$A$ radioactive sample has a half-life of $1500 \ years$. $A$ sealed tube containing $1 \ g$ of the sample will contain after $3000 \ years$:

The rate constant for a radioactive decay reaction is $\lambda$. The average life is represented by:

The half-life of a radioactive isotope is $3 \ hr$. The value of its disintegration constant is: (in $hr^{-1}$)

The half-lives of two radioactive nuclides $A$ and $B$ are $1 \ min$ and $2 \ min$ respectively. Equal weights of $A$ and $B$ are taken separately and allowed to disintegrate for $4 \ min$. What will be the ratio of weights of $A$ and $B$ disintegrated?

The half-life of radioactive $C^{14}$ is $5760 \ years$. In how many years will a $200 \ mg$ sample of $C^{14}$ be reduced to $25 \ mg$?

$A$ radioactive element has a half-life of $200 \ days$. The percentage of original activity remaining after $83 \ days$ is $....$ (Nearest integer).
(Given: $\text{antilog } 0.125 = 1.333$,$\text{antilog } 0.693 = 4.93$)