Number of nuclei of a radioactive substance at time $t = 0$ are $1000$ and $900$ at time $t = 2$ $s$. Then number of nuclei at time $t = 4$ $s$ will be

The rate of disintegration of fixed quantity of a radioactive element can be increased by

After two hours, one- sixteenth of the starting amount of a certain radioactive isotope remained undecayed. The half life of the isotope is

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as:

(where $\lambda$ is the decay constant)

Two radioactive nuclei $P$ and $Q,$ in a given sample decay into a stable nucleus $R.$ At time $t = 0,$ number of $P$ species are $4\,\, N_0$ and that of $Q$ are $N_0$. Half-life of $P$ (for conversion to $R$) is $1$ minute where as that of $Q$ is $2$ minutes. Initially there are no nuclei of $R$ present in the sample. When number of nuclei of $P$ and $Q$ are equal, the number of nuclei of $R$ present in the sample would be