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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Mathematical induction and Divisibility problems

  • question_answer
    \[{{10}^{n}}+3\,({{4}^{n+2}})+5\] is divisible by \[(n\in N)\][Kerala (Engg.) 2005]

    A) 7

    B) 5

    C) 9

    D) 17

    E) 13

    Correct Answer: C

    Solution :

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


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