1
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
$${{151} \over {13}}$$
2
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
3
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

If two straight lines whose direction cosines are given by the relations $$l + m - n = 0$$, $$3{l^2} + {m^2} + cnl = 0$$ are parallel, then the positive value of c is :

A
6
B
4
C
3
D
2
4
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
$${{25} \over {2\sqrt 3 }}$$
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