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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2002

  • question_answer
    If a, b and c are respectively the p th, q th and r th terms of an AP, then\[\left| \begin{matrix}  a & p & 1  \\    b & q & 1  \\    c & r & 1  \\ \end{matrix} \right|\]is equal to:

    A)  1                                            

    B)                         \[-1\]

    C)                         0                                            

    D)                         \[pqr\]

    E)                         \[p+q+r\]

    Correct Answer: C

    Solution :

    \[\because \]a, b, c are respectively p th, q th and r th terms of an AP, then \[a=A+(p-1)D\]         ...(i) \[b=A+(q-1)D\]        ...(ii) and        \[c=A+(r-1)D\]             ...(iii) Now,\[\left| \begin{matrix}    a & p & 1  \\    b & q & 1  \\    c & r & 1  \\ \end{matrix} \right|=a(q-r)+b(r-p)+c(p-q)\] \[=A(q-r+r-p+p-q)\] \[+D\{(p-1)(q-r)+(q-1)(r-p)+(r-1)\] \[(p-q)\}\]                 \[=A0+D0=0\]   


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