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यदि `""^(2n+1)P_(r-1):""^(2n-1)P_(n)=3:5`, तब n का मान ज्ञात कीजिए । |
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Answer» प्रश्नानुसार, `(""^(2n+1)P_(n-1))/(""^(2n-1)P_(n))=3/5` `rArr ((2n+1)!)/((n+2)!)xx((n-1)!)/((2n-1)!) = 3/5` `rArr ((2n+1)(2n)(2n-1))/((n+2)(n+1)n(n-1)!) xx((n-1)!)/((2n-1)!) =3/5` `rArr (2(2n+1))/((n+2)(n+1))=3/5` `rArr 10(2n+1)=3(n+2)(n+1)` `rArr 3n^(2) + 9n+ 6 = 20n+10` `rArr 3n^(2)-11n-4=0` `rArr (n-4)(3n+1) = 0` `n = 4` |
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