Practice questions
88551 published questions with worked solutions.
- The value of ( _ n=1 ^ 19 ^ -1 (1 + _ p=1 ^ n 2p ) ) is:
- The value of 2^2 2^3 2^ 10 2^ 10 is:
- If _ r=0 ^ 25 , ^ 50 C_r ^ 50-r C_ 25-r = K ( ^ 50 C_ 25 ), then K is equal to:
- Let a_1, a_2, a_3, , a_ 10 be in G.P. with a_i > 0 for i = 1, 2, …, 10 and S be the set of pairs (r, k), r, k ∈ N (the set of...
- Two vertices of a triangle are (0, 2) and (4, 3). If its orthocenter is at the origin, then its third vertex lies in which...
- The tangent to the curve, y = xe^ x^2 passing through the point (1, e) also passes through the point:
- The value of _ - /2 ^ /2 dx [x] + [ x] + 4 , where [t] denotes the greatest integer less than or equal to t, is:
- Let S = (x, y) R ^2 : y^2 1 + r - x^2 1 - r = 1 ; r ≠ ±1. Then S represents:
- If _0^xf(t) ,dt = x^2 + _x^1t^2f(t) ,dt, then f' ( 12 ) is:
- Let A = bmatrix 2 & b & 1 b & b^2 + 1 & b 1 & b & 2 bmatrix where b > 0. Then the minimum value of (A) b is:
- The value of λ such that sum of the squares of the roots of the quadratic equation, x^2 + (3 - )x + 2 = has the least value is:
- On which of the following lines lies the point of intersection of the line, x-4 2 = y-5 2 = z-3 1 and the plane, x + y + z = 2?
- The positive value of λ for which the co-efficient of x^2 in the expression x^2 ( x + x^2 )^ 10 is 720, is:
- Let z = ( 3 2 + i2 )^5 + ( 3 2 - i2 )^5. If R(z) and I(z) respectively denote the real and imaginary parts of z, then:
- The number of values of θ ∈ (0, π) for which the system of linear equations x + 3y + 7z = 0, −x + 4y + 7z = 0, (sin 3θ)x + (cos...
- The curve amongst the family of curves represented by the differential equation, (x^2 - y^2)dx + 2xy ,dy = 0 which passes through...
- Let f: (−1, 1) → R be a function defined by f(x) = -|x|, - 1 - x^2 . If K be the set of all points at which f is not...
- If = ( - 2) a + b and = (4 - 2) a + 3 b be two given vectors where vectors a and b are non-collinear. The value of λ for which...
- The plane which bisects the line segment joining the points (−3, −3, 4) and (3, 7, 6) at right angles, passes through which one...
- If the area of an equilateral triangle inscribed in the circle x^2 + y^2 + 10x + 12y + c = 0 is 27 3 sq units then c is equal to: