1
JEE Main 2022 (Online) 29th June Evening Shift
+4
-1

The distance of the origin from the centroid of the triangle whose two sides have the equations $$x - 2y + 1 = 0$$ and $$2x - y - 1 = 0$$ and whose orthocenter is $$\left( {{7 \over 3},{7 \over 3}} \right)$$ is :

A
$$\sqrt 2$$
B
2
C
2$$\sqrt 2$$
D
4
2
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1

The distance between the two points A and A' which lie on y = 2 such that both the line segments AB and A' B (where B is the point (2, 3)) subtend angle $${\pi \over 4}$$ at the origin, is equal to :

A
10
B
$${48 \over 5}$$
C
$${52 \over 5}$$
D
3
3
JEE Main 2022 (Online) 28th June Evening Shift
+4
-1

Let a triangle be bounded by the lines L1 : 2x + 5y = 10; L2 : $$-$$4x + 3y = 12 and the line L3, which passes through the point P(2, 3), intersects L2 at A and L1 at B. If the point P divides the line-segment AB, internally in the ratio 1 : 3, then the area of the triangle is equal to :

A
$${{110} \over {13}}$$
B
$${{132} \over {13}}$$
C
$${{142} \over {13}}$$
D
$${{151} \over {13}}$$
4
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

In an isosceles triangle ABC, the vertex A is (6, 1) and the equation of the base BC is 2x + y = 4. Let the point B lie on the line x + 3y = 7. If ($$\alpha$$, $$\beta$$) is the centroid of $$\Delta$$ABC, then 15($$\alpha$$ + $$\beta$$) is equal to :

A
39
B
41
C
51
D
63
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