Two bodies $$A$$ and $$B$$ of same mass undergo completely inelastic one dimensional collision. The body $$A$$ moves with velocity $$v_1$$ while body $$B$$ is at rest before collision. The velocity of the system after collision is $$v_2$$. The ratio $$v_1: v_2$$ is

$$ { }_{82}^{290} X \xrightarrow{\alpha} Y \xrightarrow{e^{+}} Z \xrightarrow{\beta^{-}} P \xrightarrow{e^{-}} Q $$

In the nuclear emission stated above, the mass number and atomic number of the product $$Q$$ respectively, are

If $$x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \mathrm{m}$$ represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are

A thin flat circular disc of radius $$4.5 \mathrm{~cm}$$ is placed gently over the surface of water. If surface tension of water is $$0.07 \mathrm{~N} \mathrm{~m}^{-1}$$, then the excess force required to take it away from the surface is