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81. If [x] denotes the greatest integer function (for example, [1.16] = 1 and [1.8] = 1), then ∫₁√3 (1 + [x])/(1 + x²) dx = L, then L = […]

80. From the database of a clinic it was found that out of 2000 patients who had visited the clinic in a year, 900 had high BP, 900 had high […]

79. The plane x + y + z = 0 intersects the sphere x2 + y2 + z2 = 9 along a circle. If (2, y, z) is a point […]

78. In ΔPQR, ∠Q = 60° and S is the midpoint of QR. If QS = PS and PR = 5, then (A) PQ = 5√3/3 (B) PS = 5/2 […]

77. If f(x)= ax²+b,    0≤x≤1 cx+sin(πx/2),    1≤x≤2 is continuous and differentiable at all points in the interval [0,2], and f(2)=π/4, then determine the correct option. (A) a = π/16 and b = […]

76. Consider two vectors P and Q of equal magnitude. If the magnitude of P + Q is two-times larger than that of P – Q, then the angle between […]

75. Let Z be the set of all integers and let f and g be one-one mappings from Z into itself such that For even n, f(g(n)) = g(n + […]

74. Let P(t) denote the population of a species at time t. If dP/dt = P(1 − P) and the initial population is P(0)=0.1 million, then the population at t […]

73. A line parallel to the vector passes through the point and meets the xy-plane at a point . The distance between the origin and is (A) 10 (B) 11 […]

72. From the set of 10 numbers {1, 2,…,10} three numbers are selected at random without replacement. The probability that the sum of these selected numbers is 9, is (A) […]