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JEE Main20206 Sep 2020Evening ShiftMathematicsBinomial TheoremActual

If the constant term in the binomial expansion of x - k x 2 10 is 405 , then k equals :

Options

  1. A9
  2. B1
  3. C3
  4. D2

Correct answer

C. 3

Step-by-step solution

T r + 1 = C r 10 - k x 2 r x 10 - r = C r · 10 - k r · x 5 - 5 r 2 for constant term ⇒ 5 - 5 r 2 = 0     ⇒ r = 2 ⇒ T 3 = C 2 10 · k 2 = 405 ⇒ 10 ( 9 ) 2 k 2 = 405 ⇒ k 2 = 9 ⇒ k = 3

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