Question

If E and F are independent events, then show that (i) E and F' are independent events. (ii) E' and F are also independent events.

Find : $\textstyle\int$${\frac{\left(x^{4}-x\right)^{\frac{1}{4}}}{x^{5}}}\,.$

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.

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

Show that the function f(x) = x³ – 3x² + 6x – 100 is increasing on R.

If P(A) = 0.6, P(B) = 0.5 and P(A|B) = 0.3, then find P(A ∪ B).

The volume of a sphere is increasing at the rate of 8 cm³/sec. Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm.