Binomial Theorem — Class 11 MCQs with Answers
Class 11 CBSE Mathematics · Chapter 8
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 11 CBSE Mathematics questions from Chapter 8, "Binomial Theorem". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE & Maharashtra HSC Board exams, JEE Main, MHT-CET and JEE Advanced apart.
To score well in "Binomial Theorem", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Binomial Theorem, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 11 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Binomial Theorem (Class 11 Mathematics)
The binomial theorem expands (a + b)ⁿ for a positive integer n into n + 1 terms built from the coefficients nCr. This chapter derives the expansion, isolates the general term T(r+1) to reach any single term, locates the middle term, and explores the properties and sums of the binomial coefficients.
- Binomial theorem
- (a + b)ⁿ = Σ nCr aⁿ⁻ʳ bʳ for r = 0 to n; the powers of a fall from n to 0 while the powers of b rise from 0 to n.
- Binomial coefficients
- The numbers nC0, nC1, …, nCn multiplying each term; they form the nth row of Pascal's triangle and are symmetric about the centre.
- Number of terms
- The expansion of (a + b)ⁿ has exactly n + 1 terms, and in every term the exponents of a and b add up to n.
- General term
- T(r+1) = nCr aⁿ⁻ʳ bʳ is the (r+1)th term; setting the power of the variable to a target value isolates any specific term.
Binomial Theorem — important questions & MCQs with answers (Class 11 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.
- Q1Easy
(a+b)² =
A.a²+2ab+b²✓ CorrectB.a²+b²C.a²−b²D.a²−2ab+b²Answer: A. a²+2ab+b²
Explanation: The (a+b)² identity expands to a²+2ab+b² — dropping the cross term 2ab gives the tempting but wrong a²+b², which only holds when ab=0.
- Q2Easy
Binomial theorem: (a + b)ⁿ =
A.aⁿ + bⁿB.Σ aⁿ · bⁿC.Σ C(n, r) aⁿ⁻ʳ bʳ✓ CorrectD.(ab)ⁿAnswer: C. Σ C(n, r) aⁿ⁻ʳ bʳ
Explanation: Binomial theorem: (a+b)ⁿ = Σᵣ₌₀ⁿ ⁿCᵣ·aⁿ⁻ʳ·bʳ — dropping the ⁿCᵣ weight and just summing aⁿ·bⁿ ignores that each term has its own power split.
- Q3Easy
(x + y)² =
A.x² + 2xy + y²✓ CorrectB.x² − 2xy + y²C.x² + y²D.2(x + y)Answer: A. x² + 2xy + y²
Explanation: (x+y)² = x²+2xy+y² — dropping the cross term 2xy gives the tempting but wrong x²+y², which only equals the square when xy=0.
- Q4Easy
Sum of binomial coefficients of (1 + x)ⁿ is:
A.n!B.2ⁿ✓ CorrectC.2^(n+1)D.n²Answer: B. 2ⁿ
Explanation: Sum of binomial coefficients in (1+x)ⁿ: put x=1, giving ⁿC₀+ⁿC₁+…+ⁿCₙ = (1+1)ⁿ = 2ⁿ — mistaking this sum for n! is the usual confusion.
- Q5Easy
Third term in expansion of (a + b)⁵ is:
A.5 a³b²B.10 a²b³C.5 a²b³D.10 a³b²✓ CorrectAnswer: D. 10 a³b²
Explanation: T₃ in (a+b)⁵ is Tᵣ₊₁ with r=2: ⁵C₂a³b² = 10a³b² — swapping the exponents to a²b³ (using r=2 on the wrong letter) is the common slip.
- Q6Easy
In the expansion of (a + b)⁶, the middle term is the:
A.3rd termB.5th termC.4th term✓ CorrectD.6th termAnswer: C. 4th term
Explanation: With 7 terms in all, the middle one is the 4th.
- Q7Medium
Middle term in (a+b)⁶:
A.4th term✓ CorrectB.3rdC.5thD.6thAnswer: A. 4th term
Explanation: (a+b)⁶ has n=6 (even), so there's one middle term at position n/2+1 = 4 — picking n/2=3rd instead, or counting from the wrong end, is the usual error.
- Q8Medium
Pascal's triangle row for n = 4 gives:
A.1, 5, 10, 10, 5, 1B.1, 3, 3, 1C.1, 4, 6, 4, 1✓ CorrectD.1, 4, 4, 1Answer: C. 1, 4, 6, 4, 1
Explanation: Pascal's row for n=4 is 1,4,6,4,1, giving (a+b)⁴'s coefficients — confusing it with row n=5 (1,5,10,10,5,1) by miscounting rows is the trap.
- Q9Medium
The sum of the coefficients in the expansion of (2x + 3)⁴ is:
A.81B.16C.256D.625✓ CorrectAnswer: D. 625
Explanation: Putting x = 1 gives 5⁴ = 625.
- Q10Medium
Coefficient of x⁵ in expansion of (1 + x)¹⁰:
A.84B.210C.120D.252✓ CorrectAnswer: D. 252
Explanation: Coefficient of x⁵ in (1+x)¹⁰ is ¹⁰C₅ = 10!/(5!5!) = 252 — the peak coefficient in this row, easy to undercount if the factorial cancellation is cut short.
- Q11Medium
Middle term of (1 + x)⁶:
A.15x³B.C(6, 2)·x²C.C(6, 4)·x⁴D.C(6, 3)·x³ = 20x³✓ CorrectAnswer: D. C(6, 3)·x³ = 20x³
Explanation: Middle term of (1+x)⁶: n=6 even, so it's the (6/2+1)=4th term, at r=3: ⁶C₃x³ = 20x³ — picking r=2 (the 3rd term) is the off-by-one trap.
- Q12Hard
Sum of all coefficients in (1+x)ⁿ:
A.n²B.0C.nD.2ⁿ✓ CorrectAnswer: D. 2ⁿ
Explanation: Setting a=b=1 in (a+b)ⁿ collapses every ⁿCᵣ term's variable part to 1, so ΣⁿCᵣ = (1+1)ⁿ = 2ⁿ — mistaking this sum for just n is the common slip.
- Q13Hard
Find n if coefficient of x² in (1 + 3x)ⁿ is 135.
A.8B.9C.5D.6✓ CorrectAnswer: D. 6
Explanation: Coefficient of x² in (1+3x)ⁿ is ⁿC₂·3² = 9·n(n−1)/2. Setting this to 135 gives n(n−1)=30, so n=6 — forgetting to square the 3 (using ×3 alone) misses this factor.
- Q14Hard
The sum of the coefficients of the odd powers of x in the expansion of (1 + x)⁸ is:
A.256B.128✓ CorrectC.70D.64Answer: B. 128
Explanation: The odd and even coefficients each add to half of 2⁸, that is 128.
Start this chapter free
You have 14 solved above. Sign in with Google (no card needed). You get 1 Easy + 1 Medium quiz on every chapter during your 30-day trial. After that, you keep 1 Easy quiz on every chapter, free for good, plus the full key-concept notes, formulas & exam tips.
This chapter has 90 questions (30 Easy · 30 Medium · 30 Hard), with timed scoring and instant feedback. The rest unlock with the ₹999/year plan.
Start this chapter free →Binomial Theorem — FAQs
What are the key concepts in Class 11 Mathematics Binomial Theorem?+
The binomial theorem expands (a + b)ⁿ for a positive integer n into n + 1 terms built from the coefficients nCr. This chapter derives the expansion, isolates the general term T(r+1) to reach any single term, locates the middle term, and explores the properties and sums of the binomial coefficients. Key ideas include Binomial theorem, Binomial coefficients, Number of terms, General term.
What does Class 11 Mathematics Chapter 8 (Binomial Theorem) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Binomial Theorem": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE & Maharashtra HSC Board exams, JEE Main, MHT-CET and JEE Advanced.
Are these "Binomial Theorem" questions free to practise?+
Yes. Sign in with Google to practise "Binomial Theorem" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Binomial Theorem" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Binomial Theorem" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Binomial Theorem" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip, the same negative marking as JEE Main and JEE Advanced. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Binomial Theorem (Class 11 Mathematics)?+
The questions that matter most test Binomial theorem, Binomial coefficients, Number of terms, General term. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Binomial Theorem?+
Yes — Class 11 Mathematics Binomial Theorem has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.