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AP EAMCET202317 May 2023Morning ShiftMathematicsBinomial TheoremActual

If the numerically greatest term in the expansion of (2-3 x )^9 when x =1 is P ₁^ P ₂^ P ₃^ P ₄^ ( P ₁ < P ₂ < P ₃ < P ₄ . are the first four prime numbers), then + + + =

Options

  1. A13
  2. B12
  3. C14
  4. D11

Correct answer

A. 13

Step-by-step solution

For greatest term in expansion: aligned & T _ r+1 > T _r & ^9 C_r 2^r(|-3 x|)^ 9-r > ^9 C_ r-1 2^ r-1 (|-3 x|)^ 9-(r-1) & 9 ! r !(9-r) ! 2 9 ! (r-1) !(9-r+1) ! 3 x & 2 r 3 9-r+1 x=1 & 20-2 r 3 r r 4 & r=4 & T₅= ^9 C₄(2)^4[-3]^5= 9 ! 4 ! 5 ! (2)^4 3^5 & = 9 8 7 6 4 3 6 2^4 3^5=3^7 2^5 7 & =7, =5, =1, =0 & + + + =7+5+1+0=13 aligned

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