Practice questions
88551 published questions with worked solutions.
- Let f:(1,3) R be a function defined by f(x)= x[x] 1+x^2 , where [x] denotes the greatest integer x. Then the range of f is :
- Let A and B be two events such that the probability that exactly one of them occurs is 2 5 and the probability that A or B occurs...
- If a hyperbola passes through the point P(10, 16) and it has vertices at (± 6, 0), then the equation of the normal to it at P is :
- The length of the perpendicular from the origin, on the normal to the curve, x^2+2xy-3y^2=0 at the point (2, 2) is :
- Let = -1+i 3 2 . If a=(1+ ) _ k=0 ^ 100 ^ 2k and b= _ k=0 ^ 100 ^ 3k , then a and b are the roots of the quadratic equation :
- The system of linear equations x+2y+2z=5 2 x+3y+5z=8 4x+ y+6z=10 has :
- _ x 0 _0^xt (10t) ,dt x is equal to :
- Let a = i -2 j + k and b = i - j + k be two vectors. If c is a vector such that b c = b a and c a =0, then c b is equal to :
- Let S be the set of all functions f : [0,1] → R, which are continuous on [0,1] and differentiable on (0, 1). Then for every f in...
- If the 10th term of an A.P is 1 20 and its 20th term is 1 10 , then the sum of its first 200 terms is :
- Let S be the set of all real roots of the equation, 3^x(3^x-1)+2=|3^x-1|+|3^x-2|. Then S :
- The differential equation of the family of curves, x^2=4b(y+b), b R, is :
- If a line, y = mx + c is a tangent to the circle, (x-3)^2+y^2=1 and it is perpendicular to a line L_1, where L_1 is the tangent...
- The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation...
- Let a line y = mx (m > 0) intersect the parabola, y^2=x at a point P, other than the origin. Let the tangent to it at P meet the...
- The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is...
- The sum, _ n=1 ^ 7 n(n+1)(2n+1) 4 is equal to ______.
- If 2 1+ 2 = 1 7 and 1- 2 2 = 1 10 , , (0, 2 ), then ( +2 ) is equal to _______.
- Let f(x) be a polynomial of degree 3 such that f(– 1) = 10, f(1) = – 6, f(x) has a critical point at x = – 1 and f '(x) has a...
- A heat engine is involved with exchange of heat of 1915 J, –40 J, +125 J and QJ, during one cycle achieving an efficiency of...