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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2010

  • question_answer
        If\[{{a}_{n}}\]be the nth term of an AP and if\[{{a}_{7}}=15,\]then the value of the common difference that would make\[{{a}_{2}}{{a}_{7}}{{a}_{12}}\]greatest is

    A)  9                                            

    B)  9/4

    C)  0                                            

    D)  18

    Correct Answer: C

    Solution :

                    Let d be the common difference of AP. Since,                    \[{{a}_{7}}=15\] \[\therefore \]                  \[{{a}_{2}}=15-5d\] and        \[{{a}_{12}}=15+5d\] Now, \[{{a}_{2}}{{a}_{7}}{{a}_{12}}=(15-5d)(15)(15+5d)\]                 \[=15.25(3-d)(3+d)\]                 \[=375(9-{{d}^{2}})\] Clearly, this will be greatest, if\[d=0\]


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