1
MHT CET 2023 11th May Morning Shift
+2
-0

If the angle between the lines represented by the equation $$x^2+\lambda x y-y^2 \tan ^2 \theta=0$$ is $$2 \theta$$, then the value of $$\lambda$$ is

A
0
B
1
C
$$\tan \theta$$
D
2
2
MHT CET 2023 11th May Morning Shift
+2
-0

$$\mathrm{a}$$ and $$\mathrm{b}$$ are the intercepts made by a line on the co-ordinate axes. If $$3 \mathrm{a}=\mathrm{b}$$ and the line passes through $$(1,3)$$, then the equation of the line is

A
$$x+3 y=10$$
B
$$3 x+y=6$$
C
$$x-3 y+8=0$$
D
$$3 x-2 y+3=0$$
3
MHT CET 2023 10th May Evening Shift
+2
-0

The joint equation of a pair of lines passing through the origin and making an angle of $$\frac{\pi}{4}$$ with the line $$3 x+2 y-8=0$$ is

A
$$5 x^2+24 x y-5 y^2=0$$
B
$$5 x^2-24 x y+5 y^2=0$$
C
$$5 x^2-24 x y-5 y^2=0$$
D
$$5 x^2+24 x y+5 y^2=0$$
4
MHT CET 2023 10th May Evening Shift
+2
-0

Two sides of a square are along the lines $$5 x-12 y+39=0$$ and $$5 x-12 y+78=0$$, then area of the square is

A
9 sq. units.
B
$$\frac{1}{3}$$ sq. units.
C
18 sq. units.
D
3 sq. units.
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