A radioactive sample decays by $63$% of its initial value in $10s$. It would have decayed by $50$% of its initial value in

Nuclei of a radioactive element $A$ are being produced at a constant rate $\alpha$. The element has a decay constant $\lambda$. At time $t=0$, there are $N_0$ nuclei of the element
(a) Calculate the number $N$ of nuclei of $A$ at time $t$
(b) If $\alpha =2N_0\lambda$, calculate the number of nuclei of $A$ after one half-life of $A$, and also the limiting value of $N$ as $t\to \infty$.