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NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

Let T r denote the r t h term in the expansion of 2 x + 1 4 x n . If the ratio T 3 : T 2 = 7 : 1 and the sum of the coefficients of the second and third term is 36 , then the value of x is

Options

  1. A1 2
  2. B- 1 2
  3. C- 1 4
  4. D- 1 3

Correct answer

D. - 1 3

Step-by-step solution

It is given that T 3 T 2 = 7 ⇒ n C 2 2 x n - 2 1 4 x 2 n C 1 2 x n - 1 1 4 x 1 = 7 ⇒ n - 1 2 2 - 3 x = 7 Also, n C 1 +   n C 2 = 36 ⇒   n + n n - 1 2 = 36 ⇒    n 2 + n - 72 = 0 ⇒    n = 8 ,    - 9 n = 8   ⇒   7 2   2 - 3 x = 7 ⇒ 2 - 3 x - 1 = 1 = 2 0 ⇒ - 3 x - 1 = 0 ⇒ x = - 1 3

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