1
JEE Advanced 2019 Paper 2 Offline
MCQ (Single Correct Answer)
+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?
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?
2
JEE Advanced 2019 Paper 2 Offline
MCQ (Single Correct Answer)
+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?
(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?
3
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 |
4
JEE Advanced 2018 Paper 1 Offline
MCQ (Single Correct Answer)
+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
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
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