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Two identical samples (same material and same amount initially) P and Q of a radioactive substance having mean life \( T \) are observed to have activities \( A_{P} \& A_{Q} \) respectively at the time of observation. If \( P \) is older than \( \mathrm{Q} \), then the difference in their ages is:
(A) \( T \ell n\left(\frac{A_{P}}{A_{Q}}\right) \)
(B) \( T \ell n\left(\frac{A_{Q}}{A_{P}}\right) \)
(C) \( \frac{1}{T} \ln \left(\frac{A_{P}}{A_{Q}}\right) \)
(D) \( \mathrm{T}\left(\frac{A_{P}}{A_{Q}}\right) \)
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