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KVPY Sample Paper KVPY Stream-SX Model Paper-4

  • question_answer
    If A. M. between \[{{p}^{th}}\] and \[{{q}^{th}}\] terms of an A.P. be equal to the A.M. between \[{{r}^{th}}\] and \[{{s}^{th}}\] term of the A.P. then p + q is equal to -

    A) \[r+s\]

    B) \[\frac{r-s}{r+s}\]

    C) \[\frac{r+s}{r-s}\]                      

    D) \[r+s+1\]

    Correct Answer: A

    Solution :

    [A] \[\frac{{{t}_{p}}+{{t}_{q}}}{2}=\frac{{{t}_{r}}+{{t}_{s}}}{2}\] \[\Rightarrow a+(p-1)\,\,d+a+(q-1)\,\,d\] \[=a+(r-1)\,\,d+a+(s-1)\,\,d\] \[\therefore p+q=r+s.\]              


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