Q.1999·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.2000·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.2001·Miscellaneous·2023·EasyLet f(x) = |ln x|, x ≠ 1. What is the derivative of f(x) at x = 2?View question
Q.2002·Miscellaneous·2023·EasyCentral angles p, q, r, s satisfy 9p = 3q = 2r = 6s. What is 4p - q?View question
Q.2003·Miscellaneous·2023·EasyFrom observations 4, 1, 4, 3, 6, 2, 1, 3, 4, 5, 1, 6 (dice rolls): If m = mean of lowest 8 and M = mean of highest 4, what is 2m + M?View question
Q.2004·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.2005·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.2006·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.2008·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.2009·Miscellaneous·2023·EasyWhat is the range of the function f(x) = x + |x| for all real x?View question
Q.2010·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.2011·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.2012·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.2013·Miscellaneous·2023·EasyWhat is the maximum number of points of intersection of 10 circles?View question
Q.2014·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.2015·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.2016·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