Let `f(x)=(x^(2)-6x+5)/(x^(2)-5x+6).` Then match the expressions/statements in List I with expression /statements in List II.

Answer

`a to p,r,s; b to q,s; c to q,s; d to p,r,s.`

Explanation

We have `f(x)=(x^(2)-6x+5)/(x^(2)-5x+6)=((x-5)(x-1))/((x-2)(x-3))`
`a to p, r, s.`
If `-1 lt x lt 1, " then "f(x)=((-ve)(-ve))/((-ve)(-ve))= +ve`
` :. f(x) gt 0`
Also, `f(x)-1=(-x-1)/(x^(2)-5x+6)= -((x+1))/((x-2)(x-3))`
For `-1 lt x lt 1, f(x)-1=(-(+ve))/((-ve)(-ve))= -ve`
or `f(x) -1 lt 0 or f(x) lt 1`
` :. 0 lt f(x) lt 1`
`b to q,s.`
If `1 lt x lt 2, " then " f(x)=((-ve)(+ve))/((-ve)(-ve))= -ve`
Therefore, `f(x) lt 0 " and, so, "f(x) lt 1.`
`c to q,s.`
If `3 lt x lt 5,` then
`f(x)=((-ve)(+ve))/((+ve)(+ve))= -ve`
Therefore, `f(x) lt 0 " and , so, "f(x) lt 1.`
`d to p,r,s.`
For `x gt 5, f(x) gt 0,` Also,
`f(x)-1=(-(x+1))/((x-2)(x-5)) lt 0" for " x gt 5`
`or f(x) lt 1,`
` :. 0lt f(x) lt 1`