Q.1963·Miscellaneous·2023·EasyIn this question each item consists of a sentence with an underlined word followed by four words. Select the option that is opposite in meaning to the underlined word and mark your response in your Answer Sheet accordingly. A trip to the hills was refreshing .View question
Q.1964·Miscellaneous·2023·EasyBuckminster fullerene, which looks like a football, is an allotropic form ofView question
Q.1965·Miscellaneous·2023·EasyLet p = (1/3) × (tan 3x / tan x) q = 1 – 3 tan²x, 0 < x < π, x ≠ π/2 What is pq equal to?View question
Q.1966·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.1967·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.1968·Miscellaneous·2023·EasyWhat is the number of common roots of equation-I and equation-II?View question
Q.1969·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.1970·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.1972·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.1973·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.1974·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.1975·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.1976·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.1977·Miscellaneous·2023·EasyLet f(x) = |ln x|, x ≠ 1. What is the derivative of f(f(x)), where 1 < x < 2?View question
Q.1978·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
Q.1979·Miscellaneous·2023·EasyThe value of the determinant of a matrix A of order 3 is 3. If C is the matrix of cofactors of A, then what is the value of determinant of C²?View question
Q.1980·Miscellaneous·2023·EasyWhat is the maximum number of points of intersection of 10 circles?View question