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71. Using the letters in the word TRICK a new word containing five distinct letters is formed such that T appears in the middle. The number of distinct arrangements is […]

69. Evaluate ∫₀¹ x dx + ∫₁² (2 − x) dx Evaluate ∫₀¹ x dx + ∫₁² (2 − x) dx – Detailed Solution The present problem consists of the […]

68. The positive root of the equation x4 + x2 – 2 = 0 is             .                                 How to Find the Positive Root of x⁴ + x² − 2 […]

67. Which of the following point(s) lies(lie) on the plane 2x + 3y + z = 6? (A) (0, 0, 6) (B) (0, 2, 0) (C) (1, 1, 1) (D) […]

66. lf P = {1, 2, —1, 3}, Q = (0, 4, 1, 3} and R = {1, 6, 7}, then PM(QUR)= (A) {1, 2} (B) ( 1, 3} (C) […]

65. If one of the diameters of a circle has end points (2, 0) and (4, 0), then the equation of that circle is (A) x2 — 3x + y2 […]

64. Two dice are thrown simultaneously. The probability that the sum of the numbers obtained is divisible by 7 is (A) 1/ 6               (B) 1/36 (C) 0      […]

63. If u(x) and v(x) are differentiable at x = 0, and u(0) = 5, u'(0) = -3, v(0) = -1, v'(0) = 2, then find d/dx (uv + u/v) […]

62. If [ x    y p    q u    v ] R = [ 0  0  0 0  0  0 0  0  1 ] then the order of […]

61. cos(x + yx) = (A) cos (x) cos(yx) — sin (x) sin (yx) (C) cos (x) sin (yx) — sin(x) cos (yx) (B) cos (x) cos(yx) + sin (x) […]