1
JEE Main 2025 (Online) 3rd April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the four distinct points $(4,6),(-1,5),(0,0)$ and $(k, 3 k)$ lie on a circle of radius $r$, then $10 k+r^2$ is equal to
A
34
B
32
C
35
D
33
2
JEE Main 2025 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let a circle C pass through the points (4, 2) and (0, 2), and its centre lie on 3x + 2y + 2 = 0. Then the length of the chord, of the circle C, whose mid-point is (1, 2), is:

A

4$\sqrt{2}$

B

2$\sqrt{2}$

C

2$\sqrt{3}$

D

$\sqrt{3}$

3
JEE Main 2025 (Online) 29th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the line x+y=1 meet the circle $x^2+y^2=4$ at the points A and B. If the line perpendicular to AB and passing through the mid-point of the chord AB intersects the circle at C and D, then the area of the quadrilateral ABCD is equal to :

A

$ \sqrt{14} $

B

$ 3\sqrt{7} $

C

$ 2\sqrt{14} $

D

$ 5\sqrt{7} $

4
JEE Main 2025 (Online) 28th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the equation of the circle, which touches $x$-axis at the point $(a, 0), a>0$ and cuts off an intercept of length $b$ on $y-a x i s$ be $x^2+y^2-\alpha x+\beta y+\gamma=0$. If the circle lies below $x-a x i s$, then the ordered pair $\left(2 a, b^2\right)$ is equal to

A
$\left(\alpha, \beta^2+4 \gamma\right)$
B
$\left(\alpha, \beta^2-4 \gamma\right)$
C
$\left(\gamma, \beta^2-4 \alpha\right)$
D
$\left(\gamma, \beta^2+4 \alpha\right)$
JEE Main Subjects
EXAM MAP