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1. A
   $\frac{5}{x}+\frac{4}{3x-4}-\frac{4}{3(x+5)}$
2. B
   $5+\frac{4}{3(3x-4)}-\frac{4}{3(x+5)}$
3. C
   $\frac{5}{x}+\frac{4}{3x-4}-\frac{4}{(x+5)}$
4. D
   $\frac{5}{x}+\frac{12}{3x-4}-\frac{4}{(x+5)}$

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

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1. A
   52
2. B
   26
3. C
   65
4. D
   20

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1. A
   $\frac{23}{15}$
2. B
   $17$
3. C
   $\frac{17}{15}$
4. D
   $\frac{23}{17}$

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1. A
   $\frac{35}{2}$
2. B
   $\frac{35}{2}$
3. C
   $7\sqrt{2}$
4. D
   35

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1. A
   one
2. B
   zero
3. C
   two
4. D
   infinite

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1. A
   $-\frac{7\pi}{9}$
2. B
   $-\frac{2\pi}{9}$
3. C
   $0$
4. D
   $\frac{5\pi}{9}$

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1. A
   120
2. B
   264
3. C
   270
4. D
   144

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1. A
   $180\pi\ \text{cm}^2/\text{sec}$
2. B
   $196\pi\ \text{cm}^2/\text{sec}$
3. C
   $192\pi\ \text{cm}^2/\text{sec}$
4. D
   $200\pi\ \text{cm}^2/\text{sec}$

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1. A
   $\frac{9}{8}$
2. B
   $\frac{7}{8}$
3. C
   $\frac{5}{4}$
4. D
   $\frac{3}{4}$

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1. A
   6 gm
2. B
   8 gm
3. C
   10 gm
4. D
   12 gm

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1. A
   $6x-67y-29z=0$
2. B
   $6x+67y-29z=0$
3. C
   $6x-67y+29z=0$
4. D
   $6x+67y+29z=0$

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

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1. A
   $\frac{20}{5}$
2. B
   $\frac{28}{5}$
3. C
   $\frac{48}{5}$
4. D
   $\frac{16}{5}$

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1. A
   $\frac{115}{128}$
2. B
   $\frac{63}{64}$
3. C
   $\frac{57}{64}$
4. D
   $\frac{7}{64}$

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1. A
   $\frac{2\bar{x}+1}{3}$
2. B
   $\frac{3\bar{x}-1}{4}$
3. C
   $\frac{3\bar{x}+1}{4}$
4. D
   $\frac{\bar{x}+1}{4}$

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

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1. A
   $x^2+y^2-6x-4y=27$
2. B
   $x^2+y^2-6x-4y=13$
3. C
   $x^2+y^2-6x-4y=50$
4. D
   $x^2+y^2-6x-4y=37$

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1. A
   1 and $-\frac{5}{2}$
2. B
   $-1$ and $-\frac{1}{2}$
3. C
   $2$ and $-\frac{7}{2}$
4. D
   $3$ and $-\frac{9}{2}$

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1. A
   $\left(\frac{\pi}{6},\frac{5\pi}{6}\right)$
2. B
   $\left(-1,\frac{5\pi}{6}\right)$
3. C
   $(-1,2)$
4. D
   $\left(\frac{\pi}{6},2\right)$

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1. A
   $\pm\frac{1}{\sqrt{3}}(1,1,1)$
2. B
   $\pm\frac{1}{\sqrt{3}}(-1,-1,1)$
3. C
   $\pm\frac{1}{\sqrt{6}}(1,1,-2)$
4. D
   $\pm\frac{1}{\sqrt{2}}(1,1,0)$

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1. A
   12000 cm
2. B
   24000 cm
3. C
   1200 cm
4. D
   2400 cm

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1. A
   $0$
2. B
   $-\frac{1}{|z+1|^2}$
3. C
   $\frac{z}{z+1}\cdot\frac{1}{|z+1|^2}$
4. D
   $\frac{2}{|z+1|^2}$

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1. A
   1
2. B
   -1
3. C
   2
4. D
   None of these

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1. A
   $x\geq1,\ y\leq3,\ x-2y\geq2,\ 6x+7y\leq42,\ x\geq0,\ y\geq0$
2. B
   $x\geq1,\ y\leq3,\ x-2y\geq2,\ 6x+7y\geq42,\ x\geq0,\ y\geq0$
3. C
   $x\leq1,\ y\geq3,\ x-2y\leq2,\ 6x+7y\leq42,\ x\geq0,\ y\geq0$
4. D
   $x\geq1,\ y\leq3,\ x-2y\leq2,\ 6x+7y\leq42,\ x\geq0,\ y\geq0$

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