AP EAMCET · Maths · Binomial Theorem
What is the constant term in the binomial expansion of \((1+3 x)^n\left(1+\frac{1}{3 x}\right)^n\) ?
- A \(\left(\begin{array}{c}2 n \\ n\end{array}\right)\)
- B \(\left(\begin{array}{c}2 n \\ n-1\end{array}\right)\)
- C \(\left(\begin{array}{c}2 n \\ n+1\end{array}\right)\)
- D No such term exists
Answer & Solution
Correct Answer
(A) \(\left(\begin{array}{c}2 n \\ n\end{array}\right)\)
Step-by-step Solution
Detailed explanation
\[ \text { } \begin{aligned} (1+3 x)^n\left(1+\frac{1}{3 x}\right)^n & =(1+3 x)^n\left(\frac{3 x+1}{3 x}\right)^n \\ & =\frac{(1+3 x)^n(1+3 x)^n}{(3 x)^n} \\ & =\frac{(1+3 x)^{2 n}}{(3 x)^n} \end{aligned} \] In \((1+3 x)^{2 n}\) general term is \[ T_{r+1}={ }^{2 n} C_r(3 x)^r \]…
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