Q1Single correct4 Marks15 Mar 2026

Consider the system of equations in three variables $x,y,z$: $$\begin{aligned}x+y+z&=3\\2x+3y+kz&=6\\3x+5y+(k+1)z&=9\end{aligned}$$ where $k$ is a real parameter. Consider the following statements: $S_1$: The system has a unique solution if $k\ne 2$. $S_2$: The system has no solution if $k=2$. $S_3$: The system has infinitely many solutions for some value of $k$. Choose the correct option.

A

Only $S_1$ is correct.

B

Only $S_2$ is correct.

C

Only $S_1$ and $S_3$ are correct.

D

Only $S_1$ and $S_2$ are correct.

E

$S_1$, $S_2$, and $S_3$ are all correct.