1
TG EAPCET 2025 (Online) 3rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\frac{5 \pi}{4} < x < \frac{7 \pi}{4}$, then $\int \sqrt{\frac{1-\sin 2 x}{1+\sin 2 x}} d x=$

A

$-\sec ^2\left(\frac{\pi}{4}-x\right)+C$

B

$-\log \left|\sec \left(\frac{\pi}{4}-x\right)\right|+C$

C

$\sec ^2\left(\frac{\pi}{4}-x\right)+C$

D

$\log \left|\sec \left(\frac{\pi}{4}-x\right)\right|+C$

2
TG EAPCET 2025 (Online) 3rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int x \tan ^{-1} \sqrt{\frac{1+x^2}{1-x^2}} d x= $$

A

$\frac{x^2}{4}\left(\pi-\cos ^{-1} x^2\right)+\frac{1}{4} \sqrt{1-x^2}+C$

B

$\frac{x^2}{4}\left(\pi-\cos ^{-1} x^2\right)+\frac{1}{4} \sqrt{1-x^4}+C$

C

$\frac{x^2}{4}\left(\pi+\cos ^{-1} x^2\right)-\frac{1}{4} \sqrt{1-x^4}+C$

D

$\frac{x^2}{4}\left(\pi+\cos ^{-1} x^2\right)-\frac{1}{4} \sqrt{1-x^2}+C$

3
TG EAPCET 2025 (Online) 3rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{1}{(2 \cos x+\sin x)^2} d x= $$

A

$\frac{1}{2+\tan x}+C$

B

$-\frac{1}{2 \tan x+1}+C$

C

$\frac{\cos x}{\cos x+2 \sin x}+C$

D

$-\frac{\cos x}{2 \cos x+\sin x}+C$

4
TG EAPCET 2025 (Online) 3rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\frac{x+3}{(x+1)\left(x^2+2\right)}=\frac{a}{x+1}+\frac{b x+c}{x^2+2}$, then $a-b+c=$

A

0

B

1

C

3

D

2

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