1
JEE Advanced 2023 Paper 1 Online
MCQ (Single Correct Answer)
+3
-1
Let $P$ be a point on the parabola $y^2=4 a x$, where $a>0$. The normal to the parabola at $P$ meets the $x$-axis at a point $Q$. The area of the triangle $P F Q$, where $F$ is the focus of the parabola, is 120 . If the slope $m$ of the normal and $a$ are both positive integers, then the pair $(a, m)$ 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 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
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
3
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.
![JEE Advanced 2019 Paper 2 Offline Mathematics - Parabola Question 11 English](https://app-content.cdn.examgoal.net/fly/@width/image/1kwzg4bve/b130c960-c46d-4912-bb21-59b24768127a/39a56eb0-5933-11ec-8549-cdf1b14d394a/file-1kwzg4bvf.png?format=png)
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.
![JEE Advanced 2019 Paper 2 Offline Mathematics - Parabola Question 11 English](https://app-content.cdn.examgoal.net/fly/@width/image/1kwzg4bve/b130c960-c46d-4912-bb21-59b24768127a/39a56eb0-5933-11ec-8549-cdf1b14d394a/file-1kwzg4bvf.png?format=png)
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 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 - Parabola Question 12 English](https://app-content.cdn.examgoal.net/fly/@width/image/1kwzg4bve/b130c960-c46d-4912-bb21-59b24768127a/39a56eb0-5933-11ec-8549-cdf1b14d394a/file-1kwzg4bvf.png?format=png)
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.
![JEE Advanced 2019 Paper 2 Offline Mathematics - Parabola Question 12 English](https://app-content.cdn.examgoal.net/fly/@width/image/1kwzg4bve/b130c960-c46d-4912-bb21-59b24768127a/39a56eb0-5933-11ec-8549-cdf1b14d394a/file-1kwzg4bvf.png?format=png)
Which of the following is the only CORRECT combination?
Questions Asked from Parabola (MCQ (Single Correct Answer))
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