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1. 题目序号:1
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2. 题目内容:已知集合 $A=\left\{x \mid -5 < x^{3} < 5\right\}, B=\left\{-3,-1,0,2,3\right\}$,则 $A \cap B=$
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3. 选项:
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A. $\{-1,0\}$
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B. $\{2,3\}$
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C. $\{-3,-1,0\}$
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D. $\{-1,0,2\}$
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4. 答案:A
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5. 解析:$A \cap B=\{-1,0\}$,选 A。
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1. 题目序号:2
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2. 题目内容:若 $\frac{2}{z-1}=1+i$,则 $z=$
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3. 选项:
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A. $-1-i$
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B. $-1+i$
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C. $1-i$
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D. $1+i$
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4. 答案:C
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5. 解析:无
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1. 题目序号:3
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2. 题目内容:已知向量 $\vec{a}=(0,1)$,$\vec{b}=(2,x)$,若 $\vec{b} \perp (\vec{b}-4\vec{a})$,则 $x=$
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3. 选项:
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A. $-2$
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B. $-1$
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C. $1$
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D. $2$
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4. 答案:D
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5. 解析:$\vec{b}-4\vec{a}=(2,x-4)$,$\vec{b} \perp (\vec{b}-4\vec{a})$,$\therefore \vec{b}(\vec{b}-4\vec{a})=0$,$\therefore 4+x(x-4)=0$,$\therefore x=2$,选 D。
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1. 题目序号:4
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2. 题目内容:已知 $\cos(\alpha+\beta)=m$,$\tan \alpha \tan \beta=2$,则 $\cos(\alpha-\beta)=$
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3. 选项:
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A. $-3m$
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B. $-\frac{m}{3}$
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C. $\frac{m}{3}$
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D. $3m$
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4. 答案:A
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5. 解析:$\left\{\begin{array}{l}\cos \alpha \cos \beta-\sin \alpha \sin \beta=m \\\frac{\sin \alpha \sin \beta}{\cos \alpha \cos \beta}=2\end{array}\right.$,$\therefore \left\{\begin{array}{l}\sin \alpha \sin \beta=-2m \\\cos \alpha \cos \beta=-m\end{array}\right.$,$\cos(\alpha-\beta)=\cos \alpha \cos \beta+\sin \alpha \sin \beta=-m-2m=-3m$,选 A。
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1. 题目序号:5
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2. 题目内容:已知圆柱和圆锥的底面半径相等,侧面积相等,且它们的高均为 $\sqrt{3}$,则圆锥的体积为
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3. 选项:
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A. $2\sqrt{3}\pi$
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B. $3\sqrt{3}\pi$
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C. $6\sqrt{3}\pi$
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D. $9\sqrt{3}\pi$
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4. 答案:B
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5. 解析:设它们底面半径为 $r$,圆锥母线 $l$,$\therefore 2\pi r\sqrt{3}=\pi rl$,$\therefore l=\sqrt{3}$,则圆锥的体积为 $\frac{1}{3}\pi r^{2}h$。
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