Mathematics questions
18011 published questions with worked solutions.
- A signal which can be green or red with probability 4 5 and 1 5 respectively, is received by station A and then transmitted to...
- Two parallel chords of a circle of radius 2 are at a distance 3 + 1 apart. If the chords subtend at the center, angles of k and 2...
- Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively. Suppose...Not in JEE syllabus
- Let f be a function defined on R (the set of all real numbers) such that f'(x) = 2010(x - 2009)(x - 2010)^2(x - 2011)^3(x -...
- Let a_1, a_2, a_3, , a_ 11 be real numbers satisfying a_1 = 15, 27 - 2a_2 > 0 and a_k = 2a_ k-1 - a_ k-2 for k = 3, 4, , 11. If...
- Let k be a positive real number and let A = bmatrix 2k-1 & 2 k & 2 k 2 k & 1 & -2k -2 k & 2k & -1 bmatrix and B = bmatrix 0 &...
- Let (x_0, y_0) be the solution of the following equations (2x)^ 2 = (3y)^ 3 3^ x = 2^ y . Then x_0 is
- Let a = i + j + k, b = i - j + k and c = i - j - k be three vectors. A vector v in the plane of a and b, whose projection on c is...
- Let P = : - = 2 and Q = : + = 2 be two sets. ThenNot in JEE Main syllabus
- Let the straight line x = b divide the area enclosed by y = (1 - x)^2, y = 0, and x = 0 into two parts R_1 (0 x b) and R_2 (b x...
- Let α and β be the roots of x^2 - 6x - 2 = 0, with > . If a_n = ^n - ^n for n 1, then the value of a_ 10 - 2a_8 2a_9 is
- A straight line L through the point (3, -2) is inclined at an angle 60^ to the line 3 x + y = 1. If L also intersects the x-axis,...
- The vector(s) which is/are coplanar with vectors i + j + 2 k and i + 2 j + k, and perpendicular to the vector i + j + k is/are
- Let M and N be two 3×3 non-singular skew-symmetric matrices such that MN = NM. If P^T denotes the transpose of P, then M^2N^2...
- Let the eccentricity of the hyperbola x^2 a^2 - y^2 b^2 = 1 be reciprocal to that of the ellipse x^2 + 4y^2 = 4. If the hyperbola...
- Let f : R R be a function such that f(x + y) = f(x) + f(y), x, y R . If f(x) is differentiable at x = 0, then
- Consider the parabola y^2 = 8x. Let _1 be the area of the triangle formed by the end points of its latus rectum and the point P (...
- Let a_1, a_2, a_3, , a_ 100 be an arithmetic progression with a_1 = 3 and S_p = _ i=1 ^ p a_i, 1 p 100. For any integer n with 1...
- The positive integer value of n > 3 satisfying the equation 1 ( n ) = 1 ( 2 n ) + 1 ( 3 n ) isNot in JEE Main syllabus
- Let f : [1, ) [2, ) be a differentiable function such that f(1) = 2. If 6 _1^x f(t) ,dt = 3x ,f(x) - x^3 for all x 1, then the...