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NDA2019MathematicsBinomial TheoremActual

How many terms are there in the expansion of (1+2 x+x^2 )^5+ (1+4 y+4 y^2 )^5 ?

Options

  1. A12
  2. B20
  3. C21
  4. D22

Correct answer

C. 21

Step-by-step solution

aligned & (1+2 x+x^2 )^5+ (1+4 y+4 y^2 )^5 & = [(1+x)^2 ]^5+ [(1+2 y)^2 ]^5 & =(1+x)¹⁰+(1+x y)¹⁰ & Total numbers of terms in each of them is 11 but constant & term will be added & Total terms =11+11-1 & =21 aligned

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