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

If $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ are unit coplanar vectors, then the scalar triple product $\left[\begin{array}{lll}2 \overline{\mathrm{a}}-\overline{\mathrm{b}} & 2 \overline{\mathrm{~b}}-\overline{\mathrm{c}} & 2 \overline{\mathrm{c}}-\overline{\mathrm{a}}\end{array}\right]$ has the value

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

If a random variable X has the following probability distribution values

$\mathrm{X}$ 0 1 2 3 4 5 6 7
$\mathrm{P(X):}$ 0 $\mathrm{k}$ $\mathrm{2k}$ $\mathrm{2k}$ $\mathrm{3k}$ $\mathrm{k^2}$ $\mathrm{2k^2}$ $\mathrm{7k^2+k}$

Then $P(X \geq 6)$ has the value

A
$\frac{19}{100}$
B
$\frac{81}{100}$
C
$\frac{9}{100}$
D
$\frac{91}{100}$
3
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let the vectors $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ be such that $|\bar{a}|=2,|\bar{b}|=4$ and $|\bar{c}|=4$. If the projection of $\bar{b}$ on $\bar{a}$ is equal to the projection of $\bar{c}$ on $\bar{a}$ and $\bar{b}$ is perpendicular to $\bar{c}$, then the value of $|\vec{a}+\bar{b}-\bar{c}|$ is

A
$2\sqrt5$
B
6
C
4
D
$4\sqrt2$
4
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the sum of the deviations of 50 observations from 30 is 50 , then the mean of these observations is

A
30
B
50
C
51
D
31
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