NDA 2026 · PYQ · Binomial Theorem · hard
What is the value of u?
- A.9725
- B.6971
- C.6726
- D.6725✓ Correct
Using binomial expansion: (√2 + 1)^10 + (√2 − 1)^10 = 2[C(10,0)(√2)^10 + C(10,2)(√2)^8 + C(10,4)(√2)^6 + C(10,6)(√2)^4 + C(10,8)(√2)^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, we get u = 6725.
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