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JEE Main20249 Apr 2024Evening ShiftMathematicsBinomial TheoremActual

The sum of the coefficient of x^ 2 / 3 and x^ -2 / 5 in the binomial expansion of (x^ 2 / 3 + 1 2 x^ -2 / 5 )^9 is

Options

  1. A21 / 4
  2. B63 / 16
  3. C19 / 4
  4. D69 / 16

Correct answer

A. 21 / 4

Step-by-step solution

aligned & T _ r +1 = ^9 C _ r ( x ^ 2 / 3 )^ 9- r ( x ^ -2 / 5 2 )^ r & = ^9 C _ r ( 1 2 )^ r ( r )^ (6 2 r 3 2 r 5 ) aligned for coefficient of x^ 2 / 3 , put 6- 2 r 3 - 2 r 5 = 2 3 r =5 Coefficient of x ^ 2 / 3 is = ^9 C ₅ ( 1 5 )^5 For coefficient of x^ -2 / 5 , put 6- 2 r 3 - 2 r 5 =- 2 5 r =6 Coefficient of x ^ -2 / 5 is ^9 C ₆ ( 1 2 )^6 Sum = ^9 C ₅ ( 1 2 )^5+ ^9 C ₆ ( 1 2 )^6= 21 4

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