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Manipal MET2014MathematicsBinomial Theorem

If the term free from x in the expansion of ( x - k x^2 )¹⁰ is 405 , then the value of k is

Options

  1. A1
  2. B3
  3. C4
  4. D2

Correct answer

B. 3

Step-by-step solution

General term in the expansion of ( x - k x^2 )¹⁰ is aligned T_ r+1 & = ¹⁰ C_r( x )^ 10-r ( -k x^2 )^r & = ¹⁰ C_r x^ 10-r 2 (-k)^r x^ -2 r & = ¹⁰ C_r(-k)^r x^ ( 10-5 r 2 ) aligned The term is free from x array lrl Put & 10-5 r 2 & =0 & r & =2 Now, & ¹⁰ C₂(-k)^2 & =405 & 10 9 1 2 k^2 & =405 & & k^2= 405 45 =9 & k & = 3 array

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