Chapter 5 Class 12 - Continuity and Differentiability - Short Quiz

Question 1 of 5

The function $\mathrm{f}(\mathrm{x})=\frac{4-x^2}{4 x-x^3}$ is

A discontinuous at only one point B discontinuous at exactly two points C discontinuous at exactly three points D none of these

Correct option: C

Answer: C

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Question 2 of 5

The function given by $\mathrm{f}(\mathrm{x})=\tan \mathrm{x}$ is discontinuous on the set

A $\{n \pi: n \in z\}$ B $\{2 n \pi: n \in Z\}$ C $\left\{(2 n+1) \frac{\pi}{2}: n \in Z\right\}$ D $\left\{\frac{n \pi}{2}: n \in Z\right\}$

Correct option: C

Answer: C

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Question 3 of 5

For the function $\mathrm{f}(\mathrm{x})=\mathrm{x}+\frac{1}{x}, \mathrm{x} \in[1,3]$, the value of c for mean value theorem is

A 1 B $\sqrt{3}$ C 2 D None of these

Correct option: B

Answer: B

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Question 4 of 5

If $x=t^2, y=t^3$, then $\frac{d^2 y}{d x^2}$ is

A $\frac{3}{2}$ B $\frac{3}{4 t}$ C $\frac{3}{2 t}$ D $\frac{3}{4}$

Correct option: B

Answer: B

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Question 5 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

A $\frac{\pi}{6}$ B $\frac{\pi}{4}$ C $\frac{\pi}{2}$ D $\frac{3 \pi}{4}$

Correct option: D

Answer: D

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Chapter 5 Class 12 - Continuity and Differentiability - Short Quiz