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99 Percentile Qs Bank for JEE MainMathematicsBinomial Theorem

If k is the coefficient of x^5 in the expansion of (2 x^2- 1 3 x^3 )^5 then 3 k 2 =

Options

  1. A-20
  2. B-40
  3. C20
  4. D40

Correct answer

B. -40

Step-by-step solution

Given expression (2 x^2- 1 3 x^3 )^5 . General term T _ r+1 = ^5 C _r (2 x^2 )^ 5-r ( -1 3 x^3 )^r T _ r+1 = ^5 C _r(2)^ 5-r ( -1 3 )^r x^ 10-2 r-3 r Here, 10-2 r-3 r should be equal to 5 . Then, 10-2 r-3 r=5 aligned & 5=5 r & r=1 aligned Now, T ₂= ^5 C ₁(2)⁵⁻¹ ( -1 3 )^1 x¹⁰⁻²⁻³= 5 4 ! 4 ! 16 -1 3 x^5 So, K =5 16 -1 3 = -80 3 Here, 3 ~K 2 = 3 2 -80 3 =-40 .

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