UP TGT 2021 — Mathematics (Series A)

Mathematics

1. 1. A person travels from A to B at a speed of 40 kmph and returns by increasing his speed by 50%. What is his average speed for both the trips ?

   • (a) 40 kmph
   • (b) 45 kmph
   • (c) 48 kmph
   • (d) 50 kmph
   उत्तर देखें

   उत्तर: (c)

2. 2. What is the real part of (sin x + i cos x)⁴, i = √−1 ?

   • (a) − cos 4x
   • (b) − cos 2x
   • (c) cos 4x
   • (d) cos 2x
   उत्तर देखें

   उत्तर: (c)

3. 3. is equal to

   • (a) log (3/2)
   • (b) log (9/8)
   • (c) log 2
   • (d) 1
   उत्तर देखें

   उत्तर: (b)

4. 4. If ω is an imaginary cube root of unity, then value of is

   • (a) 0
   • (b) 3
   • (c) 4
   • (d) 1
   उत्तर देखें

   उत्तर: (b)

5. 5. The sides of a triangle are 15 cm, 20 cm and 25 cm respectively, then the radius of in-circle is

   • (a) 10 cm
   • (b) 12.5 cm
   • (c) 5 cm
   • (d) 7.5 cm
   उत्तर देखें

   उत्तर: (c)

6. 6. If the arithmetic mean from the following data x: 5, 15, 25, 35, 45 f: 6, 4, 3, k, 2 is 21.5, the value of k will be

   • (a) 3
   • (b) 3.5
   • (c) 4
   • (d) 5
   उत्तर देखें

   उत्तर: (d)

7. 7. The value of [(x − y)³ + (y − z)³ + (z − x)³] / [9(x − y)(y − z)(z − x)] is

   • (a) 0
   • (b) 1/9
   • (c) 1/3
   • (d) 1
   उत्तर देखें

   उत्तर: (c)

8. 8. Find the equation of the cone with vertex at the origin and direction cosines of its generators satisfy the equation l² + 2m² − 3n² = 0.

   • (a) x² + y² − z² = 0
   • (b) x² + 2y² − 3z² = 0
   • (c) x² − 2y² + 3z² = 0
   • (d) xy + yz + zx = 0
   उत्तर देखें

   उत्तर: (b)

9. 9. A balloon is moving upward with uniform acceleration g/8 cm/sec². After half minute a body is dropped from them. The time taken by the body to reach on the ground is

   • (a) 10 seconds
   • (b) 15 seconds
   • (c) 20 seconds
   • (d) 24 seconds
   उत्तर देखें

   उत्तर: (b)

10. 10. is equal to

    • (a) 1
    • (b) e²
    • (c) e⁴
    • (d) e⁵
    उत्तर देखें

    उत्तर: (d)

11. 11. is equal to

    • (a) 1
    • (b) 0
    • (c) 2/√3
    • (d) 1/√3
    उत्तर देखें

    उत्तर: (c)

12. 12. If u⃗ = î × (a⃗ × î) + ĵ × (a⃗ × ĵ) + k̂ × (a⃗ × k̂) then u⃗ is equal to

    • (a) 0⃗
    • (b) a⃗
    • (c) 2a⃗
    • (d) 3a⃗
    उत्तर देखें

    उत्तर: (c)

13. 13. If z is a complex number of unit modulus and argument θ, then arg((1 + z)/(1 + z̄)) is equal to

    • (a) − θ
    • (b) π/2 − θ
    • (c) θ
    • (d) π − θ
    उत्तर देखें

    उत्तर: (c)

14. 14. The equations of tangents to the ellipse 3x² + 4y² = 12 which are parallel to the line y + 2x = 4 are

    • (a) y + 2x = ±4
    • (b) y + 2x = ±7
    • (c) y + 2x = ±√15
    • (d) y + 2x = ±√19
    उत्तर देखें

    उत्तर: (d)

15. 15. Which one of the following is not a measure of central tendency ?

    • (a) Mean
    • (b) Range
    • (c) Median
    • (d) Mode
    उत्तर देखें

    उत्तर: (b)

16. 16. sin⁻¹(3/5) − cos⁻¹(12/13) equals to

    • (a) sin⁻¹(56/65)
    • (b) sin⁻¹(16/65)
    • (c) 1
    • (d) 0
    उत्तर देखें

    उत्तर: (b)

17. 17. The point on the curve y² = x, the tangent at which makes an angle π/4 with x – axis, is

    • (a) (−1/4, 1/2)
    • (b) (1/4, 1/2)
    • (c) (−1/4, −1/2)
    • (d) (1/4, −1/2)
    उत्तर देखें

    उत्तर: (b)

18. 18. A sum becomes double in 5 years in C.I. When will it become 8 times at the same rate of interest ?

    • (a) 10 years
    • (b) 15 years
    • (c) 7 years
    • (d) 20 years
    उत्तर देखें

    उत्तर: (b)

19. 19. What is the principal value of sin⁻¹(sin (2π/3)) ?

    • (a) π/4
    • (b) π/2
    • (c) π/3
    • (d) 2π/3
    उत्तर देखें

    उत्तर: (c)

20. 20. is equal to

    • (a) 1
    • (b) π²/8
    • (c) π²/32
    • (d) π²/3
    उत्तर देखें

    उत्तर: (c)

21. 21. Sum of the series 2 + 3/2 + 1 + 5/8 + .... ∞ is

    • (a) 2
    • (b) 4
    • (c) 6
    • (d) 12
    उत्तर देखें

    उत्तर: (c)

22. 22. is equal to

    • (a) 2 sin θ
    • (b) 2 cos θ
    • (c) sin 2θ
    • (d) cos 2θ
    उत्तर देखें

    उत्तर: (b)

23. 23. The distances travelled by a body falling freely from rest in the first, second and third second are in the ratio

    • (a) 1 : 4 : 9
    • (b) 1 : 3 : 5
    • (c) 1 : 2 : 3
    • (d) 1 : 4 : 5
    उत्तर देखें

    उत्तर: (b)

24. 24. The number of real solutions of the equation |x|² − 3|x| + 2 = 0 is

    • (a) 4
    • (b) 1
    • (c) 3
    • (d) 2
    उत्तर देखें

    उत्तर: (a)

25. 25. In the following figure the value of θ is

    • (a) 110°
    • (b) 70°
    • (c) 60°
    • (d) 50°
    उत्तर देखें

    उत्तर: (c)

26. 26. The position vectors of the points A, B, C and D are 3î − 2ĵ − k̂, 2î + 3ĵ − 4k̂, −î + ĵ + 2k̂ and 4î + 5ĵ + λk̂ respectively. If the points A, B, C and D lie on a plane, the value of λ is

    • (a) −146/17
    • (b) −73/17
    • (c) 7
    • (d) 13
    उत्तर देखें

    उत्तर: (a)

27. 27. is equal to

    • (a) 0
    • (b) 1/3
    • (c) 2/3
    • (d) Does not exist
    उत्तर देखें

    उत्तर: (b)

28. 28. Three numbers are chosen at random from numbers 1 to 15. The probability that they are consecutive is

    • (a) 1/15
    • (b) 2/25
    • (c) 1/35
    • (d) 1/30
    उत्तर देखें

    उत्तर: (c)

29. 29. The points with position vectors 60î + 3ĵ, 40î − 8ĵ, aî − 52ĵ are collinear if a is equal to

    • (a) − 40
    • (b) 40
    • (c) 20
    • (d) 25
    उत्तर देखें

    उत्तर: (a)

30. 30. If the mean of x, x + 2, x + 4, x + 6, x + 8 is 11, then what is the mean of the last three observations ?

    • (a) 8
    • (b) 10
    • (c) 12
    • (d) 13
    उत्तर देखें

    उत्तर: (d)

31. 31. ((1 + i)/√(2))⁸ + ((1 − i)/√(2))⁸ is equal to

    • (a) 1
    • (b) 2
    • (c) 4
    • (d) 8
    उत्तर देखें

    उत्तर: (b)

32. 32. is equal to

    • (a) 2
    • (b) 6
    • (c) 0
    • (d) −2
    उत्तर देखें

    उत्तर: (b)

33. 33. The speeds of three cars are in the ratio 2 : 3 : 4. The ratios of the times taken by these cars in travelling 100 km distance will be

    • (a) 2 : 3 : 4
    • (b) 4 : 3 : 2
    • (c) 4 : 3 : 6
    • (d) 6 : 4 : 3
    उत्तर देखें

    उत्तर: (d)

34. 34. In the equation value of x is

    • (a) (a + b)/(1 + ab)
    • (b) (a − b)/(1 + ab)
    • (c) (a − b)/(1 − ab)
    • (d) None of the above
    उत्तर देखें

    उत्तर: (b)

35. 35. Integral of is

    • (a) log(sin x) + C
    • (b) log(cos x) + C
    • (c) log(log tan x) + C
    • (d) log(log sin x) + C
    उत्तर देखें

    उत्तर: (d)

36. 36. If then AB is equal to

    • (a)
    • (b)
    • (c)
    • (d) None of the above
    उत्तर देखें

    उत्तर: (a)

37. 37. In the figure ∠A is equal to

    • (a) 70°
    • (b) 45°
    • (c) 80°
    • (d) 60°
    उत्तर देखें

    उत्तर: (a)

38. 38. Find the value of ‘a’ such that the vectors 2î − ĵ + k̂, î + 2ĵ − 3k̂ and 3î + aĵ + 5k̂ are coplanar.

    • (a) 1
    • (b) 2
    • (c) 4
    • (d) − 4
    उत्तर देखें

    उत्तर: (d)

39. 39. If x₁ and x₂ are the roots of the equation then the value of x₁² + x₂² is

    • (a) 1
    • (b) 3
    • (c) 5
    • (d) 0
    उत्तर देखें

    उत्तर: (c)

40. 40. In the following figure AD is tangent of the circle and ABC is secant. If AB = 4 cm and BC = 5 cm, then the length of tangent AD is

    • (a) 3 cm
    • (b) 4 cm
    • (c) 5 cm
    • (d) 6 cm
    उत्तर देखें

    उत्तर: (d)

41. 41. A particle is projected with a velocity u so that its range on a horizontal plane is twice the greatest height attained, the range is

    • (a) 2u²/3g
    • (b) u²/2g
    • (c) 3u²/2g
    • (d) 4u²/5g
    उत्तर देखें

    उत्तर: (d)

42. 42. If f(x) = tan⁻¹x and g(x) = sin x, then (gof) (x) is equal to

    • (a) x√(1 − x²)
    • (b) x/√(1 + x²)
    • (c) √(1 + x²)/x
    • (d) 1
    उत्तर देखें

    उत्तर: (b)

43. 43. Solution of the differential equation log(dy/dx) = ax + by is

    • (a) beᵃˣ + ae⁻ᵇʸ + C = 0
    • (b) eᵃˣ/a − e⁻ᵇʸ/b + C = 0
    • (c) eᵃˣ + e⁻ᵇʸ + C = 0
    • (d) eᵃˣ⁺ᵇʸ = C(ax + by)
    उत्तर देखें

    उत्तर: (a)

44. 44. If â and b̂ are unit vectors such that â + 2b̂ and 5â − 4b̂ are perpendicular to each other, then the angle between â and b̂ is

    • (a) π/4
    • (b) cos⁻¹(1/3)
    • (c) cos⁻¹(2/7)
    • (d) π/3
    उत्तर देखें

    उत्तर: (d)

45. 45. If the mean of the observations 6, 8, 5, 7, x and 4 is 7, then the median of these observations is

    • (a) 6.5
    • (b) 6
    • (c) 5.5
    • (d) 7
    उत्तर देखें

    उत्तर: (a)

46. 46. If x₁ and x₂ are roots of x² − 2x + 4 = 0, then the value of x₁³ + x₂³ is equal to

    • (a) 16
    • (b) 8
    • (c) − 16
    • (d) 4
    उत्तर देखें

    उत्तर: (c)

47. 47. If y = log₅x + logₓ5, then what will be the value of dy/dx at x = 5 ?

    • (a) 5
    • (b) 1/5
    • (c) 0
    • (d) 1
    उत्तर देखें

    उत्तर: (c)

48. 48. If 3 men working 3 hours per day make 3 toys in 3 days, then the number of toys which can be made by 6 men working 6 hours per day in 6 days is

    • (a) 6
    • (b) 12
    • (c) 24
    • (d) 48
    उत्तर देखें

    उत्तर: (c)

49. 49. If A + iB = tan (x + iy), then tan 2x is equal to

    • (a) 2A/(1 + A² + B²)
    • (b) 2A/(1 − A² + B²)
    • (c) 2A/(1 − A² − B²)
    • (d) None of these
    उत्तर देखें

    उत्तर: (c)

50. 50. For all real x, the minimum value of (1 − x + x²)/(1 + x + x²) is

    • (a) 0
    • (b) 1/3
    • (c) 1
    • (d) 3
    उत्तर देखें

    उत्तर: (b)

51. 51. The term independent of x in the expansion of (2x + 1/(3x))⁶ is

    • (a) 160/9
    • (b) 80/9
    • (c) 160/27
    • (d) 80/3
    उत्तर देखें

    उत्तर: (c)

52. 52. Two parallel chords of a circle of radius 5 cm are in opposite side of the centre and if the chords are at distances 3 cm and 4 cm from the centre, then the difference of the lengths of the chords is

    • (a) 10 cm
    • (b) 5 cm
    • (c) 2 cm
    • (d) 1 cm
    उत्तर देखें

    उत्तर: (c)

53. 53. An aeroplane is flying at height h with horizontal velocity u. The velocity of a dropped packet on reaching the ground will be

    • (a) √(u² + 2gh)
    • (b) √(2gh)
    • (c) 2gh
    • (d) √(u² − 2gh)
    उत्तर देखें

    उत्तर: (a)

54. 54. Function f(x) = (x + 1)ᶜᵒᵗ ˣ will be continuous at x = 0 if the value of f(0) is

    • (a) 1/e
    • (b) 0
    • (c) e
    • (d) 1
    उत्तर देखें

    उत्तर: (c)

55. 55. If the equation x² + y² + (c − 2)xy − 4x − 4y + c² = 0 represents a circle, then its radius is

    • (a) 1
    • (b) 2
    • (c) 3
    • (d) 5
    उत्तर देखें

    उत्तर: (b)

56. 56. If the radius of a hemisphere is a, then its centre of gravity from its centre is at a distance

    • (a) 3a/8
    • (b) 5a/8
    • (c) a/2
    • (d) 2a/5
    उत्तर देखें

    उत्तर: (a)

57. 57. The sequence ⟨log (1/n)⟩ is

    • (a) Convergent
    • (b) Divergent to ∞
    • (c) Divergent to − ∞
    • (d) None of the above
    उत्तर देखें

    उत्तर: (c)

58. 58. Two consecutive sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0. If the equation of one diagonal is 11x + 7y = 9, the equation of other diagonal is

    • (a) x + y = 0
    • (b) 7x − 11y = 0
    • (c) 7x + 11y = 0
    • (d) x − y = 0
    उत्तर देखें

    उत्तर: (d)

59. 59. The multiplicative group {1, − 1, i, − i} is a cyclic group, its generators are

    • (a) 1 and i
    • (b) 1 and − 1
    • (c) i and − i
    • (d) only i
    उत्तर देखें

    उत्तर: (c)

60. 60. The mean weight of 9 items is 15 kg. If one more item is added then the mean weight becomes 16 kg, then the weight of tenth item will be

    • (a) 20 kg
    • (b) 15 kg
    • (c) 25 kg
    • (d) 30 kg
    उत्तर देखें

    उत्तर: (c)

61. 61. The smallest positive integer n for which ((1 + i)/(1 − i))ⁿ = 1, is

    • (a) 8
    • (b) 12
    • (c) 4
    • (d) 16
    उत्तर देखें

    उत्तर: (c)

62. 62. ∫ eˣ(x − 1)/(x + 1)³ dx equals to

    • (a) eˣ/(x + 1)² + C
    • (b) eˣ/(x + 1) + C
    • (c) −eˣ/(x + 1)² + C
    • (d) eˣ/(x − 1)² + C
    उत्तर देखें

    उत्तर: (a)

63. 63. If (b − c)², (c − a)², (a − b)² are in A.P., then 1/(b − c), 1/(c − a), 1/(a − b) will be in

    • (a) H.P.
    • (b) G.P.
    • (c) A.P.
    • (d) None of the above
    उत्तर देखें

    उत्तर: (c)

64. 64. If i = √−1, then (1 + i)⁴ − (1 − i)⁴ is equal to

    • (a) − 4i
    • (b) 4i
    • (c) 0
    • (d) 2
    उत्तर देखें

    उत्तर: (c)

65. 65. The general equation to the cone of second degree which passes through the axes, is

    • (a) x²/a + y²/b + z²/c = 0
    • (b) fyz + gzx + hxy = 0
    • (c) ax² + by² + cz² = 0
    • (d) √(fx) + √(gy) + √(hz) = 0
    उत्तर देखें

    उत्तर: (b)

66. 66. If one zero of the third degree polynomial x³ + ax² + bx + c is − 1, then the product of other two zeroes is

    • (a) b − a + 1
    • (b) b − a − 1
    • (c) a − b + 1
    • (d) a + b + 1
    उत्तर देखें

    उत्तर: (a)

67. 67. The equation of the sphere on the join of (2, −3, 1) and (3, −1, 2) as diameter is

    • (a) x² + y² + z² − 5x + 4y + 3z − 11 = 0
    • (b) x² + y² + z² + 5x − 4y + 3z − 11 = 0
    • (c) x² + y² + z² + 11 = 0
    • (d) x² + y² + z² − 5x + 4y − 3z + 11 = 0
    उत्तर देखें

    उत्तर: (d)

68. 68. Three forces P, 2P and 3P are acting along sides AB, BC and CA of equilateral Δ ABC. Magnitude of resultant force is

    • (a) P√3
    • (b) P√2
    • (c) Zero
    • (d) 2P/3
    उत्तर देखें

    उत्तर: (a)

69. 69. In a triangle ABC if cos A = sin B/(2 sin C), then triangle is

    • (a) Isosceles
    • (b) Equilateral
    • (c) Right angled
    • (d) None of the above
    उत्तर देखें

    उत्तर: (a)

70. 70. The area of the region bounded by the curves y² = x and x² = y is

    • (a) 1
    • (b) 2
    • (c) 1/3
    • (d) 2/3
    उत्तर देखें

    उत्तर: (c)

71. 71. If x² + 1/x² = 11, then value of x³ − 1/x³ may be equal to

    • (a) 22
    • (b) 25
    • (c) 33
    • (d) 36
    उत्तर देखें

    उत्तर: (d)

72. 72. The order of the element (− i) of the multiplicative group G = {1, − 1, i, − i} is

    • (a) 4
    • (b) 3
    • (c) 2
    • (d) 1
    उत्तर देखें

    उत्तर: (a)

73. 73. In ΔABC, a = 2b and |A − B| = π/3, then ∠C is

    • (a) π/2
    • (b) π/3
    • (c) π/6
    • (d) π/4
    उत्तर देखें

    उत्तर: (b)

74. 74. The area cut off the parabola 4y = 3x² by the straight line 2y = 3x + 12 is

    • (a) 15 sq. units
    • (b) 18 sq. units
    • (c) 24 sq. units
    • (d) 27 sq. units
    उत्तर देखें

    उत्तर: (d)

75. 75. If lim (x → a) (aˣ − xᵃ)/(xˣ − aᵃ) = −1, then

    • (a) a = 1
    • (b) a = 0
    • (c) a = e
    • (d) none of these
    उत्तर देखें

    उत्तर: (a)

76. 76. If y = xˣ, then dy/dx will be

    • (a) xˣ log x
    • (b) xˣ (1 − log x)
    • (c) xˣ (1 + log x)
    • (d) xˣ + log x
    उत्तर देखें

    उत्तर: (c)

77. 77. The work done in moving an object along a straight line from (3, 2, −1) to (2, −1, 4) in a force field given by F⃗ = 4î − 3ĵ + 2k̂, is

    • (a) 15 units
    • (b) 18 units
    • (c) 20 units
    • (d) 24 units
    उत्तर देखें

    उत्तर: (a)

78. 78. Equation of a circle, with center (0, 0) and 2x + 3y = 5 as a tangent, is

    • (a) x² + y² = 5
    • (b) x² + y² + 2x = 25
    • (c) x² + y² + y = 25
    • (d) 13x² + 13y² = 25
    उत्तर देखें

    उत्तर: (d)

79. 79. Sequence log x, log (x²/y), log (x³/y²), .... is

    • (a) a G.P.
    • (b) an A.P.
    • (c) a H.P.
    • (d) both G.P. and H.P.
    उत्तर देखें

    उत्तर: (b)

80. 80. If the probability for A to fail in an examination is 0.20 and that of B to fail is 0.30, then the probability that either A or B fails is

    • (a) 0.50
    • (b) 0.54
    • (c) 0.44
    • (d) 0.45
    उत्तर देखें

    उत्तर: (c)

81. 81. In a group of 300 people, 150 speak Hindi and 200 can speak English. How many can speak both Hindi and English ?

    • (a) 40
    • (b) 50
    • (c) 60
    • (d) 85
    उत्तर देखें

    उत्तर: (b)

82. 82. In a ΔABC, b = 5 cm, a = 2 cm and sin A = 3/7. How many such triangles are possible ?

    • (a) 0
    • (b) 1
    • (c) 2
    • (d) 3
    उत्तर देखें

    उत्तर: (a)

83. 83. If for a moderately symmetrical distribution mean deviation is 12, then the value of standard deviation is

    • (a) 15
    • (b) 12
    • (c) 24
    • (d) None of the above
    उत्तर देखें

    उत्तर: (a)

84. 84. d/dx (tan(cos⁻¹x))² is equal to

    • (a) −2/x³
    • (b) 2/x³
    • (c) √(1 − x²)/x
    • (d) −x/√(1 − x²)
    उत्तर देखें

    उत्तर: (a)

85. 85. In the given figure O is the centre of the circle and ∠AOB = 70° then 70° − x° is equal to

    • (a) 70°
    • (b) 35°
    • (c) 15°
    • (d) 25°
    उत्तर देखें

    उत्तर: (b)

86. 86. If α, β, γ are the roots of the equation x³ + px² + qx + r = 0, then α²β² + α²γ² + β²γ² is equal to

    • (a) q² − 2pr
    • (b) q² + 2pr
    • (c) q² + p²
    • (d) q² − p²
    उत्तर देखें

    उत्तर: (a)

87. 87. A particle is projected in vertically upward direction. If after t₁ and t₂ seconds, its height is h, then h is equal to

    • (a) (1/2)gt₁t₂
    • (b) g√(t₁t₂)
    • (c) 2g (t₁ + t₂)
    • (d) None of the above
    उत्तर देखें

    उत्तर: (a)

88. 88. If points (a, 0), (0, b) and (1, 1) are collinear, then 1/a + 1/b is equal to

    • (a) 1
    • (b) √2
    • (c) −1
    • (d) 2
    उत्तर देखें

    उत्तर: (a)

89. 89. The system of equations x + z = 3 ax + y = 2 3x + y + bz = 7 has a unique solution if (a, b) is equal to

    • (a) (1, 2)
    • (b) (2, 1)
    • (c) (1, 1)
    • (d) (− 1, 4)
    उत्तर देखें

    उत्तर: (c)

90. 90. The greatest resultant which two forces can have is P and the least is Q. If they act at an angle α, then the resultant is of magnitude

    • (a) √(P² + Q²)
    • (b) √(P² − Q²)
    • (c) √(P² cos²(α/2) + Q² sin²(α/2))
    • (d) √(P² cos² α + Q² sin² α)
    उत्तर देखें

    उत्तर: (c)

91. 91. The equation x²/(1 − r) − y²/(1 + r) = 1, |r| < 1 represents

    • (a) an ellipse
    • (b) a hyperbola
    • (c) a circle
    • (d) none of the above
    उत्तर देखें

    उत्तर: (b)

92. 92. The function defined by at x = 0 is

    • (a) continuous
    • (b) discontinuous at x = 0 and has discontinuity of first kind
    • (c) discontinuous at x = 0 and has removable discontinuity
    • (d) discontinuous at x = 0 and has discontinuity of second kind
    उत्तर देखें

    उत्तर: (b)

93. 93. A force represented by î + 2ĵ + k̂ passes through a point (2, 3, 1). The moment of the force about point (1, 2, − 1) is

    • (a) î − 2ĵ + k̂
    • (b) 3î − ĵ − k̂
    • (c) − 3î + ĵ + k̂
    • (d) 3î + ĵ − k̂
    उत्तर देखें

    उत्तर: (c)

94. 94. The tangent to the curve x = 2at²/(1 + t²), y = 2at³/(1 + t²) at the point for which t = 1/2, is

    • (a) 13x − 16y = 2a
    • (b) 13x + 16y = 2a
    • (c) 13x − 8y = 4a
    • (d) 13x + 8y = 4a
    उत्तर देखें

    उत्तर: (a)

95. 95. If x + 1/x = 2 cos (π/5), then x⁵ + 1/x⁵ is equal to

    • (a) − 2
    • (b) 0
    • (c) 1
    • (d) 5
    उत्तर देखें

    उत्तर: (a)

96. 96. A, B and C undertake to do a work for ₹ 500. A and B together do 2/5 of the work and rest is done by C alone. How much amount should C get ?

    • (a) ₹ 300
    • (b) ₹ 360
    • (c) ₹ 200
    • (d) ₹ 180
    उत्तर देखें

    उत्तर: (a)

97. 97. A body is projected with velocity 40 metre per second inclined at an angle 60° with horizontal. The velocity of the body when it is at maximum height is

    • (a) 10 m/s
    • (b) 20 m/s
    • (c) 15 m/s
    • (d) 5 m/s
    उत्तर देखें

    उत्तर: (b)

98. 98. If 1, ω, ω² are the cube roots of unity, then the value of (1 + ω²)(1 + ω⁴)(1 + ω⁸)(1 + ω¹⁶) is

    • (a) −1
    • (b) 0
    • (c) 1
    • (d) 2
    उत्तर देखें

    उत्तर: (c)

99. 99. For any two sets A and B, A − (A − B) equals

    • (a) A − B
    • (b) B
    • (c) A ∪ B
    • (d) A ∩ B
    उत्तर देखें

    उत्तर: (d)

100. 100. The distance of centre of gravity of uniform semicircular lamina of radius a, from the centre is

     • (a) a/2
     • (b) 2a/3π
     • (c) a/3
     • (d) 4a/3π
     उत्तर देखें

     उत्तर: (d)

101. 101. The intercept on the line y = x by the circle x² + y² − 2x = 0 is AB. Equation of circle with AB as diameter is

     • (a) x² + y² = 1
     • (b) x² + y² = 2
     • (c) x² + y² − x − y = 0
     • (d) x² + y² − 3x − 3y + 4 = 0
     उत्तर देखें

     उत्तर: (c)

102. 102. If A and B are two matrices such that AB = B and BA = A, then A² + B² is equal to

     • (a) 2AB
     • (b) 2BA
     • (c) A + B
     • (d) AB
     उत्तर देखें

     उत्तर: (c)

103. 103. A stone thrown up is caught by the thrower after 6 sec. What will be the velocity of stone after 2 sec of its throwing ? (g = 9.8 m/s²)

     • (a) 9.8 m/s
     • (b) 10.2 m/s
     • (c) 19.6 m/s
     • (d) 20.0 m/s
     उत्तर देखें

     उत्तर: (a)

104. 104. The equation of the directrix of the parabola y² + 4x + 4y + 2 = 0 is

     • (a) x = −1
     • (b) x = 1
     • (c) x = −3/2
     • (d) x = 3/2
     उत्तर देखें

     उत्तर: (d)

105. 105. lim (y → a) (sin ((y − a)/2) · tan (πy/2a)) is equal to

     • (a) 0
     • (b) 1
     • (c) π/a
     • (d) −a/π
     उत्तर देखें

     उत्तर: (d)

106. 106. The angle of intersection of the curves y = 4 − x² and y = x² is

     • (a) tan⁻¹(2/7)
     • (b) tan⁻¹(4√2/7)
     • (c) tan⁻¹(3√2/7)
     • (d) π/2
     उत्तर देखें

     उत्तर: (b)

107. 107. For any complex number z, the minimum value of |z + 1| + |z − 2| is

     • (a) −1
     • (b) 1
     • (c) 2
     • (d) 3
     उत्तर देखें

     उत्तर: (d)

108. 108. The number of generators of a cyclic group of order 10 is

     • (a) 2
     • (b) 3
     • (c) 4
     • (d) 5
     उत्तर देखें

     उत्तर: (c)

109. 109. Distance between the straight lines x + 2y = 5 and 2x + 4y = 11 is

     • (a) 1/√5
     • (b) 1/(2√5)
     • (c) √5
     • (d) √5/2
     उत्तर देखें

     उत्तर: (b)

110. 110. If three forces acting in one plane upon a rigid body, keep the body in equilibrium, then

     • (a) They must meet in a point
     • (b) They must be parallel
     • (c) They must either meet in a point or be parallel
     • (d) They must be perpendicular
     उत्तर देखें

     उत्तर: (c)

111. 111. The value of n, for which (aⁿ⁺¹ + bⁿ⁺¹)/(aⁿ + bⁿ) is the harmonic mean of a and b, is

     • (a) − 1
     • (b) 0
     • (c) 1
     • (d) 1/2
     उत्तर देखें

     उत्तर: (a)

112. 112. If x is a real number, then the function f(x) = x³ + x² + x + 1 has

     • (a) maximum value at x = 0
     • (b) minimum value at x = 1
     • (c) maximum value at x = − 1
     • (d) neither maximum nor minimum value
     उत्तर देखें

     उत्तर: (d)

113. 113. The minimum value of 4 cos θ + 3 is

     • (a) −3
     • (b) −1
     • (c) 0
     • (d) 1
     उत्तर देखें

     उत्तर: (b)

114. 114. Two finite sets have m and n elements respectively. The number of subsets of the first set is greater than the number of the subsets of the second by 56. Then the value of m² + n² is equal to

     • (a) 40
     • (b) 38
     • (c) 42
     • (d) None of the above
     उत्तर देखें

     उत्तर: (d)

115. 115. Ram can throw a ball vertically to a maximum height of 40 metres, then he can throw the ball in horizontal direction to which maximum distance ?

     • (a) 40√2 metre
     • (b) 20√2 metre
     • (c) 20 metre
     • (d) 80 metre
     उत्तर देखें

     उत्तर: (d)

116. 116. How many words can be formed with the letters of the word ‘POSTMAN’, if every word begins with T and ends with M ?

     • (a) 60
     • (b) 120
     • (c) 360
     • (d) 720
     उत्तर देखें

     उत्तर: (b)

117. 117. If f(x + 1/x) = x³ + 1/x³, then f(√3) is equal to

     • (a) 0
     • (b) 1
     • (c) √3
     • (d) 3√3
     उत्तर देखें

     उत्तर: (a)

118. 118. The order of the differential equation y − x(dy/dx)³ = a(y² + (dy/dx)²) is

     • (a) 3
     • (b) 1
     • (c) 2
     • (d) 4
     उत्तर देखें

     उत्तर: (b)

119. 119. If the foci of the ellipse x²/16 + y²/b² = 1 and the hyperbola x²/144 − y²/81 = 1/25 coincide, then the value of b² is

     • (a) 1
     • (b) 5
     • (c) 7
     • (d) 9
     उत्तर देखें

     उत्तर: (c)

120. 120. If A⃗ and B⃗ are two vectors, then angle between vectors A⃗ + B⃗ and A⃗ × B⃗ is

     • (a) 0°
     • (b) 60°
     • (c) 90°
     • (d) 120°
     उत्तर देखें

     उत्तर: (c)

121. 121. Which of the following is an open set ?

     • (a) S = {1, 1/2, 1/3, ....}
     • (b) N
     • (c) Z
     • (d) S = {x ∈ R : 1 < x < 3}
     उत्तर देखें

     उत्तर: (d)

122. 122. If a⃗, b⃗ and c⃗ are three vectors in such a way that a⃗ + b⃗ + c⃗ = 0⃗ and |a⃗| = 1, |b⃗| = 4, |c⃗| = 2, then the value of 2(a⃗.b⃗ + b⃗.c⃗ + c⃗.a⃗) is equal to

     • (a) 21
     • (b) −21
     • (c) 19
     • (d) −21/2
     उत्तर देखें

     उत्तर: (b)

123. 123. The co-ordinates of a moving point are (2t² + 4, 4t + 6). Its locus will be

     • (a) Circle
     • (b) Straight line
     • (c) Parabola
     • (d) None of the above
     उत्तर देखें

     उत्तर: (c)

124. 124. For all x ∈ (−1, 1), tan h⁻¹x is equal to

     • (a) log(x + √(x² + 1))
     • (b) log(x − √(x² + 1))
     • (c) (1/2) log ((1 + x)/(1 − x))
     • (d) (1/2) log ((x + 1)/(x − 1))
     उत्तर देखें

     उत्तर: (c)

125. 125. The number of generators of the cyclic group G of order 8 is

     • (a) 1
     • (b) 2
     • (c) 3
     • (d) 4
     उत्तर देखें

     उत्तर: (d)