Q42 / 155 · WBJEE 2017 · Mathematics

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

  • A
    $p !$
  • Correct answer
    B
    $q !$
  • C
    $p$
  • D
    $q$

Solution

$(p+1)(p+2)(p+3) \ldots(p+q)$ is the product of $q$ consecutive natural number ( $R$ q e $N$ ) The product of $q$ consecutive natural number is always divisible by $q!$

Hence, the correct answer is option: 'B'.

More Permutation Combination Questions