1
AP EAPCET 2025 - 26th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\int \frac{d x}{(x \tan x+1)^2}=f(x)+C$, then $\lim\limits_{x \rightarrow \frac{\pi}{2}} f(x)=$

A

$\frac{\pi}{2}$

B

$\frac{2}{\pi}$

C

$\frac{1}{\pi}$

D

$\infty$

2
AP EAPCET 2025 - 26th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \sin ^3 x \cos ^2 x d x= $$

A

$\frac{\sin ^4 x \cos x}{5}-\frac{\sin ^2 x \cos x}{15}-\frac{2 \cos x}{15}+C$

B

$-\frac{\sin ^4 x \cos x}{5}-\frac{\sin ^2 x \cos x}{15}+\frac{2 \cos x}{15}+C$

C

$\frac{\sin ^4 x \cos ^{\prime} x}{5}-\frac{\sin ^2 x \cos x}{15}+\frac{2 x}{15}+C$

D

$\frac{\sin ^4 x \cos x}{5}+\frac{\sin ^2 x \cos x}{3}-\frac{2 x}{15}+C$

3
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

  1. If $\frac{3 x^3-7 x+1}{(x-2)^5}=\frac{A}{x-2}+\frac{B}{(x-2)^2}+\frac{C}{(x-2)^3}+\frac{D}{(x-2)^4}+\frac{E}{(x-2)^5}, \text { then } A(B+C+D+E)= $
A

0

B

348

C

64

D

256

4
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int(\sqrt{\tan x}+\sqrt{\cot x}) d x= $$

A

$2 \tan ^{-1}\left(\frac{\tan x-1}{\sqrt{\tan x}}\right)+C$

B

$\tan ^{-1}\left(\frac{\tan x-2}{2 \sqrt{\tan x}}\right)+C$

C

$\sqrt{2} \tan ^{-1}\left(\frac{\tan x-1}{\sqrt{2 \tan x}}\right)+C$

D

$\sqrt{2} \tan ^{-1}\left(\frac{\tan x+1}{\sqrt{2} \tan x}\right)+C$

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