UPSC NDA Math Model Paper 6

Here, we have to find the equation of the line which makes an angle of 30° with the positive direction of the x-axis and cuts off an intercept of 4 units with the negative direction of the y - axis
As we know that, equation of a line whose slopeis m and which makes an intercept c on the Y-axis is given by: y=mx+c
Here, we have c = - 4 and m=tan‌30=

1

√3

So, the equation of the required line is: y=

1

√3

×x−4
⇒√3y=x−4√3
So, the equation of the required line is x−√3y−4√3=0
Hence, option D is the correct answer.