1
AP EAPCET 2021 - 19th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$y=x+\frac{1}{x}$$, then which among the following holds?

A
$$x^2 y^{\prime}+x y=0$$
B
$$x^2 y^{\prime}+x y+2=0$$
C
$$x^2 y^{\prime}-x y+2=0$$
D
$$x^2 y^{\prime}+x y-2=0$$
2
AP EAPCET 2021 - 19th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$y=\tan ^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right)$$, where $$x^2 \leq 1$$. Then, find $$\frac{d y}{d x}$$ is equal to

A
$$\frac{\pi}{4}+\frac{1}{2} \cos ^{-1}\left(x^2\right)$$
B
$$\frac{\pi}{4}-\frac{1}{2} \cos ^{-1}\left(x^2\right)$$
C
$$\frac{-x}{\sqrt{1-x^4}}$$
D
$$\frac{-2 x}{\sqrt{1-x^4}}$$
3
AP EAPCET 2021 - 19th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$3 \sin x y+4 \cos x y=5$$, then $$\frac{d y}{d x}$$ is equal to

A
$$\frac{3 \sin x y+4 \cos x y}{3 \cos x y-4 \sin x y}$$
B
$$\frac{3 \cos x y+4 \sin x y}{4 \cos x y-3 \sin x y}$$
C
$$\frac{-y}{x}$$
D
$$\frac{x}{y}$$
4
AP EAPCET 2021 - 19th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$f(x)=\sqrt{x^2+1}: g(x)=\frac{x+1}{x^2+1}: h(x)=2 x-3$$, then the value of $$f^{\prime}\left[h^{\prime}\left(g^{\prime}(x)\right)\right]$$ is equal to

A
$$\sqrt{5}$$
B
$$\frac{2}{\sqrt{5}}$$
C
$$\frac{\sqrt{5}}{2}$$
D
$$\frac{1}{\sqrt{5}}$$
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