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 \((3 n-1)\) th term
- B \((3 n+1)\) th term
- C \((3 n+2)\) th term
- D \((3 n)\) th term
Answer & Solution
Correct Answer
(B) \((3 n+1)\) th term
Step-by-step Solution
Detailed explanation
The given expression is \(\left(1+3x+3x^2+x^3\right)^{2n}\). Recognizing the binomial expansion, \(1+3x+3x^2+x^3 = (1+x)^3\). Substituting this into the expression, we get \(((1+x)^3)^{2n} = (1+x)^{6n}\). The expansion of \((1+x)^{6n}\) is given by…
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