Mathematics questions
18011 published questions with worked solutions.
- Given three indentical bags each containing 10 balls, whose colours are as follows : Bag I: Red 3, Blue 2, Green 5 Bag II: Red 4,...
- The line L_1 is parallel to the vector a = -3 i + 2 j + 4 k and passes through the point (7, 6, 2) and the line L_2 is parallel...
- Let f : [1, ) [2, ) be a differentiable function. If 10 _1^x f(t) ,dt = 5xf(x) - x^5 - 9 for all x 1, then the value of f(3) is :
- Let A = 1, 2, 3,...., 100 and R be a relation on A such that R = (a, b): a = 2b + 1 . Let (a_1, a_2), (a_2, a_3), (a_3, a_4), ,...
- Let the point P of the focal chord PQ of the parabola y^2 = 16x be (1, –4). If the focus of the parabola divides the chord PQ in...
- If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of...
- Let a = 2 i - 3 j + k , b = 3 i + 2 j + 5 k and a vector c be such that ( a - c ) b = -18 i - 3 j + 12 k and a c = 3. If b c = d...
- 4 _0^1 ( 1 3+x^2 + 1+x^2 )dx - 3 _e( 3 ) is equal to :
- The number of terms of an A.P. is even, the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term...
- If the system of equations 2x + λy + 3z = 5 3x + 2y – z = 7 4x + 5y + μz = 9 has infinitely many solutions, then ( ^2 + ^2) is...
- Let A be a 3 × 3 real matrix such that A^2(A - 2I) - 4(A - I) = 0, where I and O are the identity and null matrices,...
- If the sum of the first 10 terms of the series 4.1 1+4.1^4 + 4.2 1+4.2^4 + 4.3 1+4.3^4 + is m n , where gcd(m, n), then m + n is...
- If the set of all a R - 1 , for which the roots of the equation (1 - a)x^2 + 2(a - 3)x + 9 = 0 are positive is (- , - ] [ , ),...
- If y = ( 3 + ^ -1 x 2 ), then (x - y)^2 + 3y^2 is equal to
- Let y = y(x) be the solution of the differential equation dy dx + 2y ^2 x = 2 ^2 x + 3 x ^2 x such that y(0) = 5 4 . Then 12 (y (...
- Let A(4, –2), B(1, 1) and C(9, –3) be the vertices of a triangle ABC. Then the maximum area of the parallelogram AFDE, formed...
- Let a ∈ R and A be a matrix of order 3 × 3 such that det(A) = –4 and A + I = bmatrix 1 & a & 1 2 & 1 & 0 a & 1 & 2 bmatrix ,...
- Let P_n = ^n + ^n, n ∈ N. If P_ 10 = 123, P_9 = 76, P_8 = 47 and P_1 = 1, then the quadratic equation having roots 1 and 1 is :
- If S and S′ are the foci of the ellipse x^2 18 + y^2 9 =1 and P be a point on the ellipse, then min.(SP·S′P) + max.(SP·S′P) is...
- Let f : R → R be a twice differentiable function such that ( x y)(f(2x+2y)-f(2x-2y)) = ( x y)(f(2x+2y)+f(2x-2y)), for all x, y ∈...