Q.1981·Miscellaneous·2023·EasyLet f(x) = x + 6, for x ≤ 1 f(x) = px + q, for 1 < x < 2 f(x) = 5x, for x ≥ 2 If f(x) is continuous, what is the value of q?View question
Q.1982·Miscellaneous·2023·EasyLet A and B be independent events with P(A) = 0.7, P(B') = k, P(A U B) = 0.8. What is k?View question
Q.1983·Miscellaneous·2023·EasyConsider the following statements: 1.f(x) = ln x is increasing in (0, ∞) 2.g(x) = e^x + e^(1/x) is decreasing in (0, ∞) Which of the above is/are correct?View question
Q.1984·Miscellaneous·2023·EasyThree dice are thrown. What is the probability that each face shows only multiples of 3?View question
Q.1985·Miscellaneous·2023·EasyA biased coin has P(H) = 1/4. If tossed five times, what is the probability of getting tails in first four and head at last?View question
Q.1986·Miscellaneous·2023·EasyWhat is the probability that the month of December has 5 Sundays?View question
Q.1987·Miscellaneous·2023·EasyLet f(x) = x + 6, for x ≤ 1 f(x) = px + q, for 1 < x < 2 f(x) = 5x, for x ≥ 2 If f(x) is continuous, what is the value of p?View question
Q.1988·Miscellaneous·2023·EasyLet f(x) = |ln x|, x ≠ 1. What is the derivative of f(x) at x = 2?View question
Q.1989·Miscellaneous·2023·EasyA natural number n is chosen from the first 50 natural numbers. What is the probability that n + 50/n < 50 ?View question
Q.1991·Miscellaneous·2023·EasyLet f(x) = |ln x|, x ≠ 1. What is the derivative of f(f(x)), where 1 < x < 2?View question
Q.1992·Miscellaneous·2023·EasyLet f(x) = [ (x − 3)/|x − 3| + a, x < 3 a − b, x = 3 [ (x − 3)/|x − 3| + b, x > 3 f(x) be continuous at x = 3. What is the value of b ?View question
Q.1993·Miscellaneous·2023·EasyLet f(x) = [ ax(x + 1) + b, x < 1 [ x − 1, 1 ≤ x ≤ 2 If the function f(x) is differentiable at x = 1, then what is the value of (a + b) ?View question
Q.1994·Miscellaneous·2023·EasyA parabola passes through (1, 2) and satisfies the differential equation dy/dx = 2y/x, x > 0, y > 0. What is the directrix of the parabola ?View question
Q.1995·Miscellaneous·2023·EasyA parabola passes through (1, 2) and satisfies the differential equation dy/dx = 2y/x, x > 0, y > 0. What is the length of latus rectum of the parabola ?View question
Q.1996·Miscellaneous·2023·EasyLet f(x) = [ (x − 3)/|x − 3| + a, x < 3 a − b, x = 3 [ (x − 3)/|x − 3| + b, x > 3 f(x) be continuous at x = 3. What is the value of a ?View question
Q.1997·Miscellaneous·2023·EasyIf A = [ 2 –1 0 –1 3 0 1 0 1 ], then what is the value of det[adj(adj(A))]?View question
Q.1998·Miscellaneous·2023·EasyThe value of the determinant of a matrix A of order 3 is 3. If C is the matrix of cofactors of A, then what is the value of determinant of C²?View question