The coefficient of x⁵⁰ in (1 + x)¹⁰⁰ is
The Binomial Theorem in Class 11 Chapter 7 of the CBSE 2024-2025 NCERT Mathscurriculum teaches students how to expand binomial expressions efficiently. It delves into essential topics such as binomial coefficients, Pascal’s Triangle, and the formula for binomial expansion. The chapter includes MCQ questions designed to challenge students and improve their problem-solving skills. Understanding the Binomial Theorem simplifies complex algebraic expressions and strengthens logical reasoning. It not only prepares students for board exams but also builds a solid foundation for higher-level mathematics, enhancing their ability to tackle advanced mathematical problems and applications.
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Choice (b) is correct.
We know that (r + 1) term in the binomial expansion of (1 + x)ⁿ is given by
Tᵣ ₊ ₁ = ⁿCᵣ(1)ⁿ ⁻ ʳ xʳ = ⁿCᵣxʳ
In the binomial expansion of (1 + x)¹⁰⁰ is given by
Tᵣ ₊ ₁ = ¹⁰⁰Cᵣxʳ
For coefficient of x⁵⁰, put r = 50 in above, we have T ₅₀ ₊ ₁ = ¹⁰⁰ C₅₀ x⁵⁰
The coefficient x⁵⁰ = ¹⁰⁰ C₅₀
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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