The NCERT Solutions for Class 11 Maths Chapter 7 Binomial Theorem Exercise 7.1 cover every question of the first exercise, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
Exercise 7.1 is where students first use the binomial theorem for a positive integral index to expand and evaluate powers. The exercise has 14 questions built around these skills:
- Expanding an expression like (a + b)n term by term using the theorem.
- Finding a numerical value such as (96)3 or (99)5 by splitting the number.
- Writing the general term and using it to prove a divisibility or sum result.
Topics Covered in Exercise 7.1
This exercise builds the whole chapter on one formula. The binomial theorem gives a quick way to expand (a + b)n for any positive integer n, without multiplying the bracket out n times. Every question in Exercise 7.1 is a direct use of this expansion.
- Direct expansion: expanding brackets like (1 − 2x)5, (2x − 3)6 and (x + 1/x)6.
- Numerical evaluation: writing 102 as (100 + 2) and 99 as (100 − 1) before expanding.
- General term: using Tr+1 = nCr an−r br to pick out one term.
- Comparing values: deciding whether (1.1)10000 is larger than 1000.
- Proof questions: showing 9n+1 − 8n − 9 is divisible by 64.
Important: the number of terms in (a + b)n is always n + 1, one more than the power. Getting this count right decides most of the expansion questions.
Question-wise Breakdown of Exercise 7.1
The NCERT Solutions for Class 11 Maths Chapter 7 Binomial Theorem Exercise 7.1 solve all 14 questions in order. The table below shows what each question asks so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Question | What it asks | Skill tested |
|---|---|---|
| Q1–Q5 | Expand brackets such as (1−2x)5, (2x−3)6, (x+1/x)6 | Direct binomial expansion |
| Q6 | Evaluate (96)3 using the theorem | Splitting a number |
| Q7 | Evaluate (102)5 | Expansion of (100+2)5 |
| Q8 | Evaluate (101)4 | Expansion of (100+1)4 |
| Q9 | Evaluate (99)5 | Expansion of (100−1)5 |
| Q10 | Show which is larger: (1.1)10000 or 1000 | Comparing by expansion |
| Q11–Q12 | Find (a+b)4−(a−b)4 and (x+1)6+(x−1)6, then evaluate surds | Sum and difference of expansions |
| Q13 | Show 9n+1−8n−9 is divisible by 64 | Divisibility proof |
| Q14 | Prove ∑ 3r nCr = 4n | Using the theorem in reverse |
The first five questions build speed with plain expansion, while the last few reward students who spot the right split or the right general term.
Key Formulas and Definitions for Exercise 7.1
Exercise 7.1 rests on one main statement and a few supporting results. Students should learn these by heart before attempting the questions.
| Result | Statement |
|---|---|
| Binomial theorem | (a + b)n = nC0 an + nC1 an−1b + ... + nCn bn |
| General term | Tr+1 = nCr an−r br |
| Binomial coefficient | nCr = n! / [r! (n − r)!] |
| Number of terms | (a + b)n has n + 1 terms |
| Sum of coefficients | nC0 + nC1 + ... + nCn = 2n |
| Symmetry | nCr = nCn−r |
Tip: for a difference like (a − b)n, the signs alternate + − + −, because each odd power of (−b) is negative.
Common Mistakes in Exercise 7.1
Students lose easy marks in Exercise 7.1 on sign slips and coefficient errors. The list below covers the mistakes that show up most often in class tests on the NCERT Solutions for Class 11 Maths Chapter 7 Binomial Theorem Exercise 7.1.
- Forgetting the binomial coefficients and writing only the powers, so 6C2 = 15 gets dropped.
- Missing the alternating signs in a difference such as (2x − 3)6.
- Not raising the whole term to its power. In (2x)3 the 2 is also cubed, giving 8x3, not 2x3.
- Choosing an awkward split for a numerical question. Writing 102 as (100 + 2) is far quicker than (90 + 12).
Practice Questions for Exercise 7.1
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 7.1.
Practice Card: Solved Practice Questions for Class 11 Maths Binomial Theorem Exercise 7.1 — attempt each question, then check the worked solution.
Other Exercises of Chapter 7 Binomial Theorem
Chapter 7 Binomial Theorem has Exercise 7.1 plus a Miscellaneous Exercise. Use the table to move to the harder mixed questions once Exercise 7.1 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Miscellaneous Exercise | Class 11 Maths Binomial Theorem Miscellaneous Exercise Solutions |
More Class 11 Maths Binomial Theorem Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 7 Binomial Theorem are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Binomial Theorem Notes |
| Handwritten Notes | Class 11 Maths Binomial Theorem Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Binomial Theorem NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | Relations and Functions Solutions |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | Linear Inequalities Solutions |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | You are here |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | Straight Lines Solutions |
| Chapter 10: Conic Sections | Conic Sections Solutions |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 11,210 Class 11 students conducted before the 2026 exams, 64% of students said the numerical questions like (99)5 in Exercise 7.1 took them the longest, while plain expansions were rated the easiest once the coefficients were memorised.
FAQs on NCERT Solutions for Class 11 Maths Chapter 7 Binomial Theorem Exercise 7.1
Binomial Theorem NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 7 Binomial Theorem Exercise 7.1?
Ans. Exercise 7.1 has 14 questions. The first five ask for direct expansions, the next four evaluate numbers like (96)3 and (99)5, and the last five cover comparisons, surd values and short proofs such as the divisibility of 9n+1 − 8n − 9 by 64.
Ques. What is the binomial theorem used in Exercise 7.1?
Ans. The binomial theorem states that (a + b)n = nC0 an + nC1 an−1b + ... + nCn bn, for any positive integer n. Every question in Exercise 7.1 is a direct use of this expansion.
Ques. How do you evaluate a number like (102)5 using the binomial theorem?
Ans. Split the number into a round part and a small part. Write 102 = 100 + 2, then apply (100 + 2)5 using the theorem. Each term is easy to compute because 100 raised to a power is simple, and the small terms add on quickly.
Ques. What is the general term in the binomial expansion?
Ans. The (r + 1)th term of (a + b)n is Tr+1 = nCr an−r br. This single formula lets students pick out any term without writing the whole expansion, which is useful in the proof questions of Exercise 7.1.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 7 Binomial Theorem Exercise 7.1 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 7 Binomial Theorem Exercise 7.1 are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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