1
JEE Advanced 2019 Paper 2 Offline
+3
-1 Let the circles

C1 : x2 + y2 = 9 and C2 : (x $$-$$ 3)2 + (y $$-$$ 4)2 = 16, intersect at the points X and Y. Suppose that another circle C3 : (x $$-$$ h)2 + (y $$-$$ k)2 = r2 satisfies the following conditions :

(i) Centre of C3 is collinear with the centres of C1 and C2.

(ii) C1 and C2 both lie inside C3 and

(iii) C3 touches C1 at M and C2 at N.

Let the line through X and Y intersect C3 at Z and W, and let a common tangent of C1 and C3 be a tangent to the parabola x2 = 8$$\alpha$$y.

There are some expression given in the List-I whose values are given in List-II below. Which of the following is the only INCORRECT combination?
A
(III), (R)
B
(IV), (S)
C
(I), (P)
D
(IV), (U)
2
JEE Advanced 2019 Paper 2 Offline
+3
-1 Let the circle C1 : x2 + y2 = 9 and C2 : (x $$-$$ 3)2 + (y $$-$$ 4)2 = 16, intersect at the points X and Y. Suppose that another circle C3 : (x $$-$$ h)2 + (y $$-$$ k)2 = r2 satisfies the following conditions :

(i) centre of C3 is collinear with the centers of C1 and C2.

(ii) C1 and C2 both lie inside C3, and

(iii) C3 touches C1 at M and C2 at N.

Let the line through X and Y intersect C3 at Z and W, and let a common tangent of C1 and C3 be a tangent to the parabola x2 = 8$$\alpha$$y.

There are some expression given in the List-I whose values are given in List-II below. Which of the following is the only CORRECT combination?
A
(II), (T)
B
(I), (S)
C
(II), (Q)
D
(I), (U)
3
JEE Advanced 2018 Paper 2 Offline
+3
-1
Let $$H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$, where a > b > 0, be a hyperbola in the XY-plane whose conjugate axis LM subtends an angle of 60$$^\circ$$ at one of its vertices N. Let the area of the $$\Delta$$LMN be $$4\sqrt 3$$.

List - I List - II
P. The length of the conjugate axis of H is 1. 8
Q. The eccentricity of H is 2. $${4 \over {\sqrt 3 }}$$
R. The distance between the foci of H is 3. $${2 \over {\sqrt 3 }}$$
S. The length of the latus rectum of H is 4. 4
A
P $$\to$$ 4 ; Q $$\to$$ 2 ; R $$\to$$ 1 ; S $$\to$$ 3
B
P $$\to$$ 4 ; Q $$\to$$ 3 ; R $$\to$$ 1 ; S $$\to$$ 2
C
P $$\to$$ 4 ; Q $$\to$$ 1 ; R $$\to$$ 3 ; S $$\to$$ 2
D
P $$\to$$ 3 ; Q $$\to$$ 4 ; R $$\to$$ 2 ; S $$\to$$ 1
4
JEE Advanced 2018 Paper 1 Offline
+3
-1
Let S be the circle in the XY-plane defined the equation x2 + y2 = 4.

Let E1E2 and F1F2 be the chords of S passing through the point P0 (1, 1) and parallel to the X-axis and the Y-axis, respectively. Let G1G2 be the chord of S passing through P0 and having slope$$-$$1. Let the tangents to S at E1 and E2 meet at E3, then tangents to S at F1 and F2 meet at F3, and the tangents to S at G1 and G2 meet at G3. Then, the points E3, F3 and G3 lie on the curve
A
x + y = 4
B
(x $$-$$ 4)2 + (y $$-$$ 4)2 = 16
C
(x $$-$$ 4)(y $$-$$ 4) = 4
D
xy = 4
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