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If (n+1)! =90 xx(n-1)!, find n....

If `(n+1)! =90 xx(n-1)!, ` find `n`.

A

`n=11`

B

`n=8`

C

`n=10`

D

`n=9`

Text Solution

Verified by Experts

The correct Answer is:
D
We have `(n+1)! =90 xx(n-1)! `
`rArr (n+1)xxnxx(n-1)! =90xx(n-1)! `
`rArr (n+1)n=90 `
` rArr (n+1)n=10xx9 `
[ writing 90 as product of two consecutive integers]
` rArr n=9. `
Hence, `n=9. `
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