1
TS EAMCET 2022 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $x$ and $y$ are two positive integers such that $x+2 y=10$ and $x^2 y^3$ is maximum, then $x^2+2 y^3=$

A

34

B

137

C

43

D

70

2
TS EAMCET 2022 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\frac{3 \pi}{4}

A

$\frac{2^x}{\log 2}-\sin x+\cos x-\frac{1}{x}-\log x+c$

B

$2^x \log 2+\sin x-\cos x-\frac{1}{x}+\frac{1}{x^2}+c$

C

$\frac{2^x}{\log 2}+\sin x-\cos x-\frac{1}{x}-\log x+c$

D

$2^x \log 2-\sin x+\cos x-\frac{1}{x}+\frac{1}{x^2}+c$

3
TS EAMCET 2022 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\tan \alpha=\frac{4}{3}$, then $\int \frac{1}{3 \cos x-4 \sin x} d x=$

A

$\frac{1}{5} \log \left|\tan \left(\frac{x}{2}+\frac{\alpha}{2}\right)\right|+c$

B

$\frac{1}{5} \log \left|\tan \left(\frac{\pi}{4}+\frac{x}{2}+\frac{\alpha}{2}\right)\right|+c$

C

$\frac{1}{5} \log \left|\tan \left(\frac{\pi}{4}-\frac{x}{2}-\frac{\alpha}{2}\right)\right|+c$

D

$\frac{1}{5} \log |\tan (\sec x+\tan x)|+c$

4
TS EAMCET 2022 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $x \neq(2 n+1) \frac{\pi}{2}$, then $\int \frac{\cos ^3 x}{(1+\sin x)^4} d x=$

A

$-\frac{\cos ^4 x}{(1+\sin x)^3}+c$

B

$-\frac{\cos ^3 x}{(1+\sin x)^3}+c$

C

$-\frac{\cos ^4 x}{(1+\sin x)^4}+c$

D

$-\frac{\cos ^4 x}{4(1+\sin x)^4}+c$

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