The number of terms in the expansion of (a + b + c)ⁿ, where n ∈ N is
In CBSE 2024-2025 NCERT Maths for Class 11th, Chapter 7: Binomial Theorem is all about unlocking the power of binomial expansions. Students explore essential concepts like binomial coefficients, Pascal’s Triangle, and how to apply the expansion formula to simplify complex expressions. The chapter also features challenging MCQ Questions to test knowledge and boost problem-solving skills. Understanding the Binomial Theorem sharpens logical thinking and prepares students for both board exams and competitive tests. By mastering this concept, students build a strong mathematical foundation that helps tackle advanced problems with ease and confidence.
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Choice (a) is correct.
We have (a + b + c)ⁿ = {a + (b + c)}ⁿ = aⁿ + ⁿC₁aⁿ ⁻ ¹ (b + c) + ⁿC₂aⁿ ⁻ ²(b – c)² + …. + ⁿCₙ(b + c)ⁿ
On expanding each term of R.H.S., we get
Number of terms in first term = 1
Number of terms in second term = 2
Number of terms in third term = 3
Number of terms in fourth term = 4
Number of terms in (n + 1)th term = n + 1
Total number of terms = 1 + 2 + 3 + ….. + (n +1)
= (n – 1) {1 + (n + 1)}/2
= (n + 1)(n + 2) /2
This question related to Chapter 7 maths Class 11th NCERT. From the Chapter 7: Binomial Theorem. Give answer according to your understanding.
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