1. A
   $x=y=z$
2. B
   $xz=1$
3. C
   $x\neq y$ and $y=z$
4. D
   $x=y$ and $y\neq z$

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1. A
   x, 6, z
2. B
   x, 4, z
3. C
   x, 2, z
4. D
   x, 1, z

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1. A
   0
2. B
   1
3. C
   -1
4. D
   $\frac{1}{2}$

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1. A
   $\frac{b}{a}$ or $1$ or $\frac{b}{c}$
2. B
   $\frac{c}{a}$ or $\frac{c}{b}$ or $1$
3. C
   $1$ or $\frac{a}{b}$ or $\frac{a}{c}$
4. D
   $1$ or $\frac{a}{b}$ or $\frac{c}{a}$

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1. A
   only one AP
2. B
   more than one but finite numbers of APs
3. C
   infinite number of APs
4. D
   finite number of GPs

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1. A
   $(2p)^{th}$ term
2. B
   $(2q)^{th}$ term
3. C
   Twice the $p^{th}$ term
4. D
   Twice the $q^{th}$ term

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1. A
   29
2. B
   30
3. C
   32
4. D
   35

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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
   30°
2. B
   45°
3. C
   60°
4. D
   75°

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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
   $x \in \{-2\}$
2. B
   $x \in \{4\}$
3. C
   $x \in \{-2, 4\}$
4. D
   $x \in \{-4, 2\}$

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

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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
   $0$
2. B
   $1$
3. C
   $\log_{2} 5$
4. D
   $\log_{5} 2$

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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
   7
2. B
   8
3. C
   9
4. D
   10

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1. A
   $1$
2. B
   $\frac{3}{8}$
3. C
   $\frac{9}{8}$
4. D
   $\frac{9}{4}$

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1. A
   20
2. B
   10
3. C
   2
4. D
   0

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1. A
   $\frac{1}{12}$
2. B
   $\frac{1}{18}$
3. C
   $\frac{1}{36}$
4. D
   $\frac{1}{72}$

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

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1. A
   6
2. B
   5
3. C
   4
4. D
   3

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1. A
   1:2:3
2. B
   3:4:5
3. C
   3:5:4
4. D
   1:3:2

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1. A
   2k
2. B
   3k
3. C
   4k
4. D
   5k

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