1
MHT CET 2023 9th May Evening Shift
+2
-0

If the slope of one of the lines represented by $$a x^2+(2 a+1) x y+2 y^2=0$$ is reciprocal of the slope of the other, then the sum of squares of slopes is

A
$$\frac{17}{4}$$
B
$$\frac{82}{9}$$
C
$$\frac{97}{36}$$
D
2
2
MHT CET 2023 9th May Evening Shift
+2
-0

The equation of a line, whose perpendicular distance from the origin is 7 units and the angle, which the perpendicular to the line from the origin makes, is $$120^{\circ}$$ with positive $$\mathrm{X}$$-axis, is

A
$$x+\sqrt{3} y-14=0$$
B
$$x+\sqrt{3} y+14=0$$
C
$$x-\sqrt{3} y+14=0$$
D
$$x-\sqrt{3} y-14=0$$
3
MHT CET 2023 9th May Morning Shift
+2
-0

If the distance between the parallel lines given by the equation $$x^2+4 x y+p y^2+3 x+q y-4=0$$ is $$\lambda$$, then $$\lambda^2=$$

A
5
B
$$\sqrt{5}$$
C
25
D
$$\frac{9}{5}$$
4
MHT CET 2023 9th May Morning Shift
+2
-0

The distance of a point $$(2,5)$$ from the line $$3 x+y+4=0$$ measured along the line $$L_1$$ and $$L_1$$ are same. If slope of line $$L_1$$ is $$\frac{3}{4}$$, then slope of the line $$\mathrm{L}_2$$ is

A
$$-\frac{3}{4}$$
B
$$\frac{1}{3}$$
C
$$\frac{1}{4}$$
D
0
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