1
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

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

2
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

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

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

If $f(x)=\frac{1+\sec x}{2(\sec x-1)}$ for $0

A

$\operatorname{cosec} x$

B

$-\operatorname{cosec} x$

C

$2 \operatorname{cosec} x$

D

$-2 \operatorname{cosec} x$

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

If $\frac{3 x+5}{(x+1)\left(2 x^2+3\right)}=\frac{A}{x+1}+\frac{B x+C}{2 x^2+3}$ and $f(x)=A x^3+B x^2+7 x+C$, then $5 C-f^{\prime}(-2)=$

A

19

B

15

C

4

D

34

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