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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

  • question_answer
        In the expansion of\[{{(1+x)}^{n}},\]7th and 8th terms are equal, then the value of\[{{\left( \frac{7}{x}+6 \right)}^{2}}\]is

    A)  \[n\]                                    

    B)  \[{{n}^{2}}\]

    C)  \[{{n}^{3}}\]                     

    D)  \[{{n}^{4}}\]

    Correct Answer: B

    Solution :

                    Since, 7th and 8th tetras are greatest. Then,        \[^{n}{{C}_{6}}.{{x}^{6}}{{=}^{n}}{{C}_{7}}.{{x}^{7}}\] \[\Rightarrow \]               \[x=\frac{^{n}{{C}_{6}}}{^{n}{{C}_{7}}}=\frac{7}{n-6}\] \[\therefore \]  \[{{\left( \frac{7}{x}+6 \right)}^{2}}={{n}^{2}}\]


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