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1. A
   $\dfrac{1}{13}$
2. B
   $\dfrac{2}{13}$
3. C
   $\dfrac{3}{13}$
4. D
   $\dfrac{1}{52}$

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1. A
   $2\times$ Standard deviation $=5\times$ Mean deviation
2. B
   $5\times$ Standard deviation $=2\times$ Mean deviation
3. C
   $4\times$ Standard deviation $=5\times$ Mean deviation
4. D
   $5\times$ Standard deviation $=4\times$ Mean deviation

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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
   Median
2. B
   Mean
3. C
   Mode
4. D
   Geometric mean

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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
   $-\dfrac{1}{4}$
2. B
   $-\dfrac{1}{16}$
3. C
   $\dfrac{1}{16}$
4. D
   $\dfrac{1}{4}$

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1. A
   The mean and median remain the same
2. B
   The median remains the same but the mean will decrease
3. C
   The mean and median both will decrease
4. D
   The mean remains the same but median will decrease

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1. A
   $\dfrac{1}{6}$
2. B
   $\dfrac{1}{4}$
3. C
   $\dfrac{3}{4}$
4. D
   $\dfrac{5}{6}$

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1. A
   $\dfrac{1}{6}$
2. B
   $\dfrac{1}{4}$
3. C
   $\dfrac{1}{3}$
4. D
   $\dfrac{5}{12}$

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1. A
   2
2. B
   12
3. C
   18
4. D
   24

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1. A
   2, -3
2. B
   2 only
3. C
   1
4. D
   3

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1. A
   $(111)_2$ and $(100)_2$
2. B
   $(100)_2$ and $(111)_2$
3. C
   $(101)_2$ and $(101)_2$
4. D
   $(100)_2$ and $(100)_2$

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

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1. A
   $P + Q$
2. B
   $2P + 3Q$
3. C
   $2Q$
4. D
   $Q$

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1. A
   $\dfrac{r-p}{q-r},\ \dfrac{1}{2}$
2. B
   $\dfrac{p-q}{q-r},\ 1$
3. C
   $\dfrac{q-r}{p-q},\ 1$
4. D
   $\dfrac{r-p}{p-q},\ \dfrac{1}{2}$

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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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