NDA 2026 · PYQ · Binomial Theorem · medium
What is the multiplicative inverse of (√2 + 1)²⁰? [Given: (√2+1)¹⁰ = u + f, (√2-1)¹⁰ = v]
Answer
The correct answer is C: v². (√2+1)(√2-1) = 1, so (√2-1) = 1/(√2+1). Therefore 1/(√2+1)²⁰ = (√2-1)²⁰ = [(√2-1)¹⁰]² = v².
- A.v
- B.v² - 1
- C.v²✓ Correct
- D.v² + 1
(√2+1)(√2-1) = 1, so (√2-1) = 1/(√2+1). Therefore 1/(√2+1)²⁰ = (√2-1)²⁰ = [(√2-1)¹⁰]² = v².
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