1
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1

Let the point $$P(\alpha, \beta)$$ be at a unit distance from each of the two lines $$L_{1}: 3 x-4 y+12=0$$, and $$L_{2}: 8 x+6 y+11=0$$. If $$P$$ lies below $$L_{1}$$ and above $${ }{L_{2}}$$, then $$100(\alpha+\beta)$$ is equal to

A
$$-$$14
B
42
C
$$-$$22
D
14
2
JEE Main 2022 (Online) 25th July Morning Shift
+4
-1

A line, with the slope greater than one, passes through the point $$A(4,3)$$ and intersects the line $$x-y-2=0$$ at the point B. If the length of the line segment $$A B$$ is $$\frac{\sqrt{29}}{3}$$, then $$B$$ also lies on the line :

A
$$2 x+y=9$$
B
$$3 x-2 y=7$$
C
$$x+2 y=6$$
D
$$2 x-3 y=3$$
3
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
$$\sqrt 3 x - y + \sqrt 3 - 3 = 0$$
4
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
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