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AP EAMCET2011MathematicsBinomial Theorem

If the coefficients of r th and (r+1) th terms in the expansion of (3+7 x)²⁹ are equal, then r is equal to

Options

  1. A14
  2. B15
  3. C18
  4. D21

Correct answer

D. 21

Step-by-step solution

Coefficient of r th term = Coefficient of (r+1) th term 29 r-1 (3)^ 29-r+1 (7)^ r-1 = ²⁹ C_r(3)^ 29-r (7)^r aligned & 29 r-1 3 7 = ²⁹ C_r & 29 ! (r-1) !(29-r+1) ! 3 7 = 29 ! (29-r) ! r ! & 3 7(29-r+1) = 1 r & 3 r=203-7 r+7 & 10 r=210 & r=21 & aligned

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