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What is the value of \(\frac{10!}{8!}+\frac{7!}{6!}+0!\)?\(\frac{10!}{8!}+\frac{7!}{6!}+0!\) का मान क्या है?
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Correct answer:सही उत्तर: 9898
\(\frac{10!}{8!}=\frac{10\times9\times8!}{8!}=90\) and \(\frac{7!}{6!}=\frac{7\times6!}{6!}=7\). Also, by definition, \(0!=1\). Therefore, the value is \(90+7+1=98\). One may get \(97\) by incorrectly taking \(0!\) as 0. Exam tip: In factorial fractions, expand only until the common factorial terms cancel.\(\frac{10!}{8!}=\frac{10\times9\times8!}{8!}=90\) तथा \(\frac{7!}{6!}=\frac{7\times6!}{6!}=7\)। साथ ही, परिभाषा के अनुसार \(0!=1\)। अतः मान \(90+7+1=98\) है। \(97\) तब मिलता यदि \(0!\) को गलती से 0 मान लिया जाए। परीक्षा टिप: फैक्टोरियल के भिन्न में समान फैक्टोरियल पदों को काटकर शेष गुणनखंड लिखें।
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