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## Continuity and Differentiability Class 12 Multiple Choice Test

/10

Thank you for answering the multiple choice test

Continuity and Differentiability Class 12 (120501)

General Instruction:

1. There are 10 MCQ’s in the Test.

2. Passing %age is 50.

3. After time gets over, test will be submitted itself.

1 / 10

If $$x(t) = e^t$$ and $$y(t) = \ln(t)$$, what is $$\frac{dy}{dx}$$?

A) $$\frac{1}{t}$$

B) $$\frac{1}{e^t}$$

C) $$t$$

D) $$\frac{t}{e^t}$$

2 / 10

What is the derivative of $$y = \log(log(x))$$?

A) $$\frac{1}{x \log(x)}$$

B) $$x \log(x)$$

C) $$\frac{1}{x}$$

D) $$\frac{1}{y}$$

3 / 10

If $$f(x) = \sin^{-1}(e^x)$$, what is $$f'(x)$$?

A) $$\frac{e^x}{\sqrt{1-e^{2x}}}$$

B) $$\frac{e^x}{1+e^{2x}}$$

C) $$\frac{1}{\sqrt{1-e^{2x}}}$$

D) $$e^x$$

4 / 10

If $$f(x) = e^{2x}$$, what is $$f”(x)$$?

A) $$2e^{2x}$$
B) $$4e^{2x}$$
C) $$e^{2x}$$
D) $$4x \cdot e^{2x}$$

5 / 10

Given $$x^2 + y^2 = 1$$, what is $$\frac{dy}{dx}$$ at any point on the curve?

A) $$-\frac{x}{y}$$

B) $$\frac{x}{y}$$

C) $$-\frac{y}{x}$$

D) $$\frac{y}{x}$$

6 / 10

Given $$y = x^x$$, what is $$\frac{dy}{dx}$$?

A) $$x^x(\ln(x) + 1)$$

B) $$x^{x-1}$$

C) $$e^x$$

D) $$x \ln(x)$$

7 / 10

What is the derivative of $$\cos^{-1}(x)$$?

A) $$\frac{1}{\sqrt{1-x^2}}$$

B) $$\frac{1}{1+x^2}$$

C) $$-\frac{1}{\sqrt{1-x^2}}$$

D) $$\frac{1}{|x|\sqrt{x^2-1}}$$

8 / 10

What is the derivative of $$\arcsec(x)$$?

A) $$\frac{1}{x\sqrt{x^2-1}}$$

B) $$\frac{1}{\sqrt{x^2-1}}$$

C) $$\frac{1}{|x|\sqrt{x^2-1}}$$

D) $$-\frac{1}{|x|\sqrt{x^2-1}}$$

9 / 10

Given $$y = x^2 \cdot e^x$$, what is $$\frac{dy}{dx}$$?

A) $$2x \cdot e^x + x^2 \cdot e^x$$

B) $$2x \cdot e^x$$

C) $$x^2 \cdot e^x$$

D) $$e^x$$

10 / 10

Given $$x = a \cos(t)$$ and $$y = a \sin(t)$$, what is $$\frac{dy}{dx}$$?

A) $$\tan(t)$$

B) $$\cot(t)$$

C) $$\sin(t)$$

D) $$\cos(t)$$