यदि `""^(9)P_(5)+5.""^(9)P_(4)=""^(10)P_(r)`, तब `r` का मान ज्ञात कीजिए ।

Options

A. ` r = 5`
B. ` r = 6`
C. ` r = 7`
D. ` r = 8`

Answer

A

Explanation

प्रश्नानुसार, `""^(9)P_(5)+5.""^(9)P_(4)=""^(10)P_(r)`
`rArr(9!)/((9-5)!)+5'(9!)/((9-4)!)=(10!)/((10-r)!)`
`rArr(9!)/(4!)+(5)
'(9!)/(5!)=(10!)/((10-r)!)`
`rArr (9!)/(4!) +(9!)/(4!) = (10!)/((10-r)!)`
`rArr2.(9!)/(4!) = (10!)/((10-r)!)`
`rArr (5.2.9!)/(5.4!) =(10!)/((10-r)!)`
`rArr (10.9!)/(5!) = (10!)/((10-r)!) rArr (10!)/(5!) = (10!)/((10-r)!)`
`rArr (10-r)! = 5! rArr 10 -r = 5`
`rArr r = 5`