1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 ⁿCᵣ + ⁿCᵣ₋₁ = ⁿ⁺¹Cᵣ Σ ⁿCᵣ = 2ⁿ
(x+y)ⁿ
Chapter 7  ·  Class XI Mathematics  ·  MCQ Practice

MCQ Practice Arena

Binomial Theorem

Expand, Extract, Conquer — Make the General Term Your Best Friend

📋 50 MCQs ⭐ 18 PYQs ⏱ 90 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
12Easy
22Medium
16Hard
18PYQs
90 secAvg Time/Q
9Topics
Easy 24% Medium 44% Hard 32%

Why Practise These MCQs?

JEE MainJEE AdvancedCBSEBITSAT

Binomial Theorem gives 2–3 JEE Main MCQs every session. The general term Tᵣ₊₁ and coefficient extraction are the top question types. Middle term and greatest term problems appear in CBSE. JEE Advanced combines binomial with series sums. BITSAT tests numerical value calculations from expansions.

Topic-wise MCQ Breakdown

Basic Expansion5 Q
General Term Tᵣ₊₁8 Q
Specific Term / Coeff.9 Q
Middle Term5 Q
Greatest Term4 Q
Binomial Coefficients5 Q
Independent of x Term6 Q
Approximation3 Q
Binomial Series5 Q

Must-Know Formulae Before You Start

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

$\mathrm{Tᵣ₊₁ = ⁿCᵣ·x^{n−r}·y^r}$
$\mathrm{Sum\ of\ coefficients:\ put\ x=y=1 → 2^n}$
$\mathrm{Middle\ term\ (n\ even):\ T_{n/2+1}}$
$\mathrm{\sum ⁿCᵣ·(-1)^r = 0\ (alternate\ sum)}$

MCQ Solving Strategy

Write the general term Tᵣ₊₁ = ⁿCᵣ·xⁿ⁻ʳ·yʳ for every expansion MCQ and find r first. For "independent of x" questions, set the power of x to zero and solve for r. For greatest term, use Tᵣ₊₁/Tᵣ ≥ 1 and solve for r. Never expand beyond what is asked — stop at the required term.

⚠ Common Traps & Errors

Difficulty Ladder

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

① Easy

Write general term, find 3rd or 4th term of expansion

② Medium

Coefficient of xⁿ, middle term, sum of coefficients

③ Hard

Greatest term, independent of x with two variables, combined problems

★ PYQ

JEE Main — extract specific term; CBSE — middle term + binomial identities

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 Sequences & Series MCQs
🎯 Knowledge Check

Maths — BINOMIAL THEOREM

50 Questions Class 11 MCQs
1
What is the value of \((a+b)^0\), where \(a+b \ne 0\)?
(Basics | Conceptual)
2
How many terms are there in the expansion of \((a+b)^7\)?
(Basics | NCERT)
3
The coefficient of \(a^{n-r}b^r\) in \((a+b)^n\) is
(Basics | Formula-based)
4
The first term in the expansion of \((a+b)^n\) is
(Basics | Terminology)
5
The last term in the expansion of \((a+b)^n\) is
(Basics | Terminology)
6
The number of middle terms in \((a+b)^8\) is
(Moderate | Structure)
7
The middle term of \((a+b)^10\) is the
(Moderate | Structure)
8
The general term of \((a+b)^n\) is
(Basics | Formula)
9
The coefficient of \(x^3\) in \((x+2)^5\) is
(Moderate | Computation)
10
The coefficient of \(x^2\) in \((1+x)^5\) is
(Basics | Direct)
11
The sum of all coefficients in \((a+b)^n\) is
(Moderate | Property)
12
The value of \(\sum_{r=0}^n(-1)^r\,^nC_r\) is
(Moderate | Property)
13
The expansion of \((a-b)^n\) contains
(Moderate | Conceptual)
14
The coefficient of the term independent of \(x\) in \((x+\frac{1}{x})^6\) is
(Moderate | Application)
15
The greatest coefficient in \((1+x)^8\) is
(Moderate | Conceptual)
16
The number of middle terms in \((a+b)^9\) is
(Basics | Structure)
17
The coefficient of \(x^4\) in \((2x-1)^5\) is
(Moderate | Computation)
18
The term independent of \(x\) in \((2x+\frac{3}{x})^4\) is
(Moderate | Application)
19
Which identity is used in the proof of the Binomial Theorem by induction?
(Moderate | Proof-based)
20
Pascal’s Triangle is used to find
(Basics | Conceptual)
21
The remainder when \(6^n-5^n\) is divided by \(25\) is
(Advanced | Remainder)
22
The remainder when \(99^5\) is divided by \(100\) is
(Advanced | Remainder)
23
Which is larger: \((1.01)^{1000}\) or \(10\)?
(Advanced | Comparison)
24
The coefficient of \(x^5\) in \((x-2)^7\) is
(Advanced | Coefficient)
25
The term independent of \(x\) in \((x^2+\frac{1}{x})^6\) is
(Advanced | Independent Term)
26
The greatest coefficient in \((1+x)^{12}\) is
(Advanced | Greatest Term)
27
The sum of coefficients of odd powers of \(x\) in \((1+x)^{10}\) is
(Advanced | Property)
28
The value of \(\sum_{r=0}^n\,^nC_rr\) is
(Advanced | Identity)
29
The coefficient of \(x^4\) in \((2x+3)^6\) is
(Advanced | Computation)
30
The number of middle terms in \((a+b)^{15}\) is
(Advanced | Structure)
31
The coefficient of \(x^0\) in \((x+\frac{1}{x})^{10}\) is
(Advanced | Independent Term)
32
If \(^nC_2=45\), then \(n=\)
(Advanced | Combination)
33
The ratio of the middle terms of \((a+b)^8\) and \((a-b)^8\) is
(Advanced | Conceptual)
34
The sum of all coefficients in \((2x-3)^5\) is
(Advanced | Property)
35
The coefficient of the term containing \(x^7\) in \((x+1)^{10}\) is
(Advanced | Direct)
36
The remainder when \(101^6\) is divided by \(100\) is
(Advanced | Remainder)
37
Which term of \((a+b)^{12}\) contains \(a^5b^7\)?
(Advanced | Term Identification)
38
The coefficient of \(x^3\) in \((1-2x)^7\) is
(Advanced | Alternating Signs)
39
The value of \(\sum_{r=0}^n(^nC_r)^2\) is
(Advanced | Identity)
40
The greatest term in \((\frac{1}{2}+x)^8\) occurs when
(Advanced | Conceptual)
41
The coefficient of \(x^4\) in \((x^2+3x)^5\) is
(Advanced | Computation)
42
If \((1+x)^n\) has equal coefficients for \(x^r\) and \(x^{r+1}\), then \(n\) is
(Advanced | Reasoning)
43
The number of terms in \((a+b)^{20}\) is
(Basics | Structural)
44
The term independent of \(x\) in \((x^3+\frac{2}{x})^9\) is
(Advanced | Independent Term)
45
The coefficient of \(x^2\) in \((x-1)^8\) is
(Advanced | Computation)
46
The approximate value of \((1.001)^{1000}\) is
(Advanced | Estimation)
47
The coefficient of \(x^5\) in \((2x+1)^6\) is
(Advanced | Direct)
48
If \(^nC_3=35\), then \(n=\)
(Advanced | Combination)
49
The sum of all terms in \((1-x)^n\) for odd \(n\) is
(Advanced | Property)
50
The Binomial Theorem fundamentally connects algebra with
(Higher Order | Conceptual)
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Binomial Theorem Class 11: 50 MCQs with Answers, NCERT & JEE Practice
Binomial Theorem Class 11: 50 MCQs with Answers, NCERT & JEE Practice — Complete Notes & Solutions · academia-aeternum.com
Multiple Choice Questions play a crucial role in assessing conceptual clarity, analytical thinking, and problem-solving speed in Class XI Mathematics. The MCQs based on Chapter 7, Binomial Theorem, are designed to systematically evaluate a learner’s understanding of fundamental principles such as binomial coefficients, general terms, middle terms, special cases, and key identities. Beginning with basic structure-based questions and gradually progressing to higher-order applications involving…
🎓 Class 11 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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