1
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

2
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

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

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

$\int \frac{\sqrt{x-2}}{2 x+4} d x=$

A

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

B

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

C

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

D

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

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

If $\int x^{49}\left[\tan ^{-1} x^{50}+\frac{x^{50}}{1+x^{100}}\right] d x=\frac{x^n}{k} f(x)+c$, then

$$ f(x)-f\left(\sqrt[k]{x^n}\right)= $$

A

$k+n$

B

$k-n$

C

$1 / k$

D

$1 / n$

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