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Samples of two radioactive nuclides $\mathrm{A}$ and $\mathrm{B}$ are taken $\lambda_{\mathrm{A}}$ and $\lambda_{\mathrm{B}}$ are the disintegration constants of $\mathrm{A}$ and $\mathrm{B}$ respectively. In which of the following cases, the two samples can simultaneously have the same decay rate at any time?
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Initial rate of decay of $\mathrm{A}$ is twice the initial rate of decay of $B$ and $\lambda_{\mathrm{A}}>\lambda_{\mathrm{B}}$
, Initial rate of decay of $\mathrm{B}$ is same as the rate of decay of $\mathrm{A}$ at $\mathrm{t}=2 \mathrm{~h}$ and $\lambda_{\mathrm{B}} < \lambda_{\mathrm{A}}$
Initial rate of decay of $\mathrm{A}$ is twice the initial rate of decay of $B$ and $\lambda_{\mathrm{A}}>\lambda_{\mathrm{B}}$
, Initial rate of decay of $\mathrm{B}$ is same as the rate of decay of $\mathrm{A}$ at $\mathrm{t}=2 \mathrm{~h}$ and $\lambda_{\mathrm{B}} < \lambda_{\mathrm{A}}$
The two radioactive samples of the two nuclides A and $\mathrm{B}$ can have the same rate of decay at any time, if the initial rate of decay of $A$ istwiœ of decay of $B$ and $\lambda_A>\lambda_B$. So, initial rate of decay of $B$ is same as rate of decay of $A$ at $\mathrm{t}=2 \mathrm{~h}$ and decay rate can be same if $\lambda_{\mathrm{A}}>\lambda_{\mathrm{B}}$.
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