Mathematics questions
18011 published questions with worked solutions.
- Let A be the set of all function f : Z → Z and R be a relation on A such that R = (f, g : f(0) = g(1) and f(1) = g(0). Then R is :
- Let a_1, a_2, a_3, be in an A.P. such that _ k=1 ^ 12 a_ 2k-1 = - 72 5 a_1, a_1 0. If _ k=1 ^ n a_k = 0, then n is :
- If the system of linear equations 3x + y + βz = 3 2x + αy – z = –3 x + 2y + z = 4 has infinitely many solutions, then the value...
- The number of sequences of ten terms, whose terms are either 0 or 1 or 2, that contain exactly five 1s and exactly three 2s, is...
- Let A = bmatrix & -1 6 & bmatrix , α > 0, such that det(A) = 0 and α + β = 1. If I denotes 2 × 2 identity matrix, then the...
- The largest n ∈ N such that 3^n divides 50! is :
- If the function f(x) = 2x^3 - 9ax^2 + 12a^2x + 1, where a > 0, attains its local maximum and local minimum values at p and q,...
- If θ ∈ [–2π, 2π], then the number of solutions of 2 2 ^2 + (2- 6) - 3 = 0, is equal to :Not in JEE Main syllabus
- For α, β, γ ∈ R , if _ x 0 x^2 x + ( -1)e^ x^2 2x - x = 3, then β + γ – α is equal to :
- Let one focus of the hyperbola H : x^2 a^2 - y^2 b^2 = 1 be at ( 10 , 0) and the corresponding directrix be x = 9 10 . If e and l...
- If a is a non-zero vector such that its projections on the vectors 2 i - j + 2 k, i + 2 j - 2 k and k are equal, then a unit...
- If the area of the region (x, y) : |4-x^2| y x^2, y 4, x 0 is ( 80 2 - ), α, β ∈ N, then α + β is equal to ______.
- Three distinct numbers are selected randomly from the set 1, 2, 3, …, 40 . If the probability, that the selected numbers are in...
- Line L1 of slope 2 and line L2 of slope 1 2 intersect at the origin O. In the first quadrant, P1, P2 ….P12 are 12 points on line...
- Let the Mean and Variance of five observations x_1 = 1, x_2 = 3, x_3 = a, x_4 = 7 and x_5 = b, a > b, be 5 and 10 respectively....
- Let the equation x(x+2)(12-k) = 2 have equal roots. Then the distance of the point (k, k 2 ) from the line 3x + 4y + 5 = 0 is
- The integral _0^ 8x ,dx 4 ^2 x + ^2 x is equal to
- If the domain of the function f(x) = _7(1 - _4(x^2 - 9x + 18))) is ( , ) ( , ), then + + + is equal to
- Let f: R R be a function defined by f(x) = ||x+2| - 2|x||. If m is the number of points of local minima and n is the number of...
- If the probability that the random variable X takes the value x is given by P(X = x) = k(x+1) 3^ -x , x = 0, 1, 2, 3 , where k is...