1
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
$-\frac{3}{5}-\frac{1}{5} \mathrm{i}$
2
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 $$\operatorname{Re}(\mathrm{z})=10$$
3
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
$$\frac{2}{5}+\frac{4}{5} \mathrm{i}$$
4
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$(3 x+2)-(5 y-3) i$$ and $$(6 x+3)+(2 y-4) i$$ are conjugates of each other, then the value of $$\frac{x-y}{x+y}$$ is (where $$\left.i=\sqrt{-1}, x, y \in R\right)$$

A
$$-$$1
B
0
C
1
D
2
MHT CET Subjects
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