Binomial expansion uses:
- Factorization
- Roots
- Division
- Pascal triangle
Show answer and explanation
Answer: D. Pascal triangle
Binomial coefficients come from Pascal's triangle.
FSC Mathematics: Binomial Theorem, questions with answers
Practise 20 real Federal Board questions on Binomial Theorem from 2023 to 2026. See the answer and explanation as soon as you answer.
20real questions
6multiple choice
5exam sessions
About Binomial Theorem in FSC Mathematics
Binomial Theorem is one of the 14 main chapters in our Federal Board FSC Mathematics question bank (11th class), and about 4% of its real questions come from it. Tayyari Karo has 20 real questions on this chapter from 2023 to 2026; 6 are multiple choice and marked instantly, and the rest are short and long questions with a model answer. By difficulty: 9 hard, 7 medium, 4 easy.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
What is the middle term in the expansion of (x+y)⁶?
- (6 2)x³y³
- (6 3)x³y³
- (6 3)x⁴y²
- (6 2)x⁴y²
Show answer and explanation
Answer: B. (6 3)x³y³
7 terms total; middle (4th) term is ⁶C₃x³y³.
The coefficient of x² in (1+2x)³ is:
- 12
- 18
- 24
- 30
Show answer and explanation
Answer: A. 12
³C₂·2² = 3×4 = 12.
What is the coefficient of the 3rd term in the expansion of (x−1/x)⁸?
- ⁸C₃
- ⁸C₄
- 1
- ⁸C₂
Show answer and explanation
Answer: D. ⁸C₂
T₃ (r=2 term) = ⁸C₂ x^(8−2)(−1/x)² = ⁸C₂ x⁴, so the coefficient is ⁸C₂.
The sum of the odd coefficients in the expansion of (1+x)⁷ is:
- 16
- 32
- 64
- 128
Show answer and explanation
Answer: C. 64
Sum of odd‑position coefficients = [f(1) − f(−1)]/2 = [2⁷ − 0]/2 = 128/2 = 64.
The first three terms in the expansion of (1−x)^(1/2) are:
- 1 + x/2 − x²/8 + ...
- 1 − x/2 − x²/8 + ...
- 1 − x/2 + 3x²/8 + ...
- 1 − x/2 − 3x²/8 + ...
Show answer and explanation
Answer: B. 1 − x/2 − x²/8 + ...
(1+y)^(1/2) = 1 + y/2 − y²/8 + ...; put y = −x to get 1 − x/2 − x²/8 + ...
Find the remainder when 9²⁰⁵ is divided by 31 using Binomial expansion.
Show model answer
By Fermat's little theorem 9³⁰≡1(mod31); actually 9¹⁵≡1(mod31) (order 15).
205 = 15×13+10 ⇒ 9²⁰⁵≡9¹⁰(mod31)
Computing successively: 9,19,16,20,25,8,10,28,4,5
Remainder = 5
Expand (1+x)⁵ using Binomial theorem and find the coefficient of x².
Show model answer
(1+x)⁵ = 1+5x+10x²+10x³+5x⁴+x⁵
Coefficient of x² = ⁵C₂ = 10
Sessions with Binomial Theorem questions
| Session | Questions |
|---|---|
| 2026 Annual | 3 |
| 2025 1st Annual | 5 |
| 2025 2nd Annual | 6 |
| 2024 Annual | 2 |
| 2023 Annual | 4 |
Common questions
What does the Binomial Theorem chapter cover on this page?
20 real Federal Board (FBISE) Mathematics questions on Binomial Theorem from 2023 to 2026, for 11th class. Each one shows the session it came from.
Are the answers official?
No. We could not find an official FBISE marking scheme for these papers, so the answers and explanations are written by Tayyari Karo for practice. Check anything important with your teacher or textbook.
Is it free?
You can start free with no signup. A small set of papers per subject is free, and Premium unlocks the full question bank.
Other Mathematics chapters
- Differentiation 61
- Conic Sections 46
- Vectors 46
- Integration 39
- Functions and Limits 31
- Trigonometric Identities 30
- Matrices and Determinants 29
- Sequences and Series 28
- Introduction to Analytic Geometry 28
- Fundamentals of Trigonometry 26
- Quadratic Equations 21
- Permutation/Combination/Probability 19
- Number Systems 17