Let q be the maximum integral value of p in [0,10] for which the roots of the equation x²-p x+5/4 p=0 are rational. Then the area of the region \(x, y): 0 ≤ y ≤(x-q)², 0 ≤ x ≤ q is:

Integral Calculus: JEE Main 2023 Mathematics question

JEE Main 2023 · 30 Jan, Evening shift · Q2853

JEE Main 202330 Jan, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

Let

q

be the maximum integral value of

p

[0,10]

for which the roots of the equation

x^2-p x+\frac{5}{4} p=0

are rational. Then the area of the region

\left\{(x, y): 0 \leq y \leq(x-q)^2, 0 \leq x \leq q\right\}

is :