If (1 – x + x²)ⁿ = a₀ + a₁x + a₂x² + a₃x³ + …. + a₂ₙx²ⁿ, then a₁ + a₃ + a₅ …. +a₂ₙ ₋ ₁ equals
Expanding binomial expressions becomes easier with the Binomial Theorem, a key topic in Class 11 Chapter 7 of the CBSE 2024-2025 NCERT Maths syllabus. This chapter introduces fundamental ideas like binomial coefficients Pascal’s Triangle and the expansion formula. It also provides MCQ questions to test understanding and develop logical thinking. Learning this theorem helps students simplify complex algebraic expressions and improves problem-solving abilities. A strong grasp of the concept prepares students for board exams and competitive tests. Mastering the Binomial Theorem builds a solid foundation for higher mathematics and enhances analytical skills for advanced calculations.
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Choice (c) is correct.
We have, (1 + x + x²)ⁿ = a₀ + a₁x + a₂x² + a₃x³ + …. + a₂ₙx²ⁿ
Putting x = 1 and – 1 in (1), we get
1 = a₀ + a₁ + a₂ + a₃ + …. a₂ₙ
and 3ⁿ = a₀ + a₁x + a₂x² + a₃x³ + …. + a₂ₙ
Subtracting (3) from (2), we get
1 – 3ⁿ = 2(a₁ + a₃ + a₅ …. +a₂ₙ ₋ ₁)
⇒ a₁ + a₃ + a₅ …. +a₂ₙ ₋ ₁ = 1 – 3ⁿ/ 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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