Practice questions
88551 published questions with worked solutions.
- Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and...
- If the coefficients of x^3 and x^4 in the expansion of (1 + ax + bx^2)(1 - 2x)^ 18 in powers of x are both zero, then (a, b) is...
- If z is a complex number such that |z| 2, then the minimum value of |z + 1 2 |:
- The integral (1 + x - 1 x )e^ x + 1 x ,dx is equal to
- The slope of the line touching both the parabolas y^2 = 4x and x^2 = -32y is
- If [ a b b c c a ] = [ a b c ]^2 then is equal to:
- Let A and B be two events such that P( A B ) = 1 6 , P(A B) = 1 4 and P( A ) = 1 4 , where A stands for the complement of the...
- The locus of the foot of perpendicular drawn from the centre of the ellipse x^2 + 3y^2 = 6 on any tangent to it is:
- If f and g are differentiable functions in [0, 1] satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some c ]0, 1[:
- Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the...
- If g is the inverse of a function f and f'(x) = 1 1 + x^5 , then g'(x) is equal to:
- If , 0, and f(n) = ^n + ^n and vmatrix 3 & 1 + f(1) & 1 + f(2) 1 + f(1) & 1 + f(2) & 1 + f(3) 1 + f(2) & 1 + f(3) & 1 + f(4)...
- If (10)^9 + 2(11)^1(10)^8 + 3(11)^2(10)^7 + + 10(11)^9 = k(10)^9, then k is equal to:
- The angle between the lines whose direction cosines satisfy the equations + m + n = 0 and ^2 = m^2 + n^2 is -
- The variance of first 50 even natural numbers is:
- If X = 4^n - 3n - 1 : n N and Y = 9(n - 1) : n N , where N is the set of natural numbers, then X Y is equal to:
- The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature...
- The radiation corresponding to 3 2 transition of hydrogen atom falls on a metal surface to produce photoelectrons. These...
- A bob of mass m attached to an inextensible string of length is suspended from a vertical support. The bob rotates in a...
- A thin convex lens made from crown glass ( = 3 2 ) has focal length f. When it is measured in two different liquids having...