JEE Main questions
34495 published questions with worked solutions.
- The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that...
- Let ABCD be a trapezium whose vertices lie on the parabola y^2 = 4x. Let the sides AD and BC of the trapezium be parallel to...
- Two number k_1 and k_2 are randomly chosen from the set of natural numbers. Then, the probability that the value of i^ k_1 +i^...
- If f(x) = 2^x 2^x+ 2 , x R, then _ k=1 ^ 81 f ( k 82 ) is equal to
- Let A(x, y, z) be a point in xy-plane, which is equidistant from three points (0, 3, 2), (2, 0, 3) and (0, 0, 1). Let B = (1, 4,...
- The relation R = (x, y) : x, y z and x + y is even is :
- Let a_n be a sequence such that a_0 = 0, a_1 = 1 2 and 2a_ n+2 = 5a_ n+1 - 3a_n, n = 0, 1, 2, 3, .... Then _ k=1 ^ 100 a_k is...
- ( ^ -1 3 5 + ^ -1 5 13 + ^ -1 33 65 ) is equal to :
- Let T_r be the r^ th term of an A.P. If for some m, T_m = 1 25 , T_ 25 = 1 20 and 20 _ r=1 ^ 25 T_r = 13, then 5m _ r=m ^ 2m T_r...
- If the image of the point (4, 4, 3) in the line x-1 2 = y-2 1 = z-1 3 is ( , , ), then + + is equal to
- If _ - /2 ^ /2 96x^2 ^2 x (1+e^x) dx = ( ^2 + ), , Z, then ( + )^2 equals :
- The sum of all local minimum values of the function f(x) = cases 11 18 (x-4)(x-5), & x > 2 1 3 (7+2|x|), & -1 x 2 1-2x, & x < -1...
- The sum, of the squares of all the roots of the equation x^2 + |2x-3| - 4 = 0, is
- Let for some function y = f(x), _0^x t f(t) ,dt = x^2 f(x), x > 0 and f(2) = 3. Then f(6) is equal to
- Let ^nC_ r-1 = 28, ^nC_r = 56 and ^nC_ r+1 = 70. Let A(4cost, 4sint), B(2sint, –2cost) and C(3r – n, r^2 – n – 1) be the vertices...
- Let O be the origin, the point A be z_1 = 3 + 2 2 i, the point B(z_2) be such that 3 |z_2| = |z_1| and arg (z_2) = (z_1) + 6 ....
- Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate...
- Let M denote the set of all real matrices of order 3 × 3 and let S = –3, –2, –1, 1, 2 . Let S_1 = A = [a_ ij ] M : A = A^T and a_...
- If = 1 + _ r=1 ^ 6 (-3)^ r-1 ^ 12 C_ 2r-1 , then the distance of the point (12, 3 ) from the line x - 3 y + 1 = 0 is
- Let a = i + j + k , b = 2 i +2 j + k and d = a b . If c is a vector such that a . c = | c |, | c -2 a |^2 = 8 and the angle...