Let $p(x)$ be a real polynomial of least degree which has a local maximum at $x=1$ and a local minimum at $x=3$. If $p(1)=6$ and $p(3)=2$, then $p^{\prime}(0)$ is equal to :

The velocity-time graph for a body of mass 10 kg is shown in the figure. Work done on the body in the first two seconds of motion is :

For a domestic AC supply of 220 V at 50 cycles per sec, the potential difference between the terminals of a two-pin electric outlet in a room is given by

A radioactive nucleus decays as follows :

$$ X \xrightarrow{\alpha} X_1 \xrightarrow{\beta} X_2 \xrightarrow{\alpha} X_3 \xrightarrow{\gamma} X_4 $$

If the mass number and atomic number of ' $X_4$ ' are 172 and 69 respectively, then the atomic number and mass number of ' $X$ ' are