x y z (x,y,z) d=√(Δx²+Δy²+Δz²)
lim
Chapter 12  ·  Class XI Mathematics  ·  MCQ Practice

MCQ Practice Arena

Limits & Derivatives

Where Calculus Begins — Speed Through Limits, Ace the Derivative

📋 50 MCQs ⭐ 0 PYQs ⏱ 75 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
18Easy
20Medium
12Hard
0PYQs
75 secAvg Time/Q
12Topics
Easy 36% Medium 40% Hard 24%

Why Practise These MCQs?

JEE MainJEE AdvancedCBSEBITSATKVPY

Limits & Derivatives opens the calculus sequence — the dominant topic of JEE. JEE Main tests standard limits, 0/0 form simplification, and derivative rules in 4–5 MCQs. KVPY has elegant limit evaluation problems. CBSE places first-principles derivative proofs as MCQs. Mastery here guarantees success in Class XII Calculus.

Topic-wise MCQ Breakdown

Concept of Limit5 Q
Algebra of Limits6 Q
Algebraic Limits (0/0)5 Q
Trigonometric Limits9 Q
Exponential/Log Limits4 Q
Limits at Infinity2 Q
First Principles Deriv.1 Q
Derivative — Polynomials6 Q
Derivative — Trig Fns4 Q
Product Rule1 Q
Chain Rule1 Q
Conceptual Derivatives6 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$\lim\limits_{(x\to a)} (xⁿ−aⁿ)/(x−a) = naⁿ⁻¹$
$\lim\limits_{(x\to 0)} \sin x/x = 1$
$\lim\limits_{(x\to 0)} (eˣ−1)/x = 1$
$d/dx(\sin x)=\cos x, d/dx(xⁿ)=nxⁿ⁻¹$
$(uv)'=u'v+uv' \text{(Product Rule)}$

MCQ Solving Strategy

For 0/0 form algebraic limits, factorise the numerator and cancel (x−a). For trig limits, always convert to standard sinx/x or tanx/x form by multiplying and dividing. For derivative MCQs, the product rule is the most used — write it as (uv)' = u'v + uv' and identify u and v clearly before differentiating. First-principles MCQs: use f(x+h)−f(x)/h and let h→0.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Substitute directly, standard limit values, basic derivative rules

② Medium

Factorise for 0/0 form, product and quotient rule, trig limits

③ Hard

Nested limits, limits at infinity, first-principles for complex functions

★ PYQ

JEE Main — algebraic + trig limits; KVPY — elegant conceptual limits

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 🎯 PYQ Bank Previous year questions ✔️❌ True / False Concept-based True & False questions 📘✔️ Exercises Step by step Solutions to textbook exercises ➡ Next Chapter Mathematical Reasoning MCQs
🎯 Knowledge Check

Maths — LIMITS AND DERIVATIVES

50 Questions Class 11 MCQs
1
Evaluate \(\lim\limits_{x\to 2}(x+3)\).
(Basic Concept)
2
Find \(\lim\limits_{x\to 1}(2x^2-3x+1)\).
(Basic Concept)
3
Evaluate \(\lim\limits_{x\to 0}(5x)\).
(Basic Concept)
4
Find \(\lim\limits_{x\to -1}(x^2+2x+1)\).
(Basic Concept)
5
Evaluate \(\lim\limits_{x\to 3}(x^2-9)\).
(Basic Concept)
6
Find \(\lim\limits_{x\to 1}\frac{x^2-1}{x-1}\).
(Factorisation)
7
Evaluate \(\lim\limits_{x\to 2}\frac{x^2-4}{x-2}\).
(Factorisation)
8
Find \(\lim\limits_{x\to 0}\frac{\sin x}{x}\).
(Standard Limit)
9
Evaluate \(\lim\limits_{x\to 0}\frac{\tan x}{x}\).
(Standard Limit)
10
Find \(\lim\limits_{x\to 0}\frac{1-\cos x}{x^2}\).
(Standard Limit)
11
Evaluate \(\lim\limits_{x\to 0}\frac{\sin 3x}{x}\).
(Standard Limit)
12
Find \(\lim\limits_{x\to 0}\frac{\sin 5x}{\sin 2x}\).
(Standard Limit)
13
Evaluate \(\lim\limits_{x\to 1}\frac{x^2+x-2}{x-1}\).
(Factorisation)
14
Find \(\lim\limits_{x\to 0}\frac{e^x-1}{x}\).
(Standard Result)
15
Evaluate \(\lim\limits_{x\to 0}\frac{\ln(1+x)}{x}\).
(Standard Result)
16
Find the derivative of \(f(x)=x^2\) at \(x=1\).
(Derivative from First Principle)
17
The derivative of a constant function is:
(Conceptual)
18
Find \(\frac{d}{dx}(3x)\).
(Basic Derivative)
19
Evaluate \(\frac{d}{dx}(x^3)\).
(Basic Derivative)
20
Find the derivative of \(x^2+5x+1\).
(Basic Derivative)
21
The geometrical meaning of derivative at a point is:
(Conceptual)
22
If \(y=x^n\), then \(\frac{dy}{dx}\) equals:
(Formula Based)
23
Find \(\frac{d}{dx}(\sqrt{x})\).
(Intermediate)
24
Evaluate \(\lim\limits_{x\to 0}\frac{\sin x - x}{x^3}\).
(Advanced Limit)
25
Find \(\frac{d}{dx}(x^2\sin x)\).
(Product Rule – Intro)
26
Evaluate \(\lim\limits_{x\to 0}\frac{e^x-\cos x}{x}\).
(Advanced Limit)
27
Find the derivative of \(\sin x\).
(Standard Derivative)
28
The derivative of \(\cos x\) is:
(Standard Derivative)
29
Find \(\frac{d}{dx}(\tan x)\).
(Standard Derivative)
30
Evaluate \(\lim\limits_{x\to a}\frac{x^2-a^2}{x-a}\).
(Algebraic Limit)
31
If \(f'(x)=0\) for all \(x\), then \(f(x)\) is:
(Conceptual)
32
Find \(\frac{d}{dx}(1/x)\).
(Intermediate)
33
Evaluate \(\lim\limits_{x\to 0}\frac{\tan x - x}{x^3}\).
(Advanced Limit)
34
The derivative represents:
(Conceptual)
35
Find \(\frac{d}{dx}(x^4-3x^2)\).
(Intermediate)
36
Evaluate \(\lim\limits_{x\to 0}\frac{\sin x}{x}\cdot\frac{1}{\cos x}\).
(Combination of Limits)
37
Find the derivative of \(2x^3+5\).
(Intermediate)
38
If \(y=x^2\), then \(\frac{dy}{dx}\) at \(x=0\) is:
(Conceptual)
39
Evaluate \(\lim\limits_{x\to 0}\frac{1}{x}\).
(One-sided Concept)
40
Find \(\frac{d}{dx}(\ln x)\).
(Standard Derivative)
41
The derivative of \(e^x\) is:
(Standard Derivative)
42
Evaluate \(\lim\limits_{x\to 0}\frac{\sqrt{1+x}-1}{x}\).
(Advanced Limit)
43
Find \(\frac{d}{dx}(x^{-2})\).
(Intermediate)
44
If \(f(x)=x^3\), then \(f'(2)\) equals:
(Application)
45
Evaluate \(\lim\limits_{x\to 0}\frac{e^{2x}-1}{x}\).
(Advanced Limit)
46
The slope of the tangent at \(x=a\) is given by:
(Conceptual)
47
Find \(\frac{d}{dx}(x^2+1)^2\).
(Chain Rule – Intro)
48
Evaluate \(\lim\limits_{x\to 0}\frac{\sin 2x}{x}\).
(Standard Limit)
49
If \(y=x^n\), the derivative at \(x=1\) is:
(Application)
50
The limit \(\lim\limits_{x\to 0^+}\ln x\) is:
(Higher Difficulty)
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ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
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Class 11 Limits & Derivatives MCQs – Test Your Concepts with Answers
Class 11 Limits & Derivatives MCQs – Test Your Concepts with Answers — Complete Notes & Solutions · academia-aeternum.com
Limits and derivatives form the foundation of differential calculus and act as a bridge between algebraic reasoning and analytical thinking. The following set of multiple-choice questions is carefully designed to strengthen conceptual clarity while gradually enhancing problem-solving skills. Beginning with basic ideas of limits and continuity, the questions progress through standard algebraic and trigonometric limits, and finally move toward the interpretation and computation of derivatives.…
🎓 Class 11 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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