1
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1

A circle touches both the y-axis and the line x + y = 0. Then the locus of its center is :

A
$$y = \sqrt 2 x$$
B
$$x = \sqrt 2 y$$
C
$${y^2} - {x^2} = 2xy$$
D
$${x^2} - {y^2} = 2xy$$
2
JEE Main 2022 (Online) 25th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Let a circle C touch the lines $${L_1}:4x - 3y + {K_1} = 0$$ and $${L_2} = 4x - 3y + {K_2} = 0$$, $${K_1},{K_2} \in R$$. If a line passing through the centre of the circle C intersects L1 at $$( - 1,2)$$ and L2 at $$(3, - 6)$$, then the equation of the circle C is :
A
$${(x - 1)^2} + {(y - 2)^2} = 4$$
B
$${(x + 1)^2} + {(y - 2)^2} = 4$$
C
$${(x - 1)^2} + {(y + 2)^2} = 16$$
D
$${(x - 1)^2} + {(y - 2)^2} = 16$$
3
JEE Main 2022 (Online) 25th June Morning Shift
MCQ (Single Correct Answer)
+4
-1

Let a, b and c be the length of sides of a triangle ABC such that $${{a + b} \over 7} = {{b + c} \over 8} = {{c + a} \over 9}$$. If r and R are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of $${R \over r}$$ is equal to :

A
$${5 \over 2}$$
B
2
C
$${3 \over 2}$$
D
1
4
JEE Main 2021 (Online) 27th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let Z be the set of all integers,

$$A = \{ (x,y) \in Z \times Z:{(x - 2)^2} + {y^2} \le 4\}$$

$$B = \{ (x,y) \in Z \times Z:{x^2} + {y^2} \le 4\}$$

$$C = \{ (x,y) \in Z \times Z:{(x - 2)^2} + {(y - 2)^2} \le 4\}$$

If the total number of relation from A $$\cap$$ B to A $$\cap$$ C is 2p, then the value of p is :
A
16
B
25
C
49
D
9
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