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NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The coefficient of x 20 in the expansion of 1 + x 2 40 x 2 + 2 + 1 x 2 - 5 is

Options

  1. A30 C 10
  2. B30 C 15
  3. C30 C 25
  4. D30 C 20

Correct answer

C. 30 C 25

Step-by-step solution

1 + x 2 40 x 2 + 1 x 2 + 2 ⋅ x ⋅ 1 x - 5 = 1 + x 2 40 x + 1 x 2 - 5 = 1 + x 2 40 x 2 + 1 x - 10 = 1 + x 2 40 1 + x 2 - 10 x - 10 = x 10 1 + x 2 30 Coefficient of x 20 in x 10 1 + x 2 30 = coefficient of x 10 in 1 + x 2 30 1 + x 2 30 = ∑ r = 0 30 C r 30 x 2 r 2 r = 10 ⇒ r = 5 So, the required coefficient is 30 C 5 = 30 C 25

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