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.

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.

If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.

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 the sum of the order and the degree of the following differential equations : ${\frac{d^{2}y}{d x^{2}}}+{3{\sqrt\frac{{d y}}{d x}}}+(1+x)=0$

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

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