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# Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively.Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be:

$\begin{array}{1 1}(1) 1:16 \\ (2) 4:1 \\(3) 1:4 \\ (4) 5:4 \end{array}$

$N_A$ after 80 minutes $= \large\frac{N}{2^4}$
=> Number of A nuclides decayed $=\large\frac{15}{16} $$N N_B after 80 minutes = \large\frac{N}{2^4} => Number of B nuclides decayed =\large\frac{3}{4}$$N$
Required ratio $= \Large\frac{15/16}{3/4}$
$\qquad= \large\frac{5}{4}$