A capacitor of capacitance $$50 \mu \mathrm{F}$$ is connected to a.c. source $$\mathrm{e}=220 \sin 50 \mathrm{t}$$ ($$\mathrm{e}$$ in volt, $$\mathrm{t}$$ in second). The value of peak current is

Two waves are superimposed whose ratio of intensities is $$9: 1$$. The ratio of maximum and minimum intensity is

The masses and radii of the moon and the earth are $$\mathrm{M_1, R_1}$$ and $$\mathrm{M_2, R_2}$$ respectively. Their centres are at a distance $$\mathrm{d}$$ apart. What should be the minimum speed with which a body of mass '$$m$$' should be projected from a point midway between their centres, so as to escape to infinity?

A monoatomic gas $$\left(\gamma=\frac{5}{3}\right)$$ initially at $$27^{\circ} \mathrm{C}$$ having volume '$$\mathrm{V}$$' is suddenly compressed to one-eighth of its original volume $$\left(\frac{\mathrm{V}}{8}\right)$$. After the compression its temperature becomes