1
JEE Main 2024 (Online) 30th January Morning Shift
+4
-1

A line passing through the point $$\mathrm{A}(9,0)$$ makes an angle of $$30^{\circ}$$ with the positive direction of $$x$$-axis. If this line is rotated about A through an angle of $$15^{\circ}$$ in the clockwise direction, then its equation in the new position is :

A
$$\frac{y}{\sqrt{3}+2}+x=9$$
B
$$\frac{x}{\sqrt{3}+2}+y=9$$
C
$$\frac{x}{\sqrt{3}-2}+y=9$$
D
$$\frac{y}{\sqrt{3}-2}+x=9$$
2
JEE Main 2024 (Online) 29th January Evening Shift
+4
-1

Let $$\mathrm{A}$$ be the point of intersection of the lines $$3 x+2 y=14,5 x-y=6$$ and $$\mathrm{B}$$ be the point of intersection of the lines $$4 x+3 y=8,6 x+y=5$$. The distance of the point $$P(5,-2)$$ from the line $$\mathrm{AB}$$ is

A
$$\frac{13}{2}$$
B
8
C
$$\frac{5}{2}$$
D
6
3
JEE Main 2024 (Online) 29th January Evening Shift
+4
-1

The distance of the point $$(2,3)$$ from the line $$2 x-3 y+28=0$$, measured parallel to the line $$\sqrt{3} x-y+1=0$$, is equal to

A
$$3+4 \sqrt{2}$$
B
$$6 \sqrt{3}$$
C
$$4+6 \sqrt{3}$$
D
$$4 \sqrt{2}$$
4
JEE Main 2024 (Online) 29th January Morning Shift
+4
-1

In a $$\triangle A B C$$, suppose $$y=x$$ is the equation of the bisector of the angle $$B$$ and the equation of the side $$A C$$ is $$2 x-y=2$$. If $$2 A B=B C$$ and the points $$A$$ and $$B$$ are respectively $$(4,6)$$ and $$(\alpha, \beta)$$, then $$\alpha+2 \beta$$ is equal to

A
42
B
39
C
48
D
45
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