Question

If E and F be two events such that P(E) = 1/3, P(F) = 1/4, find P(E U F) if E and F are independent events.

Find the inverse of the matrix $\left(\begin{array}{l l }-3 & 2 \\ 5 & -3\end{array}\right)$ Hence, find the matrix P satisfying the matrix equation P$\left(\begin{array}{l l }-3 & 2 \\ 5 & -3\end{array}\right)$ = $\left(\begin{array}{l l }1 & 2 \\ 2 & -1\end{array}\right)$ .

Verify that ax² + by² = 1 is a solution of differential equation $x(y y_{2}+y_{1}^{2})=y y_{1}.$

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

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.

Find : $\textstyle\int{\frac{d x}{x^{2}+4x+8}}$