1.

Find the value of `r,` if (i) `.^(11)P_(r)=990` (ii) `.^(8)P_(5)+5*.^(8)P_(4)=.^(9)P_(r)`

Answer» (i) `because.^(11)P_(r)=990=11xx10xx9=.^(11)P_(3)`
`thereforer=3`
(ii) `because .^(8)P_(5)+5*.^(8)P_(4)=.^(9)P_(r)`
`implies.^(8)P_(4)((.^(8)P_(5))/(.^(8)P_(4))+5)=.^(9)P_(r)`
`implies.^(8)P_(4)(8-5+1+5)=.^(9)P_(r)` [ from note (v)]
`implies9*.^(8)P_(4)=.^(9)P_(r)`
`implies.^(9)P_(5)=.^(9)P_(r)` [from note (iii)]
`thereforer=5`


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