Question

If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.

Find : $\textstyle\int$$\frac{d x}{\sqrt{3-2\,x-x^{2}}}$

Find : $\textstyle\int$$\frac{x}{\sqrt{32-x^{2}}}\,d x$

A balloon, which always remains spherical, has a variable diameter ${\frac{2}{3}}(3x+1)$ . Find the rate of change of its volume with respect to x.

Find the integrating factor of the differential equation ${\frac{d y}{d x}}+y\ =\ {\frac{1+y}{x}}$

How many equivalence relations on the set {1, 2, 3} containing (1, 2) and (2, 1) are there in all ?Justify your answer.

The radius r of a right circular cylinder is decreasing at the rate of 3 cm/min. and its height h is increasing at the rate of 2 cm/min. When r =7 cm and h = 2 cm, find the rate of change of the volume of cylinder. $[\mathrm{Use}\:\pi=\:\frac{22}{7}\:]$