Mathematics questions
18011 published questions with worked solutions.
- The equation of a plane passing through the line of intersection of the planes x + 2y + 3z = 2 and x − y + z = 3 and at a...
- Let PQR be a triangle of area Δ with a = 2, b = 7 2 and c = 5 2 , where a, b and c are the lengths of the sides of the triangle...Not in JEE syllabus
- If a and b are vectors such that | a + b| = 29 and a (2 i + 3 j + 4 k) = (2 i + 3 j + 4 k) b, then a possible value of ( a + b)...
- If P is a 3 × 3 matrix such that P^T = 2P + I, where P^T is the transpose of P and I is the 3 × 3 identity matrix, then there...
- Let α(a) and β(a) be the roots of the equation ( [3] 1 + a - 1 )x^2 + ( 1 + a - 1 )x + ( [6] 1 + a - 1 ) = 0 where a > -1. Then _...
- Four fair dice D_1, D_2, D_3 and D_4, each having six faces numbered 1, 2, 3, 4, 5 and 6, are rolled simultaneously. The...
- The value of the integral _ - /2 ^ /2 (x^2 + + x - x ) x ,dx is
- Let a_1, a_2, a_3, be in harmonic progression with a_1 = 5 and a_ 20 = 25. The least positive integer n for which a_n < 0 is
- For every integer n, let a_n and b_n be real numbers. Let function f : R R be given by f(x) = cases a_n + x, & for x [2n, 2n + 1]...
- If f(x) = _0^x e^ t^2 (t - 2)(t - 3) ,dt for all x (0, ), then
- If the straight lines x - 1 2 = y + 1 k = z 2 and x + 1 5 = y + 1 2 = z k are coplanar, then the plane(s) containing these two...
- Let X and Y be two events such that P(X ,| ,Y) = 1 2 , P(Y ,| ,X) = 1 3 and P(X Y) = 1 6 . Which of the following is (are)...
- If the adjoint of a 3×3 matrix P is bmatrix 1 & 4 & 4 2 & 1 & 7 1 & 1 & 3 bmatrix , then the possible value(s) of the determinant...
- Let complex numbers α and 1 lie on circles (x - x_0)^2 + (y - y_0)^2 = r^2 and (x - x_0)^2 + (y - y_0)^2 = 4r^2, respectively. If...
- Four persons independently solve a certain problem correctly with probabilities 1 2 , 3 4 , 1 4 , 1 8 . Then the probability that...
- Let f : [ 1 2 , 1 ] R (the set of all real numbers) be a positive, non-constant and differentiable function such that f'(x) <...
- The number of points in (−∞, ∞), for which x^2 - x x - x = 0, is
- The area enclosed by the curves y = x + x and y = | x - x| over the interval [0, 2 ] is
- A curve passes through the point (1, 6 ). Let the slope of the curve at each point (x, y) be y x + ( y x ), x > 0. Then the...
- The value of ( _ n=1 ^ 23 ^ -1 (1 + _ k=1 ^ n 2k ) ) is