Question
Passage: Let u be a positive integer and f be a real number lying between 0 and 1. Further, ( 2 +1 )^ 10 =u+f and ( 2 -1 )^ 10 =v. Question: What is the multiplicative inverse of ( 2 +1 )^ 20 ?
NDA
Mathematics
Binomial Theorem
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. v
- B. v^2-1
- C. v^2
- D. v^2+1
Answer
C. v^2
Step-by-step solution
The multiplicative inverse of ( 2 +1 )^ 20 is 1 ( 2 +1 )^ 20 . Rationalizing the base gives 1 2 +1 = 2 -1 ( 2 +1 ) ( 2 -1 ) = 2 -1. Thus, 1 ( 2 +1 )^ 20 = ( 2 -1 )^ 20 . Given that v = ( 2 -1 )^ 10 . Squaring both sides yields v^2 = ( 2 -1 )^ 20 . Therefore, the multiplicative inverse of ( 2 +1 )^ 20 is v^2. Answer: v^2
Related: Mathematics — Binomial Theorem · All PYQ Banks