1
MHT CET 2023 14th May Morning Shift
+2
-0

$$\mathrm{p}$$ is the length of perpendicular from the origin to the line whose intercepts on the axes are a and $$\mathrm{b}$$ respectively, then $$\frac{1}{\mathrm{a}^2}+\frac{1}{\mathrm{~b}^2}$$ equals

A
$$\mathrm{p}^2$$
B
$$\frac{2}{\mathrm{p}^2}$$
C
$$\frac{1}{\mathrm{p}^2}$$
D
$$\frac{1}{2 \mathrm{p}^2}$$
2
MHT CET 2023 14th May Morning Shift
+2
-0

The perpendiculars are drawn to lines $$L_1$$ and $$L_2$$ from the origin making an angle $$\frac{\pi}{4}$$ and $$\frac{3 \pi}{4}$$ respectively with positive direction of $$\mathrm{X}$$-axis. If both the lines are at unit distance from the origin, then their joint equation is

A
$$x^2-y^2+2 \sqrt{2} y+2=0$$
B
$$x^2-y^2-2 \sqrt{2} y-2=0$$
C
$$x^2-y^2+2 \sqrt{2} y-2=0$$
D
$$x^2-y^2-2 \sqrt{2} y+2=0$$
3
MHT CET 2023 13th May Evening Shift
+2
-0

Let $$P Q R$$ be a right angled isosceles triangle, right angled at $$Q(2,1)$$. If the equation of the line $$P R$$ is $$2 x+y=3$$, then the combined equation representing the pair of lines $$P Q$$ and $$Q R$$ is

A
$$3 x^2+8 x y-3 y^2-20 x-10 y+25=0$$
B
$$3 x^2-8 x y-3 y^2-20 x-10 y-25=0$$
C
$$3 x^2+8 x y-3 y^2+20 x+10 y+25=0$$
D
$$3 x^2-8 x y-3 y^2+20 x+10 y-25=0$$
4
MHT CET 2023 13th May Evening Shift
+2
-0

$$P S$$ is the median of the triangle with vertices at $$P(2,2), Q(6,-1)$$ and $$R(7,3)$$, then the intercepts on the coordinate axes of the line passing through point $$(1,-1)$$ and parallel to PS are respectively

A
$$\frac{7}{2}, \frac{-7}{9}$$
B
$$\frac{2}{7}, \frac{9}{7}$$
C
$$\frac{-7}{2}, \frac{-7}{9}$$
D
$$-2,-9$$
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