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Consider the system of linear equations
\[
\begin{array}{l}
-x+y+2 z=0 \\
3 x-a y+5 z=1 \\
2 x-2 y-a z=7
\end{array}
\]
\( \mathrm{P} \)
W
Let \( S_{1} \) be the set of all \( a \in R \) for which the system is inconsistent and \( S_{2} \) be the set of all \( a \in R \) for which the system has infinitely many solutions. If \( n\left(S_{1}\right) \) and \( n\left(S_{2}\right) \) denote the number of elements in \( S_{1} \) and \( S_{2} \) respectively, then
[JEE Main-2021 (September)]
(a) \( n\left(S_{1}\right)=2, n\left(S_{2}\right)=2 \)
(b) \( n\left(S_{1}\right)=1, n\left(S_{2}\right)=0 \)
(c) \( n\left(S_{1}\right)=2, n\left(S_{2}\right)=0 \)
(d) \( n\left(S_{1}\right)=0, n\left(S_{2}\right)=2 \)
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