JEE Main 2023 (Online) 30th January Evening ShiftQuestion 1
Let $q$ be the maximum integral value of $p$ in $[0,10]$ for which the roots of the equation $x^{2}-px+\frac54p=0$ are rational. Then the area of the region $\{(x,y):0\le y\le(x-q)^{2},0\le x\le q\}$ is
Application of Integrals
Solution
Discriminant $p^2-5p$ must be a perfect square: $p=9$ gives $36$, $p=10$ gives $50$. So $q=9$ and area $=\int_0^9(x-9)^2dx=243$.