$A$ radioactive nucleus (initial mass number $A$ and atomic number $Z$) emits $3 \,\alpha-$ particles and $2$ positrons. The ratio of the number of neutrons to that of protons in the final nucleus will be:

Explain the structures of diborane and boric acid.

The normal freezing point $(f.p.)$ of nitrobenzene is $278.82\, K$. If a non-volatile solute is dissolved in it and a solution of $0.25\, m$ (molality) is prepared,the observed $f.p.$ of the solution is $276.82\, K$. Evaluate $K_f$ of nitrobenzene in $K\, kg\, mol^{-1}$.

The compound,found in nature in gas phase but ionic in solid state is

$A$ galvanometer of resistance $50\,\Omega$ is connected to a battery of $3\,V$ along with a resistance of $2950\,\Omega$ in series. $A$ full-scale deflection of $30$ divisions is obtained in the galvanometer. In order to reduce this deflection to $20$ divisions,the resistance in series should be.......$\Omega$.

$A$ certain radioactive substance reduces to $25\%$ of its initial value in $16$ days. Its half-life is ........ $days$.