1
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
If $${\left( {\sqrt 3 + i} \right)^{100}} = {2^{99}}(p + iq)$$, then p and q are roots of the equation :
A
$${x^2} - \left( {\sqrt 3 - 1} \right)x - \sqrt 3 = 0$$
B
$${x^2} + \left( {\sqrt 3 + 1} \right)x + \sqrt 3 = 0$$
C
$${x^2} + \left( {\sqrt 3 - 1} \right)x - \sqrt 3 = 0$$
D
$${x^2} - \left( {\sqrt 3 + 1} \right)x + \sqrt 3 = 0$$
2
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
The equation $$\arg \left( {{{z - 1} \over {z + 1}}} \right) = {\pi \over 4}$$ represents a circle with :
A
centre at (0, $$-$$1) and radius $$\sqrt 2$$
B
centre at (0, 1) and radius $$\sqrt 2$$
C
centre (0, 0) and radius $$\sqrt 2$$
D
centre at (0, 1) and radius 2
3
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
Let C be the set of all complex numbers. Let

S1 = {z$$\in$$C : |z $$-$$ 2| $$\le$$ 1} and

S2 = {z$$\in$$C : z(1 + i) + $$\overline z$$(1 $$-$$ i) $$\ge$$ 4}.

Then, the maximum value of $${\left| {z - {5 \over 2}} \right|^2}$$ for z$$\in$$S1 $$\cap$$ S2 is equal to :
A
$${{3 + 2\sqrt 2 } \over 4}$$
B
$${{5 + 2\sqrt 2 } \over 2}$$
C
$${{3 + 2\sqrt 2 } \over 2}$$
D
$${{5 + 2\sqrt 2 } \over 4}$$
4
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
Let C be the set of all complex numbers. Let

$${S_1} = \{ z \in C||z - 3 - 2i{|^2} = 8\}$$

$${S_2} = \{ z \in C|{\mathop{\rm Re}\nolimits} (z) \ge 5\}$$ and

$${S_3} = \{ z \in C||z - \overline z | \ge 8\}$$.

Then the number of elements in $${S_1} \cap {S_2} \cap {S_3}$$ is equal to :
A
1
B
0
C
2
D
Infinite
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