1
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Let $$u = {{2z + i} \over {z - ki}}$$, z = x + iy and k > 0. If the curve represented
by Re(u) + Im(u) = 1 intersects the y-axis at the points P and Q where PQ = 5, then the value of k is :
A
2
B
4
C
1/2
D
3/2
2
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
If z1 , z2 are complex numbers such that
Re(z1) = |z1 – 1|, Re(z2) = |z2 – 1| , and
arg(z1 - z2) = $${\pi \over 6}$$, then Im(z1 + z2 ) is equal to :
A
$${{\sqrt 3 } \over 2}$$
B
$${1 \over {\sqrt 3 }}$$
C
$${2 \over {\sqrt 3 }}$$
D
$${2\sqrt 3 }$$
3
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
The imaginary part of
$${\left( {3 + 2\sqrt { - 54} } \right)^{{1 \over 2}}} - {\left( {3 - 2\sqrt { - 54} } \right)^{{1 \over 2}}}$$ can be :
A
-2$$\sqrt 6$$
B
6
C
$$\sqrt 6$$
D
-$$\sqrt 6$$
4
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
The value of

$${\left( {{{1 + \sin {{2\pi } \over 9} + i\cos {{2\pi } \over 9}} \over {1 + \sin {{2\pi } \over 9} - i\cos {{2\pi } \over 9}}}} \right)^3}$$ is :
A
$${1 \over 2}\left( {\sqrt 3 - i} \right)$$
B
-$${1 \over 2}\left( {\sqrt 3 - i} \right)$$
C
$$- {1 \over 2}\left( {1 - i\sqrt 3 } \right)$$
D
$${1 \over 2}\left( {1 - i\sqrt 3 } \right)$$
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