The temperature of a gas is $-80^{\circ} \mathrm{C}$. To what temperature the gas should be heated so that the r.m.s. speed is increased by 2 times?

Two wavelength 590 nm and 596 nm of sodium light are used one after other, to study the diffraction taking place at a single slit of aperture 2.4 mm . The distance between the slit and screen is 2 m . The separation between the positions of first secondary maximum of the diffraction pattern obtained in the two cases is

For the diagram shown, the resistance between points A and B when the ideal diode ' $D$ ' is forward biased is ' $R_1$ ' and that when reverse biased is ' $R_2$ '. The ratio $\frac{R_1}{R_2}$ is

A parallel plate capacitor of capacitance ' $C$ ' is connected to a battery and charged to a potential difference ' $V$ '. Another capacitor of capacitance 3 C is similarly charged to a potential difference 3 V . The charging battery is then disconnected and capacitors are connected in parallel to each other in such a way that positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is