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

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1. A
   a is any real value and b is any real value
2. B
   a is only rational value and b is any real value
3. C
   a is only irrational value and b is any real value
4. D
   a is only rational value and b is only rational value

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1. A
   $P[X=0] = P[X=5]$
2. B
   $P[X \leq 1] = P[X \geq 4]$
3. C
   $P[X \leq 2] = P[X \geq 3]$
4. D
   $P[X \leq 2] > P[X \geq 3]$

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1. A
   60
2. B
   240
3. C
   80
4. D
   120

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1. A
   4
2. B
   4.2
3. C
   4.5
4. D
   4.4

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1. A
   If X is not an equilateral triangle, then X is not an isosceles triangle
2. B
   X is neither isosceles nor equilateral triangle
3. C
   X is isosceles but not an equilateral triangle
4. D
   If X is not an isosceles triangle, then X is not an equilateral triangle.

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1. A
   8 N
2. B
   16 N
3. C
   32 N
4. D
   64 N

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1. A
   $(3,\infty)$
2. B
   $(1,3)$
3. C
   $[3,\infty)$
4. D
   $[0,3]$

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1. A
   $x \in [2,3)$
2. B
   $x \in [2,3]$
3. C
   $x \in [2,4]$
4. D
   $x \in [2,4)$

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1. A
   18 units
2. B
   9 units
3. C
   6 units
4. D
   4 units

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1. A
   If a man is judge, then he is honest.
2. B
   If a man is not judge, then he is not honest.
3. C
   If a man is honest, then he is judge.
4. D
   If a man is not honest then, he is not judge.

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1. A
   $8x + 2y = 23$
2. B
   $34x - 8y = 40$
3. C
   $8x + 6y = 37$
4. D
   $8x + 34y = 135$

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1. A
   0.25
2. B
   3
3. C
   0.75
4. D
   1.5

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1. A
   $(2,3,4)$
2. B
   $\frac{1}{2},\frac{1}{3},\frac{1}{4}$
3. C
   $\frac{1}{6},\frac{1}{9},\frac{1}{12}$
4. D
   $\frac{3}{2},\frac{3}{3},\frac{3}{4}$

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1. A
   $\frac{1}{x^3 y}$
2. B
   $\frac{1}{xy^3}$
3. C
   $-\frac{1}{xy^3}$
4. D
   $-\frac{1}{x^3 y}$

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1. A
   $\log\tan\frac{y}{2} = C - 2\sin x$
2. B
   $\log\tan\frac{y}{4} = C - 2\sin\frac{x}{2}$
3. C
   $\log\tan\left(\frac{y}{2}+\frac{\pi}{4}\right) = C - 2\sin x$
4. D
   $\log\tan\left(\frac{y}{2}+\frac{\pi}{4}\right) = C - 2\sin\frac{x}{2}$

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1. A
   $\frac{9}{14}$
2. B
   $\frac{7}{15}$
3. C
   $\frac{5}{14}$
4. D
   $\frac{8}{15}$

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

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1. A
   7.934
2. B
   8.934
3. C
   7.022
4. D
   8.866

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

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

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1. A
   78
2. B
   210
3. C
   225
4. D
   88

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1. A
   $\frac{1}{6}[8-2\sqrt{2}]$ sq. units
2. B
   $\frac{1}{3}[8-2\sqrt{2}]$ sq. units
3. C
   $[8-2\sqrt{2}]$ sq. units
4. D
   $[8+2\sqrt{2}]$ sq. units

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1. A
   $\frac{x+3}{2}=\frac{y+1}{7}=\frac{z+2}{4}$
2. B
   $\frac{x-3}{-2}=\frac{y-1}{7}=\frac{z-2}{4}$
3. C
   $\frac{x-3}{2}=\frac{y-1}{-7}=\frac{z-2}{4}$
4. D
   $\frac{x-3}{2}=\frac{y-1}{5}=\frac{z-2}{4}$

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1. A
   $\begin{pmatrix}-1\\2\\1\end{pmatrix}$
2. B
   $\begin{pmatrix}2\\-1\\1\end{pmatrix}$
3. C
   $\begin{pmatrix}-1\\1\\2\end{pmatrix}$
4. D
   $\begin{pmatrix}-2\\1\\-1\end{pmatrix}$

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