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  4. If P(n):2n < n! Then the smallest positive integer for which P(n) is true if

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Q. If $P(n):2^n < n!$ Then the smallest positive integer for which P(n) is true if

KCETKCET 2020

Solution:

For $n =1,2,3,2^{ n }> n !$
$P(4): 2^{4}<4 !$
So, smallest positive integer, $n =4$.