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

If $\frac{x^2}{\left(x^2+2\right)\left(x^4-1\right)}=\frac{A}{x^2-1}+\frac{B}{x^2+1}+\frac{C}{x^2+2}$, then $A+B-C=$

A

0

B

$\frac{4}{3}$

C

$\frac{3}{4}$

D

2

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

If $\int \frac{5 \tan x}{\tan x-2} d x=a x+b \log |\sin x-2 \cos x|+c$, then $a+b=$

A

2

B

3

C

4

D

-1

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

$$ \int x \cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right) d x(x>0)= $$

A

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

B

$x-\left(1+x^2\right) \cot ^{-1} x+C$

C

$-x+\left(1+x^2\right) \cot ^{-1} x+C$

D

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

4
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

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

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