1
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $$\frac{\mathrm{i}^{248}+\mathrm{i}^{246}+\mathrm{i}^{244}+\mathrm{i}^{242}+\mathrm{i}^{240}}{\mathrm{i}^{249}+\mathrm{i}^{247}+\mathrm{i}^{245}+\mathrm{i}^{243}+\mathrm{i}^{241}}, (\mathrm{i}=\sqrt{-1})$$ is

A
i
B
1
C
$$-1$$
D
$$-$$i
2
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$|z-2+i| \leq 2$$, then the difference between the greatest and least value of $$|z|$$ is ________, $$(\mathrm{i}=\sqrt{-1})$$

A
$$2 \sqrt{5}+4$$
B
$$2 \sqrt{5}$$
C
4
D
8
3
MHT CET 2023 12th 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 equal to

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 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$x=\frac{5}{1-2 \mathrm{i}}, \mathrm{i}=\sqrt{-1}$$, then the value of $$x^3+x^2-x+22$$ is

A
7
B
9
C
17
D
39
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