The number of nuclei of a radioactive substance is $1000$ and $900$ at times $t = 0$ and $t = 2 \ s$,respectively. Then,the number of nuclei at time $t = 4 \ s$ will be:

The disintegration rate of a certain radioactive sample at any instant is $4250$ disintegrations per minute. $10$ minutes later,the rate becomes $2250$ disintegrations per minute. The approximate decay constant is $......... \min^{-1}$.

The half-life of a radioactive substance is $5$ years. What is the probability of decay of this element in $10$ years?

The masses of two radioactive substances are same and their half-lives are $1 \ yr$ and $2 \ yr$ respectively. The ratio of their activities after $4 \ yr$ will be

The radioactivity of a sample is $R_1$ at a time $T_1$ and $R_2$ at a time $T_2$. If the half-life of the specimen is $T$,then the number of atoms that have disintegrated in the time interval $(T_2 - T_1)$ is proportional to

The half-life of a radioactive element $X$ is equal to the mean life of another radioactive element $Y$. Initially, the number of atoms for both is the same. Then: