Circles · JEE Advanced previous year questions

2024 1 question

1. Q152024 · 26 May 2024 · Paper 1

   Let the straight line $y=2x$ touch a circle with center $(0,\alpha )$, $\alpha >0$, and radius $r$ at a point $A_1$. Let $B_1$ be the point on the circle such that the line segment $A_1{B}_1$ is a diameter of the circle. Let $\alpha +r=5+\sqrt{5}$. Match each entry in List-I to the correct entry in List-II. List-I: (P) $\alpha$ equals (Q) $r$ equals (R) $A_1$ equals (S) $B_1$ equals List-II: (1) $(-2,4)$ (2) $\sqrt{5}$ (3) $(-2,6)$ (4) 5 (5) $(2,4)$ The correct option is

   1. A.(P) $\to$ (4) \quad (Q) $\to$ (2) \quad (R) $\to$ (1) \quad (S) $\to$ (3)
   2. B.(P) $\to$ (2) \quad (Q) $\to$ (4) \quad (R) $\to$ (1) \quad (S) $\to$ (3)
   3. C.(P) $\to$ (4) \quad (Q) $\to$ (2) \quad (R) $\to$ (5) \quad (S) $\to$ (3)
   4. D.(P) $\to$ (2) \quad (Q) $\to$ (4) \quad (R) $\to$ (3) \quad (S) $\to$ (5)
   Show answer

   Answer: C