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What is the value of \(\frac{13!}{11!,2!}-\frac{6!}{4!,2!}\)?\(\frac{13!}{11!,2!}-\frac{6!}{4!,2!}\) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 6363
\(\frac{13!}{11!\,2!}=\frac{13\times12}{2}=78\), while \(\frac{6!}{4!\,2!}=\frac{6\times5}{2}=15\). Therefore, the required value is \(78-15=63\). The option 60 can result from incorrect cancellation of factorial terms. Exam tip: use \(\frac{n!}{(n-2)!\,2!}=\frac{n(n-1)}{2}\) to evaluate such terms quickly.\(\frac{13!}{11!\,2!}=\frac{13\times12}{2}=78\) और \(\frac{6!}{4!\,2!}=\frac{6\times5}{2}=15\) है। अतः आवश्यक मान \(78-15=63\) है। विकल्प 60 तब मिलता यदि गुणनखंडों को सही ढंग से सरल न किया जाए। परीक्षा टिप: \(\frac{n!}{(n-2)!\,2!}=\frac{n(n-1)}{2}\) का प्रयोग करके ऐसे पद जल्दी हल करें।
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