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NDA 2019 Maths · Mathematics · Binomial Theorem · medium

The coefficient of x^3 in the expansion of (3-2x)^5 is

Single correct option

The coefficient of x3x^3 in the expansion of (3−2x)5(3-2x)^5 is
  1. A. 720720
  2. B. −1080-1080
  3. C. −720-720
  4. D. −360-360
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Answer: (C) −720-720

The general term is (5r)35−r(−2x)r\binom5r3^{5-r}(-2x)^r. For x3x^3 take r=3r=3: (53)⋅32⋅(−2)3=10×9×(−8)=−720\binom53\cdot3^2\cdot(-2)^3=10\times9\times(-8)=-720. The sign is negative because (−2)3<0(-2)^3<0. The value 720720 forgets the sign, and −1080-1080 uses 333^3 in place of 323^2.
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Original question written in the NDA 2019 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