Question:
The greatest coefficient in the expansion of $(1+x)²n$ is ________.
The greatest coefficient in the expansion of $(1+x)²n$ is ________.
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The greatest coefficient in the expansion of $(1+x)
Updated On: Apr 15, 2026
- ${}^{2n}C_{n}$
- ${}^{2n}C_{n-1}$
- ${}^{2n}C_{n-2}$
- None of these
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The Correct Option is A
Solution and Explanation
Step 1: Concept
In $(1+x)^N$, the greatest coefficient is the middle one.
Step 2: Analysis
Here index is $2n$ (even).
Step 3: Middle Term
The middle term coefficient for an even index $N$ is ${}^NC_{N/2}$.
Step 4: Conclusion
Greatest coefficient $= {}^{2n}C_{n}$.
Final Answer: (A)
In $(1+x)^N$, the greatest coefficient is the middle one.
Step 2: Analysis
Here index is $2n$ (even).
Step 3: Middle Term
The middle term coefficient for an even index $N$ is ${}^NC_{N/2}$.
Step 4: Conclusion
Greatest coefficient $= {}^{2n}C_{n}$.
Final Answer: (A)
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