1
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $A(-4,5, P), B(3,1,4)$ and $C(-2,0, q)$ are the vertices of a triangle $A B C$ and $G(r, q, 1)$ is its centroid, then the value of $2 p+q-r$ is equal to

A
$-$3
B
$-$6
C
9
D
4
2
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

On which of the following lines lies the point of intersection of the line, $\frac{x-4}{2}=\frac{y-5}{2}=\frac{z-3}{1}$ and the plane $x+y+z=2$ ?

A
$\frac{x-1}{1}=\frac{y-3}{2}=\frac{z+4}{-5}$
B
$\frac{x-4}{1}=\frac{y-5}{1}=\frac{z-5}{-1}$
C
$\frac{x-2}{2}=\frac{y-3}{2}=\frac{z+3}{3}$
D
$\frac{x+3}{3}=\frac{4-y}{3}=\frac{z+1}{-2}$
3
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Equation of the plane containing the straight line $\frac{x}{3}=\frac{y}{2}=\frac{z}{4}$ and perpendicular to the plane containing the straight lines $\frac{x}{4}=\frac{y}{3}=\frac{z}{2}$ and $\frac{x}{2}=\frac{y}{-4}=\frac{z}{3}$ is

A
$6 x-67 y-29 z=0$
B
$6 x+67 y-29 z=0$
C
$6 x-67 y+29 z=0$
D
$6 x+67 y+29 z=0$
4
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $m$, such that $\frac{x-4}{1}=\frac{y-2}{1}=\frac{2 z-m}{3}$ lies in the plane $2 x-5 y+2 z=7$, is

A
8
B
10
C
9
D
7
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