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Limits and Derivatives Practice Questions

Class 11 · Mathematics · 996 free MCQs with instant results and detailed explanations.

996
Total
335
Easy
467
Medium
194
Hard

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Topics in Limits and Derivatives

Algebra of Limits 186
Derivatives 260
First Principle 329
Limits 221

Sample Questions from Limits and Derivatives

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the limit of (3x + 2) as x approaches 1?
A. 5
B. 7
C. 3
D. 2
Show Answer & Explanation
Correct Answer: A
Substituting x = 1 into the expression (3x + 2) gives 3(1) + 2 = 5.
Q2
Easy
What is the limit of sin(x)/x as x approaches 0?
A. 1
B. 0
C. ∞
D. undefined
Show Answer & Explanation
Correct Answer: A
The limit of sin(x)/x as x approaches 0 is a well-known limit and equals 1.
Q3
Easy
Find the limit: lim (x -> 0) (e^x - 1)/x.
A. 0
B. 1
C. e
D. undefined
Show Answer & Explanation
Correct Answer: B
Using L'Hôpital's Rule, the limit of (e^x - 1)/x as x approaches 0 equals e^0, which is 1.
Q4
Medium
Find the value of lim (x→0) (sin(5x)/x).
A. 5
B. 1
C. 0
D. undefined
Show Answer & Explanation
Correct Answer: A
Using the standard limit result lim (x→0) (sin(kx)/x) = k, we find k = 5.
Q5
Medium
Calculate lim (x→∞) (2x² + 3)/(5x² - 4).
A. 2/5
B. 1
C. 0
D. ∞
Show Answer & Explanation
Correct Answer: A
As x approaches infinity, the leading coefficients dominate, hence the limit becomes 2/5.
Q6
Medium
Evaluate the limit: lim (x→1) (x³ - 1)/(x - 1).
A. 3
B. 1
C. 0
D. undefined
Show Answer & Explanation
Correct Answer: A
The expression can be factored as (x - 1)(x² + x + 1), leading to the limit of 3 after evaluating.
Q7
Medium
Find the limit: lim(x→0) (sin(5x)/x).
A. 0
B. 5
C. 1
D. 10
Show Answer & Explanation
Correct Answer: B
Using the limit property, lim(x→0) (sin(kx)/x) = k, we have k = 5, thus the limit is 5.
Q8
Hard
Evaluate the limit: lim(x→0) (sin(3x)/x).
A. 3
B. 1
C. 0
D. 6
Show Answer & Explanation
Correct Answer: A
Using the limit property lim(x→0) (sin(kx)/x) = k, we can substitute k = 3. Thus, the limit evaluates to 3.
Q9
Hard
Evaluate the limit: lim(x→1) (x^3 - 1)/(x - 1).
A. 3
B. 2
C. 1
D. 0
Show Answer & Explanation
Correct Answer: A
Factor the numerator as (x - 1)(x^2 + x + 1). After cancelling (x - 1), the limit becomes 3 when x approaches 1.
Q10
Hard
Determine the limit: lim(x→0) (e^x - 1)/x.
A. 1
B. 0
C. e
D. ∞
Show Answer & Explanation
Correct Answer: A
Using L'Hôpital's rule, differentiate the numerator and denominator. The limit evaluates to 1.

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Limits and Derivatives — Class 11 Mathematics Practice Questions Online

This page contains 996 practice MCQs for the chapter Limits and Derivatives in Class 11 Mathematics. The questions are organized by difficulty — 335 easy, 467 medium, 194 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 4 topics, giving you comprehensive coverage of the entire chapter.