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Assertion Reasoning Quiz

Chapter 5 Class 12 Continuity and Differentiability | 5 questions | about 4 minutes

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Question 1 of 5
Question 1 of 5
Assertion (A): The function \(f(x)=x^3\) is differentiable everywhere.
Reason (R): The graph of \(y=x^3\) is smooth and has no sharp corners or breaks.
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Question 2 of 5
Assertion (A): The function \(f(x)=\cos |x|\) is differentiable at \(x=0\).
Reason (R): The cosine function is an even function, so \(\cos (-x)=\cos (x)\).
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Question 3 of 5
Assertion (A): A finction must be continuous at a point if it is differentiable at that point.
Reason (R): If the limit of a function exists at a point, it must be differentiable at that point.
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Question 4 of 5
Assertion (A): The function \(f(x)=\frac{x^2-4}{x-2}\) is not continuous at \(x=2\).
Reason (R): The function is not defined at \(x=2\).
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Question 5 of 5
Assertion (A): The function \(f(x)=|x-3|\) is continuous at \(x=3\).
Reason \((\mathrm{R})\) : Every polynomial function is continuous at every point.
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