Q.1999·Miscellaneous·2023·EasyLet f(x) = |ln x|, x ≠ 1. What is the derivative of f(f(x)), where 1 < x < 2?View question
Q.2000·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.2001·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.2002·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.2004·Miscellaneous·2023·EasyWhat is the range of the function f(x) = x + |x| for all real x?View question
Q.2005·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.2006·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.2007·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.2008·Miscellaneous·2023·EasyLet f(x) = |ln x|, x ≠ 1. What is the derivative of f(x) at x = 2?View question
Q.2009·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.2010·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.2011·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.2012·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.2013·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.2015·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.2016·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