The number of ordered pairs `(x,y)` , where `x`, `y in N` for which `4`, `x`, `y` are in `H.P.` , is equal to

Options

A. `1`
B. `2`
C. `3`
D. `4`

Answer

C

Explanation

`(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`.