UPSC NDA I 2025 Mathematics Paper

Given,
Sum of binomial coefficients =2n=256
We calculate n :
‌2n=256
‌⇒28=256
Greatest Binomial Coefficient:
For n=8 (even), the greatest binomial coefficient occurs at r=n∕2=8∕2=4.
⇒ The term index is r=4, which corresponds to the 5th term (since indexing starts from 0 ).
∴ The greatest binomial coefficient occurs in the 5th term.