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

If $\mathrm{O}(0,0), \mathrm{A}(1,2)$ and $\mathrm{B}(3,4)$ are the vertices of triangle OAB , then the joint equation of the altitude and median drawn from O is

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

The equation of the plane, passing through the point $(-1,2,-3)$ and parallel to the lines $\frac{x-1}{3}=\frac{y-2}{2}=\frac{z}{-4}$ and $\frac{x}{2}=\frac{y-1}{-3}=\frac{z-2}{2}$, is

A
$8 x-14 y-13 z-3=0$
B
$8 x-14 y+13 z+75=0$
C
$8 x+14 y+13 z+19=0$
D
$8 x+14 y-13 z-59=0$
3
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The incenter of the triangle ABC , whose vertices are $\mathrm{A}(0,2,1), \mathrm{B}(-2,0,0)$ and $\mathrm{C}(-2,0,2)$ is

A
$\left(\frac{3}{2},-\frac{1}{2},-1\right)$
B
$\left(\frac{3}{2}, \frac{1}{2}, 1\right)$
C
$\left(-\frac{3}{2}, \frac{1}{2}, 1\right)$
D
$\left(-\frac{3}{2},-\frac{1}{2},-1\right)$
4
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
$2 x^2-3 x y+2 y^2=0$
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