1
MHT CET 2025 26th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{\mathrm{d} x}{\sin ^2 x \cos ^2 x}= $$

A

$\tan x+\cot x+\mathrm{c}$, where c is the constant of integration.

B

$\tan x-\cot x+\mathrm{c}$, where c is the constant of integration.

C

$\tan x \cot x+\mathrm{c}$, where c is the constant of integration.

D

$\tan x-\cot 2 x+\mathrm{c}$, , where c is the constant of integration.

2
MHT CET 2025 26th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{\mathrm{d} x}{x^{\frac{1}{2}}+x^{\frac{1}{3}}}=\mathrm{A} x^{\frac{1}{2}}+\mathrm{B} x^{\frac{1}{3}}+\mathrm{C} x^{\frac{1}{6}}+\mathrm{D} \log \left(x^{\frac{1}{6}}+1\right)+\mathrm{k} $$

(where k is the integration constant) then values of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D are respectively,

A

$2,-3,6,-6$

B

$2,3,-6,6$

C

$2,-3,-6,6$

D

$-2,-3,6,6$

3
MHT CET 2025 26th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int x^2 \cos x d x= $$

A

$x^2 \sin x+2 x \cos x-2 \sin x+\mathrm{c}$, where c is the constant of integration

B

$x^2 \sin x-2 x \cos x-2 \sin x+\mathrm{c}$, where c is the constant of integration

C

$x^2 \sin x-2 x \cos x+2 \sin x+\mathrm{c}$, where c is the constant of integration

D

$x^2 \sin x+2 x \cos x+2 \sin x+\mathrm{c}$, where $c$ is the constant of integration

4
MHT CET 2025 26th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\int \frac{\left(x^4+1\right)}{x\left(x^2+1\right)^2} d x=A \log |x|+\frac{B}{1+x^2}+c$, then $\mathrm{A}-\mathrm{B}$ is (where c is the constant of integration)

A

0

B

1

C

2

D

-1

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