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Manipal MET2010MathematicsBinomial Theorem

The term independent of x in [ ( x 3 ) + ( 3 2 x^2 ) ]¹⁰ is

Options

  1. A1
  2. B¹⁰ C₁
  3. C5 12
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

The general term is T_ r+1 = ¹⁰ C_r ( x 3 )^ 10-r ( 3 2 x^2 )^r= ¹⁰ C_r ( 1 3 )^ 5-(r / 2) ( 3 2 )^ r / 2 x^ 5-(3 r / 2) for term independent of x . 5- 3 r 2 =0 r= 10 3 , which is not a positive integer. Hence, there is no term independent of x .

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