Let be a positive integer and be a real number lying between and . Further, and . What is the value of ? मान लीजिए एक धनात्मक पूर्णांक है तथा 0 और 1 के बीच में एक वास्तविक संख्या है। इसके अतिरिक्त, और है। का मान क्या है ?

Explanation: Let and . Using the Binomial Theorem: Summing these gives: Calculating the binomial coefficients and powers of : Since , we have: As established previously, : Conclusion: The value of is . Correct Option: (d) 6725

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NDA 2026 — Mathematics PYQ

NDA | Mathematics | 2026

Let $u$ be a positive integer and $f$ be a real number lying between $0$ and $1$ . Further, $(2 + 1)^{10} = u + f$ and $(2 - 1)^{10} = v$ .

What is the value of $u$ ?

मान लीजिए $u$ एक धनात्मक पूर्णांक है तथा 0 और 1 के बीच में $f$ एक वास्तविक संख्या है। इसके अतिरिक्त, $(2 + 1)^{10} = u + f$ और $(2 - 1)^{10} = v$ है।

$u$ का मान क्या है ?

Choose the correct answer: