1
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The differential equation of the family of circles passing through the points $$(0,2)$$ and $$(0,-2)$$ is :

A
$$2 x y \frac{d y}{d x}+\left(x^{2}-y^{2}+4\right)=0$$
B
$$2 x y \frac{d y}{d x}+\left(x^{2}+y^{2}-4\right)=0$$
C
$$2 x y \frac{d y}{d x}+\left(y^{2}-x^{2}+4\right)=0$$
D
$$2 x y \frac{d y}{d x}-\left(x^{2}-y^{2}+4\right)=0$$
2
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let the tangents at two points $$\mathrm{A}$$ and $$\mathrm{B}$$ on the circle $$x^{2}+\mathrm{y}^{2}-4 x+3=0$$ meet at origin $$\mathrm{O}(0,0)$$. Then the area of the triangle $$\mathrm{OAB}$$ is :

A
$$\frac{3 \sqrt{3}}{2}$$
B
$$\frac{3 \sqrt{3}}{4}$$
C
$$\frac{3}{2 \sqrt{3}}$$
D
$$\frac{3}{4 \sqrt{3}}$$
3
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the hyperbola $$H: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$$ pass through the point $$(2 \sqrt{2},-2 \sqrt{2})$$. A parabola is drawn whose focus is same as the focus of $$\mathrm{H}$$ with positive abscissa and the directrix of the parabola passes through the other focus of $$\mathrm{H}$$. If the length of the latus rectum of the parabola is e times the length of the latus rectum of $$\mathrm{H}$$, where e is the eccentricity of H, then which of the following points lies on the parabola?

A
$$(2 \sqrt{3}, 3 \sqrt{2})$$
B
$$\mathbf(3 \sqrt{3},-6 \sqrt{2})$$
C
$$(\sqrt{3},-\sqrt{6})$$
D
$$(3 \sqrt{6}, 6 \sqrt{2})$$
4
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let the lines

$$\frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}$$ and

$$\frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda}$$ be coplanar

and $$\mathrm{P}$$ be the plane containing these two lines.

Then which of the following points does NOT lie on P?

A
$$(0,-2,-2)$$
B
$$(-5,0,-1)$$
C
$$(3,-1,0)$$
D
$$(0,4,5)$$
JEE Main Papers
2023
2021
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12