The correct option is D (−∞,4)∪(4,5)∪(7,∞)
As line passes through the point of intersection of x−2y−2=0 and 2x−by−6=0
It can be represented as λ(x−2y−2)+(2x−by−6)=0
As it passes through the origin
−2λ−6=0
λ=−3
∴−x+(6−b)y=0
16−b
As its angle with y = 0 is less than π4
∴−1<16−b<1
⇒6−b>1or<−1⇒b<5orb>7
But b≠4 (as the lines WON'T intersect)
∴bϵ(−∞,4)∪(4,5)∪(7,∞)