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JEE Main202117 Mar 2021Morning ShiftMathematicsBinomial TheoremActual

If the fourth term in the expansion of x + x log 2 x 7 is 4480 , then the value of x where x ∈ N is equal to:

Options

  1. A2
  2. B4
  3. C3
  4. D1

Correct answer

A. 2

Step-by-step solution

Given x + x log 2 x 7 .   The general term in the expansion of x + x log 2 x 7 is C r 7 x r x log 2 x 7 - r . Then, T 4 = C 3 7 x 4 x log 2 x 3 = 4480 ⇒ 7 · 6 · 5 3 · 2 · 1 x 4 + log 2 x = 4480 ⇒ x 4 + 3 log 2 x = 128 ⇒ x 4 + 3 log 2 x = 2 7 Now, from the option only at x = 2 , LHS = RHS .

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