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99 Percentile Qs Bank for JEE MainMathematicsBinomial Theorem

If n is an even positive integer greater than 1 and x > 0 , then the condition that the greatest term in the expansion of 1 + x n may have the greatest coefficient also is

Options

  1. An - 1 n < x < n n - 1
  2. Bn n + 1 < x < n + 1 n
  3. Cn n + 3 < x < n + 3 n
  4. Dn n + 2 < x < n + 2 n

Correct answer

D. n n + 2 < x < n + 2 n

Step-by-step solution

If n is even, the greatest coefficient is n C n / 2 ∴ The greatest term = n C n / 2 x n / 2 ∴ n C n / 2 x n / 2 > n C n / 2 − 1 x n / 2 − 1 and n C n / 2 x n / 2 > n C n / 2 + 1 x n / 2 + 1 ⇒ n - n 2 + 1 n 2 x > 1 and n - n 2 + 1 + 1 n 2 + 1 x < 1 ⇒ n / 2 n / 2 + 1 < x < n 2 + 1 n 2 Hence, n n + 2 < x < n + 2 n

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