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1
MHT CET 2026 17th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The value of $\int 2x^{\frac{1}{3}} \sin \sqrt[3]{x^2}\,dx$ is
A
$\left(x^{\frac{2}{3}}\cos x^{\frac{2}{3}} + \sin x^{\frac{2}{3}}\right) + c$
B
$3\left[x^{\frac{2}{3}}\cos x^{\frac{2}{3}} - \sin x^{\frac{2}{3}}\right] + c$
C
$3\left[-x^{\frac{2}{3}}\cos x^{\frac{2}{3}} - \sin x^{\frac{2}{3}}\right] + c$
D
$3\left[-x^{\frac{2}{3}}\cos x^{\frac{2}{3}} + \sin x^{\frac{2}{3}}\right] + c$
2
MHT CET 2026 17th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
$\int x^3 \log x\,dx = $
A
$\dfrac{x^4}{16}[4\log x - 1] + c$
B
$\dfrac{x^4}{16}[4\log x + 1] + c$
C
$\dfrac{x^4}{16}[-4\log x - 1] + c$
D
$\dfrac{x^4}{16}[-4\log x + 1] + c$
3
MHT CET 2026 17th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If $f'(x) = \dfrac{(\sqrt{x}+1)e^{\sqrt{x}}}{\sqrt{x}}$ and $f(0) = e$ then $f(1) = \ldots\ldots\ldots\ldots$
A
$e$
B
$2e$
C
$3e$
D
$4e$
4
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{d x}{\cos x(1+\cos x)}= $$

A

$\quad \log (\sec x+\tan x)+2 \tan \left(\frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

B

$\quad \log (\sec x+\tan x)-2 \tan \left(\frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

C

$\log (\sec x+\tan x)+\tan \left(\frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

D

$\log (\sec x+\tan x)-\tan \left(\frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

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