1
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The joint equation of pair of lines through the origin and making an angle of $\frac{\pi}{6}$ with the line $3 x+y-6=0$ is

A
$13 x^2+12 x y+3 y^2=0$
B
$13 x^2-12 x y+3 y^2=0$
C
$13 x^2+12 x y-3 y^2=0$
D
$13 x^2-12 x y-3 y^2=0$
2
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A line $4 x+y=1$ passes through the point $\mathrm{A}(2,-7)$ meets the line BC whose equation is $3 x-4 y+1=0$ at the point $B$. The equation of the line $A C$ so that $A B=A C$ is

A
$52 x+89 y+519=0$
B
$52 x+89 y-727=0$
C
$52 x-89 y+519=0$
D
$52 x-89 y-727=0$
3
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If an equation $h x y+g x+f y+c=0$ represents a pair of lines, then

A
$\mathrm{fg}=\mathrm{ch}$
B
$\mathrm{gh}=\mathrm{cf}$
C
$\mathrm{fh}=\mathrm{cg}$
D
$\mathrm{hf}=-\mathrm{cg}$
4
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The straight line, $2 x-3 y+17=0$ is perpendicular to the line passing through the points $(7,17)$ and $(15, \beta)$, then $\beta$ equals

A
$5$
B
$\frac{35}{3}$
C
$-\frac{35}{3}$
D
$-5$
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