A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths $${\lambda _A}$$ to $${\lambda _B}$$ after the collision is:

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = $${{\lambda _1}}$$/$${{\lambda _2}}$$, is given by:

A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :

In amplitude modulation, sinusoidal carrier frequency used is denoted by $${\omega _c}$$ and the signal frequency is denoted by $${\omega _m}$$. The bandwidth ($$\Delta {\omega _m}$$) of the signal is such that $$\Delta {\omega _m}$$ < < $$\omega _c$$. Which of the following frequencies is not contained in the modulated wave?