1

IIT-JEE 2002

MCQ (Single Correct Answer)
Let $$\omega $$ $$ = - {1 \over 2} + i{{\sqrt 3 } \over 2},$$ then the value of the det.
$$\,\left| {\matrix{ 1 & 1 & 1 \cr 1 & { - 1 - {\omega ^2}} & {{\omega ^2}} \cr 1 & {{\omega ^2}} & {{\omega ^4}} \cr } } \right|$$ is
A
$$3\omega $$
B
$$3\omega \left( {\omega - 1} \right)$$
C
$$3{\omega ^2}$$
D
$$3\omega \left( {1 - \omega } \right)$$
2

IIT-JEE 2002 Screening

MCQ (Single Correct Answer)
For all complex numbers $${z_1},\,{z_2}$$ satisfying $$\left| {{z_1}} \right| = 12$$ and $$\left| {{z_2} - 3 - 4i} \right| = 5,$$
the minimum value of $$\left| {{z_1} - {z_2}} \right|$$ is
A
0
B
2
C
7
D
17
3

IIT-JEE 2001 Screening

MCQ (Single Correct Answer)
Let $${z_1}$$ and $${z_2}$$ be $${n^{th}}$$ roots of unity which subtend a right angle at the origin. Then $$n$$ must be of the form
A
$$4k + 1$$
B
$$4k + 2$$
C
$$4k + 3$$
D
$$4k$$
4

IIT-JEE 2001 Screening

MCQ (Single Correct Answer)
The complex numbers $${z_1},\,{z_2}$$ and $${z_3}$$ satisfying $${{{z_1} - {z_3}} \over {{z_2} - {z_3}}} = {{1 - i\sqrt 3 } \over 2}\,$$ are the vertices of a triangle which is
A
of area zero
B
right-angled isosceles
C
equilateral
D
obtuse-angled isosceles

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