UP TGT 2016 — Mathematics (Series A)

Mathematics

1. 1. If f(x) = cos²x/(1 + sin²x), then the value of f(π/4) − 3 f′(π/4) is

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

   उत्तर: (c)

2. 2. If a⃗, b⃗, c⃗ are three non-coplanar vectors, such that [b⃗ × c⃗, c⃗ × a⃗, a⃗ × b⃗] = 2[a⃗, b⃗, c⃗], then the value of [a⃗, b⃗, c⃗] is equal to

   • (a) 0
   • (b) 1
   • (c) 2
   • (d) 4
   उत्तर देखें

   उत्तर: (c)

3. 3. Mohan is father of 3 children with atleast one boy. The probability that he has 2 boys and 1 girl is

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

   उत्तर: (b)

4. 4. If sum of n terms of an arithmetical progression is 5n² − 3n, then its pᵗʰ term is

   • (a) 10p + 8
   • (b) 10p − 8
   • (c) 10p + 3
   • (d) 10p − 3
   उत्तर देखें

   उत्तर: (b)

5. 5. If each force F₁⃗ + F₂⃗ and F₁⃗ − F₂⃗ has magnitude √(F₁² + F₂²), then the angle between F₁⃗ and F₂⃗ is

   • (a) 90°
   • (b) 60°
   • (c) 45°
   • (d) 0°
   उत्तर देखें

   उत्तर: (a)

6. 6. Which of the following series converges ? I. Σ_(n=1)^∞ (3 + cos n)/eⁿ II. Σ_(n=1)^∞ cos(1/n)

   • (a) I only
   • (b) II only
   • (c) I and II both
   • (d) neither I nor II
   उत्तर देखें

   उत्तर: (a)

7. 7. If three forces, acting at a point, be in equilibrium, then each force is proportional to the sine of the angle between the other two. This theorem is called

   • (a) Law of triangle of forces
   • (b) Law of parallelogram of forces
   • (c) Lami’s theorem
   • (d) Trigonometrical theorem
   उत्तर देखें

   उत्तर: (c)

8. 8. A sum of money doubles itself in 4 years at compound interest. It will amount to 8 times to itself at the same rate of interest in time

   • (a) 12 years
   • (b) 16 years
   • (c) 18 years
   • (d) 24 years
   उत्तर देखें

   उत्तर: (a)

9. 9. Which one of the following is true ?

   • (a) mean = 3 median − 2 mode
   • (b) median = 3 mode − 2 mean
   • (c) mode = 2 median − 3 mean
   • (d) mode = 3 median − 2 mean
   उत्तर देखें

   उत्तर: (d)

10. 10. If the geometric mean of two numbers is 6.0 and arithmetic mean is 6.5, then the difference of squares of these numbers is

    • (a) 65
    • (b) 120
    • (c) 130
    • (d) 140
    उत्तर देखें

    उत्तर: (a)

11. 11. The smallest number among the numbers 2²⁵⁰, 3¹⁵⁰, 5¹⁰⁰ and 4²⁰⁰ is

    • (a) 4²⁰⁰
    • (b) 5¹⁰⁰
    • (c) 3¹⁵⁰
    • (d) 2²⁵⁰
    उत्तर देखें

    उत्तर: (b)

12. 12. If a : b = 2/9 : 1/3, b : c = 2/7 : 5/14 and d : c = 7/10 : 3/5, then a : b : c : d = ?

    • (a) 2 : 3 : 5 : 7
    • (b) 3 : 15 : 7 : 40
    • (c) 16 : 24 : 30 : 35
    • (d) 18 : 24 : 30 : 49
    उत्तर देखें

    उत्तर: (c)

13. 13. If ⁹P₅ + 5.⁹P₄ = ¹⁰Pᵣ, then the value of r is

    • (a) 2
    • (b) 3
    • (c) 5
    • (d) 7
    उत्तर देखें

    उत्तर: (c)

14. 14. The value of the determinant |−a² ab ac; ab −b² bc; ac bc −c²| is

    • (a) 0
    • (b) − (a² + b² + c²)
    • (c) 4 a²b²c²
    • (d) 2 (ab + bc + ca)
    उत्तर देखें

    उत्तर: (c)

15. 15. Sum of the series 1/2! + 1/4! + 1/6! + .... is

    • (a) (e + 1)²/(2e)
    • (b) (e − 1)²/(2e)
    • (c) (e² − 1)/(2e)
    • (d) (e² + 1)/(2e)
    उत्तर देखें

    उत्तर: (b)

16. 16. If the mapping f and g are given by f = {(1, 2), (3, 5), (4, 1)} g = {(2, 3), (5, 1), (1, 3)} then gof is

    • (a) {(2, 5), (5, 2), (1, 5)}
    • (b) {(1, 2), (3, 5), (4, 1)}
    • (c) {(1, 3), (3, 1), (4, 3)}
    • (d) {(2, 3), (5, 1), (1, 3)}
    उत्तर देखें

    उत्तर: (c)

17. 17. In how many ways the letter of the word BALLOON be arranged so that two L do not come together ?

    • (a) 1260
    • (b) 360
    • (c) 900
    • (d) 1060
    उत्तर देखें

    उत्तर: (c)

18. 18. The sequence {sin(nπ/2)/n}_(n=1)^∞ converges to

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

    उत्तर: (a)

19. 19. The value of (sin75° − sin15°)/(cos75° + cos15°) is

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

    उत्तर: (c)

20. 20. The value of sin(cot⁻¹(tan(cos⁻¹ x)))

    • (a) 0
    • (b) √(1 − x²)
    • (c) π
    • (d) x
    उत्तर देखें

    उत्तर: (d)

21. 21. If A + iB = tan(x + iy), then the value of tan 2x is as

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

    उत्तर: (c)

22. 22. If cos(A + B) = 3/5 and sin(A − B) = 5/13, where 0 ≤ A, B ≤ π/4, then tan 2B is equal to

    • (a) 11/34
    • (b) 21/56
    • (c) 33/56
    • (d) 1
    उत्तर देखें

    उत्तर: (c)

23. 23. AB is a chord of a circle and AOC is its diameter such that ∠ACB = 50°, if AT is tangent to the circle at the point A, then ∠BAT is equal to

    • (a) 50°
    • (b) 60°
    • (c) 65°
    • (d) None of these
    उत्तर देखें

    उत्तर: (a)

24. 24. The curve represented by the equations x = 3 (cost + sint) y = 4(cost − sint) is

    • (a) A straight line
    • (b) A circle
    • (c) A hyperbola
    • (d) An ellipse
    उत्तर देखें

    उत्तर: (d)

25. 25. The equation of sphere is x² + y² + z² − x + z − 2 = 0, its radius is

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

    उत्तर: (b)

26. 26. If the straight line x cosα + y sinα = p is tangent to the ellipse x²/a² + y²/b² = 1, then

    • (a) p² = a²b²/4
    • (b) p² = a² cos²α − b² sin²α
    • (c) p² = a² cos²α + b² sin²α
    • (d) None of these
    उत्तर देखें

    उत्तर: (c)

27. 27. Lines x = ay + b, z = cy + d and x = a′y + b′, z = c′y + d′ are perpendicular, if

    • (a) aa′ + cc′ + 1 = 0
    • (b) aa′ + cc′ − 1 = 0
    • (c) ac + a′c′ − 1 = 0
    • (d) ac + a′c′ + 1 = 0
    उत्तर देखें

    उत्तर: (a)

28. 28. If 2x − y = 5, then (2x − 3)³ − (y + 2)³ is equal to

    • (a) 0
    • (b) 25
    • (c) 40
    • (d) 125
    उत्तर देखें

    उत्तर: (a)

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

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

    उत्तर: (a)

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

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

    उत्तर: (a)

31. 31. 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)

32. 32. √(3 + 2√2) − √(3 − 2√2) is equal to

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

    उत्तर: (d)

33. 33. Which one of the following is not true ?

    • (a) |a⃗| = |b⃗| ⇒ a⃗ = b⃗
    • (b) |a⃗ × b⃗|² = (a⃗)²(b⃗)² − (a⃗ · b⃗)²
    • (c) a⃗ × (b⃗ · c⃗) is not defined
    • (d) If the adjacent sides of a parallelogram are represented by the vectors a⃗ and b⃗ respectively, then its area is |a⃗ × b⃗|
    उत्तर देखें

    उत्तर: (a)

34. 34. A particle is projected with velocity u at an inclination α with the horizontal. Then Maximum height (H) attained is

    • (a) u² sin²α / g
    • (b) 2u² sin²α / g
    • (c) u² sin²α / 2g
    • (d) u² sin2α / g
    उत्तर देखें

    उत्तर: (c)

35. 35. If |x+2 2 2; 2 x+2 2; 2 2 x+2| = 0, then values of x satisfying this equation are

    • (a) 0, − 2, − 6
    • (b) 0, −1, −2
    • (c) 0, 0, − 2
    • (d) 0, 0, − 6
    उत्तर देखें

    उत्तर: (d)

36. 36. Series Σ_(n=1)^∞ (((n+1)/n)ⁿ⁺¹ − (n+1)/n)⁻ⁿ is

    • (a) divergent
    • (b) convergent
    • (c) oscillates finitely
    • (d) oscillates infinitely
    उत्तर देखें

    उत्तर: (b)

37. 37. 10² + 11² + 12² + .... + 19² is equal to

    • (a) 1580
    • (b) 2010
    • (c) 2121
    • (d) 2185
    उत्तर देखें

    उत्तर: (d)

38. 38. The resultant force of two forces P and Q is R. If Q is doubled, R is doubled and if Q is reversed, R is again doubled. Then which one is the true relation ?

    • (a) P/√2 = Q/√3 = R/√2
    • (b) P/1 = Q/2 = R/1
    • (c) P/√3 = Q/√2 = R/√2
    • (d) P/1 = Q/1 = R/√2
    उत्तर देखें

    उत्तर: (a)

39. 39. The compound interest of ₹ 8,000 @ 10% per annum for 1.5 years, if the interest is calculated half yearly is

    • (a) ₹ 9,261
    • (b) ₹ 860
    • (c) ₹ 961
    • (d) ₹ 1,261
    उत्तर देखें

    उत्तर: (d)

40. 40. If the mean of 10 observations x₁, x₂, x₃, ..., x₁₀ is 20, then mean of x₁ + 2, x₂ + 4, x₃ + 6, ...., x₁₀ + 20 is

    • (a) 24
    • (b) 28
    • (c) 31
    • (d) 32
    उत्तर देखें

    उत्तर: (c)

41. 41. For showing the growth of population for the last 8 years, the best diagram is

    • (a) pie
    • (b) histogram
    • (c) scatter plot
    • (d) simple bar diagram
    उत्तर देखें

    उत्तर: (d)

42. 42. If non-zero a, b, c are such that a + b + c = 0, then the value of a²/bc + b²/ac + c²/ab is

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

    उत्तर: (a)

43. 43. If x + 1/x = √3, then the value of x¹⁸ + x¹² + x⁶ + 1 is

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

    उत्तर: (a)

44. 44. Factorisation of x³ − y³ is

    • (a) (x + y)(x² − xy + y²)
    • (b) (x − y)(x² − xy + y²)
    • (c) (x − y)(x² − xy − y²)
    • (d) (x − y)(x² + xy + y²)
    उत्तर देखें

    उत्तर: (d)

45. 45. The roots of the equation x³ − 12x² + 39x − 28 = 0 are in A. P., the common difference is

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

    उत्तर: (b)

46. 46. If A = [[coshx, sinhx], [−sinhx, coshx]], then trace (A²) is equal to

    • (a) 2
    • (b) − 2
    • (c) cosh 2x
    • (d) sinh 2x
    उत्तर देखें

    उत्तर: (a)

47. 47. If x − 1 and x + 3 are the two factors of x³ + ax + b, then remaining factor is

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

    उत्तर: (b)

48. 48. If A is an open set and B is a closed set, then B − A is

    • (a) Open set
    • (b) Closed set
    • (c) Both open and closed set
    • (d) None of these
    उत्तर देखें

    उत्तर: (b)

49. 49. 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)

50. 50. The value of sin 18° is

    • (a) (√5 − 1)/4
    • (b) (√5 + 1)/4
    • (c) (√5 − 1)/2
    • (d) (√5 + 1)/2
    उत्तर देखें

    उत्तर: (a)

51. 51. If sin²(x + iy) = A + iB, then value of A is

    • (a) (1/2)(1 + cos 2x cos h 2y)
    • (b) (1/2)(1 − cos 2x cos h 2y)
    • (c) (1/2)(sin 2x sin h 2y)
    • (d) − (1/2)(sin 2x sin h 2y)
    उत्तर देखें

    उत्तर: (b)

52. 52. The general solution of sinx + cosx = 1 is given by

    • (a) x = 2nπ
    • (b) x = 2nπ + π/2
    • (c) x = nπ + (−1)ⁿ π/4 − π/4
    • (d) None of these
    उत्तर देखें

    उत्तर: (c)

53. 53. In an equilateral triangle, the ratio of the radius of circumcircle to that of incircle is

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

    उत्तर: (d)

54. 54. The tangent at a point C of a circle and diameter AB when extended intersect at D, if ∠DCA = 110°, then ∠CBA is equal to

    • (a) 60°
    • (b) 70°
    • (c) 55°
    • (d) 110°
    उत्तर देखें

    उत्तर: (b)

55. 55. The equation of a normal to the parabola y² = 4x which passes through the point (6, 0) is

    • (a) y + 2x = 12
    • (b) y − 2x = 12
    • (c) y + 2x = 6
    • (d) y − 2x = 6
    उत्तर देखें

    उत्तर: (a)

56. 56. The equation 6x² − 5xy − 6y² + 14x + 5y + 4 = 0 represents

    • (a) A circle
    • (b) A hyperbola
    • (c) An ellipse
    • (d) A pair of perpendicular straight lines
    उत्तर देखें

    उत्तर: (d)

57. 57. The conic x² + xy + y² + x + y = 1 is

    • (a) an ellipse
    • (b) a hyperbola
    • (c) a parabola
    • (d) a pair of straight lines
    उत्तर देखें

    उत्तर: (a)

58. 58. If y-axis is generator line of the cone ax² + by² + cz² + 2fyz + 2gzx + 2hxy = 0, then value of b is equal to

    • (a) 1
    • (b) − 1
    • (c) 0
    • (d) None of these
    उत्तर देखें

    उत्तर: (c)

59. 59. The second degree equation 2x² + 2y² − 2x − 6y + 5 = 0 represents

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

    उत्तर: (c)

60. 60. The equation of the normal at the point (1, 1) on the curve 2y + x² = 3 is

    • (a) x + y = 0
    • (b) x + y + 1 = 0
    • (c) x − y = 0
    • (d) x − y = 1
    उत्तर देखें

    उत्तर: (c)

61. 61. The value of ∫_(π/4)^(π/3) dx/(sin²x cos²x) is

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

    उत्तर: (c)

62. 62. ∫₋₁² x|x| dx is equal to

    • (a) 0
    • (b) 2/3
    • (c) 5/3
    • (d) 7/3
    उत्तर देखें

    उत्तर: (d)

63. 63. H.C.F. of x³ − x² + 4x − 4 and x⁶ − 1 is

    • (a) x + 1
    • (b) x − 1
    • (c) x² − 1
    • (d) x³ − 1
    उत्तर देखें

    उत्तर: (b)

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

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

    उत्तर: (d)

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

    • (a) (1/2) g t₁ t₂
    • (b) g √(t₁ t₂)
    • (c) 2g (t₁ + t₂)
    • (d) none of these
    उत्तर देखें

    उत्तर: (a)

66. 66. If A = [[1, 3+x, 2], [1−x, 2, y+1], [2, 5−y, 3]] is a symmetric matrix, then 3x + y is equal to

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

    उत्तर: (a)

67. 67. If in any projectile maximum height is equal to horizontal range, then the angle of projection is

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

    उत्तर: (d)

68. 68. If ω is a complex cube root of unit, then 1 + ω + ω² + ... + ω¹⁰⁰ is equal to

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

    उत्तर: (b)

69. 69. The centre of gravity of a semi-circular disc of radius ‘a’ is

    • (a) (2a/π, 0)
    • (b) (3a/4π, 0)
    • (c) (4a/3π, 0)
    • (d) (a/2, a/2)
    उत्तर देखें

    उत्तर: (c)

70. 70. When a train travels with speed (3/5)ᵗʰ of its normal speed, it reaches its destination 4 hours late. What is the time taken by the train in travelling this distance with its normal speed ?

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

    उत्तर: (b)

71. 71. A 75 meter long train is moving at 20 km/hr. It will cross a man standing on the platform in time

    • (a) 12 seconds
    • (b) 14 seconds
    • (c) 13.5 seconds
    • (d) 15.5 seconds
    उत्तर देखें

    उत्तर: (c)

72. 72. Three dice are thrown randomly. The probability of coming 3 in at least one die is

    • (a) 180/216
    • (b) 91/216
    • (c) 5/216
    • (d) 125/216
    उत्तर देखें

    उत्तर: (b)

73. 73. If the algebraic sum of the deviations of 10 observations measured from 15 is 7, then the mean is

    • (a) 105
    • (b) 70
    • (c) 15.7
    • (d) 16.7
    उत्तर देखें

    उत्तर: (c)

74. 74. The equations 2x − ky + 7 = 0 and 6x − 12y + 15 = 0 have no solution for

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

    उत्तर: (b)

75. 75. If a + b + c = 5 and ab + bc + ca = 10, then the value of a³ + b³ + c³ − 3abc is

    • (a) − 25
    • (b) 25
    • (c) 0
    • (d) 75
    उत्तर देखें

    उत्तर: (a)

76. 76. If logₓ4 + logₓ16 + logₓ64 = 12, the value of x is

    • (a) 2
    • (b) 4
    • (c) 5
    • (d) 10
    उत्तर देखें

    उत्तर: (a)

77. 77. If a, b, c are in A. P. and x, y, z are in G. P., then the value of x^(b−c) y^(c−a) z^(a−b) is

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

    उत्तर: (b)

78. 78. 1/log₂x + 1/log₃x + 1/log₄x + .... + 1/log₅₀x, x ≠ 1, is equal to

    • (a) 50/log_(50!) x
    • (b) 49/log_(49!) x
    • (c) 1/log_(50!) x
    • (d) 1/log_(49!) x
    उत्तर देखें

    उत्तर: (c)

79. 79. If G is a group of even order, then it has an element a ≠ e, satisfying

    • (a) a² = e
    • (b) a³ = e
    • (c) a⁵ = e
    • (d) a⁷ = e
    उत्तर देखें

    उत्तर: (a)

80. 80. lim_x→1 (1 − √x)/cos⁻¹x is equal to

    • (a) 0
    • (b) 1/2
    • (c) 1/4
    • (d) 1
    उत्तर देखें

    उत्तर: (a)

81. 81. The value of Σ_(r=1)^9 sin²(rπ/18) is

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

    उत्तर: (c)

82. 82. In the equation cos⁻¹((1 − a²)/(1 + a²)) − cos⁻¹((1 − b²)/(1 + b²)) = 2tan⁻¹x, 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)

83. 83. The polar form of − 1 − √(−3) is

    • (a) 2 (cos 2π/3 − i sin 2π/3)
    • (b) 2 (cos π/3 + i sin π/3)
    • (c) 2 (cos 2π/3 + i sin 2π/3)
    • (d) 2 (cos π/3 − i sin π/3)
    उत्तर देखें

    उत्तर: (a)

84. 84. If the sides of a right angled triangle are a, ar, ar² (r < 1), then r² is equal to

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

    उत्तर: (a)

85. 85. If f(x) = cos hx + sin hx, then which one of the following is correct ?

    • (a) f(x) f(y) = f(x) + f(y)
    • (b) f(x) f(y) = f(xy)
    • (c) f(x) f(y) = f(x + y)
    • (d) f(x) f(y) = f(x/y)
    उत्तर देखें

    उत्तर: (c)

86. 86. The equation of the base of an equilateral triangle is x + y = 1 and its vertex is (1, − 1), length of its side is

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

    उत्तर: (c)

87. 87. If a straight line makes angles α, β and γ with the co-ordinate axes, then sin²α + sin²β + sin²γ is equal to

    • (a) 0
    • (b) 1
    • (c) 2
    • (d) None of these
    उत्तर देखें

    उत्तर: (c)

88. 88. If the equation 3x² + 7xy + 2y² + 5x + 5y + k = 0 represents a pair of straight lines, then the value of k is

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

    उत्तर: (b)

89. 89. The number of spheres that can be made to pass through the three given points (1, 0, 0), (0, 1, 0) and (0, 0, 1) is

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

    उत्तर: (d)

90. 90. The length of the common chord of two circles of radii 15 cm and 20 cm, whose centres are 25 cm apart, is (in cm)

    • (a) 10
    • (b) 12
    • (c) 20
    • (d) 24
    उत्तर देखें

    उत्तर: (d)

91. 91. lim_n→∞ (1 − 1/(2n))ⁿ⁺¹ is equal to

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

    उत्तर: (b)

92. 92. The derivative of the function y = 3 |x| + 1 at the point x = 0 is

    • (a) 3
    • (b) − 3
    • (c) 0
    • (d) not existing
    उत्तर देखें

    उत्तर: (d)

93. 93. The area enclosed between the curves y = sinx, y = cosx, 0 ≤ x ≤ π/2 is

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

    उत्तर: (c)

94. 94. If y(x) is a solution of the differential equation dy/dx + 4xy = x³, y(0) = 0, then lim_x→0 y(x) is

    • (a) 0
    • (b) − 2
    • (c) 1
    • (d) not existing
    उत्तर देखें

    उत्तर: (a)

95. 95. Two forces F₁⃗ = î − ĵ + k̂ and F₂⃗ = 4î + 2ĵ + 3k̂ act on a particle and displace it from the point (0, 1, 2) to (1, − 2, 3), then the total work done is

    • (a) 2 unit
    • (b) 6 unit
    • (c) 4 unit
    • (d) 8 unit
    उत्तर देखें

    उत्तर: (b)

96. 96. The moment of the force 3î + 4ĵ − 5k̂ acting through the point î − 2ĵ about the point î − ĵ + k̂ is

    • (a) 6î + 2ĵ − 5k̂
    • (b) 8î + 2ĵ − k̂
    • (c) 9î + 3ĵ − 8k̂
    • (d) 9î − 3ĵ + 3k̂
    उत्तर देखें

    उत्तर: (d)

97. 97. Value of the integral ∫₋₁¹ log((2 − x)/(2 + x)) dx is

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

    उत्तर: (d)

98. 98. If the foot of the perpendicular drawn from (−2, 1, 0) on a plane is (1, −2, 1), then the equation of the plane is

    • (a) 3x + 3y + z = 10
    • (b) 3x + 3y − z = 10
    • (c) 3x − 3y + z = 10
    • (d) 3x − 3y − z = 10
    उत्तर देखें

    उत्तर: (c)

99. 99. If â, b̂ and ĉ are unit vectors and |â + b̂|² = |b̂ + ĉ|² = |ĉ + â|² = 8, then |2â + b̂ + ĉ| is equal to

    • (a) 2
    • (b) 4
    • (c) 6
    • (d) none of the above
    उत्तर देखें

    उत्तर: (c)

100. 100. If f′(x) = g(x) and g′(x) = f(x²), then f″(x²) is equal to

     • (a) g(x²)
     • (b) f(x⁴)
     • (c) f(x³)
     • (d) g(x⁴)
     उत्तर देखें

     उत्तर: (b)

101. 101. A and B work together and complete a given work in x days. If A alone completes this work in x + 2 days and B alone completes this work in x + 8 days, then the value of x is

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

     उत्तर: (b)

102. 102. A person travels from A to B at an average speed of x km/hr and returns from B to A at an average speed of y km/hr. His average speed during the total journey, is

     • (a) (x + y)/(2xy)
     • (b) 2xy/(x + y)
     • (c) 2/(x + y)
     • (d) 1/x + 1/y
     उत्तर देखें

     उत्तर: (b)

103. 103. How much will ₹ 25,000 amount to in 2 years at compound interest, if the rate of interest for successive years be 4% and 5% per year ?

     • (a) ₹ 25,300
     • (b) ₹ 26,300
     • (c) ₹ 27,300
     • (d) ₹ 28,300
     उत्तर देखें

     उत्तर: (c)

104. 104. If the median of the distribution 10, 12, 13, 16, x, 20, 25, 30 is 18, then the value of x is

     • (a) 24
     • (b) 22
     • (c) 23
     • (d) 20
     उत्तर देखें

     उत्तर: (d)

105. 105. If x + 9/x = 6, then the value of x² + 9/x² is

     • (a) 8
     • (b) 12
     • (c) 16
     • (d) 10
     उत्तर देखें

     उत्तर: (d)

106. 106. Values of x in the equation 1/(x − 3) − 1/(x + 5) = 1/6 are

     • (a) 7, 9
     • (b) − 7, 9
     • (c) − 7, − 9
     • (d) 7, − 9
     उत्तर देखें

     उत्तर: (d)

107. 107. In the expansion of (3x − 2/x²)¹⁵ which term is free from x ?

     • (a) 4ᵗʰ
     • (b) 5ᵗʰ
     • (c) 6ᵗʰ
     • (d) 7ᵗʰ
     उत्तर देखें

     उत्तर: (c)

108. 108. If A = [[1, −1], [−1, 1]] and B = [[1, 1], [1, 1]], then the value of AB is

     • (a) [[1, −1], [−1, 1]]
     • (b) [[0, 1], [1, 0]]
     • (c) [[−1, 0], [0, −1]]
     • (d) [[0, 0], [0, 0]]
     उत्तर देखें

     उत्तर: (d)

109. 109. If |x| < 1, then x²/2 + 2x³/3 + 3x⁴/4 + ..... is equal to

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

     उत्तर: (a)

110. 110. Given : Statement A : All cyclic groups are abelian group. Statement B : The order of the cyclic group is same as the order of its generator.

     • (a) A and B are false
     • (b) A is true, B is false
     • (c) B is true, A is false
     • (d) A and B both are true
     उत्तर देखें

     उत्तर: (d)

111. 111. If f(x) = (x² − 3x + 2)/(x² − 2x), x ≠ 2 is defined and function f(x) be continuous at x = 2, then the value of f(2) is

     • (a) 0
     • (b) 1/2
     • (c) 1
     • (d) 3/4
     उत्तर देखें

     उत्तर: (b)

112. 112. The function f(x) is defined by f(x) = |x|/x , x ≠ 0 ; 0 , x = 0 then, at x = 0 it 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)

113. 113. The value of cot(cosec⁻¹(5/3) + tan⁻¹(2/3)) is

     • (a) 5/17
     • (b) 3/17
     • (c) 4/17
     • (d) 6/17
     उत्तर देखें

     उत्तर: (d)

114. 114. If r₁, r₂, r₃ are ex-radii and r the in-radius of triangle ABC and r₁ = r + r₂ + r₃, then triangle ABC is

     • (a) Isoscales triangle
     • (b) Equilateral triangle
     • (c) Right angled triangle
     • (d) None of these
     उत्तर देखें

     उत्तर: (c)

115. 115. If sin θ cos θ = 1/2, then value of sin⁶θ + cos⁶θ is

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

     उत्तर: (d)

116. 116. If ω is cube root of unity, then (3 + ω + 3ω²)⁶ is equal to

     • (a) 32
     • (b) 64
     • (c) 128
     • (d) 16
     उत्तर देखें

     उत्तर: (b)

117. 117. If AB is diameter of the circle x² + y² + 2x + 4y − 3 = 0. If co-ordinates of A are (1, 0), then co-ordinates of B are

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

     उत्तर: (d)

118. 118. The eccentricity of the ellipse, whose latus rectum is one half of its minor axis is

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

     उत्तर: (b)

119. 119. The angle between the straight lines represented by the equation y² − xy − 6x² = 0 is

     • (a) 30°
     • (b) 60°
     • (c) 45°
     • (d) 65°
     उत्तर देखें

     उत्तर: (c)

120. 120. In the conic l/r = 1 + e cosθ, the sum of the reciprocals of the segments of any focal chord is

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

     उत्तर: (d)

121. 121. The co-ordinates of the mid points of sides of a triangle are (5, 2), (3, 3) and (2, 2). Co-ordinates of its centroid is

     • (a) (7/3, 10/3)
     • (b) (10/3, 7/3)
     • (c) (7/3, 2/3)
     • (d) (2/3, 7/3)
     उत्तर देखें

     उत्तर: (b)

122. 122. In a geometric progression, first term is 7, the last term is 448 and the sum is 889. The common ratio of the geometric progression is

     • (a) 3/2
     • (b) 2
     • (c) 3
     • (d) 3.5
     उत्तर देखें

     उत्तर: (b)

123. 123. The value of ∫₀^(π/2) sinx dx/(sinx + cosx) is

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

     उत्तर: (c)

124. 124. The solution of the differential equation (x + 2y³) dy/dx = y is

     • (a) x = y³ − cy²
     • (b) x = y³ + cy
     • (c) y = x³ + cx
     • (d) y = x³ − cx²
     उत्तर देखें

     उत्तर: (b)

125. 125. Solution of the differential equation (1 + 3x) dy − (1 − 3y) dx = 0, y(1) = 0 is

     • (a) x + y + 3xy = 1
     • (b) x − y + 3xy = 1
     • (c) x − y − 3xy = 1
     • (d) x + y − 3xy = 1
     उत्तर देखें

     उत्तर: (c)