Rohit is facing North-East. He turns $45^{\circ }$ anti-clockwise, then $135^{\circ }$ clockwise and finally $90^{\circ }$ anti-clockwise. Which direction is he facing now?

Let's calculate the net angular deviation, treating clockwise (CW) as positive and anti-clockwise (ACW) as negative:
$$\text{Initial direction}=\text{North-East (NE)}$$

$$\text{Net Turn}=-45^{\circ }\text{ (ACW)}+135^{\circ }\text{ (CW)}-90^{\circ }\text{ (ACW)}$$

$$\text{Net Turn}=135^{\circ }-135^{\circ }=0^{\circ }$$

Since the net change in angle is $0^{\circ }$, Rohit remains facing his initial direction, which is North-East.