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

In positive beta decay a proton is transformed into a neutron and a positron is emitted. $$ \mathrm{p}^{+} \longrightarrow \mathrm{n}^0+\mathrm{e}^{+} $$ no. of neutrons initially was $A-Z$ no. of neutrons after decay $(A-Z)-3 \times 2$ (due to alpha particles) $+2 \times 1$ (due to positive beta decay) The no. of proton will reduce by 8 . [as $3 \times 2$ (due to alpha particles) $+2$ (due to positive beta decay)] Hence atomic number reduces by 8 .