1
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1

Let $$\alpha$$1, $$\alpha$$2 ($$\alpha$$1 < $$\alpha$$2) be the values of $$\alpha$$ fo the points ($$\alpha$$, $$-$$3), (2, 0) and (1, $$\alpha$$) to be collinear. Then the equation of the line, passing through ($$\alpha$$1, $$\alpha$$2) and making an angle of $${\pi \over 3}$$ with the positive direction of the x-axis, is :

A
$$x - \sqrt 3 y - 3\sqrt 3 + 1 = 0$$
B
$$\sqrt 3 x - y + \sqrt 3 + 3 = 0$$
C
$$x - \sqrt 3 y + 3\sqrt 3 + 1 = 0$$
D
$$\sqrt 3 x - y + \sqrt 3 - 3 = 0$$
2
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
3
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
4
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
$${{151} \over {13}}$$
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