1
MHT CET 2026 17th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The value of $\int_0^\pi \dfrac{1}{1 + 2^{\cos x}}\,dx$ is _____
A
$\dfrac{\pi}{2}$
B
$\pi$
C
$2\pi$
D
$\dfrac{3\pi}{2}$
2
MHT CET 2026 17th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If $I_n = \int_1^e (\log_e x)^n\,dx$ where $n \in Z^+$ and $I_m + mI_{2026} = e$, then $m = $
A
$2024$
B
$2025$
C
$2026$
D
$2027$
3
MHT CET 2026 16th April Evening Shift
MCQ (Single Correct Answer)
+2
-0
The value of integral $\int_0^1\cot^{-1}(1 + x^2 - x)\,dx$ is...
A
$\dfrac{\pi}{2} - \log 2$
B
$\pi - \log 2$
C
$\dfrac{\pi}{4} - \log 2$
D
$2\pi - \log 2$
4
MHT CET 2026 16th April Evening Shift
MCQ (Single Correct Answer)
+2
-0
The value of $\int_{-\pi}^{\pi}\dfrac{2x(1 + \sin x)}{1 + \cos^2 x}dx$ is...
A
$-\sqrt{2}\pi^2$
B
$\pi^2$
C
$\dfrac{\pi^2}{\sqrt{2}}$
D
$-\dfrac{\pi^2}{\sqrt{2}}$

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