Q.1999·Miscellaneous·2023·EasyCentral angles p, q, r, s satisfy 9p = 3q = 2r = 6s. What is 4p - q?View question
Q.2000·Miscellaneous·2023·EasyWhat is the range of the function f(x) = x + |x| for all real x?View question
Q.2001·Miscellaneous·2023·EasyLet f(x) = |ln x|, x ≠ 1. What is the derivative of f(f(x)), where 1 < x < 2?View question
Q.2002·Miscellaneous·2023·EasyA bivariate data set contains only two points (-1, 1) and (3, 2). What will be the line of regression of y on x?View question
Q.2003·Miscellaneous·2023·EasyIf A = [ 2 0 0 0 3 0 0 0 4 ], then which of the following statements are correct? 1. Aⁿ will always be singular for any positive integer n 2. Aⁿ will always be a diagonal matrix for any positive integer n 3. Aⁿ will always be a symmetric matrix for any positive integer n Select the correct answer using the code below:View question
Q.2004·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.2005·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.2006·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.2007·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.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·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.2011·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.2012·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.2013·Miscellaneous·2023·EasyIf (a + b), 2b, (b + c) are in HP, then which one of the following is correct?View question
Q.2014·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.2015·Miscellaneous·2023·EasyWhat is the number of common roots of equation-I and equation-II?View question