A regular hexagon of side 6 cm has a charge of $2 \mu \mathrm{C}$ at each of its vertices, what is the potential at the centre of the hexagon?

$$ \left[\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text { SI unit }\right] $$

For two different photosensitive materials having work function $\phi$ and $2 \phi$ respectively, are illuminated with light of sufficient energy to emit electrons. If the graph of stopping potential versus frequency is drawn, for these two different photosensitive materials, the ratio of slope of graph for these two materials is

The weight of man in a stationary lift is $w_1$ and when it is moving downwards with uniform acceleration ' a ' is $\mathrm{w}_2$. If the ratio $\mathrm{w}_1: \mathrm{w}_2=4: 3$, then the value of ' a ' is ( $\mathrm{g}=$ acceleration due to gravity)

The activity of radioactive sample is measured as $\mathrm{N}_0$ counts per minute at time $\mathrm{t}=0$, and $\frac{\mathrm{N}_0}{\mathrm{e}}$ counts per minute at time $\mathrm{t}=3$ minute, The activity reduces to half its value in time (in minute)