Practice questions
88551 published questions with worked solutions.
- The length of the minor axis (along y-axis) of an ellipse in the standard form is 4 3 . If this ellipse touches the line, x + 6y...
- If x=2 - 2 and y=2 - 2 , [0,2 ], then d^2y dx^2 at = is -
- If dy dx = xy x^2+y^2 ; y(1) = 1; then a value of x satisfying y(x) = e is -
- Let a – 2b + c = 1. If f(x)= vmatrix x+a & x+2 & x+1 x+b & x+3 & x+2 x+c & x+4 & x+3 vmatrix , then -
- If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain...
- The following system of linear equations 7x+6y-2z=0 3x+4y+2z=0 x-2y-6z=0, has
- If one end of a focal chord AB of the parabola y^2=8x is at A ( 1 2 ,-2 ), then the equation of the tangent to it at B is -
- Let f and g be differentiable functions on R such that fog is the identity function. If for some a, b R, g'(a) = 5 and g(a) = b,...
- If the distance between the plane, 23x – 10y – 2z + 48 = 0 and the plane containing the lines x+1 2 = y-3 4 = z+1 3 and x+3 2 =...
- If C_r= ^ 25 C_r and C_0+5 C_1+9 C_2+ +(101) C_ 25 =2^ 25 k, then k is equal to ___________.
- The number of terms common to the two A.P.'s 3, 7, 11, ….. 407 and 2, 9, 16, …. 709 is ___________.
- If the curves, x^2-6x+y^2+8=0 and x^2-8y+y^2+16-k=0, (k > 0) touch each other at a point, then the largest value of k is...
- Let a , b and c be three vectors such that | a |= 3 , | b |=5, b c =10 and the angle between b and c is 3 . If a is perpendicular...
- If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the...
- Radiation, with wavelength 6561 Å falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform...
- Two particals of equal mass m have respective initial velocities u i and u ( i + j 2 ). They collide completely inelastically....
- A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass m 2 collides with A with a...
- A quantity f is given by f= hc^5 G where c is speed of light, G universal gravitational constant of light and h is the Planck's...
- A long, straight wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic...
- An electric dipole of moment p =(- i -3 j +2 k ) 10^ -29 C.m is at the origin (0, 0, 0). The electric field due to this dipole at...