JEE Main questions
34495 published questions with worked solutions.
- Let f : R - 0 R be a function such that f(x) - 6f ( 1 x ) = 35 3x - 5 2 . If the _ x 0 ( 1 x + f(x) ) = ; , R, then + 2 is equal...
- Let S_n = 1 2 + 1 6 + 1 12 + 1 20 + ... upto n terms. If the sum of the first six terms of an A.P. with first term -p and common...
- Let f(x) = 2^ x+2 +16 2^ 2x+1 +2^ x+4 +32 . Then the value of 8 (f ( 1 15 ) + f ( 2 15 ) + ... + f ( 59 15 ) ) is equal to
- If and are the roots of the equation 2z^2 - 3z - 2i = 0, where i = -1 , then 16. Re ( ^ 19 + ^ 19 + ^ 11 + ^ 11 ^ 15 + ^ 15 ). Im...
- Let in a ABC, the length of the side AC be 6, the vertex B be (1, 2, 3) and the vertices A, C lie on the line x-6 3 = y-7 2 = z-7...
- Let y = y(x) be the solution of the differential equation (xy - 5x^2 1+x^2 )dx + (1+x^2)dy = 0, y(0) = 0. Then y( 3 ) is equal to
- Let the product of the focal distances of the point ( 3 , 1 2 ) on the ellipse x^2 a^2 + y^2 b^2 = 1, (a > b), be 7 4 . Then the...
- A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a...
- Consider the region R = (x, y): x y 9 - 11 3 x^2, x 0 . The area, of the largest rectangle of sides parallel to the coordinate...
- The area of the region (x, y) : x^2 + 4x + 2 y |x + 2| is equal to
- For a statistical data x_1, x_2, ..., x_ 10 of 10 values, a student obtained the mean as 5.5 and _ i=1 ^ 10 x_i^2 = 371. He later...
- For some n 10, let the coefficients of the 5th, 6th and 7th terms in the binomial expansion of (1 + x)^ n+4 be in A.P. Then the...
- The product of all the rational roots of the equation (x^2 - 9x + 11)^2 - (x - 4)(x - 5) = 3, is equal to :
- Let the line passing through the points (–1, 2, 1) and parallel to the line x-1 2 = y+1 3 = z 4 intersect the line x+2 3 = y-3 2...
- Let the lines 3x - 4y - = 0, 8x - 11y - 33 = 0, and 2x - 3y + = 0 be concurrent. If the image of the point (1, 2) in the line 2x...
- If the system of equations 2x – y + z = 4 5x + λy + 3z = 12 100x – 47y + μz = 212, has infinitely many solutions, then μ – 2λ is...
- Let f be a differentiable function such that 2(x + 2)^2 f(x) - 3(x + 2)^2 = 10 _0^x (t+2)f(t) , dt, x 0. Then f(2) is equal to...
- Let A be a 3 × 3 matrix such that X^T AX = O for all non-zero 3 × 1 matrices X = pmatrix x pmatrix . If A pmatrix 1 1 1 pmatrix =...
- Let S = p_1, p_2, ...., p_ 10 be the set of first ten prime numbers. Let A = S P, where P is the set of all possible products of...
- What is the relative decrease in focal length of a lens for an increase in optical power by 0.1 D from 2.5 D ? ['D' stands for...