JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • question_answer
    Let P be a prime number such that \[p\ge 11.\] Let \[n=p!+1.\] The number of primes in the list \[n+1,\] \[n+2,n+3,...n+P-1,\] is

    A) \[p-1\]

    B) 2

    C) 1

    D) None of these

    Correct Answer: D

    Solution :

    [d] For \[1\le i\le p-1,\,\,p!\] is divisible by \[(i+1)\] Thus, \[n+i=p!+(i+1)\]is divisible by \[(i+1)\] for \[1\le i\le p-1\] \[\therefore \] None of \[n+1,\,\,\,n+2,...n+p-1\] is prime.

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