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NDA2012MathematicsBinomial TheoremActual

The value of the term independent of x in the expansion of (x^2- 1 x )^9 is

Options

  1. A9
  2. B18
  3. C48
  4. D84

Correct answer

D. 84

Step-by-step solution

aligned (x^2- 1 x )^9 & t_ r+1 & = ^9 C_r (x^2 )^ 9-r ( -1 x )^r & = ^9 C_r(x)^ 18-2 r _ (-1)^r x^ -r aligned Put 18-3 r=0r=6 Put r=6 , in (1), t₇= ^9 C₆(1)^6= 9! 6!3! = 9 8 7 6! 6! 3 2 =84 .

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