UPSC NDA I 2021 Mathematics Solved Paper

CONCEPT:
Eccentricity:
The constant ratio of distance of point lying on conic from the focus to its perpendicular distance from directrix is called the eccentricity of a conic section and is denoted by e.
- For an ellipse: e<1
- For a parabola: e=1
- For a hyperbola: e>1
- For a circle: e=0
- For a pair of straight lines: e=∞
CALCULATION:
As we know that, eccentricity of a circle is 0 i.e e=0 for a circle.
So, statement 1 is correct.
We also know that, eccentricity of a parabola is equal to 1 i.e e =1 for a parabola.
So, statement 2 is also correct.
We also know that, eccentricity of an ellipse is always less than 1 i.e e<1 for an ellipse.
So, statement 3 is also correct.
Hence, correct option is 4.