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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Expansion of binomial theorem

  • question_answer
    The value of \[{{(\sqrt{5}+1)}^{5}}-{{(\sqrt{5}-1)}^{5}}\]is [MP PET 1985]

    A) 252

    B) 352

    C) 452

    D) 532

    Correct Answer: B

    Solution :

    \[{{(\sqrt{5}+1)}^{5}}-{{(\sqrt{5}-1)}^{5}}\] \[=2\left\{ ^{5}{{C}_{1}}{{(\sqrt{5})}^{4}}{{+}^{5}}{{C}_{3}}{{(\sqrt{5})}^{2}}{{+}^{5}}{{C}_{5}}.1 \right\}=352\]


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