Mathematics questions
18011 published questions with worked solutions.
- Let a_1, a_2 2 , a_3 2^2 , , a_ 10 2^9 be a G.P. of common ratio 1 2 . If a_1 + a_2 + + a_ 10 = 62, then a_1 is equal to:
- Let A = x : |x^2 - 10| 6 and B = x : |x - 2| > 1 . Then
- For a triangle ABC, let p = BC , q = CA and r = BA . If | p | = 2 3 , | q | = 2 and = 1 3 , where is the angle between p and q ,...
- Let y = y(x) be the solution of the differential equation x dy dx - 2y = 2 + 3 x, x (- 2 , 2 ), y(0) = - 7 4 . Then y ( 6 ) is...
- Let A = 2, 3, 5, 7, 9 . Let R be the relation on A defined by x R y if and only if 2x 3y. Let be the number of elements in R, and...
- If the system of equations 3x + y + 4z = 3 2x + y - z = -3 x + 2y + z = 4 has no solution, then the value of is equal to:
- The largest n N, for which 7^n divides 101!, is:
- Let [.] denote the greatest integer function and f(x) = _ n 1 n^3 _ k=1 ^ n [ k^2 3^x ]. Then 12 _ j=1 ^ f(j) is equal to _____.
- If _0^1 4 ^ -1 (1 - 2x + 4x^2) , dx = a ^ -1 (2) - b _e(5), where a, b N, then (2a + b) is equal to _____.
- Let the maximum value of ( ^ -1 x)^2 + ( ^ -1 x)^2 for x [- 3 2 , 1 2 ] be m n ^2, where (m, n) = 1. Then m + n is equal to _____.
- If ( 1 ^ 15 C_0 + 1 ^ 15 C_1 ) ( 1 ^ 15 C_1 + 1 ^ 15 C_2 ) ( 1 ^ 15 C_ 12 + 1 ^ 15 C_ 13 ) = ^ 13 ^ 14 C_0 ,^ 14 C_1 , ^ 14 C_ 12...
- If P is a point on the circle x^2 + y^2 = 4, Q is a point on the straight line 5x + y + 2 = 0 and x - y + 1 = 0 is the...
- Let AB = 2 i + 4 j - 5 k and AD = i + 2 j + k , R . Let the projection of the vector v = i + j + k on the diagonal AC of the...
- Let the relation R on the set M = 1, 2, 3, , 16 be given by R = (x, y) : 4y = 5x - 3, x, y M . Then the minimum number of...
- Let the line x = -1 divide the area of the region (x, y) : 1 + x^2 y 3 - x in the ratio m : n, (m, n) = 1. Then m + n is equal to
- Let f(x) = x^ 2025 - x^ 2000 , x [0, 1] and the minimum value of the function f(x) in the interval [0, 1] be (80)^ 80 (n)^ -81 ....
- If a random variable x has the probability distribution x: 0, 1, 2, 3, 4, 5, 6, 7 p(x): 0, 2k, k, 3k, 2k^2, 2k, k^2+k, 7k^2 then...
- The number of distinct real solutions of the equation x|x + 4| + 3|x + 2| + 10 = 0 is
- Let f : [1, ) R be a differentiable function. If 6 _1^x f(t) ,dt = 3xf(x) + x^3 - 4 for all x 1, then the value of f(2) - f(3) is
- If the line x + 2y = 1, where R , does not meet the hyperbola x^2 - 9y^2 = 9, then a possible value of is: