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The coefficient of the term independent of x in the expansion of 1 + x + 2 x 3 3 2 x 2 - 1 3 x 9 is

Options

  1. A1 3
  2. B19 54
  3. C17 54
  4. D1 4

Correct answer

C. 17 54

Step-by-step solution

Coefficient of the term independent of x is the coefficient of x 0 in 3 2 x 2 - 1 3 x 9 + x 3 2 x 2 - 1 3 x 9 + 2 x 3 3 2 x 2 - 1 3 x 9 Now, in 3 2 x 2 - 1 3 x 9 , T r + 1 = 9 C r 3 2 x 2 9 - r - 1 3 x r = 9 C r 3 2 9 - r - 1 3 r x 18 - 3 r i Coefficient of x 0 ⇒ 18 - 3 r = 0 ⇒ r = 6 Coefficient of x 0 is 9 C 6 3 2 3 - 1 3 6 i i Coefficient of x - 1 ⇒ 18 - 3 r = - 1 ⇒ r = 19 3 (not possible) i i i Coefficient of x - 3 ⇒ 18 - 3 r = - 3 ⇒ r = 7 Coefficient of x - 3 is 9 C 7 3 2 2 -

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