Mathematics questions
18011 published questions with worked solutions.
- Let the domain of the function f(x) = ^ -1 ( 4x+5 3x-7 ) be [ , ] and the domain of g(x) = _2(2 - 6 _ 27 (2x+5)) be ( , ). Then...
- Let the area of the triangle formed by the lines x+2 = y-1 = z, x-3 5 = y -1 = z-1 1 and x -3 = y-3 3 = z-2 1 be A. Then A^2 is...
- Let f be a differentiable function on R such that f(2) =1, f '(2) = 4. Let _ x 0 (f(2 + x))^ 3/x = e^ . Then the number of times...
- Consider two sets A and B, each containing three numbers in A.P. let the sum and the product of the elements of A be 36 and p...
- Let the product of _1 = (8 + i) + (7 + 4i) and _2 = (1 + 8i) + (4 + 7i) be + i , i = -1 . Let p and q be the maximum and the...
- If 1^2 ( ^ 15 C_1) + 2^2 ( ^ 15 C_2) + 3^2 ( ^ 15 C_3) + + 15^2 ( ^ 15 C_ 15 ) = 2^m 3^n 5^k, where m, n, k N , then m + n + k is...
- If a curve y = y(x) passes through the point (1, 2 ) and satisfies the differential equation (7x^4 y - e^x cosec y) dx dy = x^5,...
- Let f(x) + 2f ( 1 x ) = x^2 + 5 and 2g(x) - 3g ( 1 x ) = x, x > 0. If = _1^2 f(x)dx, and = _1^2 g(x)dx, then the value of 9 + is :
- Let A = –3, –2, –1, 0, 1, 2, 3 and R be a relation on A defined by xRy if and only if 2x - y 0, 1 . Let l be the number of...
- The centre of a circle C is at the centre of the ellipse E : x^2 a^2 + y^2 b^2 = 1, a > b. Let C pass through the foci F_1 and...
- Let the values of p, for which the shortest distance between the lines x+1 3 = y 4 = z 5 and r = (p i + 2 j + k ) + (2 i + 3 j +...
- Let the mean and the standard deviation of the observation 2, 3, 3, 4, 5, 7, a, b be 4 and 2 respectively. Then the mean...
- The sum of the infinite series ^ -1 ( 7 4 ) + ^ -1 ( 19 4 ) + ^ -1 ( 39 4 ) + ^ -1 ( 67 4 ) + is :
- If is a root of the equation x^2 + x + 1 = 0 and _ k=1 ^ n ( ^k + 1 ^k )^2 = 20, then n is equal to _____.
- If ( 1+x^2 +x)^ 10 ( 1+x^2 -x)^9 dx = 1 m (( 1+x^2 +x)^n(n 1+x^2 -x) )+c where C is the constant of integration and m, n N , then...
- Let the three sides of a triangle ABC be given by the vectors 2 i - j + k , i - 3 j - 5 k and 3 i - 4 j - 4 k . Let G be the...
- The number of solutions of the equation 2 2 + 5 2 = 2 ^3 5 2 in [- 2 , 2 ] is :Not in JEE Main syllabus
- If the orthocenter of the triangle formed by the lines y = x + 1, y = 4x – 8 and y = mx + c is at (3, –1), then m – c is:
- Let a and b be the vectors of the same magnitude such that | a + b |+| a - b | | a + b |-| a - b | = 2 +1. Then | a + b |^2 | a...
- If the area of the region (x, y) : 1 + x^2 y min x + 7, 11 – 3x is A, then 3A is equal to