Mathematics questions
18011 published questions with worked solutions.
- Let p and q be real numbers such that p 0, p^3 q and p^3 -q. If and are nonzero complex numbers satisfying + = -p and ^3 + ^3 =...
- Let f, g and h be real-valued functions defined on the interval [0, 1] by f(x) = e^ x^2 + e^ -x^2 , g(x) = xe^ x^2 + e^ -x^2 and...
- Let A and B be two distinct points on the parabola y^2 = 4x. If the axis of the parabola touches a circle of radius r having AB...
- Let ABC be a triangle such that ACB = 6 and let a, b and c denote the lengths of the sides opposite to A, B and C respectively....Not in JEE syllabus
- Let z_1 and z_2 be two distinct complex numbers and let z = (1 - t)z_1 + tz_2 for some real number t with 0 < t < 1. If Arg(w)...
- Let f be a real-valued function defined on the interval (0, ) by f(x) = n , x + _0^x 1 + t ; dt. Then which of the following...
- The number of values of in the interval (- 2 , 2 ) such that n 5 for n = 0, 1, 2 and = 5 as well as 2 = 4 isNot in JEE Main syllabus
- The maximum value of the expression 1 ^2 + 3 + 5 ^2 is
- If a and b are vectors in space given by a = i - 2 j 5 and b = 2 i + j + 3 k 14 , then the value of (2 a + b ) [ ( a b ) ( a - 2...
- The line 2x + y = 1 is tangent to the hyperbola x^2 a^2 - y^2 b^2 = 1. If this line passes through the point of intersection of...
- If the distance between the plane Ax - 2y + z = d and the plane containing the lines x-1 2 = y-2 3 = z-3 4 and x-2 3 = y-3 4 =...
- Let be the complex number 2 3 + i 2 3 . Then the number of distinct complex numbers z satisfying vmatrix z+1 & & ^2 & z+ ^2 & 1...
- Let S_k, k = 1, 2, , 100, denote the sum of the infinite geometric series whose first term is k-1 k! and the common ratio is 1 k...
- The number of all possible values of , where 0 < < , for which the system of equations (y + z) 3 = (xyz) 3 x 3 = 2 3 y + 2 3 z...Not in JEE Main syllabus
- Let f be a real-valued differentiable function on R (the set of all real numbers) such that f(1) = 1. If the y-intercept of the...
- For r = 0, 1, , 10, let A_r, B_r and C_r denote, respectively, the coefficient of x^r in the expansions of (1+x)^ 10 , (1+x)^ 20...
- Let S = 1, 2, 3, 4 . The total number of unordered pairs of disjoint subsets of S is equal to
- Let f be a real-valued function defined on the interval (-1, 1) such that e^ -x f(x) = 2 + _0^x t^4 + 1 ,dt, for all x (-1, 1),...
- If the distance of the point P(1, -2, 1) from the plane x + 2y - 2z = , where > 0, is 5, then the foot of the perpendicular from...
- Two adjacent sides of a parallelogram ABCD are given by AB = 2 i + 10 j + 11 k and AD = - i + 2 j + 2 k. The side AD is rotated...