1
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
2
JEE Main 2024 (Online) 5th April Evening Shift
+4
-1

Let $$\mathrm{A}(-1,1)$$ and $$\mathrm{B}(2,3)$$ be two points and $$\mathrm{P}$$ be a variable point above the line $$\mathrm{AB}$$ such that the area of $$\triangle \mathrm{PAB}$$ is 10. If the locus of $$\mathrm{P}$$ is $$\mathrm{a} x+\mathrm{by}=15$$, then $$5 \mathrm{a}+2 \mathrm{~b}$$ is :

A
$$-\frac{12}{5}$$
B
$$-\frac{6}{5}$$
C
6
D
4
3
JEE Main 2024 (Online) 5th April Morning Shift
+4
-1

Let two straight lines drawn from the origin $$\mathrm{O}$$ intersect the line $$3 x+4 y=12$$ at the points $$\mathrm{P}$$ and $$\mathrm{Q}$$ such that $$\triangle \mathrm{OPQ}$$ is an isosceles triangle and $$\angle \mathrm{POQ}=90^{\circ}$$. If $$l=\mathrm{OP}^2+\mathrm{PQ}^2+\mathrm{QO}^2$$, then the greatest integer less than or equal to $$l$$ is :

A
42
B
46
C
48
D
44
4
JEE Main 2024 (Online) 4th April Morning Shift
+4
-1

The vertices of a triangle are $$\mathrm{A}(-1,3), \mathrm{B}(-2,2)$$ and $$\mathrm{C}(3,-1)$$. A new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to origin is:

A
$$-x+y-(2-\sqrt{2})=0$$
B
$$x+y-(2-\sqrt{2})=0$$
C
$$x+y+(2-\sqrt{2})=0$$
D
$$x-y-(2+\sqrt{2})=0$$
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