Practice questions
88551 published questions with worked solutions.
- If x = 5 12 for some x ( , 3 2 ), then 7x ( 13x 2 + 13x 2 ) + 7x ( 13x 2 - 13x 2 ) is equal to
- Let f(t) = ( 1- ( _e t) 1- ( _e t) )dt, t>1. If f(e^ /2 ) = -e^ /2 and f(e^ /4 ) = e^ /4 , then equals
- Let R be a relation defined on the set 1,2,3,4 1,2,3,4 by R = ((a,b),(c,d)): 2a+3b = 3c+4d . Then the number of elements in R is
- Let A(1,0), B(2,-1) and C ( 7 3 , 4 3 ) be three points. If the equation of the bisector of the angle ABC is x + y = 5, then the...
- Let S = 1 25! + 1 3!23! + 1 5!21! + up to 13 terms. If 13S = 2^k n! , k N, then n+k is equal to
- Consider an A.P.: a_1, a_2, , a_n; a_1>0. If a_2 - a_1 = -3 4 , a_n = 1 4 a_1, and _ i=1 ^ n a_i = 525 2 , then _ i=1 ^ 17 a_i is...
- Let , R be such that the function f(x) = cases 2 (x^2-2)+2 x, & x<1 ( +3)x+( - ), & x 1 cases be differentiable at all x R . Then...
- The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation in this data is replaced by ,...
- The number of the real solutions of the equation : x|x+3|+|x-1|-2=0 is
- Let a line L passing through the point P(1,1,1) be perpendicular to the lines x-4 4 = y-1 1 = z-1 1 and x-17 1 = y-71 1 = z 0 ....
- The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0,1,2,5,9, if the...
- The number of 3 2 matrices A, which can be formed using the elements of the set -2,-1,0,1,2 such that the sum of all the diagonal...
- Three charges +2q, +3q and -4q are situated at (0,-3a), (2a,0) and (-2a,0) respectively in the xy plane. The resultant dipole...
- A cylindrical block of mass M and area of cross section A is floating in a liquid of density and with its axis vertical. When...
- Density of water at 4^ C and 20^ C are 1000 kg/m ^3 and respectively. The increase in internal energy of 4 kg water when it is...
- Two resistors of 100 each are connected in series with a 9 V battery. A voltmeter of 400 resistance is connected to measure the...
- The exit surface of a prism with refractive index n is coated with a material having refractive index n/2. When this prism is set...
- In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm. Total magnification...
- A spring of force constant 15 N/m is cut into two pieces. If the ratio of their length is 1:3, then the force constant of smaller...
- Given below are two statements: Statement I: For all elements, greater the mass of the nucleus, greater is the binding energy per...