Reply To: Question 45 — JEE Main 22 Jan 2026 S Ii

Solution

$\mathrm{n} \in\{1,2,3,4,5,6\}$
$\Delta=\left|\begin{array}{ccc}1 & -n & 1 \\ 1 & n-2 & n+1 \\ 0 & n-1 & 1\end{array}\right|$
$\Delta=-(\mathrm{n}-1)(\mathrm{n}-2)$
For unique solution $\Delta \neq 0 \Rightarrow n \neq 1, n \neq 2$
favourable cases $n=\{3,4,5,6\}$
Required Probability $=\frac{4}{6}=\frac{\mathrm{k}}{6}$
$\mathrm{k}=4, \mathrm{n}=3,4,5,6$
required sum $=4+3+4+5+6=22$ Answer(4)