1
TS EAMCET 2023 (Online) 14th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $y=x \sin x$ and $\frac{\frac{d y}{d x}-\frac{y}{x}}{x \frac{d y}{d x}-y}$ at $x=\alpha$ is 1 , then $\alpha=$

A

$\sqrt{2}$

B

2

C

1

D

$1 / \sqrt{2}$

2
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

On differentiation if we get $f(x, y) d y-g(x, y) d x=0$ from $2 x^2-3 x y+y^2+x+2 y-8=0$, then $\frac{g(2,2)}{f(1,1)}=$

A

$11 / 7$

B

-3

C

$-1 / 3$

D

7

3
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $f(x)=e^x, h(x)=(f \circ f)(x)$, then $\frac{h^{\prime}(x)}{h(x)}=$

A

$h(x)$

B

$\frac{1}{h(x)}$

C

$\log h(x)$

D

$-\log h(x)$

4
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\sin y=\sin 3 t$ and $x=\sin t$, then $\frac{d y}{d x}=$

A

$\frac{3}{\sqrt{4-x^2}}$

B

$\frac{3}{\sqrt{1-x^2}}$

C

$\frac{1}{\sqrt{4-x^2}}$

D

$\frac{-1}{\sqrt{4-x^2}}$

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