1
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Eight chairs are numbered 1 to 8 . Two women and three men wish to occupy one chair each. First the women choose chairs from amongst the chairs marked 1 to 4 , and then the men select the chairs from amongst the remaining. The number of possible arrangements is

A
${ }^6 \mathrm{C}_3 \times{ }^4 \mathrm{C}_2$
B
${ }^4 \mathrm{P}_2 \times{ }^6 \mathrm{P}_3$
C
${ }^4 C_2+{ }^4 P_3$
D
${ }^4 \mathrm{P}_2+{ }^6 \mathrm{P}_3$
2
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the distance between the plane Ax-2y+z $=\mathrm{d}$ and the plane containing the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ is $\sqrt{6}$ units, then $|d|$ is

A
1
B
$\sqrt{6}$
C
2
D
6
3
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Maximum value of $Z=100 x+70 y$ Subject to $2 x \geq 4, y \leq 3, x+y \leq 8, x, y \geq 0$ is

A
800
B
940
C
400
D
710
4
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Three persons $\mathrm{P}, \mathrm{Q}$ and R independently try to hit a target. If the probabilities of their hitting the target are $\frac{3}{4}, \frac{1}{2}$ and $\frac{5}{8}$ respectively, then the probability that the target is hit by P or Q but not by $R$, is

A
$\frac{15}{64}$
B
$\frac{21}{64}$
C
$\frac{39}{64}$
D
$\frac{9}{64}$
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