UPSC NDA I 2021 Mathematics Solved Paper

Concept:
Let θ be the angle between two lines of slope m1 and m2, then the acute angle between the lines is given by: tan‌θ=|‌

m2−m1

1+m1⋅m2

|
Calculatio ns:

The slope of the line x−2=0 is ∞.
The slope of the line √3x−y−2=0 is √3. Let m1=∞,m2=√3
and the angle between the given lines is θ.
⇒tan‌θ=|‌

m2−m1

1+m1⋅m2

|
⇒tan‌θ=|‌

‌ m2 m1 −1

1 m1 +m2

|
⇒tan‌θ=‌

1

√3

⇒θ=30∘
Hence, the correct option is 2 .