Mathematics questions
18011 published questions with worked solutions.
- The number of solutions of the equation ( 9 x - 9 x + 2 ) ( 2 x - 7 x + 3 ) = 0 is :
- Let y = y(x) be the solution of the differential equation x( _e( x))^2 dy + ( x - 3y x _e( x))dx = 0, x (0, 2 ). If y ( 4 ) = -1...
- Define a relation R on the interval [0, 2 ) by x R y if and only if ^2x - ^2y = 1. Then R is :
- Let the ellipse, E_1 : x^2 a^2 + y^2 b^2 = 1, a > b and E_2 : x^2 A^2 + y^2 B^2 = 1, A < B have same eccentricity 1 3 . Let the...
- Consider an A.P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies...
- Let a = i + 2 j + k and b = 2 i + 7 j + 3 k . Let L_1 : r = (- i + 2 j + k ) + a , R and L_2 : r = ( j + k ) + b , R be two...
- The value of _ n ( _ k=1 ^ n k^3+6k^2+11k+5 (k+3)! ) is :
- Let L_1 : x-1 1 = y-2 -1 = z-1 2 and L_2 : x+1 -1 = y-2 2 = z 1 be two lines. Let L_3 be a line passing through the point ( , , )...
- Let x_1, x_2,......x_ 10 be ten observations such that _ i=1 ^ 10 (x_i-2)=30, _ i=1 ^ 10 (x_i- )^2=98, > 2 and their variance is...
- Let A = [a_ ij ] = bmatrix _5 128 & _4 5 _5 8 & _4 25 bmatrix . If A_ ij is the co-factor of a_ ij , C_ ij = _ k=1 ^ 2 a_ ik A_...
- Let f : (0, ) R be a twice differentiable function. If for some a 0, _0^1 f( x)d = af(x), f(1) = 1 and f(16) = 1 8 , then 16 - f'...
- Let S = m Z : A^ m^2 + A^m = 3I - A^ -6 , where A = bmatrix 2 & -1 1 & 0 bmatrix . Then n(S) is equal to …………….. .
- The number of 6-letter words, with or without meaning, that can be formed using the letters of the word 'MATHS' such that any...
- Let S = x : ^ -1 x = + ^ -1 x + ^ -1 (2x + 1) . Then _ x S (2x-1)^2 is equal to ………….. .
- If the set of all a R, for which the equation 2x^2 + (a-5)x + 15 = 3a has no real root, is the interval ( , ), and X = x Z : < x...
- If x + ^2x = 1, x (0, 2 ), then ( ^ 12 x + ^ 12 x) + 3( ^ 10 x + ^ 10 x + ^8x + ^8x) + ( ^6x + ^6x) is equal to
- Let the area enclosed between the curves |y| = 1 - x^2 and x^2 + y^2 = 1 be . If 9 = + ; , are integers, then the value of | - |...
- If the domain of the function _5(18x - x^2 - 77) is ( , ) and the domain of the function _ (x-1) ( 2x^2+3x-2 x^2-3x-4 ) is ( , ),...
- Let a straight line L pass through the point P(2, –1, 3) and be perpendicular to the lines x-1 2 = y+1 1 = z-3 -2 and x-3 1 = y-2...
- Let S = N 0 . Define a relation R from S to R by : R = (x,y): _e y = x _e ( 2 5 ), x S, y R Then, the sum of all the elements in...