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

If $\frac{x^2+1}{\left(x^2+2\right)\left(x^2+3\right)}=\frac{A x+B}{x^2+2}+\frac{C x+D}{x^2+3}$, then $A+B+C+D=$

A

0

B

1

C

-1

D

6

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

$$ \int \frac{3^x(x \log 3-1)}{x^2} d x= $$

A

$x \cdot 3^x+C$

B

$\frac{3^x}{x^2}+C$

C

$x^2 3^x+C$

D

$\frac{3^x}{x}+C$

3
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

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

4
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

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

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