$A$ mixture consists of two radioactive materials $A_1$ and $A_2$ with half-lives of $20 \ s$ and $10 \ s$ respectively. Initially,the mixture has $40 \ g$ of $A_1$ and $160 \ g$ of $A_2$. The amount of the two in the mixture will become equal after: (in $s$)

$A$ radioactive sample has an average life of $30 \, ms$ and is decaying. $A$ capacitor of capacitance $200 \, \mu F$ is first charged and later connected with a resistor $R$. If the ratio of charge on the capacitor to the activity of the radioactive sample is fixed with respect to time,then the value of $R$ should be $.... \, \Omega$.

The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at time $t_2$. If $\lambda$ is the decay constant,then which of the following is correct?

The sample of a radioactive substance has $10^6$ nuclei. Its half-life is $20 \, s$. The number of nuclei that will be left after $10 \, s$ is nearly ...... $\times 10^5$.

In a radioactive element,the fraction of the initial amount remaining after its mean lifetime is:

The counting rate observed from a radioactive source at $t=0$ second was $1600$ counts per second and at $t=8$ seconds it was $100$ counts per second. The counting rate observed,as counts per second at $t=6$ seconds,will be