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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2010

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

    A) \[7!\]                                    

    B) \[9!\]

    C) \[6!\]                                    

    D) \[5!\]

    Correct Answer: D

    Solution :

    Given,  \[({{49}^{2}}-4)({{49}^{3}}-49)\] \[=[{{(49)}^{2}}-{{(2)}^{2}}][{{(49)}^{2}}-1].49\] \[=(49+2)(49-2)(49+1)(49-1).49\] \[=51.47.50.48.49\] \[=(51.50.49.48.47)\] Which is the product of the consecutive integers and hence it divisible by 5!


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