1
JEE Main 2025 (Online) 28th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $f$ be a real valued continuous function defined on the positive real axis such that $g(x)=\int\limits_0^x t f(t) d t$. If $g\left(x^3\right)=x^6+x^7$, then value of $\sum\limits_{r=1}^{15} f\left(r^3\right)$ is :

A

270

B

340

C

310

D

320

2
JEE Main 2025 (Online) 28th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{96 x^2 \cos ^2 x}{\left(1+e^x\right)} \mathrm{d} x=\pi\left(\alpha \pi^2+\beta\right), \alpha, \beta \in \mathbb{Z}$, then $(\alpha+\beta)^2$ equals

A
196
B
100
C
64
D
144
3
JEE Main 2025 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $I(m, n)=\int_0^1 x^{m-1}(1-x)^{n-1} d x, m, n>0$, then $I(9,14)+I(10,13)$ is

A
$I(9,1)$
B
$I(1,13)$
C
$\mathrm{I}(19,27)$
D
$\mathrm{I}(9,13)$
4
JEE Main 2025 (Online) 23rd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $\mathrm{I}=\int_0^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} \mathrm{~d} x$, then $\int_0^{2I} \frac{x \sin x \cos x}{\sin ^4 x+\cos ^4 x} \mathrm{~d} x$ equals :

A
$\frac{\pi^2}{12}$
B
$\frac{\pi^2}{4}$
C
$\frac{\pi^2}{16}$
D
$\frac{\pi^2}{8}$
JEE Main Subjects
EXAM MAP