Question
If the sum of binomial coefficients in the expansion of (x + y)^n is 256, then the greatest binomial coefficient occurs in which one of the following terms?
NDA
Mathematics
Binomial Theorem
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. Third
- B. Fourth
- C. Fifth
- D. Ninth
Answer
C. Fifth
Step-by-step solution
The sum of binomial coefficients in the expansion of (x + y)^n is 2^n. 2^n = 256 2^n = 2^8 n = 8 In the expansion of (x + y)^8, the number of terms is n + 1 = 9. The greatest binomial coefficient occurs at the middle term. Since n = 8 is even, the middle term is the ( n 2 + 1)-th term. Middle term = 8 2 + 1 = 5 The greatest binomial coefficient occurs in the fifth term. Answer: Fifth
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