1
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
If $$\omega ( \ne 1)$$ is a cube root of unity, and $${(1 + \omega )^7} = A + B\omega \,$$. Then $$(A,B)$$ equals
A
(1 ,1)
B
(1, 0)
C
(- 1 ,1)
D
(0 ,1)
2
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
The number of complex numbers z such that $$\left| {z - 1} \right| = \left| {z + 1} \right| = \left| {z - i} \right|$$ equals
A
1
B
2
C
$$\infty $$
D
0
3
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
The conjugate of a complex number is $${1 \over {i - 1}}$$ then that complex number is
A
$${{ - 1} \over {i - 1}}$$
B
$${1 \over {i + 1}}\,$$
C
$${{ - 1} \over {i + 1}}$$
D
$${1 \over {i - 1}}$$
4
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
Let R be the real line. Consider the following subsets of the plane $$R \times R$$ :
$$S = \left\{ {(x,y):y = x + 1\,\,and\,\,0 < x < 2} \right\}$$
$$T = \left\{ {(x,y): x - y\,\,\,is\,\,an\,\,{\mathop{\rm int}} eger\,} \right\}$$,

Which one of the following is true ?

A
Neither S nor T is an equivalence relation on R
B
Both S and T are equivalence relation on R
C
S is an equivalence relation on R but T is not
D
T is an equivalence relation on R but S is not
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