JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Mock Test - Principle of Mathematical Induction

  • question_answer
    The number \[({{49}^{2}}-4)({{49}^{3}}-49)\]is divisible by__

    A) 6!                   

    B) 5!

    C) 7!                   

    D) 9!

    Correct Answer: B

    Solution :

    [b] Given expression = \[({{49}^{2}}-{{2}^{2}})\times 49({{49}^{2}}-1)\]\[=51\times 47\times 49\times 50\times 48\]\[=51\times 50\times 49\times 48\times 47\] Is the product of five consecutive integers. Hence it is divisible by 5!


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