Question

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

Three cards are drawn without replacement from a pack of 52 cards. Find the probability that (i) the cards drawn are king, queen and jack respectively. (ii) the cards drawn are king, queen and jack.

Find : $\textstyle\int$$\frac{d x}{5-8\,x-x^{2}}$

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].

If A and B are two independent events, then prove that the probability of occurrence of at least one of A and B is given by 1 – P(A’) · P(B’)

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

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.