CBSE[Delhi]_XII_Mathematics_2017_Set-1

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

If A is a 3 x 3 invertible matrix, then what will be the value of k if det(A^-1) = (det A)^k.

Determine the value of the constant ‘k’ so that the function:

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

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

Show that the function f(x)=4x³–18x²+27x–7 is always increasing on R.

Find the vector equation of the line passing through the point A (1, 2, -1) and parallel to the line 5x-25=14-7y=35z.

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