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NDA 2016 Maths · Mathematics · Binomial Theorem · easy

The greatest binomial coefficient in the expansion of (1+x)^9 is

Single correct option

The greatest binomial coefficient in the expansion of (1+x)9(1+x)^9 is
  1. A. 8484
  2. B. 126126
  3. C. 252252
  4. D. 512512
Show answer and solution

Answer: (B) 126126

For odd n=9n=9 the greatest coefficients are the two middle ones, 9C4=9C5=9⋅8⋅7⋅624=126^9C_4=^9C_5=\dfrac{9\cdot8\cdot7\cdot6}{24}=126. The value 252 is 10C5^{10}C_5 and belongs to n=10n=10, while 512 is the sum of all coefficients 292^9.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake