A radioactive nucleus A has a single decay mode with half life $\tau_{\mathrm{A}}$. Another radioactive nucleus $\mathrm{B}$ has two decay modes 1 and 2. If decay mode 2 were absent, the half life of $\mathrm{B}$ would have been $\tau_{\mathrm{A}} / 2$. If decay mode 1 were absent, the half life of $\mathrm{B}$ would have been $3 \tau_{\mathrm{A}}$, then the ratio $\tau_{\mathrm{B}} / \tau_{\mathrm{A}}$ is-

• Correct answer
  A

  $3 / 7$
• B

  $7 / 2$
• C

  $7 / 3$
• D

  1

Hence, the correct answer is option: 'A'.