1
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\frac{3 x+1}{(x-1)\left(x^2+2\right)}=\frac{A}{x-1}+\frac{B x+C}{x^2+2}$, then $5(A-B)=$

A

$A+C$

B

8 C

C

$C+8$

D

$\frac{C}{8}$

2
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{\sec ^2 x}{\sin ^7 x} d x-\int \frac{7}{\sin ^7 x} d x= $$

A

$\frac{1}{\sin ^6 x \cos x}+C$

B

$\frac{\tan x}{\sin ^8 x}+C$

C

$\sin ^8 x \cos x+C$

D

$\sec x \tan ^7 x+C$

3
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\int\left(x^6+x^4+x^2\right) \sqrt{2 x^4+3 x^2+6} d x=f(x)+c$, then $f(3)=$
A

$\frac{3}{2}(95)^{3 / 2}$

B

$\frac{3}{2}(195)^{3 / 2}$

C

$\frac{3}{2}(265)^{3 / 2}$

D

$\frac{3}{2}(175)^{3 / 2}$

4
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A

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

B

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

C

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

D

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

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