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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Binomial theorem for any index

  • question_answer
    The expression \[{{[x+{{({{x}^{3}}-1)}^{1/2}}]}^{5}}+{{[x-{{({{x}^{3}}-1)}^{1/2}}]}^{5}}\] is a polynomial of degree [Pb. CET 2000]

    A) 5

    B) 6

    C) 7

    D) 8

    Correct Answer: C

    Solution :

    Given expression \[=2\,[{{x}^{5}}+{{\,}^{5}}{{C}_{2}}{{x}^{3}}{{\{{{({{x}^{3}}-1)}^{1/2}}\}}^{2}}+{{\,}^{5}}{{C}_{4}}x{{\{{{({{x}^{3}}-1)}^{1/2}}\}}^{4}}]\] = \[2[{{x}^{5}}+10{{x}^{3}}({{x}^{3}}-1)+5x{{({{x}^{3}}-1)}^{2}}]\] = \[5{{x}^{7}}+10{{x}^{6}}+{{x}^{5}}-10{{x}^{4}}-10{{x}^{3}}+5x\], which is a polynomial of degree 7.


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