Question

If P(A) = 0.4, P(B) = p, P(A U B) = 0.6 and A and B are given to the independent events, find the value of ‘p’.

The volume of a cube is increasing at the rate of 9 cm³/sec. How fast is the surface area increasing when the length of an edge is 10 cm.

The total revenue received from the sale of x units of a product is given by R(x) = 3x² + 36x + 5 in rupees. Find the marginal revenue when x = 5, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant.

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

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

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

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.