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

If $\mathrm{P}(x, y)$ denotes $\mathrm{z}=x+\mathrm{i} y x, y \in \mathbb{R}$ and $\mathrm{i}=\sqrt{-1}$ in Argand's plane and $\left|\frac{z-1}{z+2 i}\right|=1$, then the locus of P is

A
parabola
B
hyperbola
C
circle
D
straight line
2
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{a}>0$ and $\mathrm{z}=\frac{(1+\mathrm{i})^2}{\mathrm{a}-\mathrm{i}}, \mathrm{i}=\sqrt{-1}$, has magnitude $\sqrt{\frac{2}{5}}$ then $\bar{z}$ is equal to

A
$\frac{1}{5}-\frac{3}{5} \mathrm{i}$
B
$-\frac{1}{5}-\frac{3}{5} \mathrm{i}$
C
$-\frac{1}{5}+\frac{3}{5} \mathrm{i}$
D
$-\frac{3}{5}-\frac{1}{5} \mathrm{i}$
3
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $$z \in C$$ with $$\operatorname{Im}(z)=10$$ and it satisfies $$\frac{2 z-n}{2 z+n}=2 i-1, i=\sqrt{-1}$$ for some natural number $$\mathrm{n}$$, then

A
$$\mathrm{n}=20$$ and $$\operatorname{Re}(\mathrm{z})=-10$$
B
$$\mathrm{n}=40$$ and $$\operatorname{Re}(\mathrm{z})=-10$$
C
$$\mathrm{n}=40$$ and $$\operatorname{Re}(\mathrm{z})=10$$
D
$$\mathrm{n}=20$$ and $$\operatorname{Re}(\mathrm{z})=10$$
4
MHT CET 2023 14th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$a>0$$ and $$z=\frac{(1+i)^2}{a-i}, i=\sqrt{-1}$$, has magnitude $$\frac{2}{\sqrt{5}}$$, then $$\bar{z}$$ is

A
$$-\frac{2}{5}-\frac{4}{5} \mathrm{i}$$
B
$$-\frac{2}{5}+\frac{4}{5} \mathrm{i}$$
C
$$\frac{2}{5}-\frac{4}{5} \mathrm{i}$$
D
$$\frac{2}{5}+\frac{4}{5} \mathrm{i}$$
MHT CET Subjects
EXAM MAP