1. A
   $B' \cup C'$
2. B
   $B \cup C$
3. C
   $B' \cap C'$
4. D
   $B \cap C$

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1. A
   $A$
2. B
   $B$
3. C
   $C$
4. D
   $\{x : x \text{ is a multiple of } 100\}$

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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
   1 and 2 only
2. B
   2 and 3 only
3. C
   1 and 3 only
4. D
   1, 2 and 3

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1. A
   19958400
2. B
   19954800
3. C
   19952400
4. D
   39916800

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1. A
   $\begin{pmatrix}2+3i & 5 \\ 7 & 2-3i\end{pmatrix}$
2. B
   $\begin{pmatrix}2-3i & 5 \\ 7 & 2+3i\end{pmatrix}$
3. C
   $\begin{pmatrix}2-3i & 7 \\ 5 & 2+3i\end{pmatrix}$
4. D
   $\begin{pmatrix}2+3i & 5 \\ 7 & 2+3i\end{pmatrix}$

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

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1. A
   $\dfrac{1}{27}$
2. B
   $\dfrac{1}{64}$
3. C
   $\dfrac{1}{81}$
4. D
   1

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1. A
   $A$
2. B
   $2|A|I$, where $I$ is the identity matrix
3. C
   null matrix whose order is same as that of $A$
4. D
   unit matrix whose order is same as that of $A$

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1. A
   6
2. B
   36
3. C
   216
4. D
   512

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1. A
   1
2. B
   $\cos\theta$
3. C
   $\sin\theta$
4. D
   $\cos 2\theta$

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1. A
   202
2. B
   101
3. C
   51
4. D
   50

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1. A
   $2^{26}$
2. B
   $2^{49}$
3. C
   $2^{50}$
4. D
   $2^{51}$

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1. A
   $\begin{pmatrix}a^{-1} & 0 & 0 \\ 0 & b^{-1} & 0 \\ 0 & 0 & c^{-1}\end{pmatrix}$
2. B
   $\dfrac{1}{abc}\begin{pmatrix}a^{-1} & 0 & 0 \\ 0 & b^{-1} & 0 \\ 0 & 0 & c^{-1}\end{pmatrix}$
3. C
   $\dfrac{1}{abc}\begin{pmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{pmatrix}$
4. D
   $\dfrac{1}{abc}\begin{pmatrix}a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c\end{pmatrix}$

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1. A
   24 minutes
2. B
   34 minutes
3. C
   125 minutes
4. D
   135 minutes

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1. A
   1
2. B
   4
3. C
   8
4. D
   16

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1. A
   symmetric only
2. B
   symmetric and transitive only
3. C
   equivalence relation
4. D
   reflexive only

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1. A
   $x = \dfrac{y}{1+y}$
2. B
   $x = \dfrac{y}{1-y}$
3. C
   $x = \dfrac{1+y}{y}$
4. D
   $x = \dfrac{1-y}{y}$

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1. A
   $3x^2 + 8x + 16 = 0$
2. B
   $3x^2 - 8x - 16 = 0$
3. C
   $3x^2 + 8x - 16 = 0$
4. D
   $x^2 + 8x + 16 = 0$

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1. A
   $\log_e 9$
2. B
   0
3. C
   1
4. D
   $\log_e 3$

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1. A
   $24 \times 8! \times 8!$
2. B
   $(8!)^3$
3. C
   $210 \times 8! \times 8!$
4. D
   $16!$

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

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1. A
   $n,\ 2$
2. B
   $n,\ 3$
3. C
   $n+1,\ 2$
4. D
   $n+1,\ 3$

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1. A
   $a = b + c$
2. B
   $b = c + a$
3. C
   $c = a + b$
4. D
   $b = c$

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1. A
   $1+\sqrt{3}$
2. B
   $1+\sqrt{5}$
3. C
   $1-\sqrt{5}$
4. D
   $\sqrt{5}-1$

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