The number of ordered pairs `(x,y)` , where `x`, `y in N` for which `4`, `x`, `y` are in `H.P.` , is equal to
A
`1`
B
`2`
C
`3`
D
`4`
Text Solution
Verified by Experts
The correct Answer is:
C
`(c )` `4,x,y` are in `H.P.` ,brgt `(2)/(x)=(1)/(4)+(1)/(y)` `implies (2)/(x)-(1)/(4)=(1)/(y)` `implies(8-x)/(4x)=(1)/(y)` `impliesy=(4x)/(8-x)=(4(8-(8-x)))/(8-x)=(32)/(8-x)-4` `8-x` must be a factor of `32` `8-x=1impliesx=7`, `y=28` `8-x=2impliesx=6`, `y=12` `8-x=4impliesx=4`, `y=4` `8-x=8impliesx=0`, `y=0` (Not possible) `:.` Number of ordered pairs of `(x,y)` is `3`.
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CENGAGE-PROGRESSION AND SERIES-ARCHIVES (MATRIX MATCH TYPE )
