Question
If n= ^ m C_2 then what is ^ n C_2 equal to ?
NDA
Mathematics
Permutation Combination
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. ^ m+1 C_4
- B. 2 ^ m+1 C_4
- C. 3 ^ m+1 C_4
- D. ^ m+2 C_4
Answer
C. 3 ^ m+1 C_4
Step-by-step solution
Given n = ^ m C_ 2 = m(m-1) 2 Evaluating ^ n C_ 2 = n(n-1) 2 Substituting the value of n: ^ n C_ 2 = m(m-1) 2 ( m(m-1) 2 - 1 ) 2 ^ n C_ 2 = m(m-1)(m^2 - m - 2) 8 Factorizing m^2 - m - 2 = (m-2)(m+1): ^ n C_ 2 = (m+1)m(m-1)(m-2) 8 Multiplying and dividing by 3: ^ n C_ 2 = 3 (m+1)m(m-1)(m-2) 24 ^ n C_ 2 = 3 ^ m+1 C_ 4 Answer: 3 ^ m+1 C_4
Related: Mathematics — Permutation Combination · All PYQ Banks