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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2019 · Mathematics · Binomial Theorem

If the middle term in the expansion of (x^2+(1)/(x))^ 2 x 184756 x^...

If the middle term in the expansion of (x2+1x)2x184756x10\left(x^2+\frac{1}{x}\right)^{2 x}184756 x^{10}, then what is the value of nn ?

Options

  1. A10
  2. B8
  3. C5
  4. D4

Correct answer

A. 10

Step-by-step solution

(x2+1x)2n\left(x^2+\frac{1}{x}\right)^{2 n} Its index is even ∴ Middle term =Tn+1Tn+1=2nCn(x2)n(1x)n=2nCnxn=184756x10\begin{aligned} & \therefore \quad \text{ Middle term }=T_{n+1} \\ & T_{n+1}={ }^{2 n} C_n\left(x^2\right)^n\left(\frac{1}{x}\right)^n \\ & ={ }^{2 n} C_n x^n=184756 x^{10} \end{aligned}\thereforecomparingpowerofcomparing power ofxwegetwe getn=10$
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