Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass $${m \over 4}$$ . The ratio of the specific heats ($$C_V^A$$ and $$C_V^B$$ ) of gas A and B, respectively is :

If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is :

A vessel of depth 2h is half filled with a liquid of refractive index $$2\sqrt 2 $$ and the upper half with another liquid of refractive index $$\sqrt 2 $$ . The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be :

The aperture diameter of a telescope is 5m. The separation between the moon and the earth is 4 × 10⁵ km. With light of wavelength of 5500 $$\mathop A\limits^o $$, the minimum separation between objects on the surface of moon, so that they are just resolved, is close to :