1
JEE Main 2024 (Online) 8th April Evening Shift
+4
-1

If the line segment joining the points $$(5,2)$$ and $$(2, a)$$ subtends an angle $$\frac{\pi}{4}$$ at the origin, then the absolute value of the product of all possible values of $a$ is :

A
4
B
8
C
6
D
2
2
JEE Main 2024 (Online) 8th April Morning Shift
+4
-1

The equations of two sides $$\mathrm{AB}$$ and $$\mathrm{AC}$$ of a triangle $$\mathrm{ABC}$$ are $$4 x+y=14$$ and $$3 x-2 y=5$$, respectively. The point $$\left(2,-\frac{4}{3}\right)$$ divides the third side $$\mathrm{BC}$$ internally in the ratio $$2: 1$$, the equation of the side $$\mathrm{BC}$$ is

A
$$x+6 y+6=0$$
B
$$x-3 y-6=0$$
C
$$x+3 y+2=0$$
D
$$x-6 y-10=0$$
3
JEE Main 2024 (Online) 6th April Evening Shift
+4
-1

If the locus of the point, whose distances from the point $$(2,1)$$ and $$(1,3)$$ are in the ratio $$5: 4$$, is $$a x^2+b y^2+c x y+d x+e y+170=0$$, then the value of $$a^2+2 b+3 c+4 d+e$$ is equal to :

A
37
B
$$-27$$
C
437
D
5
4
JEE Main 2024 (Online) 6th April Morning Shift
+4
-1

Let a variable line of slope $$m>0$$ passing through the point $$(4,-9)$$ intersect the coordinate axes at the points $$A$$ and $$B$$. The minimum value of the sum of the distances of $$A$$ and $$B$$ from the origin is

A
30
B
15
C
10
D
25
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