1
TS EAMCET 2022 (Online) 18th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

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

A

3

B

2

C

0

D

1

2
TS EAMCET 2022 (Online) 18th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let $f(x)=\int \frac{2 x^3-3 x^2+4 x-5}{x^2} d x$ and $f(1)=1$. Then, $f(5)=$

A

$10+4 \log 5$

B

$10-4 \log 5$

C

$9+4 \log 5$

D

$9-4 \log 5$

3
TS EAMCET 2022 (Online) 18th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $x>0$ and $x \neq(2 n+1) \frac{\pi}{2}$, then $\int\left(x \sqrt{x}-e^{\log (\sec x \tan x)}+\frac{3 x^2-2 x+1}{x^2}\right) d x=$

A

$x \sqrt{x}-\sec x+3 x-2 \log x-\frac{1}{x}+c$

B

$\frac{2}{5} x^2 \sqrt{x}-\sec x+3 x+\frac{2}{x^2}-\frac{1}{x}+c$

C

$x \sqrt{x}-\sec x+3 x+\frac{2}{x^2}-\frac{1}{x}+c$

D

$\frac{2}{5} x^2 \sqrt{x}-\sec x+3 x-2 \log x-\frac{1}{x}+c$

4
TS EAMCET 2022 (Online) 18th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int(2 x-3) \sqrt{3 x+2} d x= $$

A

$\frac{2}{135}\left(54 x^2-123 x+106\right) \sqrt{3 x+2}+c$

B

$\frac{2}{135}\left(54 x^2+123 x-106\right) \sqrt{3 x+2}+c$

C

$\frac{2}{135}\left(54 x^2-123 x-106\right) \sqrt{3 x+2}+c$

D

$\frac{2}{135}\left(54 x^2-195 x-106\right) \sqrt{3 x+2}+c$

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