KCET 2026 Mathematics Solved Paper

Concept:The type of conic section depends on the relation between the semi-vertical angle $\alpha$ and the angle $\beta$ between the cutting plane and the cone's axis.Explanation:For a right circular cone, the conic is determined by comparing $\alpha$ and $\beta$.If $0 \le \beta < \alpha$, the plane cuts both nappes, giving a hyperbola.If $\beta = \alpha$, the plane is parallel to a generator, giving a parabola.If $\alpha < \beta < 90^\circ$, the plane cuts only one nappe, giving an ellipse.If $\beta = 90^\circ$, the plane is perpendicular to the axis, giving a circle.Statement-I says $\alpha > \beta \ge 0$, which is exactly $0 \le \beta < \alpha$.So the section is a hyperbola, and Statement-I is true.The angle $\beta$ is always taken between the plane and the axis, so its valid range is $0^\circ$ to $90^\circ$.Therefore, $\beta > 90^\circ$ is invalid in this context, so Statement-II is false.Answer:Statement I is true, Statement II is false.Hence, the correct option is A.