\(\begin{aligned}&\text { If system of equations }\\&& x+2 y-3 z=2 \\& 2 x+\lambda y+5 z=5 \\& 4 x+3 y+\mu z=33 \text { …

Ans. (2)
Sol.
\(\begin{aligned}& \Delta=\left|\begin{array}{lll}1 & 2 & -3 \\2 & \lambda & 5 \\4 & 3 & \mu\end{array}\right|=0 \\& 12 \lambda+\lambda \mu-4 \mu+7=0\ldots \ldots (i) \\& \Delta z=\left|\begin{array}{lll}1 & 2 & 2 \\2 & \lambda & 5 \\4 & 3 & 33\end{array}\right|=0 \\& \lambda=\frac{19}{5} \\& \text { from (i) } \mu=263 \\& \lambda+\mu=\frac{19}{5}+263=\frac{1334}{5}\end{aligned}\)