Q.1982·Miscellaneous·2023·EasyWhat is the range of the function f(x) = x + |x| for all real x?View question
Q.1983·Miscellaneous·2023·EasyLet P, Q, R represent mean, median and mode for some distribution and mode M for some distribution SP = 4Q + 2R, then what is P+Q/2P + 0.7R equal to?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·EasyThe mean and variance of five observations are 14 and 13.2 respectively. Three of them are 11, 16 and 20. What are the other two observations?View question
Q.1986·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.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 q?View question
Q.1988·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.1989·Miscellaneous·2023·EasyWhat is the probability that the month of December has 5 Sundays?View question
Q.1990·Miscellaneous·2023·EasyLet f(x) = |ln x|, x ≠ 1. What is the derivative of f(x) at x = 2?View question
Q.1991·Miscellaneous·2023·EasyFor what value of m < 0 is the area bounded by the lines y = x, y = mx, and x = 2 equal to 3?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.1994·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.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 directrix of the parabola ?View question
Q.1996·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
Q.1997·Miscellaneous·2023·EasyThe Cartesian product A × A has 16 elements among which are (0, 2) and (1, 3). Which of the following statements is/are correct? 1. It is possible to determine set A. 2. A × A contains the element (3, 2). Select the correct answer using the code given below:View question
Q.1998·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