1
JEE Main 2022 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1

If the circle $$x^{2}+y^{2}-2 g x+6 y-19 c=0, g, c \in \mathbb{R}$$ passes through the point $$(6,1)$$ and its centre lies on the line $$x-2 c y=8$$, then the length of intercept made by the circle on $$x$$-axis is

A
$$\sqrt{11}$$
B
4
C
3
D
$$2 \sqrt{23}$$
2
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1

Let the abscissae of the two points $$P$$ and $$Q$$ on a circle be the roots of $$x^{2}-4 x-6=0$$ and the ordinates of $$\mathrm{P}$$ and $$\mathrm{Q}$$ be the roots of $$y^{2}+2 y-7=0$$. If $$\mathrm{PQ}$$ is a diameter of the circle $$x^{2}+y^{2}+2 a x+2 b y+c=0$$, then the value of $$(a+b-c)$$ is _____________.

A
12
B
13
C
14
D
16
3
JEE Main 2022 (Online) 30th June Morning Shift
MCQ (Single Correct Answer)
+4
-1

Consider three circles:

$${C_1}:{x^2} + {y^2} = {r^2}$$

$${C_2}:{(x - 1)^2} + {(y - 1)^2} = {r^2}$$

$${C_3}:{(x - 2)^2} + {(y - 1)^2} = {r^2}$$

If a line L : y = mx + c be a common tangent to C1, C2 and C3 such that C1 and C3 lie on one side of line L while C2 lies on other side, then the value of $$20({r^2} + c)$$ is equal to :

A
23
B
15
C
12
D
6
4
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+4
-1

Let a triangle ABC be inscribed in the circle $${x^2} - \sqrt 2 (x + y) + {y^2} = 0$$ such that $$\angle BAC = {\pi \over 2}$$. If the length of side AB is $$\sqrt 2$$, then the area of the $$\Delta$$ABC is equal to :

A
1
B
$$\left( {\sqrt 6 + \sqrt 3 } \right)/2$$
C
$$\left( {3 + \sqrt 3 } \right)/4$$
D
$$\left( {\sqrt 6 + 2\sqrt 3 } \right)/4$$
JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination
JEE MainJEE AdvancedWB JEE
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Medical
NEET