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KVPY Sample Paper KVPY Stream-SX Model Paper-11

  • question_answer
    Let a, b and c be the 7th, 11th and 13th terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P. then \[\frac{a}{c}\]is equal to:

    A) \[\frac{1}{2}\]

    B) 4

    C) 2                                 

    D) \[\frac{7}{13}\]

    Correct Answer: B

    Solution :

    \[a=A+6d\] 
    \[b=A+10\]
    \[c=A+12\]
    a, b, c are in G.P.
    \[\Rightarrow \]   \[{{(A+10d)}^{2}}=(A+6d)(a+12d)\]
    \[\Rightarrow \]   \[\frac{A}{d}=-\,14\]
                \[\frac{a}{c}=\frac{A+6d}{A+12d}\]
    \[=\,\frac{6+\frac{A}{d}}{12+\frac{A}{d}}=\frac{6-14}{12-14}=4\]


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