Q74 / 180 · KCET 2014 · Mathematics

If \( a, b \) and \( c \) are in A.P., then the value of \( \left|\begin{array}{lll}x+2 & x+3 & x+a \\ x+4 & x+5 & x+b \\ x+6 & x+7 & x+c\end{array}\right| \) is

  • A
    \( x-(a+b+c) \)
  • B
    \( 9 x^{2}+a+b+c \)
  • Correct answer
    C
    \( 00 \)
  • D
    \( a+b+c \)

Solution

Given \( \left|\begin{array}{ccc}x+2 & x+3 & x+a \\ x+4 & x+5 & x+b \\ x+6 & x+7 & x+6\end{array}\right| \) \( R_{1} \rightarrow R_{1}-R_{2} ; R_{2} \rightarrow R_{2}-R_{3} \) \( \Delta=\left|\begin{array}{ccc}-2 & -2 & a-b \\ -2 & -2 & b-c \\ x+6 & x+7 & x+c\end{array}\right| \) Since, a, b, c are in A.P. then \( a-b=b-c \) So, \( R_{1} \equiv R_{2} \) Therefore, \( \Delta=0 \)

Hence, the correct answer is option: 'C'.

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