NDA 2026 · PYQ · Binomial Theorem · hard
What is the value of u? [Given: u is positive integer, 0 < f < 1, (√2+1)¹⁰ = u + f]
- A.9725
- B.6971
- C.6726
- D.6725✓ Correct
(√2+1)¹⁰ + (√2-1)¹⁰ = 2[C(10,0)·2⁵ + C(10,2)·2⁴ + C(10,4)·2³ + C(10,6)·2² + C(10,8)·2 + C(10,10)] = 2[32 + 45·16 + 210·8 + 210·4 + 45·2 + 1] = 2[32 + 720 + 1680 + 840 + 90 + 1] = 2[3363] = 6726. Since u + f + v = 6726 and f + v = 1, u = 6725.
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