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JEE Main202228 Jun 2022Evening ShiftMathematicsBinomial TheoremActual

The term independent of x in the expression of 1 - x 2 + 3 x 3 5 2 x 3 - 1 5 x 2 11 , x ≠ 0 is

Options

  1. A7 40
  2. B33 200
  3. C39 200
  4. D11 50

Correct answer

B. 33 200

Step-by-step solution

General term of 5 2 x 3 - 1 5 x 2 11 is T r + 1 = C r 11 5 2 x 3 11 - r - 1 5 x 2 r = C r 11 - 1 r · 5 11 - 2 r 2 11 - r · x 33 - 5 r The term independent of x in the expansion of 1 - x 2 + 3 x 3 5 2 x 3 - 1 5 x 2 11 will be the coefficient of x 0 in 5 2 x 3 - 1 5 x 2 11 - coefficient of x - 2 in 5 2 x 3 - 1 5 x 2 11 + 3 × coefficient of x - 3 in 5 2 x 3 - 1 5 x 2 11 = - C 7 11 - 1 7 · 5 - 3 2 4 = 330 5 3 · 2 4 = 33 200

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