LIMITS AND DERIVATIVES - 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)
📚
ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
Sharing this chapter
Mathematics | Maths Class 11
Mathematics | Maths Class 11 — Complete Notes & Solutions · academia-aeternum.com
🎓 Class 11 📐 Maths 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
Share on
WhatsApp
Telegram
X / Twitter
Facebook
LinkedIn
Reddit
Email
www.academia-aeternum.com/blogs/MCQs/mathematics/xi-class/limits-and%20derivatives-xi-mcqs/ Copy link
💡
Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

Frequently Asked Questions

A limit describes the value that a function \(f(x)\) approaches as \(x\) approaches a particular number, written as \(\lim_{x\to a} f(x)\).

It means that the values of \(f(x)\) can be made arbitrarily close to \(L\) by taking \(x\) sufficiently close to \(a\), but not necessarily equal to \(a\).

No, the limit depends on the behavior of the function near the point, not necessarily on the value of \(f(a)\).

The left-hand limit is \(\lim_{x\to a^-} f(x)\), where \(x\) approaches \(a\) from values less than \(a\).

The right-hand limit is \(\lim_{x\to a^+} f(x)\), where \(x\) approaches \(a\) from values greater than \(a\).

A limit exists at \(x=a\) if both left-hand and right-hand limits exist and are equal.

An infinite limit occurs when \(f(x)\) increases or decreases without bound as \(x\) approaches a value, written as \(\lim_{x\to a} f(x)=\infty\).

For a constant function \(f(x)=c\), \(\lim_{x\to a} c = c\) for any real number \(a\).

For \(f(x)=x\), \(\lim_{x\to a} x = a\).

If \(\lim_{x\to a} f(x)=L\) and \(\lim_{x\to a} g(x)=M\), then \(\lim_{x\to a} [f(x)+g(x)]=L+M\).

\(\lim_{x\to a} [f(x)-g(x)] = L-M\), provided the individual limits exist.

For a constant \(k\), \(\lim_{x\to a} kf(x)=k\lim_{x\to a} f(x)=kL\).

\(\lim_{x\to a} [f(x)g(x)] = LM\), if both limits exist.

\(\lim_{x\to a} \frac{f(x)}{g(x)}=\frac{L}{M}\), provided \(M\neq 0\).

The limit of a polynomial at \(x=a\) is found by direct substitution of \(x=a\).

Recent Posts

    --:-- ⏱ Time
    ⚡ Progress 0 / 50 answered

    LIMITS AND DERIVATIVES – Learning Resources

    Detailed Notes
    True / False
    NCERT Solutions
    Practice Advance MCQs

    Get in Touch

    Let's Connect

    Questions, feedback, or suggestions?
    We'd love to hear from you.