Mathematics questions
18011 published questions with worked solutions.
- For an integer n ≥ 2, if the arithmetic mean of all coefficients in the binomial expansion of (x+y)^ 2n-3 is 16, then the...
- Find the length of latus rectum of an ellipse, whose foci are (2, 5) and (2, –3) and the eccentricity of the ellipse is 4 5
- Let the shortest distance between the lines x-3 3 = y- -1 = z-3 1 and x+3 -3 = y+7 2 = z- 4 be 3 30 . Then the positive value of...
- Let A and B be two distinct points on the line L : x-6 3 = y-7 2 = z-7 -2 . Both A and B are at a distance 2 17 from the foot of...
- Let m and n be the number of points at which the function f(x) = x, x^3, x^5, …x^ 21 , x R , is not differentiable and not...
- Let A = z ∈ ℂ : |z − 2 − i| = 3 , B = z ∈ ℂ : Re(z − iz) = 2 and S = A∩B. Then _ z S |z|^2 is equal to _____.
- Let A = bmatrix & 0 & - 0 & 1 & 0 & 0 & bmatrix . If for some θ ∈ (0, π), A^2 = A^T, then the sum of the diagonal elements of the...
- Let the ellipse 3x^2 + py^2 = 4 pass through the centre C of the circle x^2 + y^2 - 2x - 4y - 11 = 0 of radius r. Let f_1, f_2 be...
- Let A = bmatrix 2 & 2+p & 2+p+q 4 & 6+2p & 8+3p+2q 6 & 12+3p & 20+6p+3q bmatrix If det(adj(adj(3A))) = 2^m 3^n, m, n N, then m +...
- Given below are two statements. Statement I: _ x 0 ( ^ -1 x + _e 1+x 1-x - 2x x^5 ) = 2 5 Statement II : _ x 1 (x^ 2 1-x ) = 1...
- Let a = i + 2 j + k and b = 2 i + j - k . Let c be a unit vector in the plane of the vector a and b and be perpendicular to a ....
- Let the value of for which the shortest distance between the lines x-1 2 = y-2 3 = z-3 4 and x- 3 = y-4 4 = z-5 5 is 1 6 be _1...
- Let A = 0, 1, 2, 3, 4, 5 . Let R be a relation on A defined by (x, y) R if and only if max x, y 3, 4 . Then among the statements...
- If 1 1^4 + 1 2^4 + 1 3^4 +....... = ^4 90 , 1 1^4 + 1 3^4 + 1 5^4 +....... = 1 2^4 + 1 4^4 + 1 6^4 +....... = Then is equal to
- Let the function f(x) = x 3 + 3 x +3, x 0 be strictly increasing in (- , _1) ( _2, ) and strictly decreasing in ( _3, _4) ( _4,...
- Let f(x) = x - 1 and g(x) = e^x for x R. If dy dx = (e^ -2 x g(f(f(x))) - y x ), y(0) = 0, then y(1) is
- The sum of the squares of the roots of |x-2|^2 + |x-2| - 2 = 0 and the squares of the roots of x^2 - 2|x-3| - 5 = 0, is
- Let f(x) be a positive function and I_1 = _ - 1 2 ^ 1 2xf(2x(1-2x))dx and I_2 = _ -1 ^ 2 f(x(1-x))dx. Then the value of I_2 I_1...
- The number of integral terms in the expansion of (5^ 1 2 + 7^ 1 8 )^ 1016 is
- Let be a solution of x^2 + x + 1 = 0, and for some a and b in R, [4 a b] bmatrix 1 & 16 & 13 -1 & -1 & 2 -2 & -14 & -8 bmatrix =...