1
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
2
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1

Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle. Then the area of $$\Delta$$PQR is :

A
$${{25} \over {4\sqrt 3 }}$$
B
$${{25\sqrt 3 } \over 2}$$
C
$${{25} \over {\sqrt 3 }}$$
D
$${{25} \over {2\sqrt 3 }}$$
3
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

Let the area of the triangle with vertices A(1, $$\alpha$$), B($$\alpha$$, 0) and C(0, $$\alpha$$) be 4 sq. units. If the points ($$\alpha$$, $$-$$$$\alpha$$), ($$-$$$$\alpha$$, $$\alpha$$) and ($$\alpha$$2, $$\beta$$) are collinear, then $$\beta$$ is equal to :

A
64
B
$$-$$8
C
$$-$$64
D
512
4
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
Let A be the set of all points ($$\alpha$$, $$\beta$$) such that the area of triangle formed by the points (5, 6), (3, 2) and ($$\alpha$$, $$\beta$$) is 12 square units. Then the least possible length of a line segment joining the origin to a point in A, is :
A
$${4 \over {\sqrt 5 }}$$
B
$${16 \over {\sqrt 5 }}$$
C
$${8 \over {\sqrt 5 }}$$
D
$${12 \over {\sqrt 5 }}$$
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