Let the domain of the function f(x)=\log _2 \log _4 \log _6 (3+4 x-x^2) be (a, b). If \int_{0}^{b-a} [x^2] \dx=p-\sqrt{q}-\sqrt{r}, p, q, r \in {\N}, {\gcd}(p, q, r)= 1 , where [\cdot] is the greatest integer function, then p +q+r is equal to [3 Apr 2025 Shift 1]

JEE Main 3 Apr 2025 Shift 1 Paper

Section: Mathematics

Question : 14 of 75

Marks: +1, -0

Let the domain of the function f(x)=log2log4log6(3+4x−x2) be (a,b). If

b−a

∫

[x2]‌dx=p−√q−√r,p,q,r∈N,gcd(p,q,r)= 1 , where [⋅] is the greatest integer function, then p+q+r is equal to

[3 Apr 2025 Shift 1]

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