JEE Main & Advanced Sample Paper JEE Main Sample Paper-19

  • question_answer 75) If \[a,\,\,\,b,\,\,\,c\] are in \[A.P.,\,\,\,b,\,\,\,c,\,\,\,d\] are in \[GP.\] and \[c,\,\,\,d,\,\,\,e\] are in \[H.P.\] then \[a,\,\,\,c,\,\,\,e\] are in

    A) \[A.P.\]                               

    B) \[GP.\]

    C) \[H.P.\]               

    D)  None

    Correct Answer: B

    Solution :

    \[a,\,\,b,\,\,c\]in\[A.P.\]\[\Rightarrow a+c=2b;\]  \[b,\,\,c,\,\,d\]in\[G.P.\] \[\Rightarrow \]  \[bd={{c}^{2}};\]   \[c,\,\,d,\,\,e\]in\[H.P.\]\[\Rightarrow d=\frac{ce}{c+e}\] \[\therefore \]\[\frac{a+c}{2}\times \frac{2ce}{c+e}={{c}^{2}}\Rightarrow (a+c)e=(c+e)c\Rightarrow {{c}^{2}}=ae\]Therefore, in\[G.P.\]

adversite



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