Two moles of helium are mixed with n moles of hydrogen. If $${{Cp} \over {Cv}} = {3 \over 2}$$ for the mixture, then the value of n is :

A particle executes simple harmonic motion and is located at x = a, b and c at times t₀, 2t₀ and 3t₀ respectively. The freqquency of the oscillation is :

A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let P₂ be the pressure inside the inner bubble and P₀, the pressure outside the outer bubble. Radius of another bubble with pressure difference P₂ $$-$$ P₀ between its inside and outside would be :

An oscillator of mass M is at rest in its equilibrium position in a potential
V = $${1 \over 2}$$ k(x $$-$$ X)². A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 13 collisions is : (M = 10, m = 5, u = 1, k = 1)