Question

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 the general solution of the differential equation ${\frac{d y}{d x}}+2y=e^{3x}$

Find the general solution of the differential equation ${\frac{d y}{d x}}+{\frac{2}{x}}y=x$

If P(E) = 7/13, P(F) = 9/3 and P(E' / F') = 4/3, then evaluate : (i) P(E / F) (ii) P(E / F)

The radius r of a right circular cylinder is increasing uniformly at the rate of 0.3 cm/s and its height h is decreasing at the rate of 0.4 cm/s. When r = 3.5 cm and h = 7 cm, find the rate of change of the curved surface area of the cylinder. $[\mathrm{Use}\:\pi=\:\frac{22}{7}\:]$

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.

Show that the solution of differential equation : $y=2(x^{2}-1)+c e^{-x^{2}}\,\mathrm{is}\,\frac{d y}{d x}+2x y-4x^{3}=0$