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

  • question_answer
    If \[n\in N\], then \[{{11}^{n+2}}+{{12}^{2n+1}}\] is divisible by

    A) 113

    B) 123

    C) 133

    D) None of these

    Correct Answer: C

    Solution :

    [c] Putting \[n=1\] in \[{{11}^{n+2}}+{{12}^{2n+1}}\] We get, \[{{11}^{1+2}}+{{12}^{2\times 1+1}}={{11}^{3}}+{{12}^{3}}=3059,\] which is divisible by 133.


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