Q . THE STRAIGHT LINE x + y + 2 = 0 ROTATES ABOUT A POINT WHERE IT CUTS THE Y-AXIS AND BECOMES PERPENDICULAR TO THE STRAIGHT LINE ax + by + c = 0 .IN THE NEW POSITION ITS EQUATION IS –

1. ay – bx + 2b = 0
2. ay – bx – 2a =0
3. ay – bx + 2a =0
4. none of these

The answer is ay – bx + 2a = 0
See, we have given a line x+y=2
Also it is rotated about the point where it cuts the y-axis [i.e.,(0,-2)]. So for the new line, we have a point (0,-2).
Its given that this new line is perpendicular to the ax+by=c whose slope is -a/b
So the slope of the req. line would be b/a [by the condition of perpendicularity]
Now we have all the info. we need to build up the eq. 
We have, slope = b/a and a fixed point (0,-2)
therefore, y-(-2) = b/a*(x-0)
gives, ay – bx + 2a = 0