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If x=111"...."(20 digits),y=333"...."(10...

If `x=111"...."(20 digits),y=333"...."(10digits) and z=222".....2"(10 digits), then (x-y^(2))/(z)` equals.

A

`(1)/(2)`

B

1

C

2

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
`:.x=(1)/(9)(999"...."9)=(1)/(9)(10^(20)-1)`
`y=(1)/(3)(999"...."9)=(1)/(3)(10^(10)-1)`
and `z=(2)/(9)(999"...."9)=(2)/(9)(10^(10)-1)`
`:.(x-y^(2))/(z)=((1)/(9)(10^(20)-1)-(1)/(9)(10^(10)-1)^(2))/((2)/(9)(10^(10)-1))`
`=(10^(10)+1-(10^(10)-1))/(2)=1`
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