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

  • question_answer
    \[{{10}^{n}}+3({{4}^{n+2}})+5\] is divisible by \[(n\in N)\]

    A) 7

    B) 5

    C) 9

    D) 17

    Correct Answer: C

    Solution :

    [c] \[{{10}^{n}}+3({{4}^{n+2}})+5\] Taking \[n=2;{{10}^{2}}+3\times {{4}^{4}}+5\] \[=100+768+5=873\] Therefore this is divisible by 9.


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