Chapter 5 Class 12 - Continuity and Differentiability - Short Quiz

Question 1 of 5

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

A R B \(R-\{3\}\) C \((0, \infty)\) D None of these

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Question 2 of 5

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The set of points where the function \(f\) given by \(f(x)=|2 x-1| \sin x\) is differentiable is

A R B \(R-\left\{\frac{1}{2}\right\}\) C \((0, \infty)\) D none of these

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Question 3 of 5

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The value of c in Rolle's theorem for the function \(\mathrm{f}(\mathrm{x})=\mathrm{x}^3-3 \mathrm{x}\) in the interval \([0, \sqrt{3}]\) is

A 1 B -1 C \(\frac{3}{2}\) D \(\frac{1}{3}\)

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Question 4 of 5

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Let \(f(x)=|\cos x|\). Then,

A \(f\) is everywhere differentiable. B \(f\) is everywhere continuous but not differentiable at \(\mathrm{n}=\mathrm{n} \pi, \mathrm{n} \in \mathrm{Z}\) C \(f\) is everywhere continuous but not differentiable at \(\mathrm{x}=(2 \mathrm{n}+1) \frac{\pi}{2}\), \(\mathrm{n} \in \mathrm{Z}\) D None of these

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Question 5 of 5

NCERT Exemplar

The temperature of a cup of coffee, \(T(t)\), over time \(t\) is modeled by a function. Which of the following statements best describes why \(T(t)\) must be a continuous function?

A The temperature can be measured at any instant in time. B The coffee cools down, so the function is always decreasing. C The temperature cannot jump from one value to another instantaneously. D The rate of cooling eventually slows down.

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Chapter 5 Class 12 - Continuity and Differentiability - Short Quiz