Question

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

Find the general solution of the differential equation ${\frac{d y}{d x}}+{\frac{2}{x}}y=x$

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. $[\mathrm{Use}\:\pi=\:\frac{22}{7}\:]$

If P(E) = 6/11, P(F) = 5/11 and P(E ∪ F) = 7/11 then find (i) P(E/F) (ii) P(F/E)

Find : $\textstyle\int$${\frac{e^{x}(x-3)}{(x-1)^{3}}}d x\,.$

A couple has 2 children. Find the probability that both are boys, if it is known that (i) one of them is a boy (ii) the older child is a boy.

If P(E) = 7/13, P(F) = 9/3 and P(E' / F') = 4/3, then evaluate : (i) P(E / F) (ii) P(E / F)