1
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\int \frac{\log \left(t+\sqrt{1+t^2}\right)}{\sqrt{1+t^2}} d t=\frac{1}{2}(g(t))^2+c$ where c is a constant of integration, then $\mathrm{g}(2)$ is equal to

A
$2 \log (2+\sqrt{5})$
B
$\log (2+\sqrt{5})$
C
$\frac{1}{\sqrt{5}} \log (2+\sqrt{5})$
D
$\frac{1}{2} \log (2+\sqrt{5})$
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \operatorname{cosec}(x-a) \cdot \operatorname{cosec} x d x=$$

A
$\frac{-1}{\operatorname{sina}} \log (\sin (x-\mathrm{a}) \sin x)+\mathrm{c}$, where c is a constant of integration.
B
$\frac{1}{\sin \mathrm{a}} \log (\sin (x-\mathrm{a}) \sin x)+\mathrm{c}$, where c is a constant of integration.
C
$\frac{1}{\operatorname{sina}} \log (\sin (x-a) \cdot \operatorname{cosec} x)+c$, where c is a constant of integration.
D
$\frac{-1}{\operatorname{sina}} \log (\operatorname{cosec}(x-\mathrm{a}) \cdot \sin x)+\mathrm{c}$, where c is a constant of integration.
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$\int\left(1+x-\frac{1}{x}\right) \mathrm{e}^{x+\frac{1}{x}} \mathrm{~d} x$ is equal to

A
$(x-1) \mathrm{e}^{x+\frac{1}{x}}+\mathrm{c}$, where c is a constant of integration.
B
$x \mathrm{e}^{x+\frac{1}{x}}+c$, where $c$ is a constant of integration.
C
$(x+1) \mathrm{e}^{x+\frac{1}{x}}+\mathrm{c}$, where c is a constant of integration.
D
$-x e^{x+\frac{1}{x}}+c$, where $c$ is a constant of integration.
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\int \mathrm{e}^{x^2} \cdot x^3 \mathrm{dx}=\mathrm{e}^{x^2} \mathrm{f}(x)+\mathrm{c}$ and $\mathrm{f}(1)=0$ (where c is a constant of integration), then the value of $f(x)$ is

A
$\frac{x-1}{2}$
B
$\frac{x^2+1}{2}$
C
$\frac{x+1}{2}$
D
$\frac{x^2-1}{2}$
MHT CET Subjects
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