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Maths Limits and Derivatives Class 11 Assertion and Reason Questions

Assertion Reasoning Quiz · Class 11 · Maths · CBSE

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Chapter 12 Class 11 Limits and Derivatives | 7 questions | about 6 minutes

Practise Limits and Derivatives Class 11 with Teachoo's Assertion Reasoning Quiz (Class 11 · Maths · CBSE). Practise these questions in a free interactive quiz with answer feedback.

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Question 1 of 7
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Question 1 of 7
Assertion (A): For the signum function \( f(x) = \frac{|x|}{x} \) (\( x \ne 0 \)), the limit \( \lim_{x \to 0} f(x) \) does not exist.
Reason (R): The function \( y = |x| \) is non-differentiable at \( x = 0 \).
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Question 2 of 7
Assertion (A): For the piecewise function \( f(x) = \begin{cases} x - 2 & \text{if } x < 0 \\ 0 & \text{if } x = 0 \\ x + 2 & \text{if } x > 0 \end{cases} \), the limit \( \lim_{x \to 0} f(x) = 0 \).
Reason (R): The value of the function at \( x = 0 \) is defined as \( f(0) = 0 \).
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Question 3 of 7
Assertion (A): For the function \( f(x) = \frac{1}{x^2} \) (\( x > 0 \)), the limit \( \lim_{x \to 0^+} f(x) = 0 \).
Reason (R): As positive values of \( x \) get closer and closer to 0, \( \frac{1}{x^2} \) grows arbitrarily large without bound (\( \to +\infty \)).
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Question 4 of 7
Assertion (A): The derivative of \( f(x) = x^n \) with respect to \( x \) is \( n x^{n-1} \) for any positive integer \( n \).
Reason (R): The derivative of \( g(x) = \sin x \) with respect to \( x \) is \( \cos x \).
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Question 5 of 7
Assertion (A): The derivative of \( f(x) = x \sin x \) is \( f'(x) = x \cos x + \sin x \).
Reason (R): The derivative of \( \sin x \) is \( \cos x \).
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Question 6 of 7
Assertion (A): For the cost function \( C(x) = 0.005 x^3 - 0.02 x^2 + 30x + 5000 \), the marginal cost when 100 units are produced is ₹ 176.
Reason (R): Marginal cost is the derivative \( C'(x) = 0.015 x^2 - 0.04 x + 30 \), which evaluates to \( 0.015(10000) - 0.04(100) + 30 = 150 - 4 + 30 = 176 \) at \( x = 100 \).
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Question 7 of 7
Assertion (A): \( \lim_{x \to 0} \frac{\tan x}{x} = 0 \).
Reason (R): \( \lim_{x \to 0} \frac{\sin x}{x} = 1 \) and \( \lim_{x \to 0} \cos x = 1 \).
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