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NDA 2020 Maths · Mathematics · Binomial Theorem · hard

The term independent of x in the expansion of (2x-(1)/(x^2)^9 is

Single correct option

The term independent of xx in the expansion of (2x−1x2)9\left(2x-\dfrac1{x^2}\right)^9 is
  1. A. 5376
  2. B. −672-672
  3. C. −5376-5376
  4. D. 672
Show answer and solution

Answer: (C) −5376-5376

Tr+1=(9r)(2x)9−r(−1x2)rT_{r+1}=\binom9r(2x)^{9-r}\left(-\dfrac1{x^2}\right)^r has power 9−3r9-3r, which vanishes for r=3r=3. The term is (93)⋅26⋅(−1)3=84×64×(−1)=−5376\binom93\cdot2^6\cdot(-1)^3=84\times64\times(-1)=-5376. An odd rr makes the sign negative.
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Original question written in the NDA 2020 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