1

JEE Advanced 2020 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

Let a, b and $$\lambda $$ be positive real numbers. Suppose P is an end point of the latus return of the

parabola y

parabola y

^{2}= 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 is2

JEE Advanced 2019 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

Let the circles

C

(i) Centre of C

(ii) C

(iii) C

Let the line through X and Y intersect C

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?

C

_{1}: x^{2}+ y^{2}= 9 and C_{2}: (x $$-$$ 3)^{2}+ (y $$-$$ 4)^{2}= 16, intersect at the points X and Y. Suppose that another circle C_{3}: (x $$-$$ h)^{2}+ (y $$-$$ k)^{2}= r^{2}satisfies the following conditions :(i) Centre of C

_{3}is collinear with the centres of C_{1}and C_{2}.(ii) C

_{1}and C_{2}both lie inside C_{3}and(iii) C

_{3}touches C_{1}at M and C_{2}at N.Let the line through X and Y intersect C

_{3}at Z and W, and let a common tangent of C_{1}and C_{3}be a tangent to the parabola x^{2}= 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?

3

JEE Advanced 2019 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

Let the circle C

(i) centre of C

(ii) C

(iii) C

Let the line through X and Y intersect C

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?

_{1}: x^{2}+ y^{2}= 9 and C_{2}: (x $$-$$ 3)^{2}+ (y $$-$$ 4)^{2}= 16, intersect at the points X and Y. Suppose that another circle C_{3}: (x $$-$$ h)^{2}+ (y $$-$$ k)^{2}= r^{2}satisfies the following conditions :(i) centre of C

_{3}is collinear with the centers of C_{1}and C_{2}.(ii) C

_{1}and C_{2}both lie inside C_{3}, and(iii) C

_{3}touches C_{1}at M and C_{2}at N.Let the line through X and Y intersect C

_{3}at Z and W, and let a common tangent of C_{1}and C_{3}be a tangent to the parabola x^{2}= 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?

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 |

Questions Asked from Conic Sections (MCQ (Single Correct Answer))

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