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Maths Continuity and Differentiability Class 12 Assertion and Reason Questions

Assertion Reasoning Quiz · Class 12 · Maths · CBSE

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

Practise Continuity and Differentiability Class 12 with Teachoo's Assertion Reasoning Quiz (Class 12 · Maths · CBSE). Practise these questions in a free interactive quiz with answer feedback.

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Question 1 of 5
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Question 1 of 5
Assertion (A): The function \(f(x)=[x]\) has a jump discontinuity at every integer.
Reason (R): The left-hand limit and the right-hand limit at any integer are not equal.
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Question 2 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 3 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 4 of 5
Assertion (A): The function \(f(x)=\sin \left(x^2\right)\) is a continuous function.
Reason (R): The composition of two continuous functions is a continuous function.
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Question 5 of 5
CBSE Board Exam 2025
Assertion (A) : \(\mathrm{f}(x)=\left\{\begin{array}{cc}3 x-8, & x \leq 5 \\ 2 \mathrm{k}, & x>5\end{array}\right.\) is continuous at \(x=5\) for \(\mathrm{k}=\frac{5}{2}\).
Reason (R) : For a function f to be continuous at \(x=\mathrm{a}\),

$$ \lim _{x \rightarrow \mathrm{a}^{-}} \mathrm{f}(x)=\lim _{x \rightarrow \mathrm{a}^{+}} \mathrm{f}(x)=\mathrm{f}(\mathrm{a}) $$
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