41. The derivative of the product of two functions u and v is:
(A)

(B)

(C)

(D) None of the above

42. The equation of the line that goes parallel to the x-axis and from the origin is:
(A) x/0 = y/1 = z/0
(B) x/0 = y/0 = z/0
(C) x/1 = y/0 = z/0
(D) x/0 = y/0 = z/1

43. The polar form of is :
(A) cos π + i sin π
(B) cos π/2 + i sin π/2
(C) cos π – i sin π
(D) cos π – i sin π/2

44. If   = then the value of x will be :
(A) 2
(B) 4
(C) 3
(D) 5

45. On what principle does the dynamo work?
(A) Electro magnetic induction
(B) Induced current
(C) Induced magnetism
(D) None of the above

46. The maximum value of angle of dip is :
(A) 0°
(B) 90°
(C) 45°
(D) 60°

47. The eccentricity (e) of an ellipse satisfies which of the following condition?
(A) e < 0
(B) 0 < e <l
(C) e = 1
(D) e > 1

48. A = {1, 2, 3}, then number of equivalence relations containing (1, 2) will be
(A) 1
(B) 2
(C) 3
(D) 4

49. If ‘θ’ is angle between the two vectors is and such that , when the value of θ will be
(A) 0
(B) π/4
(C) π/2
(D) π

50. The value of will be.
(A) 0
(B) π/2
(C) ½
(D) 1

51. Differentiation of function  with respect to x, will be :
(A) e^x
(B) . e^x
(C) e^-x
(D)

52. , its order and degree will be
(A) Order 3 Degree 1
(B) Degree 2 Order 3
(C) Order 3 Degree 3
(D) None of the above

53. The value of will be :
(A)
(B)
(C)
(D)

54. The velocity of sound on rainy days as compared to other days:
(A) increases
(B) decreases
(C) remains same
(D) none of the above

55. Principal value of will be:
(A) π/6
(B) π/3
(C) -π/6
(D) -π/3

56. If matrix , then:
(A) (A + A’) is a symmetric matrix
(B) (A + A’) is a skew symmetric matrix
(C) (A – A’) is a null matrix
(D) (A – A’) is an identity matrix

57. If P(A) = 7/13, P(B) = 9/13 and P(A ∩ B) = 4/13 then the value of P(A/B) will be.
(A) 4/9
(B) 5/9
(C) 3/9
(D) 2/9

58. The function is
(A) discontinuous at only one point
(B) discontinuous at exactly two points
(C) discontinuous at exactly three points
(D) none of the above

59. The value of 2 sin 5θ.cosθ will be :
(A) sin 6θ + cos 4θ
(B) sin 6θ – sin 4θ
(C) sin 6θ + sin 4θ
(D) cos 6θ + cos 4θ

60. If the mass of the bob of a simple pendulum is doubled, then its time period would become :
(A) Double
(B) Four times
(C) Remains unchanged
(D) Half