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NDA2019MathematicsBinomial TheoremActual

If the constant term in the expansion of ( x - k x^2 )¹⁰ is 405 , then what can be the values of k ?

Options

  1. A2
  2. B3
  3. C5
  4. D9

Correct answer

B. 3

Step-by-step solution

( x - k x^2 )¹⁰ according to question. Term independent of x can be calculated as aligned & ¹⁰ C_r( x )^ 10-r (- k x^2 )^r & x^ 5-r / 2-2 r =x^0 & 10-4 r-r=0 & r=2 & ¹⁰ C₂ ( x )^8 ( -k x^2 )^2=405 & ¹⁰ C₂ k^2=405 & 10! 2! 8! k^2=405 & k^2=9 & k= 3 aligned

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