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BITSAT2019MathematicsBinomial TheoremActual

Let 2 x 2 + 3 x + 4 10 = ∑ r = 0 20 a r x r , then the value of a₈ a₁₂ , is

Options

  1. A2
  2. B4
  3. C8
  4. D16

Correct answer

B. 4

Step-by-step solution

Given, 2 x 2 + 3 x + 4 10 = ∑ r = 0 20 a r x r Replacing x by 2 x , we get 8 x 2 + 6 x + 4 10 = ∑ r = 0 20 a r 2 x r ⇒ 2 10 2 x 2 + 3 x + 4 10 = ∑ r = 0 20 a r 2 r x 20 - r ⇒   2 10 ∑ r = 0 20 a r x r = ∑ r = 0 20 a r 2 r x 20 - r Comparing ccefficient of x 8 both sides, we get 2 10 a 8 = a 12 2 12 ⇒ a 8 a 12 = 2 12 2 10 = 4

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