Mathematics Tes...

If the vectors  = 5i - 2j + 4k are the sides of a triangle ABC, then the length of the median through A is

If ∫f (x) dx =Ψ(x) , then ∫x⁵f(x³) dx is equal to

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

The circle passing through (1, −2) and touching the axis of x at (3, 0) also passes through the point

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

The expression tan [A / (1 - cot A)] + [cot A / (1 - tan A)] can be written as

If y = sec(tan^-1x), then dy/dx at x = 1 is equal to

The equation of the circle passing through the foci of the ellipse x²/16 + y²/9 = 1 , and having centre at (0, 3) is