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

A wire of length 2 units is cut into two parts, which are bent respectively to form a square of side $x$ units and a circle of radius of r units. If the sum of the areas of square and the circle so formed is minimum, then

A
$2 x=(\pi+4) \mathrm{r}$
B
$(4-\pi) x=\pi \mathrm{r}$
C
$x=2 \mathrm{r}$
D
$2 x=\mathrm{r}$
2
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{L}_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2}$ and $\mathrm{L}_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3}$ be two given lines. Then the unit vector perpendicular to $L_1$ and $L_2$ is

A
$\frac{-\hat{\mathrm{i}}+7 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}}{\sqrt{99}}$
B
$\frac{-\hat{\mathrm{i}}-7 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}}{5 \sqrt{3}}$
C
$\frac{-\hat{i}+7 \hat{j}+5 \hat{k}}{5 \sqrt{3}}$
D
$\frac{7 \hat{\mathrm{i}}-7 \hat{\mathrm{j}}-7 \hat{\mathrm{k}}}{\sqrt{99}}$
3
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $a, b \in R$. If the mirror image of the point $\mathrm{p}(\mathrm{a}, 6,9)$ w.r.t. line $\frac{x-3}{7}=\frac{y-2}{5}=\frac{z-1}{-9}$ is $(20, b,-a-9)$, then $|a+b|$ is equal to

A
88
B
86
C
90
D
84
4
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A random variable $X$ has the following probability distribution

$\mathrm{X:}$ 1 2 3 4 5
$\mathrm{P(X):}$ $\mathrm{k^2}$ $\mathrm{2k}$ $\mathrm{k}$ $\mathrm{2k}$ $\mathrm{5k^2}$

Then $\mathrm{P(X > 2)}$ is equal to

A
$\frac{7}{12}$
B
$\frac{23}{36}$
C
$\frac{1}{36}$
D
$\frac{1}{6}$
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