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COMEDK2023MathematicsBinomial Theorem

The total number of terms in the expansion of (x+y)⁶⁰+(x-y)⁶⁰ is

Options

  1. A60
  2. B61
  3. C30
  4. D31

Correct answer

D. 31

Step-by-step solution

aligned (x+y)⁶⁰= ⁶⁰ C₀ x⁶⁰- ⁶⁰ C₁ x⁵⁹ y+ . . & & + 60 60 y⁶⁰ ( i ) aligned By adding Eq. (i) and Eq. (ii) aligned & (x+y)⁶⁰+(x-y)⁶⁰ & = 2 ( ⁶⁰ C₀ x^6+ ⁶⁰ C₂ x⁵⁸ y^2+ + 60 60 y⁶⁰ ) _ 31 terms aligned Hence, the expansion of (x+y)⁶⁰+(x-y)⁶⁰ has 31 terms.

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