Mathematics questions
18011 published questions with worked solutions.
- The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come...
- Let the area of a ΔPQR with vertices P(5, 4), Q(–2, 4) and R(a, b) be 35 square units. If its orthocenter and centroid are O (2,...
- If 2 x 3 4 , then ^ -1 ( 12 13 x + 5 13 x ) is equal to-
- The value of (sin70°)(cot10°cot70° – 1) is
- Marks obtains by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the...
- If A, B and (adj(A^ -1 ) + adj(B^ -1 )) are non-singular matrices of same order, then the inverse of A(adj(A^ -1 ) + adj(B^ -1...
- If the system of equations (λ – 1)x + (λ – 4)y + λz = 5 λx + (λ – 1)y + (λ –4)z = 7 (λ + 1)x + (λ + 2)y – (λ + 2)z = 9 has...
- One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked 4. Another die has one face marked 1,...
- The sum of all rational terms in the expansion of (1 + 2^ 1/3 + 3^ 1/2 )^6 is equal to _____
- Let the circle C touch the line x – y + 1 = 0, have the centre on the positive x-axis, and cut off a chord of length 4 13 along...
- If the set of all values of a, for which the equation 5x^3 - 15x - a = 0 has three distinct real roots, is the interval (α, β),...
- Let a = i + 2 j + 3 k , b = 3 i + j - k and c be three vectors such that c is coplanar with a and b . If the vector c is...
- In I(m, n) = _0^1 x^ m-1 (1-x)^ n-1 dx, m, n > 0, then I(9, 14) + I(10, 13) is
- 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...