1

JEE Advanced 2022 Paper 1 Online

MCQ (Single Correct Answer)

+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:

2

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 is3

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?

4

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?

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

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced 2022 Paper 1 Online (1)
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