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1
MHT CET 2026 18th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If $0 \leq x \leq 1$, $I_1 = \int\sin^{-1}\sqrt{1-x^2}\,dx$ and $I_2 = \int\sin^{-1}x\,dx$, then which of the following is true?
A
$I_1 = I_2$
B
$I_1 = \dfrac{\pi}{2}I_2$
C
$I_1 + I_2 = \dfrac{\pi}{2}x$
D
$I_1 + I_2 = \dfrac{\pi}{2}$
2
MHT CET 2026 18th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
$\int\sin(\log x)\,dx = $
A
$\dfrac{x}{2}[\sin(\log x) - \cos(\log x)] + c$
B
$\dfrac{x}{2}[\sin(\log x) + \cos(\log x)] + c$
C
$\dfrac{x}{2}[\cos(\log x) - \sin(\log x)] + c$
D
$\dfrac{x}{4}[\cos(\log x) - \sin(\log x)] + c$
3
MHT CET 2026 18th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The value of $\int\dfrac{n\sqrt{\text{cosec}^2 x^n - 1}}{x^{(1-n)}}\,dx$ is ...
A
$\log(\sin x) + c$
B
$\log(\sin x^n) + c$
C
$\log(\cot x^n) + c$
D
$\log(\cos x^n) + c$
4
MHT CET 2026 18th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
$\int\dfrac{(x+1)\,dx}{x(1+xe^x)} = \ldots\ldots$
A
$\log\left|\dfrac{xe^x}{1+xe^x}\right| + c$
B
$\log\left|\dfrac{1+xe^x}{xe^x}\right| + c$
C
$\log\left|\dfrac{(x+1)e^x}{xe^x}\right| + c$
D
$\log\left|\dfrac{(x+1)e^x}{1+xe^x}\right| + c$
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