COMEDK · Maths · 7. Binomial Theorem
In the expansion of \(\left(1+3 x+3 x^2+x^3\right)^{2 n}\), the term which has greatest binomial coefficient, is
- A \((3 n)\) th term
- B \((3 n+1)\) th term
- C \((3 n-1)\) th term
- D \((3 n+2)\) th term
Answer & Solution
Correct Answer
(B) \((3 n+1)\) th term
Step-by-step Solution
Detailed explanation
\(\because\) Middle term has greatest binomial coefficient. In the expansion of \(\left(1+3 x+3 x^2+x^3\right)^{2 n}\) \(=\left((1+x)^3\right)^{2 n}=(1+x)^{6 n}\) \(\because 6 n\) is even So, middle term of \((1+x)^{6 n}=T\left(\frac{6 n}{2}+1\right)\) \(=T_{(3 n+1)}=(3 n+1)\)…
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