Question

A die is rolled. If E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5}, find (a) P(E U F)/G] (b)P [(E ∩ F)/G].

A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green, is tossed. Let A be the event “number obtained is even” and B be the event “number obtained is red”. Find if A and B are independent events.

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

The length x, of a rectangle is decreasing at the rate of 5 cm/minute and the width y, is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rate of change of the area of the rectangle.

The radius r of the base of a right circular cone is decreasing at the rate of 2 cm/min. and height h is increasing at the rate of 3 cm/min. When r = 3.5 cm and h = 6 cm, find the rate of change of the volume of the cone. $[\mathrm{Use}\:\pi=\:\frac{22}{7}\:]$

if $|\stackrel{\rightarrow}{a}+\stackrel{\rightarrow}{b}|$ =60, $|\stackrel{\rightarrow}{a}-\stackrel{\rightarrow}{b}|$=40 and $\stackrel{\rightarrow}{a}\$=22,then find $\stackrel{\rightarrow}{b}\$.

If E and F are two events such that P(E) = 1/4, P(F) = 1/2 and P(E ∩ F) = 1/8, find (i) P(E or F) (ii) P(not E and not F).