1
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\int \frac{\mathrm{d} x}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$ is

A
$\left(\frac{-x^4+1}{x^4}\right)^{\frac{1}{4}}+c$, where $c$ is constant of integration.
B
$\left(x^4+1\right)^{\frac{1}{4}}+\mathrm{c}$, where c is constant of integration.
C
$-\left(x^4+1\right)^{\frac{1}{4}}+\mathrm{c}$, where c is constant of integration.
D
$-\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+c$, where $c$ is constant of integration.
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The converse of "If 3 is a prime number, then 3 is odd." is

A
If 3 is odd then it is a prime number.
B
If 3 is not a prime number then 3 is even.
C
If 3 is a prime number then 3 is even.
D
If 3 is not a prime number then 3 is not odd.
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) \mathrm{d} x=$$

A
$2 x \tan ^{-1} x-\log \left(1+x^2\right)+\mathrm{c}$, where c is a constant of integration.
B
$2\left(x \tan ^{-1} x-\log \left(1+x^2\right)\right)+\mathrm{c}$, where c is a constant of integration.
C
$x \tan ^{-1} x+\log \left(1+x^2\right)+\mathrm{c}$, where c is a constant of integration.
D
$2\left(x \tan ^{-1} x+\log \left(1+x^2\right)\right)+\mathrm{c}$, where c is a constant of integration.
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{f}(x)=\frac{a x}{x+1}, x \neq-1$, then for $\alpha=$ ________, $\mathrm{f}(\mathrm{f}(x))=x$.

A
$\sqrt{2}$
B
$-\sqrt{2}$
C
1
D
$-$1
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