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AP EAMCET201923 Apr 2019Morning ShiftMathematicsBinomial TheoremActual

If the coefficients of (r ) th and ((r+1) ) th terms in the expansion of ((1+x)²⁴ ) are in the ratio (12: 13 ), then (r ) is the root of the quadratic equation

Options

  1. A(x^2-5 x+6=0 )
  2. B(x^2-11 x+30=0 )
  3. C(x^2-14 x+13=0 )
  4. D(x^2-14 x+24=0 )

Correct answer

D. (x^2-14 x+24=0 )

Step-by-step solution

According to given information, ( 24 r-1 ²⁴ C_r = 12 13 ) ( gathered 24 ! (r-1) !(25-r) ! 24 ! r !(24-r) ! = 12 13 r 25-r = 12 13 r=12 gathered ) and since, (x^2-14 x+24=0 (x-12)(x-2)=0 ) ( x=2,12 ) Hence, option (d) is correct.

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