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Question: Answered & Verified by Expert
The greatest integer which divides $(p+1)(p+2)(p+3) \ldots(p+q)$ for all
$p \in N$ and fixed $q \in N$ is
MathematicsPermutation CombinationWBJEEWBJEE 2017
Options:
  • A $p !$
  • B $q !$
  • C $p$
  • D $q$
Solution:
1790 Upvotes Verified Answer
The correct answer is: $q !$
$(p+1)(p+2)(p+3) \ldots(p+q)$ is the product of $q$ consecutive natural number ( $R$ q e $N$ ) The product of $q$ consecutive natural number is always divisible by $q!$

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