1
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The combined equation of two lines through the origin and making an angle of $45^{\circ}$ with the line $3 x+y=0$, is

A
$2 x^2-3 x y-2 y^2=0$
B
$2 x^2+3 x y+4 y^2=0$
C
$2 x^2+3 x y-2 y^2=0$
D
$2 x^2-3 x y+2 y^2=0$
2
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The acute angle between the lines $x \cos 30^{\circ}+y \sin 30^{\circ}=3$ and $x \cos 60^{\circ}+y \sin 60^{\circ}=5$ is

A
$75^{\circ}$
B
$30^{\circ}$
C
$60^{\circ}$
D
$45^{\circ}$
3
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $4 a b=3 h^2$, then the ratio of the slope of lines represented by $a x^2+2 \mathrm{~h} x y+\mathrm{b} y^2=0$ is

A
$\sqrt{3}: 1$
B
$1: \sqrt{3}$
C
$1: 3$
D
$3: 1$
4
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The line L given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line K is parallel to line L and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between L and K is _________ units.

A
$\frac{23}{15}$
B
$\sqrt{17}$
C
$\frac{17}{\sqrt{15}}$
D
$\frac{23}{\sqrt{17}}$
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