1. A
   $\dfrac{1}{6}$
2. B
   $\dfrac{1}{36}$
3. C
   $\dfrac{1}{12}$
4. D
   $\dfrac{5}{12}$

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1. A
   $\dfrac{1}{8}$
2. B
   $\dfrac{1}{6}$
3. C
   $\dfrac{1}{4}$
4. D
   $\dfrac{1}{3}$

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1. A
   $\dfrac{6}{35}$
2. B
   $\dfrac{3}{35}$
3. C
   $\dfrac{2}{35}$
4. D
   $\dfrac{1}{35}$

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1. A
   $\dfrac{93}{100}$
2. B
   $\dfrac{47}{50}$
3. C
   $\dfrac{24}{25}$
4. D
   $\dfrac{23}{25}$

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1. A
   $2$
2. B
   $2.5$
3. C
   $3$
4. D
   $3.5$

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1. A
   $100$
2. B
   $95$
3. C
   $90$
4. D
   $85$

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1. A
   $\bar{x}-x_n+k$
2. B
   $\dfrac{n\bar{x}-\bar{x}+k}{n}$
3. C
   $\bar{x}-\dfrac{x_n-k}{n}$
4. D
   $\dfrac{n\bar{x}-x_n+k}{n}$

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1. A
   $\dfrac{5}{64}$
2. B
   $\dfrac{15}{32}$
3. C
   $\dfrac{31}{64}$
4. D
   $\dfrac{19}{32}$

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1. A
   $\dfrac{11}{20}$
2. B
   $\dfrac{7}{12}$
3. C
   -
4. D
   $1$

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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
   $\dfrac{1}{36}$
2. B
   $\dfrac{5}{36}$
3. C
   $\dfrac{7}{36}$
4. D
   $\dfrac{29}{36}$

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1. A
   $\dfrac{533}{3125}$
2. B
   $\dfrac{633}{3125}$
3. C
   $\dfrac{733}{3125}$
4. D
   $\dfrac{833}{3125}$

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1. A
   $\dfrac{5}{9}$
2. B
   $\dfrac{2}{3}$
3. C
   $\dfrac{1}{3}$
4. D
   $\dfrac{1}{2}$

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1. A
   $20$
2. B
   $18$
3. C
   $14$
4. D
   $10$

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1. A
   $18$ and $\dfrac{1}{3}$
2. B
   $9$ and $\dfrac{1}{3}$
3. C
   $18$ and $\dfrac{2}{3}$
4. D
   $9$ and $\dfrac{2}{3}$

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1. A
   The terms of $S$ form an arithmetic progression with common difference 14.
2. B
   The terms of $S$ form an arithmetic progression with common difference 6.
3. C
   The terms of $S$ form a geometric progression with common ratio $\frac{10}{7}$.
4. D
   The terms of $S$ form a geometric progression with common ratio $\frac{11}{4}$.

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1. A
   One
2. B
   Two
3. C
   Three
4. D
   More than three

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1. A
   $3$
2. B
   $6$
3. C
   $9$
4. D
   $12$

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1. A
   $0$
2. B
   $1$
3. C
   $4$
4. D
   $5$

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

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

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1. A
   $(1111001)_2$
2. B
   $(1001111)_2$
3. C
   $(1)_2$
4. D
   $(0)_2$

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

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1. A
   None
2. B
   One
3. C
   Two
4. D
   All three

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1. A
   $-10$
2. B
   $-6$
3. C
   $0$
4. D
   $6$

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