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AP EAMCET2002MathematicsBinomial Theorem

If the coefficient of x is in expansion of (x^2+ k x )^5 is 270 , then k is equal to

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

C. 3

Step-by-step solution

General term in the expansion of (x^2+ k x )^5 is aligned T_ r+1 & = ^5 C_r (x^2 )^ 5-r ( k x )^r & = ^5 C_r x^ 10-3 r k^r aligned Let this term contains x then, 10-3 r=1 3 r=9 r=3 , then coefficient of x= ^5 C₃ k^3=10 k^3 Given that 10 k^3=270 k^3=27 k=3

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