1
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int\left(\frac{x+2}{x+4}\right)^2 \cdot e^x \mathrm{~d} x=$$

A
$\mathrm{e}^x\left(\frac{x}{x+4}\right)+\mathrm{c}$, where c is a constant of integration.
B
$\mathrm{e}^x\left(\frac{x+2}{x+4}\right)+\mathrm{c}$, where c is a constant of integration.
C
$\mathrm{e}^x\left(\frac{x-2}{x+4}\right)+\mathrm{c}$, where c is a constant of integration.
D
$\mathrm{e}^x\left(\frac{2 x}{x+4}\right)+\mathrm{c}$, where c is a constant of integration.
2
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$\int \frac{\mathrm{d} x}{3-2 \cos 2 x}=\frac{\tan ^{-1}(\mathrm{f}(x))}{\sqrt{5}}+\mathrm{c}$, (where c is a constant of integration), then $f(\pi / 4)$ has the value

A
$-\sqrt{5}$
B
$\sqrt{5}$
C
$\frac{2}{\sqrt{5}}$
D
$\frac{1}{\sqrt{5}}$
3
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $$\int \mathrm{e}^x\left(\frac{x^2+4 x+4}{(x+4)^2}\right) \mathrm{d} x$$ is :

A
$$\mathrm{e}^x\left(\frac{x}{x+4}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$\mathrm{e}^x\left(\frac{4}{x+4}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$\mathrm{e}^x\left(\frac{x}{(x+4)^2}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
D
$$\mathrm{e}^x\left(\frac{4}{(x+4)^2}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
4
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\int \frac{x^2}{\sqrt{1-x}} \mathrm{~d} x=\mathrm{p} \sqrt{1-x}\left(3 x^2+4 x+8\right)+\mathrm{c}$$ where $$\mathrm{c}$$ is a constant of integration, then the value of $$p$$ is

A
$$\frac{-2}{15}$$
B
$$\frac{2}{15}$$
C
$$\frac{4}{15}$$
D
$$\frac{-4}{15}$$
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