1. A
   $1$
2. B
   $-1$
3. C
   $i$
4. D
   $-i$

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1. A
   $-2$
2. B
   $-1$
3. C
   $0$
4. D
   $2$

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1. A
   $\begin{pmatrix}1 & 1 \\ 1 & 2\end{pmatrix}$
2. B
   $\begin{pmatrix}-1 & -1 \\ -1 & 2\end{pmatrix}$
3. C
   $\begin{pmatrix}1 & -1 \\ -1 & 2\end{pmatrix}$
4. D
   $\begin{pmatrix}-1 & -1 \\ -1 & -2\end{pmatrix}$

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1. A
   3
2. B
   2
3. C
   1
4. D
   0

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1. A
   They are collinear
2. B
   They lie on a circle of radius $\sqrt{3}$
3. C
   They form an equilateral triangle
4. D
   None of the above

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1. A
   1
2. B
   -1
3. C
   $2i$
4. D
   $-2i$

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1. A
   8
2. B
   6
3. C
   4
4. D
   2

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1. A
   1
2. B
   $-k$
3. C
   $k^2$
4. D
   $-k^2$

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1. A
   $-1$
2. B
   $0$
3. C
   $1$
4. D
   $3$

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1. A
   1 only
2. B
   2 only
3. C
   Both 1 and 2
4. D
   Neither 1 nor 2

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1. A
   $\sqrt{3}$
2. B
   $\sqrt{2}$
3. C
   1
4. D
   $\frac{4}{\sqrt{3}}$

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1. A
   $\sqrt{3}$
2. B
   $\sqrt{2}$
3. C
   1
4. D
   $\frac{1}{\sqrt{3}}$

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1. A
   $\dfrac{\gamma}{\alpha}$
2. B
   $\dfrac{\gamma}{\beta}$
3. C
   $\dfrac{2\gamma}{\alpha}$
4. D
   $\dfrac{2\gamma}{\beta}$

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1. A
   6
2. B
   4
3. C
   2
4. D
   None

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1. A
   -1
2. B
   0
3. C
   1
4. D
   4

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1. A
   -2
2. B
   -1
3. C
   0
4. D
   2

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1. A
   $6ab$
2. B
   $3ab$
3. C
   $a^2+b^2$
4. D
   $1$

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1. A
   $0$
2. B
   $1$
3. C
   $2$
4. D
   $3$

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1. A
   $10(1-\omega),\;10(10-\omega^2),\;100$
2. B
   $10(10-\omega),\;10(10-\omega^2),\;90$
3. C
   $10(1-\omega),\;10(10-\omega^2),\;1000$
4. D
   $(1+\omega),\;10+\omega^2,\;-1$

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1. A
   (A) and (B) only
2. B
   (B) and (C) only
3. C
   (A) and (C) only
4. D
   (A), (B) and (C)

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1. A
   $2^{100}\omega^{2}$
2. B
   $2^{100}\omega$
3. C
   $2^{100}$
4. D
   $-2^{100}$

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1. A
   $0$
2. B
   $\omega$
3. C
   $\omega^2$
4. D
   $1-\omega^2$

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