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1

### IIT-JEE 1998

MCQ (More than One Correct Answer)
If $$\,\left| {\matrix{ {6i} & { - 3i} & 1 \cr 4 & {3i} & { - 1} \cr {20} & 3 & i \cr } } \right| = x + iy$$ , then
A
x = 3, y = 2
B
x = 1, y = 3
C
x = 0, y = 3
D
x = 0, y = 0
2

### IIT-JEE 1998

MCQ (More than One Correct Answer)
The value of the sum $$\,\,\sum\limits_{n = 1}^{13} {({i^n}} + {i^{n + 1}})$$ , where i = $$\sqrt { - 1}$$, equals
A
i
B
i - 1
C
- i
D
0
3

### IIT-JEE 1998

MCQ (More than One Correct Answer)
If $${\omega}$$ is an imaginary cube root of unity, then $${(1\, + \omega \, - {\omega ^2})^7}$$ equals
A
$$128\omega$$
B
$$- 128\omega$$
C
$$128{\omega ^2}$$
D
$$- 128{\omega ^2}$$
4

### IIT-JEE 1987

MCQ (More than One Correct Answer)
The value of $$\sum\limits_{k = 1}^6 {(\sin {{2\pi k} \over 7}} - i\,\cos \,{{2\pi k} \over 7})$$ is
A
- 1
B
0
C
- i
D
i

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