1
JEE Advanced 2020 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Change Language
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
$${{2 \over 5}}$$
2
JEE Advanced 2019 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Change Language
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.

JEE Advanced 2019 Paper 2 Offline Mathematics - Conic Sections Question 23 English

Which of the following is the only INCORRECT combination?
A
(III), (R)
B
(IV), (S)
C
(I), (P)
D
(IV), (U)
3
JEE Advanced 2019 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Change Language
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.

JEE Advanced 2019 Paper 2 Offline Mathematics - Conic Sections Question 24 English

Which of the following is the only CORRECT combination?
A
(II), (T)
B
(I), (S)
C
(II), (Q)
D
(I), (U)
4
JEE Advanced 2018 Paper 2 Offline
MCQ (Single Correct Answer)
+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
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