1
JEE Main 2018 (Offline)
+4
-1
If $$\alpha ,\beta \in C$$ are the distinct roots of the equation
x2 - x + 1 = 0, then $${\alpha ^{101}} + {\beta ^{107}}$$ is equal to
A
2
B
-1
C
0
D
1
2
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
If |z $$-$$ 3 + 2i| $$\le$$ 4 then the difference between the greatest value and the least value of |z| is :
A
$$2\sqrt {13}$$
B
8
C
4 + $$\sqrt {13}$$
D
$$\sqrt {13}$$
3
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
The set of all $$\alpha$$ $$\in$$ R, for which w = $${{1 + \left( {1 - 8\alpha } \right)z} \over {1 - z}}$$ is purely imaginary number, for all z $$\in$$ C satisfying |z| = 1 and Re z $$\ne$$ 1, is :
A
an empty set
B
{0}
C
$$\left\{ {0,{1 \over 4}, - {1 \over 4}} \right\}$$
D
equal to R
4
JEE Main 2017 (Offline)
+4
-1
Let $$\omega$$ be a complex number such that 2$$\omega$$ + 1 = z where z = $$\sqrt {-3}$$. If

$$\left| {\matrix{ 1 & 1 & 1 \cr 1 & { - {\omega ^2} - 1} & {{\omega ^2}} \cr 1 & {{\omega ^2}} & {{\omega ^7}} \cr } } \right| = 3k$$,

then k is equal to
A
z
B
-1
C
1
D
-z
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