Practice questions
88551 published questions with worked solutions.
- If , C are the distinct roots, of the equation x^2 - x + 1 = 0, then ^ 101 + ^ 107 is equal to
- If vmatrix x-4 & 2x & 2x 2x & x-4 & 2x 2x & 2x & x-4 vmatrix = (A + Bx)(x - A)^2, then the ordered pair (A, B) is equal to :
- If the system of linear equations x + ky + 3z = 0 3x + ky - 2z = 0 2x + 4y - 3z = 0 has a non-zero solution (x, y, z) then xz y^2...
- From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a...
- The sum of the co-efficients of all odd degree terms in the expansion of (x + x^3 - 1 )^5 + (x - x^3 - 1 )^5, (x > 1) is
- Let a_1, a_2, a_3, , a_ 49 be in A.P. such that _ k=0 ^ 12 a_ 4k+1 = 416 and a_9 + a_ 43 = 66. If a_1^2 + a_2^2 + + a_ 17 ^2 =...
- Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 1^2 + 2 2^2 + 3^2 + 2 4^2 + 5^2 + 2...
- For each t R , let [t] be the greatest integer less than or equal to t. Then _ x 0^+ x ( [ 1 x ] + [ 2 x ] + + [ 15 x ] )
- Let S = t R : f(x) = |x - | (e^ |x| - 1) |x| is not differentiable at t . Then the set S is equal to :
- If the curves y^2 = 6x, 9x^2 + by^2 = 16 intersect each other at right angles, then the value of b is :
- Let f(x) = x^2 + 1 x^2 and g(x) = x - 1 x , x R - -1, 0, 1 . If h(x) = f(x) g(x) , then the local minimum value of h(x) is
- The integral ^2 x ^2 x ( ^5 x + ^3 x ^2 x + ^3 x ^2 x + ^5 x)^2 ,dx is equal to (where C is a constant of integration)
- The value of _ - /2 ^ /2 ^2 x 1 + 2^x ,dx is :
- Let g(x) = x^2, f(x) = x , and , ( < ) be the roots of the quadratic equation 18x^2 - 9 x + ^2 = 0. Then the area (in sq. units)...
- Let y = y(x) be the solution of the differential equation x dy dx + y x = 4x, x (0, ). If y ( 2 ) = 0, then y ( 6 ) is equal to:
- A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and...
- Let the orthocenter and centroid of a triangle be A(–3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle,...
- If the tangent at (1, 7) to the curve x^2 = y - 6 touches the circle x^2 + y^2 + 16x + 12y + c = 0 then the value of c is:
- Tangent and normal are drawn at P(16, 16) on the parabola y^2 = 16x, which intersect the axis of the parabola at A and B,...
- Tangents are drawn to the hyperbola 4x^2 - y^2 = 36 at the points P and Q. If these tangents intersect at the point T(0, 3) then...