1
MHT CET 2026 11th April Evening Shift
MCQ (Single Correct Answer)
+2
-0
$\int \sqrt{4^x(4^x + 4)}\, dx = \cdots$
A
$\dfrac{1}{\log 2}\left[\dfrac{2^x}{2}\sqrt{4^x + 4} + 2\log|2^x + \sqrt{4^x + 4}|\right] + c$
B
$\dfrac{2^x}{2}\sqrt{4^x + 4} + 2\log|2^x + \sqrt{4^x + 4}| + c$
C
$\dfrac{1}{\log 2}\left[\dfrac{2^x}{2}\sqrt{4^x + 4} + \log|2^x + \sqrt{4^x + 4}|\right] + c$
D
$\left[\dfrac{2^x}{\log 4}\sqrt{4^x + 4} + \log|2^x + \sqrt{4^x + 4}|\right] + c$
2
MHT CET 2026 11th April Evening Shift
MCQ (Single Correct Answer)
+2
-0
The value of $\int \dfrac{1}{x^2 - 5x + 8} dx$ is equal to...
A
$\dfrac{2}{\sqrt{7}}\tan^{-1}\left(\dfrac{2x+5}{\sqrt{7}}\right) + c$
B
$-\dfrac{2}{\sqrt{7}}\tan^{-1}\left(\dfrac{2x-5}{\sqrt{7}}\right) + c$
C
$\dfrac{2}{\sqrt{7}}\tan^{-1}\left(\dfrac{2x-5}{\sqrt{7}}\right) + c$
D
$-\dfrac{2}{\sqrt{7}}\tan^{-1}\left(\dfrac{2x+5}{\sqrt{7}}\right) + c$
3
MHT CET 2026 11th April Evening Shift
MCQ (Single Correct Answer)
+2
-0
$\int \dfrac{2x}{4 - 3x - x^2} dx = \cdots$
A
$\dfrac{8}{5}\log|4 + x| - \dfrac{2}{5}\log|1 - x| + c$
B
$2\log|4 + x| + \dfrac{2}{5}\log|1 - x| + c$
C
$-\log|4 + x| + \dfrac{2}{5}\log|1 - x| + c$
D
$-\dfrac{8}{5}\log|4 + x| - \dfrac{2}{5}\log|1 - x| + c$
4
MHT CET 2026 11th April Evening Shift
MCQ (Single Correct Answer)
+2
-0
If $\int_{2}^{e}\left[\dfrac{1}{\log x} - \dfrac{1}{(\log x)^2}\right] dx = a + \dfrac{b}{\log 2}$, then values of $a$ and $b$ are
A
$a = e, b = 2$
B
$a = -e, b = 2$
C
$a = e, b = -2$
D
$a = -e, b = -2$

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