Q.1981·Miscellaneous·2023·EasyLet X + Y = 100, and X ~ B(100, 4/5). What is the variance of Y?View question
Q.1982·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.1983·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.1984·Miscellaneous·2023·EasyIf regression lines are x + 4y + 1 = 0 and 4x + 9y + 7 = 0, find x when y = -3:View question
Q.1985·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.1986·Miscellaneous·2023·EasyThree dice are thrown. What is the probability that each face shows only multiples of 3?View question
Q.1987·Miscellaneous·2023·EasyWhat is the probability that the month of December has 5 Sundays?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) = [ 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.1993·Miscellaneous·2023·EasyA function is defined by f(x) = | x + 1 2 3 | | 2 x + 4 6 | | 3 6 x + 9 | The function attains local minimum value at :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·EasyConsider the following statements: 1. A = (A ∪ B) ∪ (A – B) 2. A ∪ (B – A) = (A ∪ B) 3. B = (A ∪ B) – (A – B) Which of the statements given above are correct?View question
Q.1997·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.1998·Miscellaneous·2023·EasyConsider the following statements: 1. The relation f defined by f(x) = { x³, 0 ≤ x ≤ 2 4x, 2 ≤ x ≤ 8 } is a function. 2. The relation g defined by g(x) = { x², 0 ≤ x ≤ 4 3x, 4 ≤ x ≤ 8 } is a function. Which of the statements given above is/are correct?View question