JEE MAIN - Mathematics (2023 - 25th January Evening Shift - No. 4)
Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that $$N-2,\sqrt{3N},N+2$$ are in geometric progression be $$\frac{k}{48}$$. Then the value of k is :
8
16
2
4
Explanation
$n-2, \sqrt{3 n}, n+2 \rightarrow$ G.P.
$3 n=n^{2}-4$
$\Rightarrow n^{2}-3 n-4=0$
$\Rightarrow n=4,-1$ (rejected)
$P(S=4)=\frac{3}{36}=\frac{1}{12}=\frac{4}{48}$
$\therefore k=4$
$3 n=n^{2}-4$
$\Rightarrow n^{2}-3 n-4=0$
$\Rightarrow n=4,-1$ (rejected)
$P(S=4)=\frac{3}{36}=\frac{1}{12}=\frac{4}{48}$
$\therefore k=4$
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