If A is an invertible matrix, then what will be the value of k if

Determine the value of the constant ‘k’ so that the function is continuous at

Evaluate:

If a line makes angle 90^{o} and 60^{o} respectively with the positive directions of x and y-axes, find the angle which it makes with the positive direction z-axis.

Show that all the diagonal elements of a skew-symmetric matrix are zero.

Find at if

The volume of a sphere is increasing at the rate of 3 cubic centimetre per second. Find the rate of increase of its surface area, when the radius is 2 cm.

Show that the function f(x) = 4x^{3} − 18x^{2} + 27x − 7 is always increasing on IR.

Find the vector equation of the line passing through point A(1, 2, -1) and parallel to the line

Prove that if E and F are independent events, then the events E and F are also independent.