Teachoo Quiz

Maths Limits and Derivatives Class 11 MCQ and Assertion Questions

10 Question MCQ (including Assertion) · Class 11 · Maths · CBSE

Preparing for CBSE

Chapter 12 Class 11 Limits and Derivatives | 10 questions | about 8 minutes

Practise Limits and Derivatives Class 11 with Teachoo's 10 Question MCQ (including Assertion) (Class 11 · Maths · CBSE). Practise these questions in a free interactive quiz with answer feedback.

Attempt time 0:00
This question 0:00
Question 1 of 10
Advertisement
Question 1 of 10
Find the derivative of \( f(x) = \sqrt{x} \) at \( x = 4 \) from the first principle.
Select an option to see the answer, or skip this question.
Question 2 of 10
Assertion (A): \( \lim_{x \to 0} \frac{1 - \cos 2x}{x^2} = 2 \).
Reason (R): The identity for \( 1 - \cos 2x \) is \( 1 - \cos 2x = \cos^2 x - \sin^2 x \).
Select an option to see the answer, or skip this question.
Question 3 of 10
Evaluate \( \lim_{x \to 0} \frac{ax + x \cos x}{b \sin x} \) where \( b \ne 0 \).
Select an option to see the answer, or skip this question.
Question 4 of 10
Let \( f(x) = \begin{cases} x + 2 & \text{if } x \ne 1 \\ 0 & \text{if } x = 1 \end{cases} \). What is \( \lim_{x \to 1} f(x) \)?
Select an option to see the answer, or skip this question.
Question 5 of 10
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 \( f(0) = 0 \).
Select an option to see the answer, or skip this question.
Question 6 of 10
Find the derivative of \( f(x) = \frac{a + b \sin x}{c + d \cos x} \).
Select an option to see the answer, or skip this question.
Question 7 of 10
Find \( \lim_{x \to 0} f(x) \), where \( f(x) = \begin{cases} \frac{|x|}{x}, & x \ne 0 \\ 0, & x = 0 \end{cases} \).
Select an option to see the answer, or skip this question.
Question 8 of 10
Compute the derivative of \( h(x) = \frac{x^5 - \cos x}{\sin x} \) for all \( x \) where \( \sin x \ne 0 \).
Select an option to see the answer, or skip this question.
Question 9 of 10
If the function \( f(x) \) satisfies \( \lim_{x \to 1} \frac{f(x) - 2}{x^2 - 1} = \pi \), what is the value of \( \lim_{x \to 1} f(x) \)?
Select an option to see the answer, or skip this question.
Question 10 of 10
An expanding circular oil spill has area \( A(r) = \pi r^2 \). What is the rate of change of the area with respect to radius \( r \) when \( r = 5 \text{ cm} \)?
Select an option to see the answer, or skip this question.

Frequently asked questions

Who is this Limits and Derivatives Class 11 quiz for?

This 10 Question MCQ (including Assertion) covers Limits and Derivatives Class 11 for Class 11 · Maths · CBSE. Practise the questions in the interactive quiz and check your answers.

Is this quiz free?

Yes. This online quiz is free to attempt. Teachoo Black is not required to take the quiz.

How many questions will I get?

The current selection contains 10 questions. The questions and count can vary with the available question bank and grouped questions.

Can I check my answers and score?

Yes. In quiz mode, check your answer to receive feedback. Submit the quiz to review your score and answers. Full Teachoo solution links are shown where available.

Will I get the same questions when I retry?

Questions can change between attempts. Teachoo uses your previous practice when available to prioritise new questions and revision; a completely new set is not guaranteed.

Practice · Limits and Derivatives Class 11

Stuck? Keep your progress moving.