Practice questions
88551 published questions with worked solutions.
- Let a = i + 2 j + k and b = 2 i + j - k . Let c be a unit vector in the plane of the vector a and b and be perpendicular to a ....
- Let the value of for which the shortest distance between the lines x-1 2 = y-2 3 = z-3 4 and x- 3 = y-4 4 = z-5 5 is 1 6 be _1...
- Let A = 0, 1, 2, 3, 4, 5 . Let R be a relation on A defined by (x, y) R if and only if max x, y 3, 4 . Then among the statements...
- If 1 1^4 + 1 2^4 + 1 3^4 +....... = ^4 90 , 1 1^4 + 1 3^4 + 1 5^4 +....... = 1 2^4 + 1 4^4 + 1 6^4 +....... = Then is equal to
- Let the function f(x) = x 3 + 3 x +3, x 0 be strictly increasing in (- , _1) ( _2, ) and strictly decreasing in ( _3, _4) ( _4,...
- Let f(x) = x - 1 and g(x) = e^x for x R. If dy dx = (e^ -2 x g(f(f(x))) - y x ), y(0) = 0, then y(1) is
- The sum of the squares of the roots of |x-2|^2 + |x-2| - 2 = 0 and the squares of the roots of x^2 - 2|x-3| - 5 = 0, is
- Let f(x) be a positive function and I_1 = _ - 1 2 ^ 1 2xf(2x(1-2x))dx and I_2 = _ -1 ^ 2 f(x(1-x))dx. Then the value of I_2 I_1...
- The number of integral terms in the expansion of (5^ 1 2 + 7^ 1 8 )^ 1016 is
- Let be a solution of x^2 + x + 1 = 0, and for some a and b in R, [4 a b] bmatrix 1 & 16 & 13 -1 & -1 & 2 -2 & -14 & -8 bmatrix =...
- Let the domain of the function f(x) = ^ -1 ( 4x+5 3x-7 ) be [ , ] and the domain of g(x) = _2(2 - 6 _ 27 (2x+5)) be ( , ). Then...
- Let the area of the triangle formed by the lines x+2 = y-1 = z, x-3 5 = y -1 = z-1 1 and x -3 = y-3 3 = z-2 1 be A. Then A^2 is...
- A rod of linear mass density ' ' and length 'L' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its...
- In a young's double slit experiment, the source is white light. One of the slits is covered by red filter and another by a green...
- For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as
- A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm...
- A quantity Q is formulated as X^ -2 Y^ 3 2 Z^ - 2 5 . X, Y and Z are independent parameters which have fractional errors of 0.1,...
- A monoatomic gas having = 5 3 is stored in a thermally insulated container and the gas is suddenly compressed to ( 1 8 )^ th of...
- Two strings with circular cross section and made of same material are stretched to have same amount of tension. A transverse wave...
- An infinitely long wire has uniform linear charge density = 2nC/m. The net flux through a Gaussian cube of side length 3 cm, if...