Q.1981·Miscellaneous·2023·EasyWhat is the probability that the month of December has 5 Sundays?View question
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 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.1984·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.1985·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.1986·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.1987·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.1988·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.1989·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.1990·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.1991·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.1992·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.1994·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.1995·Miscellaneous·2023·EasyA set S contains (2n + 1) elements. There are 4096 subsets of S which contain at most n elements. What is n equal to?View question
Q.1996·Miscellaneous·2023·EasyWhat is the maximum number of points of intersection of 10 circles?View question
Q.1997·Miscellaneous·2023·EasyIf all elements of a third order determinant are equal to 1 or –1, then the value of the determinant is:View question
Q.1998·Miscellaneous·2023·EasyIf A = [ 2 –1 0 –1 3 0 1 0 1 ], then what is the value of det[adj(adj(A))]?View question