1
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

2
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

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

If $\int \frac{\mathrm{d} x}{x^4+5 x^2+4}=\mathrm{A} \tan ^{-1} x+\mathrm{B} \tan ^{-1} \frac{x}{2}+\mathrm{c}$ where c is a constant of integration, then

A
$\mathrm{A}=\frac{1}{2}, \mathrm{~B}=\frac{1}{4}$
B
$\mathrm{A}=\frac{1}{3}, \mathrm{~B}=-\frac{1}{6}$
C
$\mathrm{A}=\frac{1}{3}, \mathrm{~B}=\frac{1}{6}$
D
$\quad \mathrm{A}=\frac{1}{2}, \mathrm{~B}=-\frac{1}{4}$
4
MHT CET 2025 26th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{\sqrt{\tan x}}{\sin x \cdot \cos x} d x= $$

A

$2 \sqrt{\sec x}+c$, where c is a constant of integration

B

$2 \sqrt{\tan x}+c$, where $c$ is a constant of integration

C

$\frac{2}{\sqrt{\tan x}}+\mathrm{c}$, where c is a constant of integration

D

$\frac{2}{\sqrt{\sec x}}+\mathrm{c}$, where c is a constant of integration

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