1
JEE Advanced 2022 Paper 1 Online
+3
-1 Consider the ellipse

$$\frac{x^{2}}{4}+\frac{y^{2}}{3}=1$$$Let$H(\alpha, 0), 0<\alpha<2$, be a point. A straight line drawn through$H$parallel to the$y$-axis crosses the ellipse and its auxiliary circle at points$E$and$F$respectively, in the first quadrant. The tangent to the ellipse at the point$E$intersects the positive$x$-axis at a point$G$. Suppose the straight line joining$F$and the origin makes an angle$\phi$with the positive$x$-axis. List-I List-II (I) If$\phi=\frac{\pi}{4}$, then the area of the triangle$F G H$is (P)$\frac{(\sqrt{3}-1)^{4}}{8}$(II) If$\phi=\frac{\pi}{3}$, then the area of the triangle$F G H$is (Q) 1 (III) If$\phi=\frac{\pi}{6}$, then the area of the triangle$F G H$is (R)$\frac{3}{4}$(IV) If$\phi=\frac{\pi}{12}$, then the area of the triangle$F G H$is (S)$\frac{1}{2 \sqrt{3}}$(T)$\frac{3 \sqrt{3}}{2}$The correct option is: A$(\mathrm{I}) \rightarrow(\mathrm{R}) ;(\mathrm{II}) \rightarrow(\mathrm{S}) ;(\mathrm{III}) \rightarrow(\mathrm{Q}) ;(\mathrm{IV}) \rightarrow(\mathrm{P})$B (I)$\rightarrow$(R); (II)$\rightarrow(\mathrm{T}) ;(\mathrm{III}) \rightarrow(\mathrm{S}) ;(\mathrm{IV}) \rightarrow(\mathrm{P})$C (I)$\rightarrow(\mathrm{Q}) ;(\mathrm{II}) \rightarrow(\mathrm{T}) ;(\mathrm{III}) \rightarrow(\mathrm{S}) ;(\mathrm{IV}) \rightarrow(\mathrm{P})$D (I)$\rightarrow$(Q); (II)$\rightarrow$(S); (III)$\rightarrow$(Q); (IV)$\rightarrow\$ (P)
2
JEE Advanced 2020 Paper 1 Offline
+3
-1 Let a, b and $$\lambda$$ be positive real numbers. Suppose P is an end point of the latus return of the
parabola y2 = 4$$\lambda$$x, and suppose the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ passes through the point P. If the tangents to the parabola and the ellipse at the point P are perpendicular to each other, then the eccentricity of the ellipse is
A
$${1 \over {\sqrt 2 }}$$
B
$${{1 \over 2}}$$
C
$${{1 \over 3}}$$
D
$${{2 \over 5}}$$
3
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)
4
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)
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