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BITSAT2023MathematicsBinomial TheoremActual

The middle term in the expansion of ( 10 x + x 10 )¹⁰ is

Options

  1. A¹⁰ C ₅
  2. B¹⁰ C ₆
  3. C¹⁰ C ₅ 1 x¹⁰
  4. D¹⁰ C ₅ x ¹⁰

Correct answer

A. ¹⁰ C ₅

Step-by-step solution

General term =T_ r+1 = ¹⁰ C _r ( 10 x )^ 10-r ( x 10 )^r Here n=10 , which is an even number. Now, [ 10 2 +1 ]^ th term i.e. 6^ th term is the middle term. Hence, middle term =T₆ T _ 5+1 = ¹⁰ C ₅ ( 10 x )¹⁰⁻⁵ ( x 10 )^5 = ¹⁰ C ₅ ( 10 x )^5 ( x 10 )^5= ¹⁰ C ₅ .

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