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COMEDK2024MathematicsBinomial Theorem

The total number of terms in (x-y)²⁰+(x+y)²⁰ is

Options

  1. A10
  2. B20
  3. C21
  4. D11

Correct answer

D. 11

Step-by-step solution

By using binomial expansion (x+y)²⁰= ²⁰ C₀ x²⁰+ ²⁰ C₁ x¹⁹ y+ ²⁰ C₂ x¹⁸ y^2+ 20 20 y²⁰ ...(i) and (x-y)²⁰= ²⁰ C₀ x²⁰- ²⁰ C₁ x¹⁹ y+ ²⁰ C₂ x¹⁸ y^2 - + 20 20 y²⁰ ...(ii) Add both the Eqs. (i) and (ii), array r (x+y)²⁰+(x-y)²⁰=2 [ ²⁰ C₀ x²⁰+ ²⁰ C₂ x¹⁸ y^2 + + 20 20 y²⁰ ] array Total number of terms =11

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