1
TS EAMCET 2020 (Online) 14th September Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int\left[\frac{x^4-x}{x^{20}}\right]^{1 / 4} d x= $$

A

$\frac{4}{15}\left(\frac{\left(x^3-1\right)^5}{x^{15}}\right)^{1 / 4}+C$

B

$\frac{4}{15}\left(\frac{x^4+1}{x^4}\right)^{1 / 4}+C$

C

$\frac{\sqrt{x^4+x^2+1}}{x}+C$

D

$\frac{3}{4}\left(x^{4 / 3}+x^{1 / 3}\right)+C$

2
TS EAMCET 2020 (Online) 11th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

If the partial fractions decomposition of $\frac{x^4+24 x^2+28}{\left(x^2+1\right)^3}$ is $\frac{A}{x^2+1}+\frac{B}{\left(x^2+1\right)^2}+\frac{C}{\left(x^2+1\right)^3}$ then $B-2 A+C=$

A

23

B

24

C

25

D

26

3
TS EAMCET 2020 (Online) 11th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{x^2}{\left(\sqrt{4-x^2}\right)^3} d x= $$

A

$\frac{x^2}{\sqrt{4-x^2}}-\sin ^{-1}\left(\frac{x}{2}\right)+C$

B

$\frac{x}{\sqrt{4-x^2}}-\tan ^{-1}\left(\frac{x}{\sqrt{4-x^2}}\right)+C$

C

$\frac{x}{\sqrt{4-x^2}}+\sin ^{-1}\left(\frac{2}{\sqrt{4-x^2}}\right)+C$

D

$\sqrt{4-x^2}-\tan ^{-1}\left(\frac{x}{2}\right)+C$

4
TS EAMCET 2020 (Online) 11th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{d x}{x \ln (x) \ln ^2(x) \ln ^3(x) \ldots \ln ^m(x)}=\frac{(\ln (x))^K}{K}+C \Rightarrow 2 K= $$

A

$(m+1)(m+2)$

B

$(2-m)(1-m)$

C

$(m+1)(2-m)$

D

$(m+2)(1-m)$

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