Mathematics questions
18011 published questions with worked solutions.
- If the system of equations x + 2y - 3z = 2 2x + + 5z = 5 14x + 3y + = 33 has infinitely many solutions, then + is equal to :
- Let (2, 3) be the largest open interval in which the function f(x) = 2 _e(x - 2) - x^2 + ax + 1 is strictly increasing and (b, c)...
- Suppose A and B are the coefficients of 30th and 12th terms respectively in the binomial expansion of (1+x)^ 2n-1 . If 2A = 5B,...
- Let a = 3 i - j +2 k , b = a ( i -2 k ) and c = b k . Then the projection of c -2 j on a is :
- For some a, b, let f(x) = vmatrix a+ x x & 1 & b a & 1+ x x & b a & 1 & b+ x x vmatrix , x 0, _ x 0 f(x) = + a + b. Then ( + +...
- Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can...
- Let A = [a_ ij ] be a square matrix of order 2 with entries either 0 or 1. Let E be the event that A is an invertible matrix....
- If the equation of the parabola with vertex V ( 3 2 ,3 ) and the directrix x + 2y = 0 is x^2 + y^2 - xy - 30x - 60y + 225 = 0,...
- Number of functions f : 1, 2, , 100 0, 1 , that assign 1 to exactly one of the positive integers less than or equal to 98, is...
- Let P be the image of the point Q(7, -2, 5) in the line L : x-1 2 = y+1 3 = z 4 and R(5, p, q) be a point on L. Then the square...
- Let y = y(x) be the solution of the differential equation 2 x dy dx = 2x - 4y x, x (0, 2 ). If y ( 3 )=0, then y' ( 4 )+y ( 4 )...
- Let H_1 : x^2 a^2 - y^2 b^2 =1 and H_2 : x^2 A^2 + y^2 B^2 =1 be two hyperbolas having length of latus rectums 15 2 and 12 5...
- If 2x^2+5x+9 x^2+x+1 dx = x x^2+x+1 + x^2+x+1 + _e |x+ 1 2 + x^2+x+1 | + C, where C is the constant of integration, then + 2 is...
- 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...