1
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the line $\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$ lies in the plane $x+3 y-\alpha z+\beta=0$, then $(\alpha, \beta)=$

A
$(6,-7)$
B
$(-6,7)$
C
$(5,-15)$
D
$(-5,15)$
2
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Mean and variance of six observations are 6 and 12 respectively. If each observation is multiplied by 3, then new variance of the resulting observations is

A
288
B
36
C
18
D
108
3
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Words of length 10 are formed by using the letters A, B, C, D, E, F, G, H, I, J. Let $x$ be number of such words where no letter is repeated and $y$ be number of such words where exactly two letters are repeated twice and no other letter is repeated, then the value of $\frac{y}{x}$ is

A
45
B
415
C
315
D
215
4
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$\triangle \mathrm{OAB}$ is formed by the lines $x^2-4 x y+y^2=0$ and the line $A B$. The equation of line $A B$ is $2 x+3 y-1=0$. Then the equation of the median of the triangle drawn from the origin is

A
$7 x+8 y=0$
B
$7 x-8 y=0$
C
$8 x+7 y=0$
D
$8 x-7 y=0$
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