1
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

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

A

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

B

$-\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+C$

C

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

D

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

2
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \sin ^{-1}\left(\sqrt{\frac{x}{a+x}}\right) d x= $$

A

$(a+x) \tan ^{-1} \sqrt{\frac{x}{a}}+a x+C$

B

$(a+x) \tan ^{-1} \sqrt{\frac{x}{a}}+\sqrt{a x}+C$

C

$(a+x) \tan ^{-1} \sqrt{\frac{a}{x}}-\sqrt{a x}+C$

D

$(a+x) \tan ^{-1} \sqrt{\frac{x}{a}}-\sqrt{a x}+C$

3
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int \frac{x}{x \tan x+1} d x=\log f(x)+k$, then $f\left(\frac{\pi}{4}\right)=$

A

$\frac{\pi}{4 \sqrt{2}}$

B

$\pi+\frac{\pi}{2 \sqrt{2}}$

C

$\frac{\pi+4}{4 \sqrt{2}}$

D

$\frac{\pi-4}{4 \sqrt{2}}$

4
AP EAPCET 2025 - 26th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\frac{2 x^4-3 x^2+4}{\left(x^2+1\right)\left(x^2+2\right)}=a+\frac{p x+q}{x^2+1}+\frac{m x+n}{x^2+2}$, then $\frac{n}{q}=$

A

$p+m-a$

B

$\frac{p+m}{a}$

C

$\frac{a}{p+m}$

D

$p+m+a$

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