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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        The first three terms in the expansion of \[{{(1+ax)}^{n}}(n\ne 0)\]are\[1,6x\]and\[16{{x}^{2}}\]. Then, the value of a and n are respectively

    A)  2 and 9

    B)  3 and 2

    C)  2/3 and 9

    D)  3/2 and 6

    Correct Answer: C

    Solution :

                    Given, \[{{T}_{1}}{{=}^{n}}{{C}_{0}}=1\]                                ?.(i) \[{{T}_{2}}{{=}^{n}}{{C}_{1}}ax=6x\] \[\Rightarrow \]             \[nax=6x\]                                            ...(ii) and        \[{{T}_{3}}{{=}^{n}}{{C}_{2}}{{(ax)}^{2}}=16{{x}^{2}}\] \[\Rightarrow \]               \[\frac{n(n-1)}{2}{{a}^{2}}{{x}^{2}}=16{{x}^{2}}\]                              ?.(iii) On solving Eqs. (ii) and (iii), we get \[a=\frac{2}{3}\]and \[n=9\]


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