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

If $\int \frac{\mathrm{d} x}{\cos ^3 x \sqrt{2 \sin 2 x}}=(\tan x)^A+C(\tan x)^B+\mathrm{k}$ where k is a constant of integration, then $A+B+C$ equals

A
$\frac{27}{10}$
B
$\frac{16}{5}$
C
$\frac{27}{5}$
D
$\frac{21}{5}$
2
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The integral $\int \frac{2 x^3-1}{x^4+x} \mathrm{~d} x$ is equal to

A
$\log \frac{\left|x^3+1\right|}{x^2}+c$, (where c is a constant of integration)
B
$\frac{1}{2} \log \frac{\left(x^3+1\right)^2}{\left|x^3\right|}+\mathrm{c}$, (where c is a constant of integration)
C
$\quad \log \left|\frac{x^3+1}{x}\right|+\mathrm{c}$, (where c is a constant of integration)
D
$\frac{1}{2} \log \frac{\left|x^3+1\right|}{x^2}+\mathrm{c}$, (where c is a constant of integration)
3
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
$\frac{1}{2} \log (2+\sqrt{5})$
4
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.
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