1
MHT CET 2024 10th 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 6 7 8
$\mathrm{P(X=}x)$ 0.15 0.23 0.12 0.10 0.20 0.08 0.07 0.05

For the events $\mathrm{E}=\{\mathrm{X}$ is prime number $\}$

$$\mathrm{F}=\{\mathrm{X}<4\}$$

Then $P(E \cup F)=$

A
0.87
B
0.77
C
0.35
D
0.50
2
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y=a x^{n+1}+b x^{-n}$, then $x^2 \frac{d^2 y}{d x^2}=$

A
$\mathrm{n}(\mathrm{n}+1) y$
B
  $(\mathrm{n}+1)(\mathrm{n}-2) y$
C
$\mathrm{n}(\mathrm{n}-2) y$
D
$(\mathrm{n}+1) \mathrm{y}$
3
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\bar{A}, \bar{B}, \bar{C}$ be vectors of lengths 3 units, 4 units, 5 units respectively. let $\bar{A}$ be perpendicular to $\overline{\mathrm{B}}+\overline{\mathrm{C}}, \overline{\mathrm{B}}$ be perpendicular to $\overline{\mathrm{C}}+\overline{\mathrm{A}}$ and $\overline{\mathrm{C}}$ be perpendicular to $\bar{A}+\bar{B}$, then the length of vector $\overline{\mathrm{A}}+\overline{\mathrm{B}}+\overline{\mathrm{C}}$ is

A
$2 \sqrt{5}$
B
$\sqrt{30}$
C
$\sqrt{45}$
D
$5 \sqrt{2}$
4
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The approximate value of $x^3-2 x^2+3 x+2$ at $x=2.01$ is

A
8.07
B
8.27
C
8.007
D
8.17
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