Nuclei question for NEET / JEE Main, with solution

Answer: (C) $\dfrac{1}{e}$

Concept. $N = N_0e^{-\lambda t}$, and the mean life is $\tau = \dfrac{1}{\lambda}$.

Step 1. Substitute $t = \tau$.
$$\frac{N}{N_0} = e^{-\lambda \cdot 1/\lambda} = e^{-1} \approx 0.37$$

Answer. $\dfrac1e$ (Option C).

Solution by Sreeraj P, M.Sc Physics