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NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

If only the 4 t h term in the expansion of 2 + 3 x 8 10 has the greatest numerical value, then the integral values of x are

Options

  1. A- 3 , - 2 , 2 , 3
  2. B- 2 , - 1 , 1 , 2
  3. C- 3 , 3
  4. D- 3 , - 2 , - 1 , 0 , 1 , 2 , 3

Correct answer

C. - 3 , 3

Step-by-step solution

T 3 < T 4 > T 5 ⇒ T 4 T 3 > 1 and T 5 T 4 < 1 T r + 1 = C r 10 2 10 - r 3 x 8 r T 4 T 3 = C 10 3 2 7 3 x 8 3 C 10 2 2 8 3 x 8 2 = x 2 T 5 T 4 = C 10 4 2 6 3 x 8 4 C 10 3 2 7 3 x 8 3 = 21 64 x x 2 > 1 ⇒ x > 2 or x < - 2 21 64 x < 1 ⇒ - 64 21 < x < 64 21 Taking intersection, we get, x ∈ - 64 21 , - 2 ∪ 2 , 64 21 Hence, integral values of x = - 3 , + 3

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