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CLAT Sample Paper CLAT Sample Paper-5

  • question_answer
    If the pth, gth and rth terms of an AP are a, b and c respectively, then the value of \[(q-r)+(r-p)+c(p-r)\] is

    A)  0

    B)  1

    C)  \[abc\]

    D)  \[pqr\]

    Correct Answer: A

    Solution :

    \[{{T}_{p}}={{a}_{1}}+(p-1)d\] \[{{T}_{q}}={{q}_{a}}+(q-1)d\] \[\therefore \] \[LHS=a(q-r)+b(r-p)+c(p-q)\] \[=\{{{a}_{1}}+(p-1)d\}\,(q-r)+\{{{a}_{1}}+(q-1)d\}\] \[(r-p)+\{{{a}_{1}}+(r-1)d\}(p-q)\] \[={{a}_{1}}\cdot (q-r+r-p+p-q)+d\,[(p-1)\] \[=(q-r)+(q-1)\,(r-p)+(r-1)\,(p-q)]=0\]


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