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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2022 · Mathematics · Binomial Theorem

In the expansion of (x+(1)/(x))^ 2 n , what is the (n+1) th term...

In the expansion of (x+1x)2n\left(x+\frac{1}{x}\right)^{2 n}, what is the (n+1)(n+1) th term from the end (when arranged in descending powers of xx )?

Options

  1. AC(2n,n)xC(2 n, n) x
  2. BC(2n,n−1)xC(2 n, n-1) x
  3. CC(2n,n)C(2 n, n)
  4. DC(2n,n−1)C(2 n, n-1)

Correct answer

C. C(2n,n)C(2 n, n)

Step-by-step solution

(x+1)^{\text{th }}termfromtheendofexpressionterm from the end of expression\left(\mathrm{x}+\frac{1}{\mathrm{x}}\right)^{2 \mathrm{n}}=(\mathrm{n}+1)^{\text{th }}termfrombeginingofexpressionterm from begining of expression\left(\frac{1}{x}+x\right)^{2 n}\therefore(\mathrm{n}+1)^{\text{lh }}termof(1x+x)2nterm of \left(\frac{1}{\mathrm{x}}+\mathrm{x}\right)^{2 \mathrm{n}} is Tn+1=2nCn(1x)nxn=2nCn\mathrm{T}_{\mathrm{n}+1}={ }^{2 \mathrm{n}} \mathrm{C}_{\mathrm{n}}\left(\frac{1}{\mathrm{x}}\right)^{\mathrm{n}} \mathrm{x}^{\mathrm{n}}={ }^{2 \mathrm{n}} \mathrm{C}_{\mathrm{n}}
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