You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
|
|
|
|
1.
|
|
|
|
|
题目序号:1
|
|
|
|
|
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 \(A \cap B=\)
|
|
|
|
|
选项:
|
|
|
|
|
A. \(\{-1,0\}\)
|
|
|
|
|
B. \(\{2,3\}\)
|
|
|
|
|
C. \(\{-3,-1,0\}\)
|
|
|
|
|
D. \(\{-1,0,2\}\)
|
|
|
|
|
答案:A
|
|
|
|
|
解析:\(A \cap B=\{-1,0\}\),选 A。
|
|
|
|
|
|
|
|
|
|
2.
|
|
|
|
|
题目序号:2
|
|
|
|
|
题目内容:若 \(\frac{2}{z-1}=1+i\),则 \(z=\)
|
|
|
|
|
选项:
|
|
|
|
|
A. \(-1-i\)
|
|
|
|
|
B. \(-1+i\)
|
|
|
|
|
C. \(1-i\)
|
|
|
|
|
D. \(1+i\)
|
|
|
|
|
答案:C
|
|
|
|
|
解析:
|
|
|
|
|
|
|
|
|
|
3.
|
|
|
|
|
题目序号:3
|
|
|
|
|
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 \(x=\)
|
|
|
|
|
选项:
|
|
|
|
|
A. \(-2\)
|
|
|
|
|
B. \(-1\)
|
|
|
|
|
C. \(1\)
|
|
|
|
|
D. \(2\)
|
|
|
|
|
答案:D
|
|
|
|
|
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。
|
|
|
|
|
|
|
|
|
|
4.
|
|
|
|
|
题目序号:4
|
|
|
|
|
题目内容:已知 \(\cos(\alpha+\beta)=m\),\(\tan \alpha \tan \beta=2\),则 \(\cos(\alpha-\beta)=\)
|
|
|
|
|
选项:
|
|
|
|
|
A. \(-3m\)
|
|
|
|
|
B. \(-\frac{m}{3}\)
|
|
|
|
|
C. \(\frac{m}{3}\)
|
|
|
|
|
D. \(3m\)
|
|
|
|
|
答案:A
|
|
|
|
|
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。
|
|
|
|
|
|
|
|
|
|
5.
|
|
|
|
|
题目序号:5
|
|
|
|
|
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
|
|
|
|
|
选项:
|
|
|
|
|
A. \(2\sqrt{3}\pi\)
|
|
|
|
|
B. \(3\sqrt{3}\pi\)
|
|
|
|
|
C. \(6\sqrt{3}\pi\)
|
|
|
|
|
D. \(9\sqrt{3}\pi\)
|
|
|
|
|
答案:B
|
|
|
|
|
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 \(\frac{1}{3}\pi r^{2}h\)。
|