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

If $y=\frac{e^{\sin x}+\sinh ^3 x}{\cosh x-\tan x}$, then $y^{\prime}(0)=$

A

0

B

1

C

-1

D

2

2
TS EAMCET 2022 (Online) 19th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A

$\frac{-2}{3}$

B

$\frac{2}{3}$

C

$\frac{1}{3}$

D

$\frac{-1}{3}$

3
TS EAMCET 2022 (Online) 19th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \frac{d}{d x}\left[\left(x^{\frac{5}{2}}-x^{\frac{3}{2}}+1\right)\left(x^2-3 x+5\right)\right]= $$

A

$\frac{9}{2} x^{7 / 2}-14 x^{5 / 2}+20 x^{3 / 2}-\frac{15}{2} x^{1 / 2}+2 x-3$

B

$\frac{9}{2} x^{7 / 2}-7 x^{5 / 2}+5 x^{3 / 2}-\frac{3}{2} x^{1 / 2}+2 x-3$

C

$9 x^{7 / 2}-14 x^{5 / 2}+20 x^{3 / 2}-15 x^{1 / 2}+2 x-3$

D

$\frac{9}{2} x^{7 / 2}-\frac{7}{2} x^{5 / 2}+\frac{5}{2} x^{3 / 2}-\frac{15}{2} x^{1 / 2}+2 x-3$

4
TS EAMCET 2022 (Online) 19th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

The value of $\frac{d}{d x}\left[\log \left(\sin \sqrt{\frac{x^2+1}{x^2+2}}\right)\right]$ when $x=\sqrt{2}$, is

A

$\frac{\sqrt{2} \cot \left(\frac{\sqrt{3}}{2}\right)}{6 \sqrt{3}}$

B

$\frac{\sqrt{2} \tan \left(\frac{\sqrt{3}}{2}\right)}{6 \sqrt{3}}$

C

$\frac{\sqrt{2} \cot \left(\frac{\sqrt{3}}{2}\right)}{8 \sqrt{3}}$

D

$\frac{\sqrt{2} \tan \left(\frac{\sqrt{3}}{2}\right)}{8 \sqrt{3}}$

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