1
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
If $${{3 + i\sin \theta } \over {4 - i\cos \theta }}$$, $$\theta$$ $$\in$$ [0, 2$$\theta$$], is a real number, then an argument of
sin$$\theta$$ + icos$$\theta$$ is :
A
$$\pi - {\tan ^{ - 1}}\left( {{3 \over 4}} \right)$$
B
$$- {\tan ^{ - 1}}\left( {{3 \over 4}} \right)$$
C
$${\tan ^{ - 1}}\left( {{4 \over 3}} \right)$$
D
$$\pi - {\tan ^{ - 1}}\left( {{4 \over 3}} \right)$$
2
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
If $${\mathop{\rm Re}\nolimits} \left( {{{z - 1} \over {2z + i}}} \right) = 1$$, where z = x + iy, then the point (x, y) lies on a :
A
straight line whose slope is $${3 \over 2}$$
B
straight line whose slope is $$-{2 \over 3}$$
C
circle whose diameter is $${{\sqrt 5 } \over 2}$$
D
circle whose centre is at $$\left( { - {1 \over 2}, - {3 \over 2}} \right)$$
3
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
Let z $$\in$$ C with Im(z) = 10 and it satisfies $${{2z - n} \over {2z + n}}$$ = 2i - 1 for some natural number n. Then :
A
n = 20 and Re(z) = –10
B
n = 40 and Re(z) = 10
C
n = 40 and Re(z) = –10
D
n = 20 and Re(z) = 10
4
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
The equation |z – i| = |z – 1|, i = $$\sqrt { - 1}$$, represents :
A
B
the line through the origin with slope – 1
C
a circle of radius $${1 \over 2}$$
D
the line through the origin with slope 1
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