABC and ΔDEF are 30 cm and 18 cm respectively. If length of DE = 36 cm, then length of AB is
A. 60 cm
B. 40 cm
C. 45 cm
D. 50 cm
Question 724
If cos -225° = x, then the value of x is
A. 1/2
B. √3/2
C. -2/√3
D. -1/√2
Question 725
If sin θ + sin 5θ = sin 3θ and 0 < θ < (π/2), then what is the value of θ (in degrees)?
A. 30
B. 45
C. 60
D. 75
Question 726
What is the simplified value of sec4θ – sec2θ tan2θ?
A. cosec2θ
B. Cot2θ
C. sec2 θ
D. secθ tan θ
Question 727
P(3,1) and R(-7,5) are vertices of a rhombus PQRS. What is the equation of diagonal QS?
A. 5x - 2y = 16
B. 5x - 2y = -16
C. 5x + 2y = -16
D. 5x + 2y = 16
Question 728
If pq(p+q) = 1, then the value of 1p3q3-p3-q3 is equal to
A. 1
B. 2
C. 3
D. 4
Question 729
What should be added to 8(3x - 4y) to obtain 18x - 18y?
A. 6x - 14y
B. 14y + 6x
C. 14y - 6x
D. 6xy
Question 730
What is the value of Cot 45° + Cosec 60°?
A. (√6 + 1)/√3
B. (1 + √3)/2
C. 5/√3
D. (√3 + 2)/√3
Question 731
What is the value of tan150°?
A. -√3
B. 1/√3
C. √3
D. -1/√3
Question 732
What is the equation of line whose slope is -1/2 and passes through the intersection of the lines x - y = -1 and 3x - 2y = 0?
A. x + 2y = 8
B. 3x + y = 7
C. x + 2y = -8
D. 3x + y = -7
Question 733
If cotA = x, then the value of x is
A. √(sec2A + 1)
B. √(cosec2A + 1)
C. √(sec2A - 1)
D. √(cosec2A - 1)
Question 734
If tan2A / (secA - 1)2 = x, then the value of x is
A. (1+cosecA) / (1-cosecA)
B. (1+cosA)(1-cosA)
C. (1+cosA) / (1-cosA)
D. (1+cosecA)(1-cosecA)
Question 735
What is the value of 643 × 121289 - 169 ?
A. 12
B. 11
C. 1/11
D. 1/12
Question 736
If 16% of an electricity bill is deducted, Rs 1806 is still to be paid. How much was the bill?
A. Rs 1557
B. Rs 2186
C. Rs 1593
D. Rs 2150
Question 737
If 3a – (3/a) – 3 = 0, then what is the value of a3 – (1/a3) + 2?
A. 0
B. 2
C. 4
D. 6
Question 738
If α and β are the roots of equation x2 – 2x + 4 = 0, then what is the equation whose roots are α3/β2 and β3/α2?
A. x2 – 4 x + 8 = 0
B. x2 – 32 x + 4 = 0
C. x2 – 2 x + 4 = 0
D. x2 – 16 x + 4 = 0
Question 739
If x2 + y2 + 6x + 5 = 4(x - y) then x - y is
A. 1
B. -1
C. 0
D. 4
Question 740
If ab-1b=cb-1c=ac-1a, then ac+ba+cb
A. 1
B. 2
C. 3
D. 4
Question 741
If (x – 2)2 + (y + 3)2 + (z – 15)2 = 0, then what is the value of x + y + z – 5?
A. 5
B. 9
C. 15
D. 20
Question 742
If x+19x=4, then 9x2+19x2 is
A. 140
B. 142
C. 144
D. 146
Question 743
What is the value of [12/(√5 + √3)] + [18/(√5 – √3)]?
A. 15(√5 – √3)
B. 3(5√5 + √3)
C. 15(√5 + √3)
D. 3(3√5 + √3
Question 744
Find the value of 'y' if y84 = 225
A. 10
B. 12
C. 15
D. 18
Question 745
A box weighs 8.5 kg when full of sand and weighs 5.5 kg when it is half filled with sand . Weight of the empty box is
A. 5 kg
B. 6 kg
C. 2.5 kg
D. 4.5 kg
Question 746
Mayur can complete a work in 27 hours. If he is joined by Jayantika who is 100% more efficient, in what time will they together finish the work?
A. 6 hours
B. 3 hours
C. 9 hours
D. 10 hours
Question 747
Δ ABC is right angled at B. If m∠A = 60°, then what is the value of 2 Sec C x 1/2 Sin A?
A. 1/2
B. 1/3
C. 1
D. 1/√2
Question 748
What is the value of (tan60 + 1/3) ?
A. (2√2+1)/2
B. (√3+1)/√3
C. (3√3+1)/3
D. (3+√2)/3√2
Question 749
Cost of 4 pens, 6 note books and 9 files is Rs 305. Cost of 3 pens, 4 notebooks and 2 files is Rs 145. What is the cost (in Rs) of 5 pens, 8 notebooks and 16 files?
A. 415
B. 465
C. 440
D. Cannot be determined
Question 750
If tan A = 1/2 and tan B = 1/3, then what is the value of tan (2A + B)?
A. 1
B. 3
C. 5
D. 9
Question 751
In ΔXYZ measure of angle Y is 90 deg. If cot X = 5/12, and XY = 2.5 cm, then what is the length (in cm) of side XZ?
A. 6
B. 4
C. 5.6
D. 6.5
Question 752
If a = √2 + 1, b = √2 - 1 then the value of 1a+1+1b+1 ?
A. 0
B. 1
C. 2
D. 3
Question 753
What is the value of cos (90 – B) sin (C – A) + sin (90 + A) cos (B + C) – sin (90 – C) cos (A + B)?
A. 1
B. sin ( A + B – C)
C. cos ( B + C – A)
D. 0
Question 754
Arrange them in ascending order 64, 33 and 43
A. 33 < 64 > 43
B. 33 > 64 > 43
C. 33 > 43 > 64
D. 33 < 64 < 43
Question 755
If cosec 4π/3 = x, then the value of x is
A. √2
B. 2/√3
C. √2
D. -1/√3
Question 756
The value of 2.33+0.0272.33-0.69+0.09
A. 2
B. 2.27
C. 2.33
D. 2.6
Question 757
If 5x/2 - [7(6x - 3/2)]/4 = 5/8, then what is the value of x?
A. 1/4
B. -1/4
C. 4
D. -4
Question 758
A 8 cm long perpendicular is drawn from the centre of a circle to a 12 cm long chord. The diameter of the circle is
A. 10 cm
B. 12 cm
C. 16 cm
D. 20 cm
Question 759
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
A. 160
B. 175
C. 180
D. 195
Question 760
∆XYZ is right angled at Y. If CosecX = 17/15, then what is the value of CotZ?
A. 17/15
B. 8/17
C. 17/8
D. 15/8
Question 761
What is the value of (cot45 - √2) ?
A. (√3-1)/2√3
B. (√3-1)/2
C. 1-√2
D. 1-√3
Question 762
On dividing 8a2b2c2 by 4a2, we get
A. 2b2
B. 2c2
C. 2b2c2
D. 2
Question 763
If the zeroes of the polynomial x2 - ax + b are 3 and 4, then 'a' and 'b' are respectively equal to
A. 4, 3
B. 12, 7
C. 3, 4
D. 7, 12
Question 764
The price of 2 oranges, 3 bananas and 4 apples is Rs. 15. The price of 3 oranges, 2 bananas and 1 apple is Rs. 10. What will be price of 4 oranges, 4 bananas and 4 apples ?
A. Rs. 10
B. Rs. 15
C. Rs. 20
D. Rs. 25
Question 765
If 2x- 3(4-2x) < 4x - 5 < 4x + 2x/3, then x can take which of the following values?
A. 2
B. 8
C. 0
D. -8
Question 766
Let a = (4 ÷ 3) ÷ 3 ÷ 4, b = 4 ÷ (3 ÷ 3) ÷ 4, c = 4 ÷ 3 ÷ (3 ÷ 4), The maximum value among the above three is?
A. a
B. b
C. c
D. All equal
Question 767
What is the value of (-7776)25
A. 16
B. 36
C. 64
D. 21
Question 768
(1 + sec 20° + cot 70°)(1 - cosec 20° + tan70°) is equal to
A. 0
B. 1
C. 2
D. 3
Question 769
If cot2A = x, then x is
A. 2cotA/(cot2A - 1)
B. (cot2A - 1)/2cotA
C. (cot2A + 1)/2cotA
D. 2cotA/(1 - cot2A)
Question 770
If A = (1/0.4) + (1/0.04) + (1/0.004) + ... upto 8 terms, then what is the value of A?
A. 27272727.5
B. 25252525.5
C. 27777777.5
D. 25555555.5
Question 771
(0.2 x 0.2 x 0.2)(0.06 x 0.06 x 0.06) / (0.12 x 0.12 x 0.12) = ?
A. 0.008
B. 0.001
C. 0.002
D. 0.006
Question 772
A T.V was sold at a profit of 5% If it had been sold at a profit of 10% , the profit would have been Rs. 1000 more. What is its cost price ?
A. Rs.20000
B. Rs.5000
C. Rs.10000
D. Rs.15000
Question 773
In ∆UVW measure of angle V is 900. If cosecU = 13/12, and UV = 2.5 cm, then what is the length (in cm) of side VW?
A. 6.5
B. 6
C. 4
D. 5.6
Question 774
If a+b=3 then the value of a3+b3+9ab-27 is
A. 24
B. 25
C. 0
D. 27
Question 775
The value of 2.31 x 0.34 = ?
A. 1.7854
B. 0.7854
C. 0.7845
D. 0.7584
Question 776
4 + 16 x -12 x 24 - 13 - 3 ÷ 20 - 4 = ?
A. 4
B. 6
C. 5
D. 3
Question 777
If x = a + 1a, y = a - 1a ,(a>0), then the value of x4+y4-2x2y2 is
A. 16
B. 20
C. 10
D. 5
Question 778
What is the value of 1+aa1/2+a-1/2-a1/2+a-1/21+a+a-1/2 ?
A. √a
B. 1/√a
C. 0
D. √a+1
Question 779
In each of the following questions two equations I and II are given. Solve both the equations and give answer: I. x2+2x-195=0II. y2+30y+225=0
A. x = y or relation can’t be established between x and y
B. x > y
C. x < y
D. x ≥ y
Question 780
If a - b = 10 and ab =-21, then what is the value of a3-b3 ?
A. 316
B. 370
C. 185
D. 158
Question 781
If ab+ba=1, then the value of a3+b3 is
A. 1
B. 0
C. -1
D. 2
Question 782
If cot A = [sin B/(1 – cos B)], then what is the value of cot 2A?
A. cot(B/2)
B. cot 2B
C. cot B
D. tan B
Question 783
If (x + y)/z = 2, then what is the value of [y/(y – z)] + [x/(x – z)]?
A. 0
B. 1
C. 2
D. – 1
Question 784
For triangle ABC, find equation of median AD if coordinates of points A, B and C are (2,4), (3,0) and (5,2) respectively?
A. 3x - 2y = 14
B. 3x - 2y = 2
C. 3x + 2y = 14
D. 3x + 2y = 2
Question 785
What is the value of 2 - 2z + z22 + 2z - z2, when z+2z = 2 ?
A. 0
B. 2
C. 4
D. 8
Question 786
What is the value of 2sec2A?
A. secA/(cosecA - 1) + secA/(cosecA +1)
B. cosecA/(secA -1) + cosecA/(secA +1)
C. cosecA/(cosecA - 1) + cosecA/(cosecA +1)
D. secA/(secA - 1) + secA/(secA +1)
Question 787
ABCD is a parallelogram. Co-ordinates of A, B and C are (5,0), (-2,3) and (-1,4) respectively. What will be the equation of line AD?
A. y = 2x - 5
B. y = x + 5
C. y = 2x + 5
D. y = x - 5
Question 788
What is the value of (1/2) Sec 30° + √2 Tan 60°?
A. (1 + 3√2)/√3
B. (√3 + 2)/√3
C. √3 + 2
D. (√3 + 2)/2
Question 789
If x = a + 1/a, y = a - 1/a, then the value of x4+y4-2x2y2
A. 4
B. 8
C. 16
D. 64
Question 790
If cosA = x, then x is
A. √(1 - cos2A)
B. √(1 + sin2A)
C. √(1 + cos2A)
D. √(1 - sin2A)
Question 791
What is the simplified value of 18 - 12 ?
A. 5/√2
B. 5√2
C. 2√5
D. 2/√5
Question 792
∆PQR is right angled at Q. If sinP = 12/13, then what is the value of tanR?
A. 5/13
B. 13/5
C. 13/12
D. 5/12
Question 793
What is the value of sin(11π/6)?
A. 2/√3
B. -2/√3
C. -1/2
D. 1/2
Question 794
What is the value of 1xp-q+1+1xq-p+1?
A. 0
B. 1
C. x
D. cant determine
Question 795
The value of 8(sin6θ + cos6θ) - 12(sin4θ + cos4θ) is equal to
A. 20
B. -20
C. 4
D. -4
Question 796
If P = 7 + 4√3 and PQ = 1, then what is the value of (1/P2) + (1/Q2)?
A. 148
B. 189
C. 194
D. 204
Question 797
What is the total number of points in the plane of triangle ABC which is equidistant from the vertices of the triangle?
A. 0
B. 1
C. 2
D. 3
Question 798
A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:
A. 22
B. 23
C. 24
D. 26
Question 799
5 + 2 x 10/2 = ?
A. 15
B. 35
C. 10
D. 20
Question 800
2*[0.3(1.3 + 3.7)] of 0.8 = ?
A. 1.92
B. -0.72
C. 2.16
D. -2.4
Question 801
What is the area of the sector whose central angle is 90° and radius of the circle is 14 cm?
A. 308 sq cm
B. 77 sq cm
C. 154 sq cm
D. 231 sq cm
Question 802
If 12x = 192- 112, what is the value of x?
A. 20
B. 17
C. 13
D. 11
Question 803
If a + b + c = 13, a2+b2+c2=69 then find the ab + bc + ca :
A. 10
B. 30
C. 50
D. 70
Question 804
In ∆XYZ measure of angle Y is 90 deg. If cosecX = 13/12, and XY = 1cm, then what is the length ( in cm ) of side YZ?
A. 2.6
B. 1.5
C. 2.4
D. 2
Question 805
The two lines 4x+3y=0 and 7x+5y=0 will ______ in their graphical representation.
A. be parallel to each other
B. intersect each other at one point only
C. intersect each other at three points only
D. coincide each other
Question 806
When [x + (1/x)] = 5, then what is the value of [x – (1/x)]?
A. 11
B. ± √22
C. 21
D. ± √21
Question 807
Factors of x2 + 7x + 10 are
A. (x-5)(x-2)
B. (x+5)(x+2)
C. (x-5)(x+2)
D. (x-4)(x+2)
Question 808
The length of a median of an equilateral triangle is 12√3 cms. Then the area of the triangle is
A. 144 sq. cms
B. 288√3 sq. cms
C. 144√3 sq. cms
D. 288sq.cms
Question 809
If sin(A/2) = x, then the value of x is
A. √[(1 + cosA)/2]
B. √[(1 - cosA)/2]
C. √[(1 - sinA)/2]
D. √[(1 + sinA)/2]
Question 810
If cos 135° = x, then the value of x is
A. -1/√2
B. -√3/2
C. -1/2
D. 2
Question 811
If √(1 + cot2A)/cotA = x, then the value of x is
A. sinA
B. cosecA
C. secA
D. cosA
Question 812
What is the value of sinAtanA/(1 - cosA)?
A. 1 - secA
B. 1 + secA
C. 1 + cotA
D. 1 - cotA
Question 813
The value of cos220°+cos270° is
A. 0
B. 1
C. 1/2
D. 13
Question 814
At what point does the line 3x + 2y = 12 cuts the Y-axis?
A. (0, 6)
B. (0, -6)
C. (6, 0)
D. (-6, 0)
Question 815
Compute : 28854 / 458 / 9
A. 70
B. 567
C. 7
D. 576
Question 816
ax + 3y = 6 has slope -2/3. What is the value of a?
A. -2
B. 2
C. 3
D. -3
Question 817
If 2x + 3y = 0 and 3x - 4y = 34, then x - y = ______
A. 10
B. -10
C. 2
D. -2
Question 818
If Cos θ = 35/37 , then what is the value of Cot θ?
A. 12/35
B. 35/12
C. 37/12
D. 12/37
Question 819
If Cot θ = 24/7, then what is the value of Sec θ?
A. 7/25
B. 25/24
C. 8/25
D. 9/25
Question 820
Simplify x5 ÷ x43 ÷ x
A. x3
B. x2
C. X
D. 1/X
Question 821
If secA/√(sec2A - 1) = x, then value of x is
A. tanA
B. cosecA
C. sinA
D. cosA
Question 822
What is the value of (cosec30 - 1/√3)?
A. (2√3-1)/√3
B. (√3-4)/2√3
C. -1/√3
D. 2/√3
Question 823
If 3+12=x+3y, then the x+y is
A. 2
B. 4
C. 6
D. 8
Question 824
The simplified form of (x + 3)2 + (x - 1)2 is
A. (x2 + 2x + 5)
B. 2(x2 + 2x + 5)
C. (x2 - 2x + 5)
D. 2(x2 - 2x + 5)
Question 825
If 2x-y2+(3y-2z)2=0, then the ratio of x:y:z is
A. 1 : 3 : 2
B. 1 : 2 : 3
C. 3 : 1 : 2
D. 3 : 2 : 1
Question 826
(798+579)2- (798-579)2798 x 579 =
A. 2
B. 6
C. 4
D. 8
Question 827
A telephone bill costs Rs.13 for 19 minutes. What is the cost in rupees for 15 minutes 50 seconds?(rounded to one decimal)
A. 10.8
B. 10.7
C. 10.6
D. 10.9
Question 828
If Sin 31° = xy, then the value of Sec 31° - Sin 59° is
A. x2yy2-x2
B. -x2yy2-x2
C. -y2y2-x2
D. x
Question 829
sin(A+B) - sin(A-B) is equal to
A. 2sinAcosB
B. 2cosAcosB
C. 2cosAsinB
D. 2sinAsinB
Question 830
If cos 45° - sec 60° = x, then the value of x is
A. (√3-4)/2√3
B. 1
C. (1-2√2)/√2
D. (√3+√2)/2
Question 831
If cos 240° = x, then value of x is
A. -1/√2
B. -√3/2
C. 1/2
D. -1/2
Question 832
If (1/4 of x) - (4/5 of 6/7) equals - 9/7, then value of x is
A. -12
B. -2.4
C. -3.6
D. -14
Question 833
If x-1x = 10, then find the value of x4+1x2
A. 98
B. 100
C. 102
D. 106
Question 834
If (5x – y)/(5x + y) = 3/7, then what is the value of (4x2 + y2 – 4xy)/(9x2 + 16y2 + 24xy) ?
A. 0
B. 3/7
C. 18/49
D. 1/6
Question 835
What is the simplified value of sec6 A – tan6 A – 3 sec2 A tan2 A?
A. -1
B. 0
C. 1
D. sec A tan A
Question 836
217 x 217 + 183 x 183 = ?
A. 84521
B. 87487
C. 80578
D. 78458
Question 837
What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(-4, 0) and C(3, -4)?
A. ( 0, 3)
B. ( 0, -3)
C. ( 0, -5)
D. ( 0, 5)
Question 838
At what point does the line 2x + 5y = -6 cuts the X-axis?
A. (3, 0)
B. (0, 3)
C. (-3, 0)
D. (0, -3)
Question 839
Find the unit digit in the given product (4211)102 x (361)52.
A. 3
B. 1
C. 4
D. 7
Question 840
What is the equation of the line which passes through the points (3,2) and (5,3)?
A. 5x - 2y = -19
B. 5x - 2y = 19
C. 5x + 2y = 31
D. 5x + 2y = -31
Question 841
What is the value of x3-1x3+8 when 8x-8x-16=0 ?
A. 6
B. 8
C. 16
D. 22
Question 842
The value of sec2θ + 2tanθcotθ - tan2θ is
A. 0
B. 1
C. 2
D. 3
Question 843
Δ DEF is right angled at E. If m∠F = 45, then what is the value of Sin F x Tan F?
A. √2
B. 1/√3
C. 1/√2
D. 2/√3
Question 844
If cosA/(1 - sinA) = x, then the value of x is
A. secA - tanA
B. cosecA + tanA
C. secA + tanA
D. cosecA - tanA
Question 845
A fraction is greater than its reciprocal by (72)/(77). What is the fraction?
A. 7/11
B. 11/7
C. 4/7
D. 7/4
Question 846
What is the value of [(sin 7x – sin 5x)÷(cos 7x + cos 5x)] – [(cos 6x – cos 4x)÷(sin 6x + sin 4x)]?
A. 1
B. 2 tan x
C. tan 2 x
D. tan (3 x/2)
Question 847
What should be added to 3(x - 2y) to obtain 2(3x + y) - 5(2x + 3)?
A. 8y - 7x - 15
B. 8y - 7x + 15
C. 8y + 7x + 15
D. 8y + 7x - 15
Question 848
What is the value of cosec -150°?
A. -2
B. 2/√3
C. 2
D. -2/√3
Question 849
If a3+1a3 = 2, then the value of a2+1a?
A. 1
B. 2
C. 3
D. 4
Question 850
If p/q = (x+3)/(x-3), then what is the value of p2+q2p2-q2 ?
A. x+9
B. x2+96x
C. x2+186x
D. 0
Question 851
The value of 14 ÷ 5 of 2 - 3 x 47 - 2 is
A. 44
B. 40
C. 1/10
D. 14/19
Question 852
Reflection of the point (2,7) in the yaxis is
A. (2,7)
B. (-2,-7)
C. (-7,2)
D. (7,2)
Question 853
cot2A + cos2A is equal to
A. (cosecA - sinA)2(cosecA + sinA)
B. (cosecA + sinA)(cosecA - sinA)
C. (secA + sinA)(secA - sinA)
D. (secA - sinA)2(secA + sinA)
Question 854
The value of the expression 2(sin6θ+cos6θ) - 3(sin4θ+cos4θ) + 1 is
A. -1
B. 0
C. 1
D. 2
Question 855
What is the smplified value of Sin2A/1+Cos2A ?
A. tan A
B. cot A
C. sin A
D. cos A
Question 856
What is the value of tan4A + tan2A?
A. sec4A - sec2A
B. sec4A + sec2A
C. cosec4A - sec2A
D. sec4A + cosec2A
Question 857
If a3 + b3 = 19 and ab = -6 , then what is the value of a + b?
A. 5
B. 7
C. 1
D. -5
Question 858
If sinA/(1 + cosA) = x, then x is
A. cosecA + cotA
B. secA - cotA
C. secA + cotA
D. cosecA - cotA
Question 859
Point A (4 , 2) divides segment BC in the ratio 2:5. Co-ordinates of B are (2 , 6) and C are (7 , y). What is the value of y?
A. 8
B. -8
C. 6
D. -6
Question 860
If x + y = 13 and x2 + y2 = 89, then find xy is
A. 80
B. 169
C. 258
D. 40
Question 861
The point R(a,b) is first reflected in origin to R1 and R1 is reflected in x-axis to (-3,4). The co-ordinates of point R are
A. (3,4)
B. (-3,-4)
C. (-3,4)
D. (3,-4)
Question 862
The total of 324 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is :
A. 50
B. 100
C. 150
D. 200
Question 863
What are the coordinates of the centroid of a triangle, whose vertices are A(2,5), B(4,4) and C(7,3)?
A. (4,-3)
B. (-1,0)
C. (-3,-3)
D. (3,-2)
Question 864
If Cosec θ = 25/7 , then what is the value of Cot θ?
A. 24/25
B. 7/24
C. 7/25
D. 24/7
Question 865
If secθ + tanθ = 4, then secθ - tanθ = ?
A. 1
B. 0.25
C. 0.5
D. 0.75
Question 866
For triangle ABC, what would be the equation of median AD if co-ordinates of A, B and C are (-5,4), (-4,0) and (-2,2) respectively?
A. 3x - 2y = -11
B. 3x + 2y = 7
C. 3x + 2y = -7
D. 3x - 2y = 11
Question 867
What is the slope of the line 4x - 8y = 3?
A. -1/2
B. 2
C. 1/2
D. -2
Question 868
What is the value of 7293 + 441 - 3433 ?
A. 48
B. 23
C. 7
D. 41
Question 869
Simplify : -21973 × -1253 ÷ 275123
A. 492/7
B. 520/3
C. 554/7
D. 571/5
Question 870
If a + b = 4 and ab = 3, then what is the value of a3 + b3?
A. 21
B. 17
C. 28
D. 31
Question 871
Find the value of 491321973
A. 17/13
B. 13/17
C. 13/7
D. 17/7
Question 872
If 5x + 1/x = 10, then x2 + 125x2 is equal to
A. 215
B. 335
C. 315
D. 235
Question 873
ΔABC is right angled at B. If m∠A = 45 deg, then find the value of (tanC + √3/2).
A. 4/√3
B. (2+√3)/2
C. (√2+2)/2√2
D. (2+√3)/3
Question 874
tan(A/2) is equal to
A. cosecA + cotA
B. secA - cotA
C. cosecA - cotA
D. secA + cotA
Question 875
Geetha weighs 11.235 kg. Her sister weighs 1.4 times her weight. Find their combined weight?
A. 15.729 kg
B. 25.964 kg
C. 26.964 kg
D. 26.946 kg
Question 876
If a+1/a = 3, then a3+1a3?
A. 12
B. 18
C. 9
D. 6
Question 877
If (8x - 4) = (3x + 6), then the numerical value of (x + 1)3 is
A. 3
B. 9
C. 27
D. 81
Question 878
How many times the keys of a typewriter have to be pressed in order to write numbers from 121 to 1346?
A. 3675
B. 4018
C. 4021
D. 4025
Question 879
If (cotAcotB - 1) / (cotB + cotA) = x, then the value of x is
A. cot(A - B)
B. tan(A + B)
C. cot(A + B)
D. tan(A - B)
Question 880
If (6x - 1) - (8x - 5) = 7, then the value of x is _______ .
A. -3/2
B. 3/2
C. 11/2
D. -11/2
Question 881
If x = a cosθ+ b sinθ and y = b cosθ- a sinθ, then x2 + y2 is equal to
A. ab
B. a2+b2
C. a2-b2
D. 1
Question 882
What is the value of tan -240°?
A. -√3
B. 1/√3
C. -1/√3
D. √3
Question 883
You purchased two pieces of cloth measring 1.2 m and 1.3 m each at Rs. 330 and Rs. 270 per meter respectively and gave Rs. 1000 at the payment counter. How much cash will you get back?
A. Rs. 253
B. Rs. 604
C. Rs. 649
D. Rs. 235
Question 884
What is the value of [(cos 7A + cos 5A)÷(sin 7A – sin 5A)]?
A. tan A
B. tan 4 A
C. cot 4 A
D. cot A
Question 885
A 1.6 m tall observer is 45 meters away from a tower. The angle of elevation from his eye to the top of the tower is 30°, then the height of the tower in meters is
A. 25.98
B. 26.58
C. 27.58
D. 27.98
Question 886
25 - 1/2{5 + 4 - (3 + 2 - 1 + 3)} = ?
A. 21
B. 23
C. 22
D. 24
Question 887
If x = √2+1, then the value of x4-1/x4
A. 8√2
B. 18√2
C. 6√2
D. 24√2
Question 888
Which of the following points lies on the line 3x - 4y = -13?
A. (5,7)
B. (-5,7)
C. (5,-7)
D. (-5,-7)
Question 889
What is the value of sin 5π/3?
A. √3/2
B. 2/√3
C. 1/√3
D. -2/√3
Question 890
In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 130 marks, the no of questions he attempts correctly is :
A. 35
B. 38
C. 40
D. 42
Question 891
Expanded and simplification of (x + 3)(x - 1) will be equal to
A. x2+ 2x - 3
B. x2 + 3x + 2
C. x2 - 2x + 3
D. x2 + 3x - 2
Question 892
45 - [38 - {60 / 3 - (6 - 9 / 3)/ 3}]= ?
A. 24
B. 25
C. 26
D. 21
Question 893
If a + b = 10 and ab = 24, then the value of a3 + b3 is
A. 280
B. 370
C. 520
D. 730
Question 894
If 7x - (3/2) * (4x - 9) = 6.5, then the value of x is?
A. 7
B. 20
C. -7
D. -20
Question 895
If a.sin 45°.cos 45°.tan60° = tan 245° cos60° then find the value of a ?
A. 13
B. 3
C. 1
D. 32
Question 896
If x - 2y = 2 and 3x + y = 20, then the value of (x,y) is
A. (6, 2)
B. (4, 1)
C. (3, 2)
D. (5, 5)
Question 897
The value of (0.00000729/0.00000027) is
A. 0.27
B. 0.027
C. 2.7
D. 27
Question 898
The value of (0.3)2/100=?
A. 0.09
B. 0.0009
C. 0.009
D. 0.9
Question 899
If a + b = 9 and a2+ b2= 61, then ab is
A. 20
B. 10
C. 81
D. 142
Question 900
What is the value of (4a2 + 8b + 14c + 2)/2 ?
A. 2a2 + 4b + 7c + 1
B. a2 + 4b + 7c + 1
C. 2a2 + 4b + 7c + 2
D. a2 + 4b + 7c + 2
Question 901
Find the value of 'a' for which x+3x+a24 is a perfect square.
A. √3
B. 2√3
C. 3√3
D. 4√3
Question 902
If x + y = 12 and xy = 32, then what is the value of x2 + y2 ?
A. 24
B. 144
C. 128
D. 80
Question 903
If n + n2 + n4 + n8 = 45, then find the value of 'n' which will satisfy the equation.
A. 16
B. 24
C. 36
D. 48
Question 904
Simplify: (213 x 213 + 187 x 187)
A. 80338
B. 80438
C. 60338
D. 60438
Question 905
If x + y = 3, then what is the value of x3 + y3 + 9xy?
A. 15
B. 81
C. 27
D. 9
Question 906
If cot 240° = x, then the value of x is
A. -1
B. -1/√3
C. 1/√3
D. √3
Question 907
What is the value of 23+5252-23 ?
A. 9
B. 49
C. 561
D. 571
Question 908
What is the value of |3(1) - 6|?
A. 3
B. 0
C. -3
D. 4
Question 909
What is the value of 3.6×1.62+0.48×3.61.8×0.8+10.8×0.3-2.16 ?
A. 2.4
B. 2
C. 4
D. 3
Question 910
If 4x + 1x = 5, (x≠0), then the value of 5x4x2+10x+1 is
A. 1/2
B. 1/3
C. 2/3
D. 3
Question 911
If a-1a=1, then a2 + 1a2 ?
A. 1
B. 3
C. 2
D. 4
Question 912
1/(tanA + cotA) is equal to
A. (cosecA + sinA)(secA - cosA)
B. √[(cosecA - sinA)(secA - cosA)]
C. √[(cosecA + sinA)(secA - cosA)]
D. (cosecA - sinA)(secA - cosA)
Question 913
If 7x - 5y = 13 and 2x - y = 5, then (x - y) is
A. 3
B. 4
C. 5
D. 1
Question 914
If cos -300° = x, then the value of x is
A. 1/2
B. -1/√2
C. -1/2
D. √3/2
Question 915
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
A. 20
B. 80
C. 100
D. 200
Question 916
A factory produced 18,58,509 cassettes in the month of January, 7623 more cassettes in the month of February and owing to short supply of electricity produced 25,838 less cassettes in March than in February. Find the total production in all?
A. 55,57,312
B. 59,83,245
C. 55,64,935
D. 56,08,988
Question 917
What are the roots of the quadratic equation: x2 + 3x - 154 = 0
A. 11, 14
B. 11, -14
C. 14, -11
D. 14, -22
Question 918
If A = (-14 + 4) and B = 4 - 14, then AB =
A. 0
B. -100
C. 100
D. -1
Question 919
Which of the following is not a quadratic equation?
A. 3x(x + 5) 11 = 2x(x - 2) + 6
B. 4x(x + 3) + 7 = 4x(x - 11) + 9
C. x(x + 2) 15 = x(2x - 5) + 11
D. 4x - 6x + 9 = 0
Question 920
If a + b = 10 and ab- 13 = -ba - 11, then what is the value of 3ab + 4a2 + 5b2 ?
A. 450
B. 300
C. 600
D. 750
Question 921
Simplify (2/7 + 3/5) / (2/5 + 2/7)
A. 31/24
B. 24/31
C. 26/25
D. 12/13
Question 922
By how much is three-fifth of 350 greater than four-seventh of 210 ?
A. 90
B. 100
C. 110
D. 120
Question 923
What is the equation of a line of slope 1/3 and y-intercept 5?
A. x - 3y = -15
B. x - 3y = 15
C. x + 3y = -15
D. x + 3y = 15
Question 924
Which of the following numbers is completely divisible by 99?
A. 57717
B. 57627
C. 55162
D. 56982
Question 925
If x = at2 and y = 2at then
A. x2 = 4ay
B. y2 = 4ax
C. x2 + y 2 = a2
D. x 2 - y2 = a 2
Question 926
If x varies as y and x = 8 when y = 15 then the value of x when y = 10 is:
A. 5
B. 15/8
C. 8/15
D. 16/3
Question 927
If a - b = -1 and ab = 6, then what is the value of a3- b3?
A. 33
B. -19
C. 18
D. 35
Question 928
In ∆DEF measure of angle E is 90°. If secD = 25/7, and DE = 1.4cm, then what is the length (in cm) of side DF?
A. 5
B. 4.8
C. 4
D. 5.6
Question 929
1747 + 13212 - ? = 1123
A. 16
B. 17
C. 18
D. 19
Question 930
What is the value of tan3A?
A. (3tanA - tan3A)/(1 - 3tan2A)
B. (3tanA + tan3A)/(1 + 3tan2A)
C. (3tanA - tan3A)/(1 + 3tan2A)
D. (3tanA + tan3A)/(1- 3tan2A)
Question 931
If x=2+3, then the value of x2-x+1x2+x+1 is
A. 2/3
B. 3/4
C. 4/5
D. 3/5
Question 932
Expand and simplify (x + 4)2 + (x - 2)2
A. 2(x2 + 2x + 10)
B. 2(x2 + 2x - 10)
C. 2(x2 - 2x + 10)
D. 2(x2 - 2x - 10)
Question 933
A man spends in 8 months as much as he earns in 6 months. He saves Rs. 6000 in a year. His average monthly income is
A. Rs. 2400
B. Rs. 2000
C. Rs. 2150
D. Rs. 1800
Question 934
What is the reflection of the point (5, 2) in the line x = -3?
A. (-11 ,2)
B. (-11 ,-2)
C. (11 ,-2)
D. (11 ,2)
Question 935
Simplify 4(x-1) -3x
A. 7x - 4
B. 7x + 4
C. x + 4
D. x - 4
Question 936
If √x - √y = 1 , √x + √y = 17 then √xy = ?
A. √72
B. 72
C. 32
D. 24
Question 937
What is the value of 4cos90-A sin390+A - 4sin90+A cos390-Acos180+8A2 ?
A. 1
B. -1
C. 0
D. 2
Question 938
What is the difference between the total sale of English newspapers and the total sale of Hindi newspapers in all the localities together.
A. 7500
B. 5600
C. 6500
D. 5700
Question 939
If a : b = c : d = 1 : 6, then what is the value of a2+c2b2+d2?
A. 1/600
B. 1/60
C. 1/36
D. 1/360
Question 940
If sinθ+cosθsinθ-cosθ=3, then the value of sin4θ-cos4θ is
A. 4/3
B. 3/4
C. 5/3
D. 3/5
Question 941
If a+bab=21 , then the value of (a-b) is
A. 1
B. 0
C. -1
D. 2
Question 942
If 2x + 6y = 3xy and 10x - 3y = 4xy, find x, y.
A. 3, 2
B. 2, 3
C. 4, 6
D. 6, 4
Question 943
Given that ( 12 + 22 + 32 + .......... + 102 ) = 385, then the value of ( 22 + 32 + 42 + .......... + 202 ) is equal to = ?
A. 770
B. 1155
C. 1540
D. (385)2
Question 944
If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what is the value of (a + c)/b?
A. 9/5
B. 11/7
C. 7/11
D. 7/4
Question 945
If a + b = 1 and ab = -6, then what is the value of a3+ b3?
A. 17
B. 15
C. 19
D. 13
Question 946
If (sinA + CosA)/(sin A - cos A) = 5/4, the value of (tan2A + 1)/(tan2A - 1) = ?
A. 41/40
B. 12/13
C. 40/41
D. -31/49
Question 947
The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a distance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 60°. The height of the tower in meters is
A. √3
B. 5√3
C. 10√3
D. 20√3
Question 948
If cosθ1-sinθ+cosθ1+sinθ = 4, then the value of θ (0°<θ<90°)?
A. 60°
B. 45°
C. 30°
D. 35°
Question 949
If cos 21° = x/y, then cosec 21° - cos 69° is equal to
A. x2yy2-x2
B. y2xy2-x2
C. y2xx2-y2
D. x2yx2-y2
Question 950
On dividing 24a2b2 by 6b2, we will get
A. 4b
B. 4ab
C. 4
D. 4a2
Question 951
If 1+121+141+161+181-131-151-17 = 1+ 1x, then what is the value of x?
A. 6
B. 8
C. 5
D. 7
Question 952
The first and last terms of an arithmetic progression are 25 and 52. What is the sum of the series if it has 12 terms?
A. -162
B. -110
C. 162
D. 110
Question 953
In ΔUVW measure of angle V is 90 deg. If sinU = 24/25, and UV = 0.7cm, then what is the length (in cm) of side VW?
A. 2.5
B. 3
C. 2.4
D. 4
Question 954
The value of sinθ+sin∅cosθ+cos∅ + cosθ-cos∅sinθ-sin∅ is
A. 1
B. 2
C. 1/2
D. 0
Question 955
If 60/75 is equivalent to 4/x, then the value of x is
A. 5
B. 4
C. 15
D. 18
Question 956
Simplify 486b3x2a4z3/27a3b2z
A. 18bx2az2
B. 18bx2a2z
C. 36ba2z
D. 36bxaz
Question 957
Calculate the value of 61681 x 61681 - 31681 x 3168130000?
A. 93352
B. 94362
C. 93362
D. 95362
Question 958
Find the value of x3 - y3, if x - y = 4 and xy = 12.
A. 198
B. 208
C. 218
D. 228
Question 959
What is the value of (32 cos6x – 48 cos4x + 18 cos2x – 1)/[4 sin x cos x sin (60 – x) cos (60 – x) sin (60 + x) cos (60 + x)]?
A. 4 tan 6x
B. 4 cot 6x
C. 8 cot 6x
D. 8 tan 6x
Question 960
Calculate the value of 55-5, if the value of √5 = 2.236.
A. 0.809
B. 0.89
C. 0.089
D. 0.807
Question 961
2660 of 17 of 12 of 19.5 of 12 = ?
A. 1
B. 10
C. 0.1
D. 100
Question 962
What is the value of Sin 30- √2 Cos 30
A. (1 - √6)/√2
B. (1 - √6)/2
C. (3 - √6)/2
D. (3 - √6)/√2
Question 963
If (x – 2)2 + (y + 3)2 + (z – 15)2 = 0, then what is the value of x + y + z – 5?
A. 5
B. 9
C. 15
D. 20
Question 964
The point R(a,b) is first reflected in origin to R1 and R1 is reflected in xaxis to (-4,2). The co-ordinates of point R are
A. (4,-2)
B. (-4,2)
C. (4,2)
D. (-4,-2)
Question 965
38% of 7500 + ?% of 375 = 50% of 6000
A. 50
B. 40
C. 60
D. 45
Question 966
If x + (1/x) = 2, then what is the value of x21 + (1/x1331)?
A. 0
B. 1
C. 2
D. 3
Question 967
If [2(4x/5 - 3/4)]/3 - 5/3 = -1/6, then the value of x is?
A. 4/15
B. -15/4
C. -4/15
D. 15/4
Question 968
Find the value of y(y4 - y2 - y) when y = 5.
A. 2900
B. 2975
C. 2925
D. 2995
Question 969
Triangle PQR is inscribed in a circle such that P, Q and R lie on the circumference. If PQ is the diameter of the circle and ∠PQR = 40°, then what is the value (in degrees) of ∠QPR?
A. 40
B. 45
C. 50
D. 55
Question 970
Reciprocal of 235?
A. 235
B. 532
C. 513
D. 335
Question 971
Simplify 437bxaz / 23ab.
A. 17xzb
B. 9xz
C. 19xz
D. 19ab
Question 972
In ∆ABC if the median AD=1/2 BC, then ∠BAC is
A. 90°
B. 45°
C. 60°
D. 75°
Question 973
Square of (7 - 4x) is
A. 16x2 - 28x + 49
B. 49 - 28x - 16x2
C. 49 - 56x - 16x2
D. 16x2 - 56x + 49
Question 974
Which of the following value of 'x' satisfies the equation 814x+4 = 2432x+8?
A. 3
B. 4
C. 5
D. 6
Question 975
Which of the following quadratic equations has real roots?
A. 3x2 - 5x + 2 = 0
B. 3x2 - 4x + 2 = 0
C. 4x2 - 3x + 2 = 0
D. 5x2 - 2x + 2 = 0
Question 976
Sum of twice a fraction and its reciprocal is 17/6. What is the fraction?
A. 4/3
B. 5/4
C. 3/4
D. 4/5
Question 977
The line passing through the point (5,a) and point (4,3) is perpendicular to the line x - 6y = 8. What is the value of 'a'?
A. -3
B. -2
C. 4
D. 5
Question 978
The sum of 6xy(2x - 4z) , 3yz(2x - 3z) and 4xz(3y - 2y2) is
A. 12x2y - 6xyz - 9yz2 + 8xy2z
B. 12x2y - 6xyz + 9yz2 - 8xy2z
C. 12x2y - 6xyz - 9yz2 - 8xy2z
D. 12x2y + 6xyz - 9yz2 - 8xy2z
Question 979
If a - b = 4 and ab = -3, then what is the value of a3- b3?
A. 21
B. 28
C. 23
D. -20
Question 980
What is the value of (cos 45 - 1/3) ?
A. 2-√3
B. 2/√3
C. (3-√2)/3√2
D. 1/2√3
Question 981
If the difference between the roots of the equation Ax2 – Bx + C = 0 is 4, then which of the following is TRUE?
A. B2 – 16A2 = 4AC + 4B2
B. B2 – 10A2 = 4AC + 6A2
C. B2 – 8A2 = 4AC + 10A2
D. B2 – 16A2 = 4AC + 8B2
Question 982
Reflection of the point (3,-6) in the y-axis is
A. (3,6)
B. (3,-6)
C. (-3,-6)
D. (-3,6)
Question 983
p3 + q3 + r3 – 3pqr = 4. If a = q + r, b = r + p and c = p + q, then what is the value of a3 + b3 + c3 – 3abc?
A. 4
B. 8
C. 2
D. 12
Question 984
Which of the following is correct?
A. (3x - 2y)2 = 9x2 - 12xy + 4y2
B. (3x - 2y)2 = 9x2 - 6xy + 4y2
C. (3x + 2y)2 = 9x2 - 12xy + 4y2
D. (3x + 2y)2 = 9x2 - 6xy + 4y2
Question 985
What is the value of (1/√2) Cot 45° + (1/√3) Cosec 60°?
A. (√6 + 1)/√3
B. √3
C. (1 + 3√2)/√3
D. (3 + 2√2)/3√2
Question 986
What is the value of (√3 - sec60) ?
A. √3-2
B. (1-√6)/√2
C. (2√3-√6)/2√2
D. (1-3√2)/3
Question 987
If sin π/6 + sec π/6 = x, then x is
A. (2√2-1)/2
B. 5/√3
C. (√6-1)/√2
D. (√3+4)/2√3
Question 988
A line passing through the origin perpendicularly cuts the line 2x + 3y = 6 at point M. Find M?
A. (6/11, 9/11)
B. (6/7, 9/7)
C. (6/11, -9/11)
D. (-6/7, 9/7)
Question 989
If l + m + n = 9 and l2+m2+n2 = 31, then the value of lm + mn + nl will be
A. 22
B. 50
C. 25
D. -25
Question 990
The value of Sin 60 is
A. √1/2
B. √3/2
C. 1/√2
D. 1/2
Question 991
If (23)2= 4x then 3x is equal to
A. 3
B. 6
C. 9
D. 27
Question 992
What is the value of (cosecA - cotA) / (secA + tanA)?
A. (secA + tanA)/(cosecA - cotA)
B. √[(secA - tanA)/(cosecA + cotA)]
C. (secA - tanA)/(cosecA + cotA)
D. √[(secA + tanA)/(cosecA - cotA)]
Question 993
Δ LMN is right angled at M. If m∠N = 60 deg., then Tan L =______.
A. 1/2
B. 1/√3
C. 1/√2
D. 2
Question 994
If 1 + (1/2) + (1/3) + ... + (1/20) = k, then what is the value of (1/4) + (1/6) + (1/8) + ... + (1/40)?
A. k/2
B. 2k
C. (k – 1)/2
D. (k + 1)/2
Question 995
Reduce 3596 / 4292 to lowest terms.
A. 29/37
B. 17/43
C. 31/37
D. 19/23
Question 996
If (x/5) + (5/x) = – 2, then what is the value of x3?
A. –125
B. 5
C. 1/125
D. 625
Question 997
If -3/2 + (2/3)(3x + 9) = x/2, then what is the value of x?
A. -9
B. 11
C. 9
D. -3
Question 998
What is the reflection of the point (6, -1) in the line y = 2?
A. (-2 , -1)
B. (-6 , 5)
C. (-2 , 1)
D. (6 , 5)
Question 999
If A + B = 90 deg and Cos B = 1/3, then the value of Sin A is
A. 1/2
B. 1/4
C. 1/3
D. 2/3
Question 1000
If Sin θ = 12/13, then what is the value of Cot θ?
A. 13/12
B. 5/13
C. 5/12
D. 13/5
Question 1001
If (4x - 5) = (3x - 1), then the numerical value of (x + 4)2
A. 16
B. 64
C. 32
D. 8
Question 1002
What is the value of sin225°+ sin265°?
A. 0
B. 1
C. 2
D. 4
Question 1003
If 3n = 2187, then the value of n is:
A. 13
B. 14
C. 15
D. 16
Question 1004
A root of equation ax2 + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3√3. What is the value of (a2 + b2 + c2)/(a + b + c)?
A. 35/3
B. 37/3
C. – 105/11
D. – 105/13
Question 1005
ΔPQR is right angled at Q. If m∠R = 45°, then find the value of (tanP - 1/2).
A. (2-√3)/√3
B. (2√3-√6)/2√2
C. 1/2
D. (√6-6)/3√3
Question 1006
Consider a regular hexagon ABCDEF. Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is 30 deg, and the angle of elevation to the top of the tower at C is 45 deg. What is the ratio of the height of towers at B and C?
A. 1:√3
B. 1:3
C. 1:2
D. 1:2√3
Question 1007
Which of the following is correct?
A. (4x - 5y)2 = 16x2 - 20xy + 25y2
B. (4x - 5y)2 = 16x2 + 40xy - 25y2
C. (4x - 5y)2 = 16x2 - 40xy + 25y2
D. (4x - 5y)2 = 16x2 - 20xy - 25y2
Question 1008
If a - b = 2 and ab = 24, then what is the value of a3- b3?
A. 280
B. 124
C. 140
D. 152
Question 1009
If a=101 then the value of a(a2-3a+3) is
A. 1000000
B. 1010101
C. 1000001
D. 999999
Question 1010
A line passing through the origin perpendicularly cuts the line 3x - 2y = 6 at point M. Find M?
A. (18/13, 12/13)
B. (18/13, -12/13)
C. (-18/13, -12/13)
D. (-18/13, 12/13)
Question 1011
Reflection of the point (-3,6) in the x-axis is
A. (3,6)
B. (6,-3)
C. (-3,-6)
D. (-6,3)
Question 1012
A bag contains coins of denominations Rs.1, Rs.5 and Rs.10. Assuming there are equal number of Rs.1, Rs.5 and Rs.10, what will be the total number of coins in the bag be if the total money is Rs. 368?
A. 69
B. 96
C. 56
D. 65
Question 1013
If 3 dozen guavas cost Rs. 90, how many guavas can be bought for Rs. 240?
A. 98
B. 96
C. 102
D. 90
Question 1014
If x = 6+26, then what is the value of x-1 + 1x-1 ?
A. 2√3
B. 3√2
C. 2√2
D. 3√3
Question 1015
What is the value of Tan 45° + 4/√3 Sec 60°?
A. (√3 + 8)/√3
B. (√3 + 8)/3
C. (√3 - 8)/√3
D. (√3 - 8)/3
Question 1016
What is the reflection of the point (4 , -3) in the line y = 1?
A. (4, -5)
B. (4, 5)
C. (-4, -5)
D. (-4, 5)
Question 1017
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed :
A. 30 birds
B. 60 birds
C. 72 birds
D. 90 birds
Question 1018
What is the value of cosec 3π/4?
A. -√2
B. √2
C. 2/√3
D. -2/√3
Question 1019
The difference of 18 and its reciprocal is equal to :
A. 1/8
B. 4/3
C. 15/16
D. 105/304
Question 1020
If x = 4aba+b, then what is the value of x+2ax-2a+x+2bx-2b ?
A. 0
B. 2
C. 4
D. 1
Question 1021
The slopes of two lines are 1 and √3. What is the angle between these two lines?
A. 15°
B. 30°
C. 45°
D. 60°
Question 1022
Factorise x2 + 3x - 18
A. (x+18)(x-1)
B. (x-1)(x+18)
C. (x+6)(x-3)
D. (x-6)(x+3)
Question 1023
Determine the value of 'x' in x = 11+2+12+3+13+2
A. -1
B. 0
C. 1
D. 2
Question 1024
If tanα = 2 - 1, then the value of tanα - cotα = ?
A. -2
B. √2 + 1
C. 1
D. 2√2
Question 1025
The value of -261+(-380)-(-521)+821-(-121)
A. 833
B. 825
C. 822
D. 800
Question 1026
Determine the value of y-1y2 when y4+1y4=34
A. 1
B. 2
C. 3
D. 4
Question 1027
Ifab=45andbc=1516, then c2-a2c2+a2 is :
A. 7/5
B. 7/25
C. 7/125
D. 7
Question 1028
If x3+ 2x2– 5x + k is divisible by x + 1, then what is the value of k?
A. -6
B. -1
C. 0
D. 6
Question 1029
If a--b = 4 and ab = 45, find the value of a3 - b3
A. 604
B. 370
C. 253
D. 199
Question 1030
What is the value of cosec 5π/3?
A. √2
B. -2/√3
C. -√2
D. 1/√3
Question 1031
(secA - 1)/(secA + 1) is equal to?
A. (1 - sinA)/(1 + sinA)
B. (1 + cosA)/(1 - cosA)
C. (1 + sinA)/(1 - sinA)
D. (1 - cosA)/(1 + cosA)
Question 1032
What is the value of (4/3) cot2 (p/6) + 3 cos2 (150) – 4 cosec2 45 + 8 sin (p/2)?
A. 25/4
B. 1
C. – 7/2
D. 13/2
Question 1033
What is the sum of a3+b3+c3-3abc, when the value of a=4, b=2 and c=-6?
A. 0
B. 2
C. 4
D. 6
Question 1034
What is the simplified value of 22433+393-11253?
A. 593
B. 493
C. 793
D. 1193
Question 1035
If 5 3x < 4 x and 5(2 x) > 2 2x, then x can take which of the following values?
A. 0
B. 1
C. 3
D. -1
Question 1036
What is the area (in square units) of the figure enclosed by the x-axis, the y-axis and the line x + 2y = 6 ?
A. 3
B. 6
C. 9
D. 12
Question 1037
Product of 6ab, 3b and 4a is
A. 72a2b2
B. 144ab
C. 72ab
D. 144a2b2
Question 1038
If (333 + 333 + 333) (233 + 233) = 6x, then what is the value of x?
A. 34
B. 35
C. 33
D. 33.5
Question 1039
What is the simplified value of (sec A + cos A)(sec A – cos A)?
A. 2 tan2A
B. 2 sin2 A
C. sin2 A tan2 A
D. sin2A + tan2 A
Question 1040
Find x, if 5x-6+5x+6 = 6
A. -4
B. 0
C. 2
D. 4
Question 1041
In ∆ABC, ∠B=35°, ∠C=65° and the bisector of ∠BAC meets BC in D. Then ADB is
A. 40°
B. 75°
C. 90°
D. 105°
Question 1042
A = (x8 – 1)/(x4 + 1) and B = (y4 – 1)/(y2 + 1). If x = 2 and y = 9, then what is the value ofA2 + 2AB + AB2?
A. 96475
B. 98625
C. 92425
D. 89125
Question 1043
Factorise 24x2 - 54x - 15
A. 3(2x + 5)(4x - 1)
B. 3(2x - 5)(4x + 1)
C. 2(3x - 5)(4x + 1)
D. 4(2x - 5)(3x + 1)
Question 1044
If x + y = 10 and xy = 4, then what is the value of x4 + y4?
A. 8464
B. 8432
C. 7478
D. 6218
Question 1045
What is the equation of the line whose y-intercept is 3/4 and making an angle of 45° with the positive x-axis?
A. 4x - 4y = 3
B. 4x - 4y = -3
C. 3x - 3y = 4
D. 3x - 3y = -4
Question 1046
What is the equation of the line which intercepts xaxis and yaxis at 3/4 and 2/3 respectively?
A. 8x + 9y = 6
B. 9x + 8y = 12
C. 8x - 9y = 6
D. 9x + 8y = -12
Question 1047
tan3A is equal to
A. 3tanA - tan3A(1 - 3tan2A)
B. 3tanA + tan3A(1 - 3tan2A)
C. 3tanA - tan3A(1 + 3tan2A)
D. 3tanA + tan3A(1 + 3tan2A)
Question 1048
78 of 448 + 67 of 3374 = ?
A. 3084
B. 3184
C. 3584
D. None of these
Question 1049
If x2+1x2 = 2, then the value of x - 1x is
A. -2
B. 0
C. 1
D. -1
Question 1050
For triangle PQR, what is the equation of altitude PS if coordinates of P, Q and R are (5,1), (0,4) and (2,3) respectively?
A. 7x + 2y = 33
B. 2x - 7y = 9
C. 2x - 7y = -3
D. 7x + 2y = -33
Question 1051
What is the value of (1 + cotA)2 + (1 - cotA)2?
A. 2cosec2A
B. 2sec2A
C. 1 - 2cosec2A
D. 1 - 2sec2A
Question 1052
If sin x + cos x = √2 sin x, then the value of tan x is
A. √2 - 1
B. √2 + 1
C. 1
D. √2
Question 1053
If θ is positive acute angle and 7cos2Ɵ + 3sin2Ɵ = 4, then the value of θ is
A. 60°
B. 30°
C. 45°
D. 90°
Question 1054
Find the value of '?' in 512 × 125 ÷ 15625 = 3125 × 25?
A. 4
B. 3
C. 2
D. 1
Question 1055
If x2 – 4x + 1 = 0, then what is the value of x9 + x7 – 194x5 – 194x3?
A. 4
B. – 4
C. 1
D. – 1
Question 1056
What is the value of sin6θ + cos6θ + 3 sin2θ cos2θ –1?
A. 0
B. 1
C. 2
D. 4
Question 1057
If x2+ x = 19, then what is the value of (x + 5)2+ [1/(x + 5)2]?
A. 77
B. 79
C. 81
D. 83
Question 1058
What is the simplified value of 0.072+0.292-0.02030.073+0.293
A. 0.6
B. 0.06
C. 1/0.6
D. 1/0.06
Question 1059
Determine the value of ‘r’ for which the equation 13x + 5 = rx + 18 has no solution.
A. 0
B. 5
C. 13
D. 18
Question 1060
Coefficient of x in (x + 11)(3 - 5x) is _____.
A. 33
B. -5
C. 3
D. -52
Question 1061
The value of(1(p-n)(n-q)+1(n-q)(q-p)+1(q-p)(p-n)) is
A. 1
B. 0
C. p+q+n
D. 2np+q
Question 1062
Solve the following equation to find x: (x − 2)2 − 36 = 0 : xεN
A. 4
B. 8
C. -4
D. -8
Question 1063
What is the value of 1sin490-θ+1cos290-θ - 1 ?
A. tan2θ sec2θ
B. sec4θ
C. tan4θ
D. tan2θ sin2θ
Question 1064
What is the value of Tan 45° - 1/√3 Sec 60°?
A. (1 - 2√3)/2
B. (√2 - √3)/√6
C. (3 - 2√3)/3
D. (1 - 2√2)/2
Question 1065
5 + 2 x 10 =
A. 70
B. 20
C. 25
D. 52
Question 1066
Find the greatest number that will divide 390, 495 and 300 without leaving a remainder
A. 5
B. 15
C. 25
D. 35
Question 1067
If Cot θ = 21/20, then what is the value of Cosec θ?
A. 21/29
B. 29/21
C. 20/29
D. 29/20
Question 1068
Find the value of 0.0112 - 0.0012 of 0.14 + 0.25 × 0.20.02 × 0.01
A. 257
B. 25.7
C. 2.57
D. 0.0257
Question 1069
If 1/√(1+tan2A) = x, then value of x is
A. cosA
B. sinA
C. cosecA
D. secA
Question 1070
If a2b+c=b2c+a=c2a+b=1 then the value of 21+a+21+b+21+c
A. 0
B. 1
C. 2
D. 3
Question 1071
Reflection of the point (2,5) in the x axis is
A. (2,5)
B. (-2,5)
C. (2,-5)
D. (-2,-5)
Question 1072
What is the value of sec 30° + cot 30°?
A. (√6-1)/√2
B. √3+2
C. 5/√3
D. (√3-2√2)/√6
Question 1073
If sin -330° = x, then the value of x is
A. √3/2
B. 1/2
C. -2/√3
D. √2
Question 1074
If P = 99, then the value of P(P2+ 3P + 3) is
A. 9999
B. 999999
C. 99999
D. 9999999
Question 1075
If Tan A = 15/8 and Tan B = 7/24, then Tan (A - B) = ?
A. 304/297
B. 304/425
C. 416/87
D. 87/416
Question 1076
If 3√2 + √18 + √50 = 15.55, then what is the value of √32 + √72?
A. 13.22
B. 10.83
C. 14.13
D. 16.54
Question 1077
If 5+x+5-x5+x-5-x = 3,then what is the value of x ?
A. 5/2
B. 25/3
C. 4
D. 3
Question 1078
The value of sec217°-1tan273°-sin17°sec73°
A. 1
B. 0
C. -1
D. 2
Question 1079
If secA = x, then the value of x is
A. √(1 - cot2A)
B. √(1 - tan2A)
C. √(1 + cot2A)
D. √(1 + tan2A)
Question 1080
The slope of the line passing through the points (2,-1) and (x,5) is -1. Find x?
A. 4
B. -4
C. 8
D. -8
Question 1081
The distance between the points (7,7) and (k,-5) is 13. Find k?
A. -2
B. 4
C. -4
D. 2
Question 1082
If 4(4x + 5) > 2x - 1 > 4x - 3, then the value of x is
A. 2
B. 3
C. -2
D. 0
Question 1083
If cosαcosβ=m and cosαsinβ=n, then the value of m2+n2 cos2β is
A. n2
B. m2
C. mn
D. 1
Question 1084
The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
A. Rs. 3500
B. Rs. 3750
C. Rs. 3840
D. Rs. 3900
Question 1085
1$ = Rs.67.89. Money changer adds a margin of RS. 1.11. What will be the cost of $150?
A. RS. 10,183
B. RS. 10,350
C. RS. 10,330
D. RS. 10,450
Question 1086
If 31x + 31y = 403, then what is the average of x and y?
A. 3.5
B. 5
C. 6.5
D. 13
Question 1087
If 2cosAsinB = x, then the value of x is?
A. sin(A+B) + sin(A-B)
B. cos(A+B) + cos(A-B)
C. sin(A+B) - sin(A-B)
D. cos(A-B) - cos(A+B)
Question 1088
A tetrahedron has 4 vertices. How many edges does it have?
A. 8
B. 12
C. 6
D. 10
Question 1089
Calculate the sum of squares from 1 to 9.
A. 284
B. 285
C. 385
D. 380
Question 1090
If 2x -3(x + 2) < 5 - 2x < -x + 2, then find the value of x.
A. 2
B. 0
C. 10
D. 12
Question 1091
A triangular prism has 9 edges. How many vertices does it have?
A. 8
B. 6
C. 12
D. 10
Question 1092
If x – 3 + [1/(x – 3)] = 4, what is the value of [(x – 3)3+ [1/(x – 3)3]?
A. 14
B. 18
C. 52
D. 76
Question 1093
XYZ is a right angled triangle and ∠Y = 90°. If XY = 2.5 cm and YZ = 6 cm then the circumradius of ∆XYZ is
A. 6.5 cm
B. 3.25 cm
C. 3 cm
D. 2.5 cm
Question 1094
If a - b = 3 and a^2 + b^2 = 29, find the value of ab.
A. 10
B. 12
C. 15
D. 18
Question 1095
When a number is increased by 28, it becomes 107% of itself. What is the number?
A. 336
B. 420
C. 400
D. 252
Question 1096
What is the simplified value of 12-13 ?
A. 5√3
B. 5/√3
C. 3√5
D. 3/√5
Question 1097
If 3x + 2y = 7 and 4x - y = 24, then x - y = ______.
A. 9
B. 1
C. -9
D. -1
Question 1098
Simplify (b5x2a3z4)*(b3x2a4z5) / (a2b3z2)
A. b5x4a5z5
B. b5x4a5z7
C. b5x4a4z7
D. b4x4a5z7
Question 1099
If a2+1a2 = 38, then find the value of a-1a?
A. 2
B. 4
C. 6
D. 8
Question 1100
P is a point outside the circle at distance of 6.5 cm from centre O of the circle. PR be a secant such that it intersects the circle at Q and R. If PQ = 4.5 cm and QR = 3.5 cm, then what is the radius (in cm) of the circle?
A. 1.5
B. 2
C. 2.5
D. 3
Question 1101
If sec (3x – 20°) = cosec (3y + 20°), then what is the value of tan (x + y)?
A. 1
B. √3
C. 1/√3
D. 2√3
Question 1102
125 - 73 + 48 - 137 + 99 = ?
A. 237
B. 62
C. -37
D. 52
Question 1103
Find the roots of the quadratic equation 27x2 + 57x - 14 = 0
A. 2/9, 7/3
B. 2/9, -7/3
C. 9/2, -3/7
D. -9/2, 3/7
Question 1104
If a + b + c = 9, ab + bc + ca = 26, a3 + b3 = 91, b3 + c3 = 72 and c3 + a3 = 35, then what is the value of abc?
A. 48
B. 24
C. 36
D. 42
Question 1105
If sin3A = x, then value of x is
A. 3sinA + 4sin3A
B. 4sin3A - 3sinA
C. 4sin3A + sinA
D. 3sinA - 4sin3A
Question 1106
The point Q(a,b) is first reflected in yaxis to Q1 and Q1 is reflected in xaxis to (6,2). The coordinates of point Q are
A. (-6,2)
B. (2,-6)
C. (6,-2)
D. (-2,6)
Question 1107
If -3[1-(x/2)] + 5x/3 = 1/6, then what is the value of x?
A. 2
B. -1
C. 1
D. -2
Question 1108
Mr. Ankit is on tour to Siachin and he has Rs. 360 for his expenditure. If he exceeds his tour by 4 days, he must trim down his daily expenditure by Rs.3. Forhow many days is Mr. Ankit is on tour?
A. 20
B. 22
C. 24
D. 26
Question 1109
Out of the 60 students of a class, 29 took Mathematics, 32 took Biology and 8 took none of the two subjects. How many students took both Mathematics and Biology?
A. 8
B. 9
C. 7
D. 6
Question 1110
What is the equation of the line passing through the point (1,3) and making an angle of -45° with the positive x-axis?
A. x + y = 4
B. x + y = 2
C. x - y = 4
D. x - y = 2
Question 1111
If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ?
A. 500
B. 1000
C. 1500
D. 2000
Question 1112
Find co-ordinates of the mid point of the segment joining points C (3,-5) and D (-7,3).
A. (-2, -1)
B. (5, -4)
C. (-5, 4)
D. (2, 1)
Question 1113
What is the value of tan 7π/4?
A. √3
B. -1/2
C. √3/2
D. -1
Question 1114
[15% of 300% of 560] × 2 ÷ 5 =
A. 100
B. 90
C. 85
D. 105
Question 1115
PQ is a tangent to the circle at T. If TR = TS where R and S are points on the circle and ∠RST = 65°, the ∠PTS =
A. 65°
B. 130°
C. 115°
D. 55°
Question 1116
If 27x + 27[x–(1/3)] = 972, then what is the value of x?
A. 2
B. 3
C. 4
D. 5
Question 1117
In ΔPQR measure of angle Q is 90°. If tanP = 4/3, and PQ = 1.5cm, then what is the length (in cm) of side PR?
A. 2
B. 2.5
C. 3
D. 4.8
Question 1118
If Sec θ = 13/12, then what is the value of Sin θ?
A. 5/13
B. 12/5
C. 12/13
D. 5/12
Question 1119
For x > 0, what is the minimum value of x + x+22x?
A. 1
B. 2
C. 2.5
D. 1.5
Question 1120
What is the value of (1+cosA)/(1-cosA)?
A. (cosecA - cotA)2
B. (cosecA + cotA)2
C. (secA + cotA)2
D. (secA - cotA)2
Question 1121
If cosec4A - cosec2A = x, then value of x is?
A. tan4A + tan2A
B. cot4A + cot2A
C. cot4A - cot2A
D. tan4A - tan2A
Question 1122
A man has Rs.480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
A. 45
B. 60
C. 75
D. 90
Question 1123
If (6x - 5) = (4x + 7), then the numerical value of (x + 1)3 is
A. 216
B. 125
C. 64
D. 343
Question 1124
(secA - tanA)/(cosecA + cotA) is equal to
A. (secA - cotA) / (cosecA + tanA)
B. (secA - cosA) / (cosecA + sinA)
C. (cosecA - cotA) / (secA + tanA)
D. (secA + cosA) / (cosecA - sinA)
Question 1125
If Cos θ = 5/13, then Cosec θ = ?
A. 5/12
B. 12/5
C. 13/5
D. 13/12
Question 1126
If the simple interest on Rs. 1 for 1 month is 1 paisa, then the rate percent per annum will be
A. 10%
B. 8%
C. 12%
D. 6%
Question 1127
What is the value of 1/√2 Cot 30° + 1/√3 Cosec 60°?
A. (3√3 + 2√2)/3√2
B. (3√3 - 2√2)/3√2
C. (3√3 + 2√2)/√2
D. (3√3 - 2√2)/√2
Question 1128
If x2 – 12x + 33 = 0, then what is the value of (x – 4)2 + [1/(x – 4)2]?
A. 16
B. 14
C. 18
D. 20
Question 1129
If cot(A/2) = x, then x is equal to
A. tanA/(1 + secA)
B. 1/(secA + cotA)
C. tanA/(1 + cosecA)
D. 1/(cosecA - cotA)
Question 1130
If x3-2x=3x, then the value of x2+1x2 will be
A. 3 1/9
B. 3 2/9
C. 2 1/9
D. 2 4/9
Question 1131
If a + b = 8 and ab = 15, then what is the value of a3 + b3?
A. 98
B. 152
C. 124
D. 260
Question 1132
If √(1 - sin2A) = x, then the value of x is
A. tanA
B. cosA
C. cosecA
D. secA
Question 1133
If √(1 + cot2A) = x, then the value of x is
A. secA
B. sinA
C. cosecA
D. cosA
Question 1134
If 56 × 75 × 60 × 84 × 210 = 2p × 3q × 5r × 7s, then what is the value of [(p + q)/s] + r?
A. 6
B. 8
C. 12
D. 10
Question 1135
If sec2θ+tan2θ=3, then sec4θ-tan4θ =
A. 1/√3
B. 1
C. √3
D. 0
Question 1136
Solve the following: (−18)[36÷7−(−2)]÷{}(−4)19−(−3)×(−5)={}?
A. -4.5
B. 4.5
C. -2.5
D. 2.5
Question 1137
The sum of two positive integers is 80 & difference between them is 20. Then what is difference of squares of those numbers ?
A. 1400
B. 1600
C. 1800
D. 2000
Question 1138
If (1/cos θ) – (1/cot θ) = 1/P, then what is the value of cos θ?
A. (P + 1)/(P – 1)
B. (P2+ 1)/2P
C. 2(P2+ 1)/P
D. 2P/(P2+ 1)
Question 1139
Expand : S + 23
A. S3+3S2+12S+8
B. S3+3S2+6S+8
C. S3+6S2+12S+8
D. S3+6S2+6S+8
Question 1140
What is the value of cosec 11π/6?
A. -2/√3
B. √2
C. -2
D. -√2
Question 1141
What is the value of sec -2π/3 ?
A. -2
B. 2
C. 2/√3
D. -2/√3
Question 1142
If 2x+29x = 4, then the value of 27x3+127x3
A. 180
B. 198
C. 234
D. 252
Question 1143
What is the value of 4600+540+1280+250+36 ?
A. 69
B. 68
C. 70
D. 72
Question 1144
If 493/29 = 17, then 4.93/0.0017 = ?
A. 290
B. 0.29
C. 2.9
D. 2900
Question 1145
If 7x + 6y = 5xy and 10x - 4y = 4xy, then value of x and y is
A. 3, 2
B. 2, 3
C. 4, 2
D. 5, 6
Question 1146
If a+b=5 then the value of a-37+b-27 is
A. 27
B. 37
C. 1
D. 0
Question 1147
A fraction, when taken away from 1/3 gives 1/12. The fraction is
A. 5/12
B. 1/4
C. 3/4
D. 1/9
Question 1148
If price of oranges is increased by 30%, then a person can buy 12 oranges less for Rs 208. What is the original price (in Rs) of an orange?
A. 2
B. 4
C. 8
D. 3
Question 1149
If a+1b= b+1c = c+1a (a , b, c are not equal) then the value of abc =
A. + 1
B. - 1
C. +1 & -1
D. None of the options
Question 1150
Δ XYZ is right angled at Y. If m∠Z = 60°, what is the length of YZ (in cm), if ZX = 3√3 cm?
A. 3√3/2
B. 3√3
C. 9
D. 6
Question 1151
A complete factorisation of x4 + 64 is
A. (x2 + 8)2
B. (x2 + 8)(x2 - 8)
C. (x2 - 4x + 8)(x2 -4x - 8)
D. (x2 + 4x + 8)(x2 - 4x + 8)
Question 1152
What is the value of (sin60° - 2/√3) ?
A. -1/2√3
B. -1/2
C. 1/√3
D. (1-2√3)/2
Question 1153
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
A. 10
B. 35
C. 62.5
D. Cannot be determined
Question 1154
If Cot θ = 24/7, then Sin θ = ?
A. 24/25
B. 8/25
C. 7/25
D. 9/25
Question 1155
If Cot θ = 21/20, then what is the value of Sec θ?
A. 29/21
B. 21/29
C. 29/20
D. 20/29
Question 1156
What is the value of Cot 45°+ 1/3 Cosec 60°?
A. √3 + 2
B. (9 + 2√3)/9
C. √3
D. (2√2 + 3)/√6
Question 1157
The coordinates of the point that divides the line segment joining the points (-5, 5) and (7,-3) internally in the ratio 3 : 1 are given by
A. (-2, 3)
B. (4, -1)
C. (5/2, 0)
D. (1, 1)
Question 1158
If 3a+4b3c+4d = 3a-4b3c-4d, then
A. ab = cd
B. ad = bc
C. ac = bd
D. a = b = c ≠ d
Question 1159
A circle is inscribed in a square. If the length of the diagonal of the square is 14√2 cm, what is the area of the circle?
A. 308 sq cm
B. 462 sq cm
C. 154 sq cm
D. 616 sq cm
Question 1160
If (x + y)2 = xy + 1 and x3 – y3 = 1, then what is the value of x – y?
A. 1
B. 0
C. -1
D. 2
Question 1161
Slope of the line AB is -2/3. Co-ordinates of points A and B are (x , -3) and (5 , 2) respectively. What is the value of x?
A. 4
B. -14
C. 12.5
D. -4
Question 1162
If a+b+c = 0, then (a^3 + b^3 + c^3)^2 = ?
A. 27abc
B. 9abc
C. 3abc
D. 9a^2b^2c^2
Question 1163
Point P (-2, 5) is the midpoint of segment AB. Co-ordinates of A are (-5, y) and B are (x, 3). What is the value of x?
A. 1
B. -1
C. 2
D. -2
Question 1164
If one more cobbler is hired the output of a shoe making unit will increase from 50 pairs of shoes to 55 pairs per day, but then the shoe making unit will have to reduce the price of a pair of shoes from Rs 3200 to Rs 3000 per pair to sell the additional output, the marginal revenue product of the last cobbler is
A. Rs 1000
B. Rs 5000
C. Rs 4000
D. Rs 200
Question 1165
In an examination, a student scores 4 marks for every correct answer and loses I mark for every wrong answer. If he attempts in all 60 questions and secures 130 marks, the number of questions he attempts correctly, is:
A. 35
B. 38
C. 40
D. 42
Question 1166
In a slip test, K got the 15th rank and he was 44th from the bottom of the list of passed students. 4 students did not take up the slip test and 3 students were failed. What is the total strenght of the class ?
A. 63
B. 62
C. 64
D. 65
Question 1167
If x(2x + 3) = 90 and 7y-1/2+ 2y-1/2= y1/2 (x and y are positive numbers), then what is the value of x2+ y2?
A. 45
B. 109
C. 117
D. 126
Question 1168
What is the value of ( 1/2 - cot45) ?
A. (2√2-√3)/2
B. 3/2
C. (3√3-1)/3
D. -1/2
Question 1169
What is the equation of the line if its slope is 4/3 and it passes through the point (-7 , 2)?
A. 4x - 3y = -22
B. 4x + 3y = -34
C. 4x + 3y = -22
D. 4x - 3y = -34
Question 1170
∆LMN is right angled at M. If m ∠N = 45°. What is the length (in cm) of MN, if NL = 6√2 cm?
A. 3
B. 4
C. 2
D. 6
Question 1171
What is the reflection of the point (3,-5) in the origin?
A. (-3, -5)
B. (5,-3)
C. (-5,-3)
D. (-3, 5)
Question 1172
If x + y = 5, x3 + y3 = 35, then what is the positive difference between x and y?
A. 0
B. 1
C. 5
D. 6
Question 1173
Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
A. 1/7
B. 1/8
C. 1/9
D. 7/8
Question 1174
If x + 1/x = √13, then 3x(x2-1) equal to
A. 3√13
B. √13/3
C. 1
D. 3
Question 1175
What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)? √580×∛510+ 49.999 x 3.999=?
A. 384
B. 392
C. 410
D. 372
Question 1176
Find the degree of the polynomial 8x4 + 2x2y3 + 4
A. 4
B. 5
C. 0
D. 1
Question 1177
cos3A is equal to
A. cos3A - 3sin2cosA
B. cos3A + 4sin2cosA
C. cos3A + 3sin2cosA
D. cos3A - 4sin2cosA
Question 1178
If each median of an equilateral triangle has a length of 12cm. Then what will be the value of in-radius (in cm) of the equilateral triangle?
A. 3
B. 4
C. 5
D. 6
Question 1179
If 2cos2A - 1 = x, then the value of x is
A. cosec4A - sin4A
B. cos4A - sin4A
C. cos4A - tan4A
D. cosec4A - tan4A
Question 1180
The value of x for which the expressions 7x + 13 and 13x - 7 become equal is _____
A. -10/3
B. 3/10
C. -3/10
D. 10/3
Question 1181
If 123 x 356 = 43788, then 1.23 x 0.356 = ?
A. 437.88
B. 4.3788
C. 0.43788
D. 0.043788
Question 1182
A bag contain equal number of 1 rupee, 50 paisa and 25 paisa coins. If the total amount is Rs 105, then how many coins of each type are there?
A. 15
B. 45
C. 60
D. 80
Question 1183
What is the equation of the line whose y-intercept is 4 and making an angle of 45° with the positive x-axis?
A. x + y = -4
B. x - y = 4
C. x + y = 4
D. x - y = -4
Question 1184
If a – b = 11 and ab = 24, then value of a2 + b2 is
A. 169
B. 37
C. 73
D. 48
Question 1185
If x + 3y - 2z4 = 6, x + 232y + 3z = 33 and 17x + y +z + 2z =9, then what is the value of 46x+ 131y ?
A. 414
B. 364
C. 384
D. 464
Question 1186
Δ XYZ is right angled at Y. If m∠Z = 60°, then what is the value of (1/√2) Sec X?
A. 2/√3
B. 1/√6
C. 1/√3
D. 2/√6
Question 1187
What is the simplified value of (sin A – cosec A)(sec A – cos A) (tan A + cot A)?
A. 1
B. -1
C. 0
D. 2
Question 1188
Sec 45% + Tan 30% =
A. (√6 + 1)/√3
B. (1 + √3)/2
C. (√3 + 2)/√3
D. 5/√3
Question 1189
If 2+aa + 2+bb + 2+cc = 4, then the value of ab+bc+caabc is
A. 2
B. 1
C. 0
D. 1/2
Question 1190
43% of 616.6 + 37% of 217 =?
A. 345.428
B. 354.428
C. 344.428
D. 364.428
Question 1191
What is the simplified value of (cos4 A – sin4 A)?
A. 0
B. 2 cos2 A
C. cos2A
D. 1
Question 1192
If C+1C = 3, then what is the value of C3+1C3 = ?
A. 0
B. 3√3
C. 1/√3
D. 6√3
Question 1193
The average revenues of 13 consecutive years of a company is Rs 70 lakhs. If the average of first 7 years is Rs 65 lakhs and that of last 7 years is Rs 77 lakhs, find the revenue for the 7th year.
A. Rs 86 lakhs
B. Rs 84 lakhs
C. Rs 82 lakhs
D. Rs 80 lakhs
Question 1194
Twenty times a positive integer is less than its square by 96. What is the integer ?
A. 42
B. 36
C. 48
D. 24
Question 1195
On dividing 111a2b2c2 by 37a2, we get ______.
A. 2c2
B. 2b2
C. 3
D. 3b2c2
Question 1196
What is the value of 128 + 7232
A. 3.5
B. 7
C. 4.5
D. 9
Question 1197
What is the value of Tan 60 + Cosec 60?
A. 5/3
B. 2/√3
C. 5/√3
D. 2/3
Question 1198
If 14.35 - (1.956 - x ) - 83.92 = 3.858 then what is the value of x?
A. -92.456
B. 75.384
C. 71.472
D. 104.084
Question 1199
If a/(a+b) = 15/21, what is (a+b)/(a-b) is equal to?
A. 13/9
B. 23/11
C. 14/5
D. 21/9
Question 1200
If the value 5 = 2.236,then calculate the value of 405 - 1280-125
A. 2.236
B. 4.472
C. 1.118
D. 8.994
Question 1201
When x2+ax+b is divided by (x-1), the remainder is 15 and when x2+bx+a is divided by (x+1), the remainder is -1, then the value of a2+b2 is
A. 10
B. 20
C. 8
D. 16
Question 1202
If X = 423 + 32 then find the value of ( X + 1X ).
A. 103 + 15212
B. (103 - 52)12
C. -103 - 33212
D. (103+332)12
Question 1203
Tan 45° + Cosec 60° =
A. (1 + 2√2)/2
B. (√3 + 2)/√6
C. 5/√3
D. (3 + 2√3)/3
Question 1204
If -5x3+2 = x-6, then find the value of x?
A. 1
B. 2
C. 3
D. 4
Question 1205
If 3x+22x+1 = a2x+1+bx+2 be an identity, then the value of b
A. 0
B. -1
C. 2
D. 3
Question 1206
A bag contains 25 paise, 50 paise and 1 Rs coins. There are 220 coinsinall and the total amount in the bag is Rs. 160. If there arethrice as many 1 Rs. coins as there are 25 paise coins, then what is the number of 50 paise coins?
A. 60
B. 40
C. 120
D. 80
Question 1207
If (tanA + tanB)/(1 tanAtanB) = x, then the value of x is
A. tan(A + B)
B. tan(A - B)
C. cot(A + B)
D. cot(A - B)
Question 1208
If 10x/3 + 5/2(2 - x/3) = 7/2, then the value of x is?
A. 3/5
B. -5/3
C. 5/3
D. -3/5
Question 1209
What is the value of √[(1 - sinA)/(1 + sinA)]?
A. cosA/(1 - sinA)
B. cosecA/(1 + sinA)
C. cosA/(1 + sinA)
D. cosecA/(1 - sinA)
Question 1210
What is the slope of the line perpendicular to the line passing through the points (-2, 3) and (2, 0)?
A. 4/3
B. 3/4
C. -3/4
D. -4/3
Question 1211
If a + b + c = 7/12, 3a – 4b + 5c = 3/4 and 7a – 11b – 13c = – 7/12, then what is the value of a + c?
A. 1/2
B. 5/12
C. 3/4
D. 1/4
Question 1212
If x/3 - [5(7x/5 - 4/3)]/2 = -x/6, then what is the value of x?
A. 10/9
B. -10/9
C. -9/10
D. 9/10
Question 1213
If xy = 22 and x2+ y2= 100, then what will be the value of (x + y)?
A. 12
B. 144
C. 72
D. 6
Question 1214
97 x 97 = ?
A. 9391
B. 9409
C. 9049
D. 9309
Question 1215
The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
A. Rs. 1200
B. Rs. 2400
C. Rs. 4800
D. Cannot be determined
Question 1216
If secA + tanA = x, then the value of x is
A. cosA/(1 + sinA)
B. √[cosA/(1 - sinA)]
C. √[cosA/(1 + sinA)]
D. cosA/(1 - sinA)
Question 1217
tanAcosec2A is equal to
A. (1 + tan2A)cotA
B. (1 - tan2A)cotA
C. √[(1 + tan2A)cotA]
D. √[(1 - tan2A)cotA]
Question 1218
If 2x - 5y = 5 and 2x - y = 9, then x - y is ______.
A. 2
B. 4
C. 6
D. 3
Question 1219
Derivative of sinx by first principle?
A. -sinx
B. -cosx
C. cosx
D. sinx
Question 1220
The value of cos (1110°) is
A. √3/2
B. 1/2
C. 1/√2
D. 1
Question 1221
What is the square root of 5041?
A. 79
B. 81
C. 71
D. 69
Question 1222
If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (c/a) + (a/c), then what is the value of xyz – x2 – y2 – z2?
A. – 4
B. 2
C. – 1
D. – 6
Question 1223
In a party there are male and female members. If 15 female quit then the number of females will become double the number of males. If 45 males quit no. of female becomes five times the number of males. Find the number of females ?
A. 175
B. 145
C. 165
D. 135
Question 1224
What is the value of cos 4π/3?
A. -1/2
B. √3/2
C. - 1/√2
D. √3/2
Question 1225
For triangle ABC, find equation of median AD if co-ordinates of points A, B and C are (2,4), (3,0) and (5,2) respectively?
A. 3x - 2y = 14
B. 3x - 2y = 2
C. 3x + 2y = 14
D. 3x + 2y = 2
Question 1226
If the value of √30 is approximately 5.477, then what is the approximate value of 56 ?
A. 0.853
B. 0.891
C. 0.913
D. 0.937
Question 1227
If √(1 - cos2A)/cosA = x, then the value of x is
A. cotA
B. cosecA
C. tanA
D. secA
Question 1228
If θ is acute angle and tan θ – cot θ = 0, then what is the value of tan26θ + cot100θ?
A. -2
B. 0
C. 1
D. 2
Question 1229
If p and q are the roots of the equation x2 –15x + r = 0 and p –q = 1, then what is the value of r ?
A. 55
B. 56
C. 60
D. 64
Question 1230
What should be added to 5(2x-y) to obtain 4(2x - 3y) + 5(x + 4y)?
A. 3x - 13y
B. 3x + 13y
C. 13x - 3y
D. 13x + 3y
Question 1231
Point P is the midpoint of segment AB. Co-ordinates of P are (5, -1) and A are (2, -4). What are the co-ordinates of point B?
A. (6, 4)
B. (8, 2)
C. (1,-2)
D. (-6, -2)
Question 1232
If sin - 4π/3 = x, then the value of x is
A. -2
B. -2/√3
C. √3/2
D. √2
Question 1233
If a - b = 1 and ab = 6, then what is the value of a3- b3?
A. 21
B. 23
C. 19
D. 25
Question 1234
The value of x for which the expressions 15x + 4 and 13x - 2 become equal is ______
A. -1
B. 1
C. -3
D. 3
Question 1235
If x - y = -8 and xy = 45, then (x2 + y2) is
A. 154
B. 64
C. 90
D. 26
Question 1236
In the given figure, AB is a diameter of the circle with center O and XY is the tangent at a point C. If ACX = 35 deg, then what is the value (in deg) of CAB?
A. 45
B. 35
C. 55
D. 65
Question 1237
The expenses of a person increase by Rs. 50000 for every month in February and March. If his expenses in January was Rs. 50000, calculate his average expenditure (in Rs.) from January to March.
A. 100000
B. 150000
C. 75000
D. 50000
Question 1238
-70 + 28 / (7 - 3) = ?
A. -9
B. -69
C. -10.5
D. -63
Question 1239
Compute of 69696 x 9999 =
A. 696980304
B. 666890304
C. 696809304
D. 696890304
Question 1240
If the value of 3-1.732, then calculate the value of 243-12108-147
A. 1.732
B. -1.464
C. 3.464
D. -1.732
Question 1241
If Sin θ = 20/29 , then what is the value of Sec Sin θ ?
A. 29/21
B. 29/20
C. 21/20
D. 21/29
Question 1242
2sin[(C+D)/2].sin[(D-C)/2] is equal to
A. cosC + cosD
B. cosC - cosD
C. sinC - sinD
D. sinC + sinD
Question 1243
D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:5 and area of ΔADE is 8 cm sq, what is the area (in sq cm) of quadrilateral BDEC?
A. 98
B. 94
C. 90
D. 86
Question 1244
Which of the following equations has the sum of its roots as 11?
A. x2 - 11x + 18 = 0
B. x2 - 7x + 10 = 0
C. x2 + 2x - 26 = 0
D. x2 + 5x - 6 = 0
Question 1245
Simplify 0.1x0.1x0.1 + 0.3x0.3x0.30.3x0.3 - 0.3x0.1 + 0.1x0.1
A. 0.09
B. 0.03
C. 0.05
D. 0.04
Question 1246
What is the value of Sin 30° + Cos 30°?
A. (√6 + 1)/√3
B. (√3 + 2)/√3
C. (1 + √3)/2
D. 5/√3
Question 1247
If 2/3(6x/5 - 1/4) + 1/3 = 9x/5, then what is the value of x?
A. 1/6
B. -1/6
C. 1/5
D. -1/5
Question 1248
If 2x + 5 > 2 + 3x and 2x - 3 ≤ 4x - 5, then x can take which of the following values?
A. -2
B. 2
C. -4
D. 4
Question 1249
If 3.5x = 0.07y, then find the result of [y-x / y+x]
A. 51/49
B. 49/53
C. 49/51
D. 53/57
Question 1250
If 2x+2x=3, then the value of x3+1x3+2 is
A. 3/4
B. 4/5
C. 5/8
D. 7/8
Question 1251
If x = (√5) + 1 and y = (√5) – 1, then what is the value of (x2/y2) + (y2/x2) + 4[(x/y) + (y/x)] + 6?
A. 31
B. 23√5
C. 27√5
D. 25
Question 1252
α and β are the roots of quadratic equation. If α + β = 8 and α – β = 2√5, then which of the following equation will have roots α4 and β4?
A. x2 – 1522x + 14641 = 0
B. x2 + 1921x + 14641 = 0
C. x2– 1764x + 14641 = 0
D. x2+ 2520x + 14641 = 0
Question 1253
If x2+y2+z2-8x+6y-4z+29 = 0, then find the value of z(x+y).
A. 1
B. 2
C. 3
D. 4
Question 1254
What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)?(55.01+16.0003)×22.01÷10.998 =?
A. 190
B. 130
C. 110
D. 142
Question 1255
Slope of the line AB is -4/3. Co-ordinates of points A and B are (x, -5) and (-5, 3) respectively. What is the value of x?
A. -1
B. 2
C. -2
D. 1
Question 1256
What is the slope of the line 2x - 5y = 12?
A. 2/5
B. 5/2
C. -2/5
D. -5/2
Question 1257
For what value of k, the expression x6– 18x3 + k will be a perfect square?
A. -9
B. 81
C. 9
D. -81
Question 1258
If (cosecA - 1)/(cosecA + 1) = x, then the value of x is
A. (sinA/(1 + cosA))2
B. cosA/(1 + sinA)
C. (cosA/(1 + sinA))2
D. sinA/(1 + cosA)
Question 1259
If cotA/√(1 + cot2A) = x, then the value of x is
A. sinA
B. cosecA
C. secA
D. cosA
Question 1260
The distance between the points (11,5) and (k,0) is 13. Find k.
A. k = 1 or 23
B. k = -1 or 23
C. k = 1 or -23
D. k = -1 or -23
Question 1261
What is the value of [sin (90– 10θ) – cos (p – 6θ)]/ [cos (p/2 – 10θ) – sin (p – 6θ)]?
A. tan 2θ
B. cot 2θ
C. cot θ
D. cot 3θ
Question 1262
What is the value of cosecA/√(cosec2A - 1)?
A. sinA
B. secA
C. tanA
D. cosA
Question 1263
If x = y + 2 then x3 - y3 - z3 is
A. 0
B. 3xyz
C. -3xyz
D. 1
Question 1264
If 3x + 4y – 11 = 18 and 8x – 6y + 12 = 6, then what is the value of 5x – 3y – 9?
A. 18
B. – 9
C. – 27
D. – 18
Question 1265
If a2+b2+c2=14 and a+b+c=6, then the value of ab+bc+ca is,
A. 11
B. 12
C. 13
D. 14
Question 1266
If sin = 2/3, find the value of secθ and cotθ
A. √5/2, 2/√5
B. 2/√5, 3/5
C. 3√5/5, √5/2
D. 3/5, 3√5/5
Question 1267
If x + 1x = -2, then the value of x631 + 1x632?
A. -2
B. -1
C. 0
D. 2
Question 1268
If x=aCosθCosΦ, y = aCosθSinΦ and z= aSinθ, then the value of x2+ y2 + z2 is
A. 2a2
B. 0
C. 4a2
D. a2
Question 1269
What is the value of [(cos32θ + 3 cos 2θ)÷(cos6θ – sin6θ)]?
A. 0
B. 1
C. 2
D. 4
Question 1270
What is the equation of a line which has 3 as x-intercept and -5 as y-intercept?
A. 3x - 5y = 15
B. 5x - 3y = 15
C. 5x + 3y = 15
D. 3x + 5y = 15
Question 1271
If sin P + cosec P = 2, then the value of sin7P + cosec7P is
A. 1
B. 2
C. 3
D. 0
Question 1272
If tan 45° + cosec 30° = x, then find the value of x.
A. √3
B. (1-2√2)/√2
C. (√3-4)/2√3
D. 3
Question 1273
0.196 + 1.96 + 19.6 + 196 = ?
A. 217.756
B. 216.856
C. 216.756
D. 217.676
Question 1274
If x – 4y = 0 and x + 2y = 24, then what is the value of (2x + 3y)/(2x – 3y)?
A. 9/5
B. 11/5
C. 13/7
D. 9/7
Question 1275
AB is the diameter of a circle with center O and P be a point on its circumference. If ∡POA = 120°, then the value of ∡PBO is
A. 30°
B. 60°
C. 50°
D. 40°
Question 1276
Value of (cos 53° - sin 37°) is
A. 2 sin 37 ̊
B. 2 cos 53 ̊
C. 0
D. 1
Question 1277
Given w = -2, x = 3, y = 0 & z = -1/2. Find the value of (z/w) + x.
A. 13/4
B. -13/4
C. 3.2
D. 3.5
Question 1278
If xy = 48 and x2 + y2 = 100, then (x + y) is
A. 12
B. 16
C. 18
D. 14
Question 1279
If X + 2Y = 27 and X - 2Y = -1, find the value of Y.
A. 13
B. 14
C. 7
D. 26
Question 1280
If cotA + cotB = x, then value of x is
A. (cotAcotB + 1)/(cotB - cotA)
B. (cotAcotB + 1)/(cotB + cotA)
C. (cotAcotB - 1)/(cotB + cotA)
D. (cotAcotB - 1)/(cotB - cotA)
Question 1281
The value of 1/64 is equal to square of
A. 0.125
B. 0.135
C. 0.145
D. 0.225
Question 1282
What is the value of cot 5π/3?
A. 1/√3
B. -1/√3
C. √3
D. -√3
Question 1283
If x1/4 + x-1/4 = 2, then what is the value of x81 + (1/x81)?
A. -2
B. 0
C. 1
D. 2
Question 1284
If (x – y) = 7, then what is the value of (x – 15)3 – (y – 8)3?
A. 0
B. 343
C. 392
D. 399
Question 1285
If a - b = 3 and a2 + b2 = 29, find the value of ab.
A. 10
B. 12
C. 15
D. 18
Question 1286
√(1 + tan2A)/tanA is equal to
A. secA
B. sinA
C. cosecA
D. cosA
Question 1287
If 3x2 = 102 - 52, find the value of x?
A. 7
B. 5
C. 9
D. 11
Question 1288
What is the equation of the line if its slope is 1/4 and y-intercept is -3?
A. x - 4y = 12
B. x + 4y = 12
C. x - 4y = -12
D. x + 4y = -12
Question 1289
If (1 - cosA)/(1 + cosA) = x, then the value of x is
A. (cotA + cosecA)2
B. (cotA - cosecA)2
C. cotA - cosecA
D. cotA + cosecA
Question 1290
If 5x - 5(3x - 2) < 4x - 1 < 2 + 2x, then x can take which of the following values?
A. 2
B. 1
C. -1
D. -2
Question 1291
Determine the value of z in the equation: z = 20+20+20+20+...∞
A. 4
B. 5
C. 20
D. 25
Question 1292
What is the value of 13×7+17×11+111×15+...+1899×903 ?
A. 21/509
B. 18/403
C. 25/301
D. 29/31
Question 1293
If θ>0, be an acute angle, then the value of it in degrees satisfying cos2θ-3cosθ+2sin2θ=1 is
A. 90°
B. 30°
C. 45°
D. 60°
Question 1294
If a + b = 10 and ab = 24, then what is the value of a3 + b3?
A. 280
B. 152
C. 140
D. 72
Question 1295
On dividing 256a2b2c2 by 64a2, we get
A. 2cxc
B. 2bxb
C. 4 bxb.cxc
D. 4
Question 1296
A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook ?
A. 15
B. 20
C. 10
D. 8
Question 1297
If x=8+215, then what is the value of x+1x?
A. 2√15
B. 3√5
C. (3√5+√3)/2
D. 3√2+3
Question 1298
If SinX-CosX=1, where 'X' is an acute angle, the value of SinX+CosX is
A. 0
B. 1
C. 1/2
D. 2
Question 1299
Find the common factor of (3757+4357) and (3737+4337) ?
A. (43 - 37)
B. (43 + 37)
C. (37 + 37)
D. 10
Question 1300
What is the simplified value of [2/(cot A – tan A)]?
A. sin A cos A
B. tan 2A
C. sin2 A
D. cos2 A
Question 1301
If 9x - [5(2x + 1)/2] = 9/2, then the value of x is?
A. 7/4
B. -7/4
C. 4/7
D. -4/7
Question 1302
If 2x+14x = 1, then the value of x2+164x2 is
A. 0
B. 1
C. 1/4
D. 2
Question 1303
Simplify 413 + 215 + 414 = ?
A. 10 47/60
B. 11 45/73
C. 11 47/36
D. 10 35/48
Question 1304
What is the value of 26 + 152?
A. 17
B. 19
C. 15
D. 21
Question 1305
If A = 30°, B = 60° and C = 135°, then what is the value of sin3A + cos3B + tan3C – 3sin A cos B tan C?
A. 0
B. 1
C. 8
D. 9
Question 1306
What is the value of Cot 60 - Sec 30?
A. -1/3
B. -1/√3
C. 1/√3
D. 1/3
Question 1307
5 sin(x)+ 12 cos(x) + r is always greater than or equal to zero. What is the smallest value satisfied by 'r' ?
A. -13
B. 11
C. 13
D. -11
Question 1308
What is the equation of the line if its slope is 2/5 and y-intercept is 6?
A. 2x + 5y = 6
B. 2x + 5y = 30
C. 2x - 5y = 6
D. 2x + 5y = -30
Question 1309
If Tan θ = 4/3, then what is the value of Sin θ?
A. 1.25
B. 0.8
C. 4/3
D. 3/4
Question 1310
Two numbers are such that the sum of twice the first number and thrice the second number is 36 and the sum of thrice the first number and twice the second number is 39. Find the difference between the numbers?
A. 15
B. 3
C. 9
D. 6
Question 1311
If x = 1 + √2 + √3, then the value of x2-2x-4=0
A. √6
B. 2√3
C. 3√2
D. 2√6
Question 1312
In a triangle PQR, ∠Q = 90°. If PQ = 12 cm and QR = 5 cm, then what is the radius (in cm) of the circum circle of the triangle?
A. 5
B. 6
C. 6.5
D. 6√2
Question 1313
2 - (cosA + sinA)2 is equal to
A. (cosecA - sinA)2
B. cosA - sinA
C. cosecA - sinA
D. (cosA - sinA)2
Question 1314
If 4x + 5y = 14 and x - 5y = 16 then the value of x and y are
A. 10 and -6/5
B. 6 and 2
C. 10 and 6/5
D. 6 and -2
Question 1315
If 9x = 24311, then what is the value of x?
A. 5/11
B. 5/22
C. 5/7
D. 5/33
Question 1316
If Sec θ = 13/12, then Cot θ = ?
A. 12/5
B. 13/5
C. 5/13
D. 5/12
Question 1317
An owner of a Dry fruits shop sold small packets of mixed nuts for Rs. 150 each and large packets for Rs. 250 each. One day he sold 5000 packets, for a total of Rs. 10.50 lakh. How many small packets were sold ?
A. 2000
B. 3000
C. 2500
D. 3500
Question 1318
If angles M and N measure 60 deg and 30 deg respectively, (sinM) x (cotN) = ?
A. 1/2
B. √3/2
C. 3/2
D. 0
Question 1319
What is the value of cos2A/(1 + sinA)?
A. 1 + sinA
B. 1 - sinA
C. 1 - secA
D. 1 + secA
Question 1320
If P=9, Q=17 then the value of p2-q2-13
A. 4
B. 1/4
C. 3
D. 1/3
Question 1321
tan2Asin2A is equal to
A. tan2A - sin2A
B. tan2A + sin2A
C. cot2A - sin2A
D. cot2A + sin2A
Question 1322
If x = 1.1, then what is the value of 4x2 -4x + 1 ?
A. 1.21
B. 1.331
C. 2.21
D. 1.2
Question 1323
What is the value of {sin (90 – x) cos [π – (x – y)]} + {cos (90 – x) sin [π – (y – x)]}?
A. -cos y
B. -sin y
C. cos x
D. tan y
Question 1324
What is the value of (cos45° + 1/3) ?
A. 2+√3
B. (2√2+1)/√2
C. (3+√2)/3√2
D. 5/√3
Question 1325
If cosθ + sinθ = m, secθ + cosecθ = n, what is m/n?
A. 1
B. sinθ cosθ
C. secθ cosecθ
D. cotθ tanθ
Question 1326
What is the reflection of the point (-1 , 5) in the line x = 1?
A. (3 , -5)
B. (-3 , -5)
C. (3 , 5)
D. (-3 , 5)
Question 1327
In a farm, in addition to 48 hens there are 42 sheep and 11 oxen with some shepherds. If the total number of feet be 224 more than the number of heads, find the number of shepherd.
A. 11
B. 13
C. 15
D. 17
Question 1328
If x = 11, the value of x5 - 12x4 + 12x3 - 12x2 + 12x - 1 is
A. 11
B. 10
C. 12
D. -10
Question 1329
ΔXYZ is right angled at Y. If m∠Z = 60°, then Cosec X =
A. 2
B. 1/2
C. 1/√2
D. 1/√3
Question 1330
5 bottles cost as much as 2 bags. The cost of 15 bottles and 4 bags is Rs 2,000. What is the price (in Rs.) of a single bag?
A. 200
B. 215
C. 240
D. 250
Question 1331
The sum of 2xy(3x + 4y - 5z) and 5yz(2x - 3y) is
A. 6x2y - 8xy2 + 15y2z
B. 6x2y + 8xy2 - 15y2z
C. 6x2y + 8xy2 - 15y2z - 20xyz
D. 6x2y - 8xy2 + 15y2z + 20xyz
Question 1332
If aq-r+br-p-cp-q, then find the value of (pa + qp + rc) is
A. 0
B. 1
C. 2
D. -1
Question 1333
If 5 sin2θ+ 4 cos2θ= 9/2 and 0 <θ<Π/2 then tanθ is equal to?
A. 1
B. 0
C. -1
D. 1/4
Question 1334
Point A divides segment BC in the ratio 4:1. Co-ordinates of B are (6 , 1) and C are (7/2 , 6). What are the co-ordinates of point A?
A. (4 , 3)
B. (4 , 5)
C. (2 , 5)
D. (3 , 5)
Question 1335
The sum of the parallel sides of a trapezium is 12.4 cm. If the distance between the parallel sides is 3.5 cm, what is the area of this trapezium?
A. 43.4 sq cm
B. 86.8 sq cm
C. 130.2 sq cm
D. 21.7 sq cm
Question 1336
What is the simplified value of Sec ACot A + Tan A2 ?
A. 1 – cos2A
B. 2sin2A
C. sec2A
D. 0
Question 1337
If 1/√(cosec2A - 1) = x, then value of x is
A. cotA
B. tanA
C. sinA
D. cosA
Question 1338
What is the value of [sin (y – z) + sin (y + z) + 2 sin y]/[sin (x – z) + sin (x + z) + 2 sin x]?
A. cos x sin y
B. (sin y)/(sin x)
C. sin z
D. sin x tan y
Question 1339
A bag has Rs 30.8 in the form of 1 rupee, 50 paise and 10 paise coins in the ratio of 6:3:2. What is the number of 50 paise coins?
A. 8
B. 24
C. 12
D. 4
Question 1340
What is the value of sin 330°?
A. 2
B. 2/√3
C. √2
D. -1/2
Question 1341
ΔDEF is right angled at E. If cosecD = 5/4, then what is the value of cosecF?
A. 5/3
B. 3/4
C. 4/5
D. 4/3
Question 1342
What is the perimeter of the sector whose central angle is 60° and radius of the circle is 21 cm?
A. 128 cm
B. 96 cm
C. 64 cm
D. 32 cm
Question 1343
What is the value of 0.55 x 4.5/0.81 ?
A. 3.555
B. 55/18
C. 3.05
D. 55/81
Question 1344
∆ABC is right angled at B. If m∠A = 30°, then find the value of (sinC + 1/3).
A. 4/3
B. (√3+1)/2
C. (√3+2)/√3
D. (3√3+2)/6
Question 1345
5.16 x 3.2 =
A. 15.502
B. 16.512
C. 17.772
D. 17.52
Question 1346
If (5/9 of x) - (2/5 of 9/4) equals -4/5 then find x.
A. 0.18
B. 0.12
C. 2
D. 0.54
Question 1347
The value of x for which the expressions 15 7x and 15x + 7 become equal is _____.
A. -4/11
B. 11/4
C. -11/4
D. 4/11
Question 1348
What is the value of sin (90° + 2A)[4 – cos2(90° – 2A)]?
A. 2(cos3 A – sin3 A)
B. 2(cos3 A + sin3 A)
C. 4(cos6 A+ sin6 A)
D. 4(cos6 A – sin6 A)
Question 1349
Which of the following quadratic equations has real roots?
A. 4x2 - 3x + 6 = 0
B. 2x2 + 7x + 6 = 0
C. x2 - 2x + 4 = 0
D. 3x2 - 4x + 3 = 0
Question 1350
If cos 2π/3c = x, then the value of x is
A. -1/2
B. 1/2
C. -√3/2
D. √3/2
Question 1351
If cot 135° = x, then the value of x is
A. -1/√3
B. -√3
C. -1
D. -1/2
Question 1352
Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 4 cm, then what is the area (in cm2) of an equilateral triangle with side equal to the bigger diagonal of the rhombus?
A. 6
B. 9√3
C. 12
D. 12√3
Question 1353
If α and βare the zeros of the polynomial 5x2 - 7x + 2 then the sum of their reciprocals is
A. 5/2
B. 7/5
C. 2/5
D. 7/2
Question 1354
If 1aa2+1 = 3, then the value of a6+1a3 is
A. 9
B. 18
C. 27
D. 1
Question 1355
What is the reflection of the point (5, -2) in the line x = -1?
A. (-7 , -2)
B. (5 , 0)
C. (7 , -2)
D. (5 , 2)
Question 1356
19 x 23 = 437. Then 190 x 0.023 = ?
A. 43.7
B. 4.37
C. 0.0437
D. 0.437
Question 1357
Simplyfiy : 314÷114-12212-14+16
A. 78
B. 88
C. 98
D. 108
Question 1358
There are 10 dozen apples, 15 dozen mangoes and 20 dozen oranges for selling. If 1/2, 1/3 and 1/4 of them are sold respectively. How many of the total fruits are remaining?
A. 420
B. 380
C. 180
D. 360
Question 1359
If a - b = -7 and a2+ b2= 85, then find ab.
A. 18
B. -30
C. -44
D. 60
Question 1360
If sinθ+cosecθ=2, the value of sinnθ+cosecnθ is
A. 2
B. 0
C. 1
D. 1/n
Question 1361
If 17/3 + [3(2x - 5/3)]/2 = 1/6, then what is the value of x?
A. 1
B. 3
C. -3
D. -1
Question 1362
In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group ?
A. 6
B. 10
C. 8
D. 12
Question 1363
The orthocentre of an obtuseangled triangle lies
A. inside the triangle
B. outside the triangle
C. on one side of a triangle
D. none of these
Question 1364
If Sin x = 4/5, then Cosec x + Cot x =
A. 31/12
B. 35/12
C. 2
D. 1/2
Question 1365
In a farm, there are goats and peacocks. If the number of heads are 60 and the number of feet are 170, then the number of goats = ?
A. 18
B. 20
C. 23
D. 25
Question 1366
If a:b = 3:8, find the value of (5a 3b)/(2a + b).
A. 9/14
B. 14/9
C. -9/14
D. -14/9
Question 1367
Coefficient of x2 in (x + 7)(5 - 3x)(3x - 6) is
A. 96
B. -30
C. 42
D. -18
Question 1368
If a3 + b 3 = 35 and ab = 6, then what is the value of a + b?
A. 5
B. 8
C. 2
D. -8
Question 1369
If x2 + (1/x2) = 1, then what is the value of x48 + x42 + x36 + x30 + x24 + x18 + x12 + x6 + 1?
A. -9
B. 0
C. 1
D. 9
Question 1370
An angle is thrice its complementary angle. What is the measure of the angle?
A. 22.5°
B. 135°
C. 45°
D. 67.5°
Question 1371
If 2x+4-2x+2=3, then the value of x?
A. 0
B. 2
C. -1
D. -2
Question 1372
What is the value of cos [(180 – θ)/2] cos [(180 – 9θ)/2] + sin [(180 – 3θ)/2] sin [(180 – 13θ)/2]?
A. sin 2θ sin 4θ
B. cos 2θ cos 6θ
C. sin 2θ sin 6θ
D. cos 2θ cos 4θ
Question 1373
What are the components of X6 - X4 - X5 - X4 + X2 - 4?
A. (X - 1)
B. (X + 2)
C. Both 1 and 2
D. Neither 1 nor 2
Question 1374
A sum of Rs. 1360 has been divided among A, B and C such that A gets 2/3 of what B gets and B gets 1/4 of what C gets. B's share is:
A. Rs. 120
B. Rs. 160
C. Rs. 240
D. Rs. 300
Question 1375
If 5x - 40 = 3x, then the numerical value of 2x - 11 is
A. 29
B. 39
C. 19
D. 9
Question 1376
If a3+ b3 = 19 and a + b = 1, then what is the value of ab?
A. 5
B. -6
C. 7
D. -9
Question 1377
On dividing a number by 38, we get 70 as quotient and 12 as remainder. What is the number?
A. 2648
B. 2636
C. 2684
D. 2672
Question 1378
Shaan got a total of Rs. 912 in the denomination of equal numbers of Rs. 1, Rs. 5 and Rs. 10 coins. How many coins do Shaan posses?
A. 16
B. 57
C. 171
D. 323
Question 1379
If x = 999, y = 1000, z = 1001, then the value of x3+y3+z3-3xyzx-y+z is
A. 1000
B. 9000
C. 1
D. 9
Question 1380
What is the value of [tan (90 – A) + cot (90 – A)]2/[2 sec2(90 – 2A)]?
A. 0
B. 1
C. 2
D. – 1
Question 1381
If 3x + [1/(5x)] = 7, then what is the value of 5x/(15x2+ 15x + 1)?
A. 1/5
B. 1/10
C. 2/5
D. 10
Question 1382
For which value of ‘g’ the linear graph of 6x + 12y +9 = 0 and 2x + gy + 3 =0 has infinite number of solutions?
A. 3
B. 4
C. 6
D. 9
Question 1383
If x and y are natural numbers such that x + y = 2017, then what is the value of (– 1)x+ (– 1)y?
A. 2
B. – 2
C. 0
D. 1
Question 1384
Find the unit place in 194102+294103
A. 0
B. 6
C. 8
D. 2
Question 1385
What is the simplified value of 0.042+0.212-0.00840.043+0.213
A. 0.5
B. 2
C. 10.25
D. 10.3
Question 1386
Simplify (b2x 3a2z4 ) × (b2x 4a4z3 )/(a3b2z4 )
A. b2x7a3z3
B. b3x7a3 z3
C. b2x5a3 z3
D. b2x7a3z2
Question 1387
What value of 'p' will satisfy the equation p540 = 240p ?
A. 6
B. 10
C. 6√10
D. √10
Question 1388
If x = 5 + 15 - 1 & y = 5 - 15 + 1 , then find the value of x2 - y2.
A. √5
B. 2√5
C. 3√5
D. 4√5
Question 1389
Coefficient of x in (x + 9)(8 - 5x) is
A. 37
B. -53
C. -37
D. 53
Question 1390
If sec 300° = x, then value of x is
A. √2
B. 1/√3
C. 2
D. 1
Question 1391
In ΔABC measure of angle B is 90 deg. If cosA = 5/13, and AB = 10 cm, then what is the length (in cm) of side BC?
A. 26
B. 24
C. 25
D. 5
Question 1392
If x+1x:x-1x=5:3 then the value of x is
A. +- 1
B. +-2
C. +-3
D. +-4
Question 1393
Δ ABC is right angled at B. If m∠A = 60°, then what is the value of sec C.sin A?
A. 2/√3
B. √3/2
C. 2/3
D. 1
Question 1394
If cosec π/4 - sin π/3 = x, then the value of x is
A. 4/√3
B. (2√2-√3)/2
C. (1-√3)/√3
D. √3+2
Question 1395
If (8 - 10x) - (13x - 2) = -9, then the value of x is
A. -19/23
B. 19/23
C. -1/23
D. 1/23
Question 1396
If X + Y + Z = 9 then the value of (X - 4)3 + (Y - 2)3 + (Z - 3)3 - 3 (X - 4) (Y - Z) (Z - 3) is
A. 6
B. 9
C. 0
D. 1
Question 1397
What is the value of ( 1/√3 + cot60) ?
A. 3√3/2
B. 7/2√3
C. (4+√3)/2√3
D. 2/√3
Question 1398
If a2+b2=80 and ab = 32, then calculate the value of a-b/a+b.
A. 0.337
B. 0.339
C. 0.333
D. 0.335
Question 1399
The point P (a,b) is first reflected in origin to P1 and P1 is reflected in Yaxis to (4,3). The co-ordinates of point P are
A. (4,3)
B. (-4,3)
C. (-3,4)
D. (3,-4)
Question 1400
What is the value of Sin 30° - Cosec 45°?
A. (2√6 - 1)/√3
B. (1 - 2√3)/2
C. (√2 - √3)/√6
D. (1 - 2√2)/2
Question 1401
If the expression px3 – 2x2 – qx + 18 is completely divisible by (x2 – 9), then what is the ratio between p and q respectively?
A. 1:9
B. 1:3
C. 3:1
D. 9:1
Question 1402
The cost of 15 kg of groundnuts and 4 kg of cashews is Rs.7,000. The cost of 10 kg of cashews is equal to 25 kg of groundnuts. Find the cost of groundnut per kg.
A. Rs.320
B. Rs.700
C. Rs.540
D. Rs.280
Question 1403
If x = 222, y = 223, z = 225 then the value of x3 + y3 + z3 - 3xyz is
A. 4590
B. 4690
C. 4950
D. 4960
Question 1404
What is the value of {[sin (x + y) – 2 sin x + sin (x – y)]/[cos (x – y) + cos (x + y) – 2 cos x]} × [(sin 10x – sin 8x)/(cos 10x + cos 8x)]?
A. 0
B. tan2x
C. 1
D. 2 tan x
Question 1405
If sin (3x 20°) = cos (3y + 20°), then find the value of (x + y).
A. 90°
B. 60°
C. 120°
D. 30°
Question 1406
If cos -4π/3 = x, then the value of x is
A. √3/2
B. 1/2
C. -√3/2
D. -1/2
Question 1407
What is the value of {(sin 4x + sin 4y) [(tan 2x – 2y)]}/(sin 4x – sin 4y)?
A. tan 2 (2x + 2y)
B. tan2
C. cot (x – y)
D. tan (2x + 2y)
Question 1408
Solve : 12 - [26 - {2 + 5 x (6 - 3)}]
A. 2
B. 3
C. 7
D. 8
Question 1409
There are 90 coins, comprising of 5 and 10 paisa coins. The value of all the coins is Rs. 7. How many 5 paisa coins are there?
A. 50
B. 45
C. 40
D. 35
Question 1410
9876-?+5431=5553
A. 9754
B. 9765
C. 8754
D. 9854
Question 1411
If 4x = √5+ 2, then the value of x - 1/16x is
A. 1
B. -1
C. 4
D. 2√5
Question 1412
If 3x + 5y + 7z = 49 and 9x + 8y + 21z = 126, then what is the value of y?
A. 4
B. 2
C. 3
D. 5
Question 1413
If tan(A/2) = x, then the value of x is
A. √[(1 + cosA)/(1 - cosA)]
B. (1 - cosA)/(1 + cosA)
C. (1 + cosA)/(1 - cosA)
D. √[(1 - cosA)/(1 + cosA)]
Question 1414
In ΔABC, D and E are points on side AB and AC respectively. DE is parallel to BC. If lengths of AD, DB and DE are 9 cm, 6 cm and 5.4 cm respectively find length of BC?
A. 3.6 cm
B. 4.8 cm
C. 11.2 cm
D. 9 cm
Question 1415
∆XYZ is right angled at Y. If m ∠Z = 60. What is the length (in cm) of YZ, if ZX = 9√3 cm?
A. 3√3
B. 3√3/2
C. 9√3/2
D. √3
Question 1416
If 2x + 3y – 5z = 18, 3x + 2y + z = 29 and x + y + 3z = 17, then what is the value of xy + yz + zx?
A. 32
B. 52
C. 64
D. 46
Question 1417
Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?
A. 4/5
B. 9/4
C. 4/9
D. 5/4
Question 1418
An angle is four times its complementary angle. What is the measure of the angle?
A. 72°
B. 108°
C. 54°
D. 36°
Question 1419
Divya and Kriti have total 46 candies. If Divya has 10 candies more than kriti, then find the total number of candies Divya have?
A. 20
B. 24
C. 28
D. 32
Question 1420
If 3sinθ+4cosθ=5 (0<θ<90°) then the value of sinθ is
A. 1/5
B. 2/5
C. 3/5
D. 4/5
Question 1421
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
A. 20
B. 80
C. 100
D. 120
Question 1422
1422 ÷ 1260.25 = ?
A. 586
B. 578
C. 568
D. 566
Question 1423
What is the value of 5.6x0.36+0.42x3.20.8 x 2.1 ?
A. 2
B. 1
C. 3
D. 3/2
Question 1424
If a+1b = 1 and b+1c = 1 then c+1a = ?
A. 0
B. 2
C. 1
D. 3
Question 1425
If x - y = -9 and xy = -20, then find x2 + y2 ?
A. 61
B. 41
C. 81
D. 51
Question 1426
What is the value of (cos30° + 1/2) ?
A. (√3+1)/√3
B. (√2+1)/√2
C. (√3+1)/2
D. (2√3+1)/√3
Question 1427
If a + b = 8 and a2 + b2 = 34, then value of ab is
A. 30
B. 64
C. 98
D. 15
Question 1428
ΔABC is right angled at B. If m ∠A = 60°, then what is the value of 1/√3 Cosec C?
A. 2/√3
B. 2/3
C. √2/√3
D. √2/3
Question 1429
What is the value of 36+729381+643
A. 5/12
B. 5/9
C. 4/9
D. 4/15
Question 1430
Which of the following quadratic equations has real roots?
A. 4x2 - 9x + 6 = 0
B. 3x2 - 2x + 6 = 0
C. 2x2 - 7x + 6 = 0
D. x2 - 2x + 2 = 0
Question 1431
For x = 462+3, what is the value of x+22x-22+x+23x-23
A. 1
B. √2
C. √3
D. 2
Question 1432
The two roots of a quadratic equation are given as x = 1/7 and x = -1/8 . The equation can be written as:
A. (7x − 1)(8x − 1) = 0
B. (7x − 1)(8x + 1) = 0
C. (7x + 1)(8x − 1) = 0
D. (7x + 1)(8x + 1) = 0
Question 1433
The slope of the line passing through the points (7,-2) and (x,1) is -3/10. Find x.
A. 4
B. 2
C. -4
D. -3
Question 1434
If sec2A + cosec2A = X, then the value of X is
A. tan2A cot2A
B. sinA cosA
C. secA cosecA
D. sec2A cosec2A
Question 1435
What is the value of sec 4π/3?
A. 2
B. -2
C. 2/√3
D. -2/√3
Question 1436
If 3x - 10 = -(2x + 5), then the numerical value of (x - 4)3 is
A. 27
B. 125
C. -125
D. -27
Question 1437
What is the value 32cos 39sin 51-sin239 + sin251
A. 1/2
B. 5/2
C. 0
D. Both 1/2 and 5/2
Question 1438
If tanA - cotA = x, then value of x is?
A. (1 + 2cos2A)/(sinA cosA)
B. (sinA cosA)/(1 - 2cos2A)
C. (sinA cosA)/(1 + 2cos2A)
D. (1 - 2cos2A)/(sinA cosA)
Question 1439
If Cosec θ = 17/8, then what is the value of Cos θ?
A. 15/8
B. 15/17
C. 8/15
D. 17/15
Question 1440
If 5x = 30-y = 6z, then what is the value of (xy + yz + zx)/xyz?
A. 0
B. 1
C. 2
D. 3
Question 1441
If 3x - 8(2 - x) = -19, then the value of x is
A. -3/11
B. -33/11
C. -3/5
D. -33/5
Question 1442
What is the equation of the line which has 3/2 and -4/7 as x and y intercept respectively?
A. 8x - 21y = -12
B. 8x + 21y = 14
C. 8x - 21y = 12
D. 8x + 21y = -14
Question 1443
If 1/(1 + cosA) + 1/(1 - cosA) = x , then value of x is
A. 2sec2A
B. 2cosecA
C. 2cosec2A
D. 2secA
Question 1444
The value of 16 - [5 - 2{14 of 2 - (8 ÷ 4 x 2 - 1 + 3}] is
A. -12
B. -9
C. -10
D. -14
Question 1445
The average of 100 observations was calculated as 35.It was found later, that one of the observation was misread as 83 instead of 53. The correct average is :
A. 32.7
B. 34.7
C. 35.7
D. 36.7
Question 1446
If 3x - 7 = 5x - 1, then the numerical value of (x - 4)2 is
A. 1
B. 49
C. -1
D. -49
Question 1447
cosA/(1 - sin A) is equal to
A. (secA - tanA)
B. (secA + tanA)
C. √[(secA + tanA)]
D. √[(secA - tanA)]
Question 1448
1/(secA + tanA) is equal to
A. cosecA - cotA
B. sinA - cosA
C. secA - tanA
D. sinA + cosA
Question 1449
The inradius of a equilateral triangle is 10 cm. What is the circum-radius (in cm) of the same triangle?
A. 5
B. 10√3
C. 20
D. 20√3
Question 1450
Two parallel chords on the same side of the centre of a circle are 5 cm apart. If the chords are 20 and 28 cm long, what is the radius of the circle?
A. 14.69 cm
B. 15.69 cm
C. 18.65 cm
D. 16.42 cm
Question 1451
A tower stands on the top of a building which is 40 metres high. The angle of depression of a point situated on the ground from the top and bottom of the tower are found to be 60 and 45 deg respectively. What is the height (in metres) of tower?
A. 20√3
B. 30(√3 + 1)
C. 40(√3 – 1)
D. 50(√3 – 1)
Question 1452
Solve : (x + 2y) (2x - y)
A. 2x2 + 5xy + 2y2
B. 2x2 + 3xy - 2y2
C. x2 + 4xy + y2
D. x2+ 4xy - y2
Question 1453
When 721+722+723+724 is divided by 25 the remainder is:
A. 5
B. 17
C. 7
D. 0
Question 1454
If 2560.256 = 25.6x, then what will be the value of x?
A. 2.56
B. 25.6
C. 0.256
D. 0.0256
Question 1455
What is the simplified value of cosec 2A + cot 2A?
A. sec A
B. sec (A/2)
C. cot A
D. cot2 A
Question 1456
Expand and simplify (3x + 2)2*(4x - 3) - (2x3 - 9x2 + 12x - 24)
A. 34x3 + 30x2 - 32x - 12
B. 34x3 + 30x2 - 32x + 12
C. 34x3 - 30x2 - 32x + 12
D. 34x3 - 30x2 + 32x - 12
Question 1457
If 9x2 + 16y2 = 60 and 3x + 4y = 6, then the value of xy is
A. -1
B. 1
C. -2
D. 2
Question 1458
If 22x - 40 = 207 + 3x, then x = ?
A. 14
B. 13
C. 12
D. 11
Question 1459
What is the reflection of the point (4, 7) in the line y = -1?
A. (-6 , 7)
B. (-4 , -9)
C. (4 , -9)
D. (-6 , -7)
Question 1460
The value of cos0 deg is
A. 0
B. infinite
C. not defined
D. 1
Question 1461
If 2x - 6 ≤ x - 3 and 1+3x < 4x + 4, then x can take which of the following values?
A. 4
B. -4
C. -6
D. 2
Question 1462
If a+1b=1 and b+1c=1 , then the value of c+1a is
A. 0
B. 1
C. -1
D. 2
Question 1463
The co-ordinates of the centroid of a triangle ABC are (3,-2). What are the co-ordinates of vertex C if co-ordinates of A and B are (-2,5) and (6,-2) respectively?
A. (-5,-9)
B. (5,-9)
C. (5,9)
D. (-5,9)
Question 1464
ΔABC is right angled at B. If m∠A = 45°, then find the value of (cosecC + 1/√3).
A. (3√2+1)/3
B. (2+√3)/2
C. 5/√3
D. (√6+1)/√3
Question 1465
For what value of C, the system of equation 6x + 2y = 2 & 3x + y = C will be coincident?
A. 4
B. 0
C. 2
D. 1
Question 1466
What is the value of 13313 + 729 - 5123
A. 15
B. 20
C. 30
D. 23
Question 1467
Given 17 x 29 = 493, then 170 x 0.029 = ?
A. 0.0493
B. 4.93
C. 0.493
D. 49.3
Question 1468
2sin[(C+D)/2].cos[(C-D)/2] is equal to
A. sinC - sinD
B. cosC + cosD
C. cosC - cosD
D. sinC + sinD
Question 1469
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ?
A. 52.5
B. 62.5
C. 72.5
D. 82.5
Question 1470
If (4x - 3) - (2x + 1) = 4, then the value of x is
A. 0
B. 1
C. 2
D. 3
Question 1471
If (x/a) + (y/b) = 3 and (x/b) – (y/a) = 9, then what is the value of x/y?
A. ( b + 3 a)/( a – 3 b)
B. ( a + 3 b)/( b – 3 a)
C. (1 + 3 a)/( a + 3 b)
D. ( a + 3 b2)/( b – 3 a2)
Question 1472
Find the value of 532+108
A. 732
B. 1732
C. 2732
D. 3732
Question 1473
If cosec θ + cot θ= 2, then cosec θ= ?
A. 1.5
B. 1.25
C. 1
D. 2
Question 1474
If ax= by= cz and b2= ac, then what is 1x+1z equal to ?
A. 1/y
B. -1/y
C. 2/y
D. -2/y
Question 1475
What is the value of sin 75°+ sin 15°?
A. √3
B. 2√3
C. √(3/2)
D. 3/√2
Question 1476
What is the simplified value of (1– sin A cos A)(sin A + cos A)?
A. sin2A – cos2A
B. sin3A + cos3A
C. 0
D. 1
Question 1477
If [a + (1/a)]2 – 2[a – (1/a)] = 12, then which of the following is a value of 'a'?
A. – 8 + √3
B. – 8 – √3
C. – 8 + √5
D. None of these
Question 1478
If (x/y)a-4 = (y/x)2a-5, then what is the relation between x and y?
A. x > y
B. Cannot be determined
C. x < y
D. x = y
Question 1479
In a circle with centre O, AB is a diameter and CD is a chord which is equal to the radius OC. AC and BD are extended in such a way that they intersect each other at a point P, exterior to the circle. The measure of ∠APB is
A. 30°
B. 45°
C. 60°
D. 90°
Question 1480
tan(A/2) is equal to
A. tanA/(1 + secA)
B. 1/(cosecA + cotA)
C. tanA/(1 + cosecA)
D. 1/(secA + cotA)
Question 1481
Sin6A + Cos6A - 1 is equal to
A. -3Sin2ACos2A
B. 1 - 3 SinACosA
C. 1 + 3Sin2ACos2A
D. 0