1
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of the integral $\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\left(x^2+\log \frac{\pi-x}{\pi+x}\right) \cos x d x$ is equal to

A
0
B
$\frac{\pi^2}{2}-4$
C
$\frac{\pi^2}{2}$
D
$\frac{\pi^2}{2}+4$
2
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\int_\limits0^{\frac{\pi}{3}} \frac{\tan \theta}{\sqrt{2 k \sec \theta}} d \theta=1-\frac{1}{\sqrt{2}},(k>0)$, then the value of $k$ is

A
2
B
1
C
$\frac{1}{2}$
D
4
3
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\mathrm{I}=\int_\limits{\sqrt{\log _{\mathrm{e}}}}^{\sqrt{\log _{\mathrm{e}} 3}} \frac{x \sin x^2}{\sin x^2+\sin \left(\log _{\mathrm{e}} 6-x^2\right)} d x$ is

A
$\frac{1}{4} \log _{\mathrm{e}} \frac{3}{2}$
B
$\frac{1}{2} \log _e \frac{3}{2}$
C
$ \log _e \frac{3}{2}$
D
$\frac{1}{6} \log _{\mathrm{e}} \frac{3}{2}$
4
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $f$ and $g$ be continuous functions on $[0, a]$ such that $f(x)=f(a-x)$ and $g(x)+g(a-x)=4$, then $\int_0^a f(x) g(x) d x$ is equal to

A
$4 \int_\limits0^a f(x) \mathrm{d} x$
B
$\int_\limits0^2 \mathrm{f}(x) \mathrm{d} x$
C
$2 \int_\limits0^2 f(x) \mathrm{d} x$
D
$-3 \int_\limits0^2 f(x) d x$
MHT CET Subjects
EXAM MAP