Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationFundamental PrincipleMedium2 minQB

MathematicsMediumsingle choice

Number of positive integer $n$ , less than 17 , for which $n! + (n + 1)! + (n + 2)$ ! is an integral multiple of 49 is

Answer:

Solution:

$n! + (n + 1)! + (n + 2)! = n! (n + 2)^{2}$

⇒ Either 7 divides $(n + 2)$ or 49 devides n !

$\Rightarrow n = 5, 12, 14, 15, 16$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Fundamental Principle

⏱ 2mℹ️ Source: QB

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