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JEE Main2005MathematicsBinomial TheoremActual

If the coefficients of r th, (r+1) th and (r+2) th terms in the binomial expansion of (1+y)^m are in A.P., then m and r satisfy the equation

Options

  1. Am^2-m(4 r-1)+4 r^2-2=0
  2. Bm^2-m(4 r+1)+4 r^2+2=0
  3. Cm^2-m(4 r+1)+4 r^2-2=0
  4. Dm^2-m(4 r-1)+4 r^2+2=0

Correct answer

C. m^2-m(4 r+1)+4 r^2-2=0

Step-by-step solution

Given ^m C, ^m C, ^m C_ r+1 are in A.P. aligned & 2 ^m C_r= ^m C_ r-1 + ^m C_ r+1 & 2= ^m C_ r-1 ^m C_r + ^m C_ r+1 ^m C_r & = r m-r+1 + m-r r+1 & m^2-m(4 r+1)+4 r^2-2=0 aligned

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