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JEE Main202125 Jul 2021Evening ShiftMathematicsBinomial TheoremActual

The sum of all those terms which are rational numbers in the expansion of 2 1 3 + 3 1 4 12 is:

Options

  1. A89
  2. B27
  3. C35
  4. D43

Correct answer

D. 43

Step-by-step solution

r th term in the expansion of 2 1 3 + 3 1 4 12 is T r + 1 = C r 12 2 r 3 · 3 12 - r 4 Since, T r + 1 will be rational number, when r   =   0 , 3 , 6 , 9 , 12   and r   =   0 , 4 , 8 , 12   ⇒ r = 0 , 12 for rational term of the expansion Therefore, T 1 + T 13 = 1 × 3 3 + 1 × 2 4 × 1 = 27 + 16 = 43 .

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