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JEE Main & Advanced JEE Main Online Paper (Held On 08 April 2018)

  • question_answer
    The sum of the co-efficient of all odd degree terms in the expansion of \[{{\left( x+\sqrt{{{x}^{3}}-1} \right)}^{5}}+{{\left( x-\sqrt{{{x}^{3}}-1} \right)}^{5}},(x>1)\] is: [JEE Main Online 08-04-2018]

    A)  1                                

    B)  2

    C)  -1                               

    D)  0

    Correct Answer: B

    Solution :

    \[\left[ ^{5}{{C}_{0}}{{x}^{5}}{{+}^{5}}{{C}_{2}}{{x}^{3}}({{x}^{3}}-1){{+}^{5}}{{C}_{4}}{{x}^{1}}{{({{x}^{3}}-1)}^{2}} \right]\] \[=2\left[ ^{5}{{C}_{0}}{{-}^{5}}{{C}_{2}}{{+}^{5}}{{C}_{4}} \right]\] \[=2\left[ \underbrace{1+10}_{{}}-10 \right]\] \[=2\]


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