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NCERT Exemplar MCQ Quiz

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Chapter 5 Class 12 Continuity and Differentiability | 7 questions

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Question 1 of 7
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Question 1 of 7
NCERT Exemplar
If \(f(\mathrm{x})=\left\{\begin{array}{c}m x+1, \text { if } x \leq \frac{\pi}{2} \\ \sin x+n, \text { if } x>\frac{\pi}{2}\end{array}\right.\), is continuous at \(\mathrm{x}=\frac{\pi}{2}\), then
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Question 2 of 7
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The value of c in Mean value theorem for the function \(f(\mathrm{x})=\mathrm{x}(\mathrm{x}- 2), x \in[1,2]\) is
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Question 3 of 7
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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
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Question 4 of 7
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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
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Question 5 of 7
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The derivative of \(\cos ^{-1}\left(2 x^2-1\right)\) w.r.t. \(\cos ^{-1} x\) is
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Question 6 of 7
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Differential coefficient of \(\sec \left(\tan ^{-1} x\right)\) w.r.t. \(x\) is
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Question 7 of 7
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Let \(f(x)=|\cos x|\). Then,
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