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1
TS EAMCET 2023 (Online) 13th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

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

A

$\log \frac{\sqrt{x^2+1}}{|x-2|}+2 \tan ^{-1} x+C$

B

$\log \frac{|x-2|}{x^2+1}+2 \tan ^{-1} x+C$

C

$\frac{1}{5}\left[\log \frac{|x-2|}{\sqrt{7+x^2}}+2 \tan ^{-1} x\right]+C$

D

$\frac{1}{5}\left[\log \frac{|x-2|}{\sqrt{1+x^2}}-2 \tan ^{-1} x\right]+C$

2
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$-\frac{1}{2}$
B
$\frac{1}{2}$
C
1
D
$\frac{3}{2}$
3
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \text { Match the following items from List I into List II } $$
List-I List-II
1. ∫ sin 2 ⁡ x cos 4 ⁡ x d x ∫ sin 2 ⁡ x cos 4 ⁡ x d x int(sin^(2)x)/(cos^(4)x)dx A. tan 2 ⁡ x 2 + ln ⁡ | cos ⁡ x | + C tan 2 ⁡ x 2 + ln ⁡ | cos ⁡ x | + C quad(tan^(2)x)/(2)+ln |cos x|+C
2. ∫ sin 4 ⁡ x cos 2 ⁡ x d x ∫ sin 4 ⁡ x cos 2 ⁡ x d x int(sin^(4)x)/(cos^(2)x)dx B. cos ⁡ x + sec ⁡ x + C cos ⁡ x + sec ⁡ x + C cos x+sec x+C
3. ∫ sin 3 ⁡ x cos 2 ⁡ x d x ∫ sin 3 ⁡ x cos 2 ⁡ x d x int(sin^(3)x)/(cos^(2)x)dx C. tan 3 ⁡ x 3 + C tan 3 ⁡ x 3 + C (tan^(3)x)/(3)+C
4. ∫ sin 3 ⁡ x cos 3 ⁡ x d x ∫ sin 3 ⁡ x cos 3 ⁡ x d x int(sin^(3)x)/(cos^(3)x)dx D. tan ⁡ x + sin ⁡ 2 x 4 − 3 x 2 + C tan ⁡ x + sin ⁡ 2 x 4 − 3 x 2 + C tan x+(sin 2x)/(4)-(3x)/(2)+C
E. cos ⁡ x − sec ⁡ x + C cos ⁡ x − sec ⁡ x + C cos x-sec x+C
Select the correct choice
A
1-C, 2-E, 3-B, 4-A
B
1,-C, 2-D, 3-B, 4-A
C
1-D, 2-C, 3-A, 4-B
D
1-C, 2-E, 3-A, 4-D
4
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\int \frac{x}{(a+x)^5} d x=\frac{1}{k(a+x)^4}(f(x))+C$, then $\frac{f(-a)}{a k}=$
A
$1 / 3$
B
$1 / 2$
C
$5 / 6$
D
$1 / 4$
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