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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2018 · Mathematics · Binomial Theorem

What is the number of non-zero terms in the expansion of (1+2 3 x)^...

What is the number of non-zero terms in the expansion of (1+23x)11+(1−23x)11(1+2 \sqrt{3} x)^{11}+(1-2 \sqrt{3} x)^{11} \quad (after simplification)?

Options

  1. A4
  2. B5
  3. C6
  4. D11

Correct answer

C. 6

Step-by-step solution

We know, in the expansion of (x+y)n+(x−y)n(x+y)^n+(x-y)^n, of n=\mathrm{n}= even, then number of non zero terms is n2+1n=\frac{\mathrm{n}}{2}+1\mathrm{n}= odd, then number of non zero terms in n+12\frac{\mathrm{n}+1}{2}. Here, n=11\mathrm{n}=11 which is odd. ∴\therefore number of non zero terms =11+12=6=\frac{11+1}{2}=6.
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