UPSC NDA Math Model Paper 6

Here, we have to find the equation of a line which cuts off an intercept of 4 units on negative direction of the Y-axis and makes an angle of 120° with the positive direction of the x-axis.
As we know that, equation of a line whose slope is m and which makes an intercept c on the Y-axis is given by: y = mx + c
Here, c = - 4 and m = tan 120° = tan (180° - 60°) = - tan 60° = - √3
So, the equation of the required line is: y=−√3x−4
So, the required equation is √3x+y+4=0
Hence, option C is the correct answer.