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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]

  1. A.v
  2. B.v² - 1
  3. C.✓ Correct
  4. D.v² + 1

Explanation

(√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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