A monoatomic ideal gas, initially at temperature T₁ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T₂ by releasing the piston suddenly. If l₁ and l₂ are the lengths of the gas column, before and after the expansion respectively, then the value of $${{{T_1}} \over {{T_2}}}$$ will be :

A ray of laser of a wavelength 630 nm is incident at an angle of 30$$^\circ$$ at the diamond-air interface. It is going from diamond to air. The refractive index of diamond is 2.42 and that of air is 1. Choose the correct option.

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y₁ and Y₂. The combination behaves as a single wire then its Young's modulus is :

The half-life of $${}^{198}Au$$ is 3 days. If atomic weight of $${}^{198}Au$$ is 198 g/mol then the activity of 2 mg of $${}^{198}Au$$ is [in disintegration/second] :