Q5
Probability Definitions
Set Operations
View
5. After the examination ends, submit both this test paper and the answer sheet together. I. Multiple Choice Questions: This section has 12 questions, each worth 5 points, for a total of 60 points. For each question, only one of the four options is correct.
1. Given sets $M = \{ x \mid - 4 < x < 2 \} , N = \left\{ x \mid x ^ { 2 } - x - 6 < 0 \right\}$, then $M \cap N =$
A. $\{ x \mid - 4 < x < 3 \}$
B. $\{ x \mid - 4 < x < - 2 \}$
C. $\{ x \mid - 2 < x < 2 \}$
D. $\{ x \mid 2 < x < 3 \}$
2. Let complex number $z$ satisfy $| z - \mathrm { i } | = 1$, and the point corresponding to $z$ in the complex plane is $( x , y )$, then
A. $( x + 1 ) ^ { 2 } + y ^ { 2 } = 1$
B. $( x - 1 ) ^ { 2 } + y ^ { 2 } = 1$
C. $x ^ { 2 } + ( y - 1 ) ^ { 2 } = 1$
D. $x ^ { 2 } + ( y + 1 ) ^ { 2 } = 1$
3. Given $a = \log _ { 2 } 0.2 , b = 2 ^ { 0.2 } , c = 0.2 ^ { 0.3 }$, then
A. $a < b < c$
B. $a < c < b$
C. $c < a < b$
D. $b < c < a$
4. In ancient Greece, people believed that the most beautiful human body has the ratio of the length from the top of the head to the navel to the length from the navel to the sole of the foot equal to $\frac { \sqrt { 5 } - 1 } { 2 } \left( \frac { \sqrt { 5 } - 1 } { 2 } \approx 0.618 \right.$, called the golden ratio), and the famous ``Venus de Milo'' exemplifies this. Furthermore, the ratio of the length from the top of the head to the throat to the length from the throat to the navel is also $\frac { \sqrt { 5 } - 1 } { 2 }$. If a person satisfies both golden ratio proportions, with a shoulder width of 105 cm and the length from the top of the head to the chin of 26 cm, then their height could be [Figure]
A. 165 cm
B. 175 cm
C. 185 cm
D. 190 cm
5. The graph of the function $f ( x ) = \frac { \sin x + x } { \cos x + x ^ { 2 } }$ on $[ - \pi , \pi ]$ is approximately
A. [Figure]
B. [Figure]
C. [Figure]
D. [Figure]