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

If $\mathrm{w}=\frac{-1+i \sqrt{3}}{2}$, where $\mathrm{i}=\sqrt{-1}$, then the value of $\left(3+w+3 w^2\right)^4$ is

A
16
B
$-16$
C
16w
D
16w$^2$
2
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $|\overline{\mathrm{a}}|=2,|\overline{\mathrm{~b}}|=3$ and $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ are mutually perpendicular vectors, then the area of the triangle whose vertices are $0, a+2 b, a-2 b$ is

A
6 sq.units
B
12 sq.units
C
24 sq.units
D
8 sq.units
3
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y$ is a function of $x$ and $\log (x+y)=2 x y$, then the value of $y^{\prime}(0)$ is

A
1
B
$-$1
C
2
D
0
4
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
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