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

If $\left|\frac{\mathrm{z}}{1+\mathrm{i}}\right|=2$, where $\mathrm{z}=x+\mathrm{i} y, \mathrm{i}=\sqrt{-1}$ represents a circle, then centre ' $C$ ' and radius ' $r$ ' of the circle are

A
$\mathrm{C} \equiv(3,0), \mathrm{r}=4$
B
$\mathrm{C} \equiv(6,0), \mathrm{r}=2$
C
$\mathrm{C} \equiv(0,3), \mathrm{r}=8$
D
$ \mathrm{C} \equiv(0,0), \mathrm{r}=2 \sqrt{2}$
2
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\left(-2-\frac{1}{3} \mathrm{i}\right)^3=\frac{x+\mathrm{i} y}{27}, \mathrm{i}=\sqrt{-1}$, where $x$ and $y$ are real numbers, then $(y-x)$ has the value

A
$-91$
B
$-85$
C
$85$
D
$91$
3
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $z^2+z+1=0$ then $\left(z^3+\frac{1}{z^3}\right)^2+\left(z^4+\frac{1}{z^4}\right)^2=$ where $z=w=$ complex cube root of unity

A
4
B
1
C
5
D
2
4
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $|z|=1$ and $w=\frac{z-1}{z+1}$ (where $\left.z \neq-1\right)$, then $\operatorname{Re}(w)$ is

A
0
B
$-\frac{1}{|z+1|^2}$
C
$\left|\frac{z}{z+1}\right| \cdot \frac{1}{|z+1|^2}$
D
$\frac{\sqrt{2}}{|z+1|^2}$
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