IPMAT Indore 2025 — Question 6

Compute $A^2=\left[\begin{array}{cc}4+4n& 3n\\ 12& 4n+1\end{array}\right]$, then $A^3$. Match against $27$ times the target matrix.

Solving gives $n=5$, $q=5$, $p=4$, $r=3$. Sum = $5+4+3=12$.