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Chapter 5 Class 12 - Continuity and Differentiability - Short Quiz

Chapter 5 Class 12 Continuity and Differentiability | 5 questions

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Question 1 of 5
Question 1 of 5
The function $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{ll}\frac{\sin x}{x}+\cos \mathrm{x} & , \text { if } \mathrm{x} \neq 0 \\ k & , \text { if } \mathrm{x}=0\end{array}\right.$ is continuous at $\mathrm{x}=0$, then the value of k is

Correct option: B

Answer: B

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Question 2 of 5
The value of c in Rolle's Theorem for the function $\mathrm{f}(\mathrm{x})=e^x \sin x$, $x \in[0, \pi]$ is

Correct option: D

Answer: D

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Question 3 of 5
If $f(x)=2 x$ and $g(x)=\frac{x^2}{2}+1$, then which of the following can be a discontinuous function

Correct option: D

Answer: D

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Question 4 of 5
The set of points where the functions $f$ given by $f(x)=|x-3| \cos x$ is differentiable is

Correct option: B

Answer: B

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Question 5 of 5
If $\mathrm{u}=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$ and $\mathrm{v}=\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$, then $\frac{d u}{d v}$ is

Correct option: D

Answer: D

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