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**JEE Mains**

The activity of a radioactive sample falls from $700s_{−1}$ to $500s_{−1}$ in $30$ minutes. Its half life is close to :

Half lives of two radioactive nuclei $A$ and $B$ are $10$ minutes and $20$ minutes, respectively. If, initially a sample has equal number of nuclei, then after $60$ minutes, the ratio of decayed numbers of nuclei A and B will be:

Two radioactive substances A and B have decay constants $5λ$ and $λ$ respectively. At $t=0$ they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be $(e1 )_{2}$ after a time interval

Two radioactive materials $A$ and $B$ have decay constants $10λ$ and $λ$, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $A$ to that of $B$ will be $1/e$ after a time:

At a given instant, say t = 0, two radioactive substances A and B have equal activities. The ratio $R_{A}R_{B} $ of their activities after time t itself decays with time t as $e_{−3t}.$ If the half-life of A is $ln2$, the half-life of B is:

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At $t=0$ it was $1600$ counts per second and $t=8$ seconds it was $100$ counts per second. The count rate observed, as counts per second, at $t=6$ seconds is close to

Consider the nuclear fission, $Ne_{20}→2He_{4}+C_{12}$

Given that the binding energy/nucleon of $Ne_{20}$, $He_{4}$ and $C_{12}$ are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement:

Given that the binding energy/nucleon of $Ne_{20}$, $He_{4}$ and $C_{12}$ are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement:

At some instant, a radioactive sample $S_{1}$ having an activity $5μCi$ has twice the number of nuclei as another sample $S_{2}$ which has an activity of $10μCi$. The half lives of $S_{1}$ and $S_{2}$ are

A solution containing active cobalt $_{27}Co$ having activity of $0.8μCi$ and decay constant $λ$ is injected in an animal's body. If $1cm_{3}$ of blood is drawn from the animal's body after $10$ hrs of injection, the activity found was $300$ decays per minute. What is the volume of blood that is flowing in the body? ($1Ci=3.7×10_{10}$ decay per second and at $t=10hrs$ $e_{−λt}=0.84$)