The RD Sharma Solutions for Class 11 Maths Chapter 18 – Binomial Theorem are designed to help students build a clear understanding of core concepts. A binomial expression is defined as an algebraic expression that consists of exactly two terms. To support conceptual clarity, these solutions have been carefully prepared by expert educators, aiming to address common student doubts and enhance comprehension.
These step-by-step solutions not only help students solve problems correctly but also improve their confidence and problem-solving abilities — a key requirement for success in exams.
Chapter 18 focuses on the Binomial Theorem and includes two exercises. The RD Sharma solutions offer precise and structured answers for each question, making it easier for students to follow the correct method. Learners who want to understand the proper approach to solving problems efficiently can benefit from these solutions, which are available in PDF format and aligned with the latest 2025–26 syllabus.
RD Sharma Solutions Class 11 Maths Chapter 18 - Overview
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Binomial Theorem for Positive Integral Indices
- Important Properties Derived from the Theorem
- General Term and Middle Term in a Binomial Expansion
These topics lay a strong foundation for algebraic reasoning and are essential for higher-level mathematics.
RD Sharma Solutions Class 11 Maths Binomial Theorem Question with Answers
🔹 Basic Concept & Expansion
Q1. Expand (1 + x)5.
Ans: (1 + x)5 = 1 + 5x + 10x² + 10x³ + 5x⁴ + x⁵
Q2. Write the 4th term in the expansion of (2 + x)6.
Ans: 4th term = 160x³
Q3. Find the number of terms in the expansion of (a + b)10.
Ans: 11 terms
Q4. Expand (1 - 2x)4.
Ans: 1 - 8x + 24x² - 32x³ + 16x⁴
Q5. Find the coefficient of x³ in (1 + 2x)5.
Ans: 80
🔹 General Term
Q6. Write the general term Tr+1 in (x + a)n.
Ans: Tr+1 = C(n, r) xn-r ar
Q7. Find the 5th term in the expansion of (3x - 2)6.
Ans: 2160x²
Q8. What is the general term of the expansion of (2x - 1)8?
Ans: Tr+1 = C(8, r) · (2x)8–r · (–1)r
Q9. Find the term independent of x in the expansion of (x² + 1/x)9.
Ans: Term = 84
Q10. In (1 + x)8, find the term containing x5.
Ans: 56x⁵
🔹 Middle Term & Symmetry
Q11. How many middle terms are there in (a + b)10?
Ans: 2 (T₆ and T₇)
Q12. Find the middle term in (x + 3)7.
Ans: 945x⁴
Q13. In (1 - x)8, find the coefficient of the middle term.
Ans: 70
Q14. Show that coefficients of equidistant terms from start and end in (1 + x)n are equal.
Ans: C(n, r) = C(n, n–r)
Q15. Find the middle term of (2 – 3x)6.
Ans: –4320x³
🔹 Properties & Applications
Q16. Evaluate ∑C(n, k) from k = 0 to n.
Ans: 2ⁿ
Q17. Show that sum of coefficients in (x + a)n is (1 + a)n.
Ans: Put x = 1
Q18. Find the sum of coefficients in (2x – 1)5.
Ans: 1
Q19. Find the sum of all coefficients in (1 + x + x²)3.
Ans: 27
Q20. Evaluate ∑C(5, k)·2k from k = 0 to 5.
Ans: 243
🔹 Advanced Pattern & Simplification
Q21. Find coefficient of x⁴ in (1 + x)²(1 + x)³.
Ans: 5
Q22. Find ∑C(7, k) from k = 0 to 7.
Ans: 128
Q23. Prove ∑(–1)k·C(n, k) = 0
Ans: Follows from (1 – 1)n = 0
Q24. In (a + b)n, total number of terms is?
Ans: n + 1
Q25. What is the sum of alternate terms in (1 + x)4?
Ans: 8
🔹 Objective & Application-Based
Q26. Which term has the greatest coefficient in (1 + x)6?
Ans: T₄ with coefficient 20
Q27. General term of (x + 1/x)10?
Ans: Tr+1 = C(10, r) · x10 – 2r
Q28. Which term in (x + 2/x)7 is independent of x?
Ans: None (no integer r gives x⁰)
Q29. Coefficient of x⁰ in (x + 1/x)6?
Ans: 20
Q30. Coefficient of x⁻³ in (x – 2/x)8?
Ans: 0
Q31. Constant term in (x³ + 1/x²)7?
Ans: 35
Q32. Coefficient of x⁰ in (2x + 1/x)12?
Ans: 59136
Q33. Find term with x⁵ in (1 + 2x)6.
Ans: 192x⁵
Q34. Total terms in (x + x² + x³)4?
Ans: 9
Q35. In (1 + x)n, for which r is Tr+1 greatest?
Ans: r = ⌊n/2⌋ when x = 1
Frequently Asked Questions
The Binomial Theorem has real-life applications in:
- Probability and Statistics: Binomial distributions
- Computer Algorithms: Combinatorial calculations
- Finance: Compound interest and growth models
- Physics: Expansions in Taylor or Maclaurin series
- Engineering: Signal processing, data modeling
Binomial Theorem is important in Class 11 because:
- It builds a foundation for algebraic manipulations.
- It improves problem-solving skills in higher-order polynomial expansions.
- It is essential for board exam preparation and forms the base for JEE and Olympiad-level problems.
- It is also applied in Calculus (Class 12) for approximations.
Yes, the Binomial Theorem is extremely important for JEE Main, JEE Advanced, and other competitive exams like BITSAT. It helps with algebraic simplification, term identification, and mathematical reasoning. While NEET doesn’t focus heavily on this chapter, strong basics are still beneficial in analytical thinking and problem solving.
The RD Sharma Class 11 Binomial Theorem chapter includes over 150 practice questions, divided into different exercises covering basic expansion, general term, middle term, properties, and miscellaneous problems. In the above resource, we’ve shared 35 carefully selected solved questions across all difficulty levels to help students prepare effectively.