Question:
Let $a-2 b+c=1$
If $f(x)=\left|\begin{array}{lll}x+a & x+2 & x+1 \\ x+b & x+3 & x+2 \\ x+c & x+4 & x+3\end{array}\right|$, then :
Correct Option: , 4
Solution:
If $f(x)=\left|\begin{array}{lll}x+a & x+2 & x+1 \\ x+b & x+3 & x+2 \\ x+c & x+4 & x+3\end{array}\right|$
$R_{1}=R_{1}+R_{3}-2 R_{2}$
$\Rightarrow \quad f(x)=\left|\begin{array}{ccc}1 & 0 & 0 \\ x+b & x+3 & x+2 \\ x+c & x+4 & x+3\end{array}\right|$
$\Rightarrow f(x)=1 \Rightarrow f(50)=1$
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