1
MHT CET 2023 11th May Morning Shift
+2
-0

If $$\mathrm{z}=x+\mathrm{i} y$$ and $$\mathrm{z}^{1 / 3}=\mathrm{p}+\mathrm{iq}$$, where $$x, y, \mathrm{p}, \mathrm{q} \in \mathrm{R}$$ and $$\mathrm{i}=\sqrt{-1}$$, then value of $$\left(\frac{x}{\mathrm{p}}+\frac{y}{\mathrm{q}}\right)$$ is

A
$$\mathrm{p}^2-\mathrm{q}^2$$
B
$$4\left(\mathrm{p}^2-\mathrm{q}^2\right)$$
C
$$\mathrm{p}^2+\mathrm{q}^2$$
D
$$4\left(\mathrm{p}^2+\mathrm{q}^2\right)$$
2
MHT CET 2023 10th May Evening Shift
+2
-0

The argument of $$\frac{1+i \sqrt{3}}{\sqrt{3}+i}, i=\sqrt{-1}$$ is

A
$$\frac{\pi}{3}$$
B
$$\frac{\pi}{4}$$
C
$$\frac{\pi}{6}$$
D
$$\frac{\pi}{2}$$
3
MHT CET 2023 10th May Morning Shift
+2
-0

If $$w=\frac{z}{z-\frac{1}{3} i}$$ and $$|w|=1, i=\sqrt{-1}$$, then $$z$$ lies on

A
circle.
B
line.
C
parabola.
D
ellipse.
4
MHT CET 2023 9th May Evening Shift
+2
-0

If $$Z_1=2+i$$ and $$Z_2=3-4 i$$ and $$\frac{\overline{Z_1}}{\overline{Z_2}}=a+b i$$, then the value of $$-7 a+b$$ is (where $$i=\sqrt{-1}$$ and $$a, b \in R)$$

A
1
B
$$-$$1
C
$$\frac{-3}{25}$$
D
$$\frac{-9}{25}$$
EXAM MAP
Medical
NEET