MikaStars39/nano-eval huggingface dataset:
After expanding the expression $(1+x^{5}+x^{7})^{20}$ and combining like terms, what are the coefficients of $x^{17}$ and $x^{18}$?

Options:
A. The coefficient of $x^{17}$ is 1230, and the coefficient of $x^{18}$ is 50.
B. The coefficient of $x^{17}$ is 3420, and the coefficient of $x^{18}$ is 20.
C. The coefficient of $x^{17}$ is 2500, and the coefficient of $x^{18}$ is 500.
D. The coefficient of $x^{17}$ is 3400, and the coefficient of $x^{18}$ is 100.
E. The coefficient of $x^{17}$ is 3420, and the coefficient of $x^{18}$ is 0.
F. The coefficient of $x^{17}$ is 1420, and the coefficient of $x^{18}$ is 200.
G. The coefficient of $x^{17}$ is 1000, and the coefficient of $x^{18}$ is 3420.
H. The coefficient of $x^{17}$ is 700, and the coefficient of $x^{18}$ is 300.
I. The coefficient of $x^{17}$ is 5000, and the coefficient of $x^{18}$ is 3420.
J. The coefficient of $x^{17}$ is 2400, and the coefficient of $x^{18}$ is 3420.
Answer: E
Solve the equation $3-7 \ \operatorname{cos}^{2} x \ \operatorname{sin} x-3 \ \operatorname{sin}^{3} x=0$.

Options:
A. $x = \frac{\pi}{2} + k\pi$ and $x = (-1)^k \frac{\pi}{8} + k\pi$
B. $x = \frac{\pi}{12} + 2k\pi$ and $x = (-1)^k \frac{\pi}{3} + k\pi$
C. $x = \frac{\pi}{6} + k\pi$ and $x = (-1)^k \frac{\pi}{2} + k\pi$
D. $x = \frac{\pi}{4} + 2k\pi$ and $x = (-1)^k \frac{\pi}{3} + k\pi$
E. $x = \frac{\pi}{8} + 2k\pi$ and $x = (-1)^k \frac{\pi}{4} + k\pi$
F. $x = \frac{\pi}{3} + 2k\pi$ and $x = (-1)^k \frac{\pi}{4} + k\pi$
G. $x = \frac{\pi}{5} + 2k\pi$ and $x = (-1)^k \frac{\pi}{2} + k\pi$
H. $x = \frac{\pi}{7} + 2k\pi$ and $x = (-1)^k \frac{\pi}{5} + k\pi$
I. $x = \frac{\pi}{2} + 2k\pi$ and $x = (-1)^k \frac{\pi}{6} + k\pi$
J. $x = \frac{\pi}{3} + k\pi$ and $x = (-1)^k \frac{\pi}{6} + k\pi$
Answer: I
Given that the piston has a diameter of $d = 0.14 \, \text{m}$ and a length of $l = 0.16 \, \text{m}$. The piston reciprocates within the cylinder with a clearance of $\delta = 0.4 \, \text{mm}$ between the piston and the inner wall of the cylinder, which is filled with a lubricant of viscosity $\mu = 0.1 \, \text{Pa} \cdot \text{s}$. The velocity of the piston's motion is $1.5 \, \text{m/s}$, and the speed of the lubricant in the clearance follows a linear distribution. Calculate the frictional resistance experienced by the piston.

Options:
A. $$
2 8. 4 6 \mathrm{N}
$$
B. $$
3 0. 7 2 \mathrm{N}
$$
C. $$
2 9. 6 0 \mathrm{N}
$$
D. $$
3 2. 4 9 \mathrm{N}
$$
E. $$
2 5. 1 9 \mathrm{N}
$$
F. $$
2 6. 3 8 \mathrm{N}
$$
G. $$
2 2. 5 1 \mathrm{N}
$$
H. $$
1 8. 7 5 \mathrm{N}
$$
I. $$
1 9. 8 4 \mathrm{N}
$$
J. $$
2 4. 3 9 \mathrm{N}
$$
Answer: F
Given that the velocity distribution of turbulent flow in a circular pipe is $u_{x} \,=\, u_{m} \left( \frac{r_{{0}}-r} {r_{{0}}} \right)^{n}, u_{{y}} \,=\, 0 \,, u_{z} \,=\, 0$, find the angular velocities $\omega_{x}, \omega_{y}, \omega_{z}$?

Options:
A. $\omega_{x}=0, \omega_{y}=-{\frac{n u_{m}} {2 r_{0} r}} \bigl( 1-{\frac{r} {r_{0}}} \bigr)^{n-1} x \neq0$ , $\omega_{z}={\frac{m u_{n}} {2 r_{0} r}} {\big(} 1-{\frac{r} {r_{0}}} {\big)}^{r-1} y \neq0$
B. $\omega_{x}=0, \omega_{y}=-{\frac{n u_{m}} {2 r_{0} r}} \Bigl( 1-{\frac{r} {r_{0}}} \Bigr)^{n-1} z \neq0$ , $\omega_{z}={\frac{m u_{n}} {2 r_{0}}} {\Big(} 1-{\frac{r} {r_{0}}} {\Big)}^{r-1} y \neq0$
C. $\omega_{x}=0, \omega_{y}=-{\frac{n u_{m}} {2 r_{0} r}} \Bigl( 1-{\frac{r} {r_{0}}} \Bigr)^{n-1} z \neq0$ , $\omega_{z}={\frac{m u_{n}} {r_{0} r}} {\Big(} 1-{\frac{r} {r_{0}}} {\Big)}^{r-1} x \neq0$
D. $\omega_{x}=0, \omega_{y}=-{\frac{m u_{n}} {2 r_{0} r}} \Bigl( 1-{\frac{r} {r_{0}}} \Bigr)^{r-1} x \neq0$ , $\omega_{z}={\frac{n u_{m}} {r_{0} r}} {\Big(} 1-{\frac{r} {r_{0}}} {\Big)}^{n-1} y \neq0$
E. $\omega_{x}=0, \omega_{y}=-{\frac{m u_{n}} {2 r_{0}}} \Bigl( 1-{\frac{r} {r_{0}}} \Bigr)^{r-1} z \neq0$ , $\omega_{z}={\frac{n u_{m}} {2 r_{0} r}} {\Big(} 1-{\frac{r} {r_{0}}} {\Big)}^{n-1} x \neq0$
F. $\omega_{x}=0, \omega_{y}=-{\frac{n u_{m}} {2 r_{0} r}} \Bigl( 1-{\frac{r} {r_{0}}} \Bigr)^{n-1} x \neq0$ , $\omega_{z}={\frac{m u_{n}} {r_{0} r}} {\Big(} 1-{\frac{r} {r_{0}}} {\Big)}^{r-1} y \neq0$
G. $\omega_{x}=0, \omega_{y}=-{\frac{m u_{n}} {2 r_{0} r}} \Bigl( 1-{\frac{r} {r_{0}}} \Bigr)^{r-1} z \neq0$ , $\omega_{z}={\frac{n u_{m}} {2 r_{0} r}} {\Big(} 1-{\frac{r} {r_{0}}} {\Big)}^{n-1} y \neq0$
H. $\omega_{x}=0, \omega_{y}=-{\frac{m u_{n}} {r_{0} r}} \Bigl( 1-{\frac{r} {r_{0}}} \Bigr)^{n-1} y \neq0$ , $\omega_{z}={\frac{n u_{m}} {2 r_{0} r}} {\Big(} 1-{\frac{r} {r_{0}}} {\Big)}^{r-1} x \neq0$
I. $\omega_{x}=0, \omega_{y}=-{\frac{m u_{n}} {2 r_{0} r}} \Bigl( 1-{\frac{r} {r_{0}}} \Bigr)^{r-1} y \neq0$ , $\omega_{z}={\frac{n u_{m}} {2 r_{0}}} {\Big(} 1-{\frac{r} {r_{0}}} {\Big)}^{n-1} x \neq0$
J. $\omega_{x}=0, \omega_{y}=-{\frac{n u_{m}} {2 r_{0} r}} \bigl( 1-{\frac{r} {r_{0}}} \bigr)^{n-1} y \neq0$ , $\omega_{z}={\frac{m u_{n}} {2 r_{0} r}} {\big(} 1-{\frac{r} {r_{0}}} {\big)}^{r-1} x \neq0$
Answer: G
There are two water pipes, A and B. Pipe A has a diameter of 200 mm, an equivalent roughness of 0.86 mm, and a flow rate of 0.00094 $\mathrm{m^{3} / s}$; Pipe B has a diameter of 40 mm, an equivalent roughness of 0.19 mm, and a flow rate of 0.0035 m*/s, with the water temperature at 15°C. If the flow is in the hydraulically smooth zone, use the Blasius equation to calculate A. If it is in the transitional zone, you can first use the Jain equation to calculate the hydraulic gradient $J$ for both pipes.

Options:
A. 0.532
B. 0.308
C. 0.379
D. 0.657
E. 0.562
F. 0.489
G. 0.249
H. 0.274
I. 0.412
J. 0.701
Answer: B
A circular pipe with a diameter of 20 cm transports oil with a kinematic viscosity of $\upsilon\!=\! 0.4 \, \mathrm{cm}^{2} / \mathrm{s}$ and a flow rate of 121 L/s. If a 5 cm circular pipe is used in a model test and water at 20°C is used as the test fluid, what would be the flow rate of the model? Assume that the primary acting force is the viscous force.

Options:
A. 0.150 (L/s)
B. 0.650 (L/s)
C. 2.125 (L/s)
D. 0.915 (L/s)
E. 1.350 (L/s)
F. 1.500 (L/s)
G. 1.000 (L/s)
H. 0.825 (L/s)
I. 1.275 (L/s)
J. 0.762 (L/s)
Answer: J
There is a trapezoidal cross-section channel with a bottom slope of $i = 0.0005$, a side slope coefficient of $m = 1$, and a roughness coefficient of $n = 0.027$, with a water cross-sectional area $A = 10m^{2}$. Determine the hydraulically optimal cross-section.

Options:
A. $12.00\mathrm{m}^{3}/$s
B. $8.50\mathrm{m}^{3}/$s
C. $6.90\mathrm{m}^{3}/$s
D. $11.45\mathrm{m}^{3}/$s
E. $9.19\mathrm{m}^{3}/$s
F. $7.35\mathrm{m}^{3}/$s
G. $8.85\mathrm{m}^{3}/$s
H. $10.70\mathrm{m}^{3}/$s
I. $7.75\mathrm{m}^{3}/$s
J. $10.25\mathrm{m}^{3}/$s
Answer: E
The elevation of the flat bottom spillway slab of the reservoir is 122.0 m. It is required that the outflow discharge is $Q \!=\! 1150 \, \mathrm{m}^{3} / \mathrm{s}$ when the reservoir's extreme water level is 130.4 m. Assuming the total width of the spillway is the same as the upstream diversion channel, the net width of each bay $b$ does not exceed 6.0 m, the thickness does not exceed 1.5 m, the side piers and the pier heads are circular, and the sluice chamber is followed by a steep chute. How many bays should be set up for this spillway?

Options:
A. $$
b \!=\! 3.5 \mathrm{m} \,, \, \, \, n \!=\! 8 \,, \, \, \, d \!=\! 1. \, 5 \mathrm{m}
$$
B. $$
b \!=\! 7 \mathrm{m} \,, \, \, \, n \!=\! 3 \,, \, \, \, d \!=\! 2. \, 5 \mathrm{m}
$$
C. $$
b \!=\! 5 \mathrm{m} \,, \, \, \, n \!=\! 5 \,, \, \, \, d \!=\! 1. \, 5 \mathrm{m}
$$
D. $$
b \!=\! 2 \mathrm{m} \,, \, \, \, n \!=\! 10 \,, \, \, \, d \!=\! 1. \, 5 \mathrm{m}
$$
E. $$
b \!=\! 6 \mathrm{m} \,, \, \, \, n \!=\! 4 \,, \, \, \, d \!=\! 2. \, 0 \mathrm{m}
$$
F. $$
b \!=\! 4 \mathrm{m} \,, \, \, \, n \!=\! 7 \,, \, \, \, d \!=\! 1. \, 5 \mathrm{m}
$$
G. $$
b \!=\! 8 \mathrm{m} \,, \, \, \, n \!=\! 3 \,, \, \, \, d \!=\! 1. \, 0 \mathrm{m}
$$
H. $$
b \!=\! 4.5 \mathrm{m} \,, \, \, \, n \!=\! 6 \,, \, \, \, d \!=\! 1. \, 8 \mathrm{m}
$$
I. $$
b \!=\! 5.5 \mathrm{m} \,, \, \, \, n \!=\! 4 \,, \, \, \, d \!=\! 2. \, 0 \mathrm{m}
$$
J. $$
b \!=\! 3 \mathrm{m} \,, \, \, \, n \!=\! 9 \,, \, \, \, d \!=\! 1. \, 5 \mathrm{m}
$$
Answer: C
Under the Froude similarity criterion and the Reynolds similarity criterion, the velocity scale ratio $\lambda_{v}$ and the time scale ratio $\lambda_{\iota}$ are respectively _.

Options:
A. Forchheimer: $\lambda_{v}=\lambda_{l}^{0.5} \quad\lambda_{l}=\lambda_{l}^{2}$ Reynolds: $\lambda_{v}=\lambda_{l}^{1} \quad\lambda_{l}=\lambda_{l}^{0}$
B. Forchheimer: $\lambda_{v}=\lambda_{l}^{2 / 3} \quad\lambda_{l}=\lambda_{l}^{2 / 3}$ Reynolds: $\lambda_{v}=\lambda_{l}^{0.5} \quad\lambda_{l}=\lambda_{l}^{1.5}$
C. Forchheimer: $\lambda_{v}=\lambda_{l}^{1 / 2} \quad\lambda_{l}=\lambda_{l}^{1 / 2}$ Reynolds: $\lambda_{v}=\lambda_{l}^{-1} \quad\lambda_{l}=\lambda_{l}^{2}$
D. Forchheimer: $\lambda_{v}=\lambda_{l}^{1 / 3} \quad\lambda_{l}=\lambda_{l}^{1}$ Reynolds: $\lambda_{v}=\lambda_{l}^{0} \quad\lambda_{l}=\lambda_{l}^{1 / 3}$
E. Forchheimer: $\lambda_{v}=\lambda_{l}^{-1 / 2} \quad\lambda_{l}=\lambda_{l}^{1 / 4}$ Reynolds: $\lambda_{v}=\lambda_{l}^{1} \quad\lambda_{l}=\lambda_{l}^{0}$
F. Forchheimer: $\lambda_{v}=\lambda_{l}^{2} \quad\lambda_{l}=\lambda_{l}^{2}$ Reynolds: $\lambda_{v}=\lambda_{l}^{0.5} \quad\lambda_{l}=\lambda_{l}^{0.5}$
G. Forchheimer: $\lambda_{v}=\lambda_{l}^{0} \quad\lambda_{l}=\lambda_{l}^{0}$ Reynolds: $\lambda_{v}=\lambda_{l}^{3} \quad\lambda_{l}=\lambda_{l}^{3}$
H. Forchheimer: $\lambda_{v}=\lambda_{l}^{0.5} \quad\lambda_{l}=\lambda_{l}^{0.5}$ Reynolds: $\lambda_{v}=\lambda_{l}^{0} \quad\lambda_{l}=\lambda_{l}^{1.5}$
I. Forchheimer: $\lambda_{v}=\lambda_{l}^{3 / 2} \quad\lambda_{l}=\lambda_{l}^{3 / 2}$ Reynolds: $\lambda_{v}=\lambda_{l}^{2} \quad\lambda_{l}=\lambda_{l}^{-1}$
J. Forchheimer: $\lambda_{v}=\lambda_{l}^{2} \quad\lambda_{l}=\lambda_{l}^{0.5}$ Reynolds: $\lambda_{v}=\lambda_{l}^{0.5} \quad\lambda_{l}=\lambda_{l}^{0.5}$
Answer: C
A thin plate with an area of 1.6m² is moving on the water surface at a speed of $u=1.5 \mathrm{m / s}$. Given that the water depth $h=$ 0.05m and the water temperature is 10°C, with the water flow velocity following a linear distribution, find the drag force $F$ on the plate.

Options:
A. $F=8 3. 5 7 1 \times$ $1 0^{-3} \mathrm{N} )$
B. $F=4 5. 3 8 2 \times$ $1 0^{-3} \mathrm{N} )$
C. $F=7 0. 4 2 8 \times$ $1 0^{-4} \mathrm{N} )$
D. $F=5 1. 9 4 6 \times$ $1 0^{-4} \mathrm{N} )$
E. $F=9 1. 6 5 0 \times$ $1 0^{-3} \mathrm{N} )$
F. $F=6 2. 7 8 4 \times$ $1 0^{-3} \mathrm{N} )$
G. $F=3 7. 9 1 2 \times$ $1 0^{-3} \mathrm{N} )$
H. $F=5 8. 1 0 9 \times$ $1 0^{-3} \mathrm{N} )$
I. $F=6 4. 2 9 7 \times$ $1 0^{-5} \mathrm{N} )$
J. $F=7 2. 8 5 3 \times$ $1 0^{-2} \mathrm{N} )$
Answer: F
To design a sluice gate below a breast wall, arrange two beams such that each beam bears an equal force. Given $h_{1}=3 \mathrm{m}$, $h_{2}=6 \mathrm{m}$, find the total hydrostatic pressure on each beam.

Options:
A. $$
1 2 1. 5 \ ( \mathrm{k N} )
$$
B. $$
1 3 0. 9 \ ( \mathrm{k N} )
$$
C. $$
1 5 0. 7 \ ( \mathrm{k N} )
$$
D. $$
1 2 8. 0 \ ( \mathrm{k N} )
$$
E. $$
1 1 7. 4 \ ( \mathrm{k N} )
$$
F. $$
1 3 2. 3 \ ( \mathrm{k N} )
$$
G. $$
1 4 3. 8 \ ( \mathrm{k N} )
$$
H. $$
1 4 0. 2 \ ( \mathrm{k N} )
$$
I. $$
1 5 5. 1 \ ( \mathrm{k N} )
$$
J. $$
1 3 5. 6 \ ( \mathrm{k N} )
$$
Answer: F
Within the region centered at the origin with a radius $r \! \leqslant\! 2 \mathrm{m}$, the velocity field can be expressed as $u_{x}=x^{2} \,, \, \, \, u_{y}=y^{2}$, $u_{z}=z^{2}$. Find the acceleration at the spatial point (1, 1, 1) .

Options:
A. $$
3 \, {\sqrt{2}} \, \ ( \, \mathrm{m / s^{2} \,} )
$$
B. $$
2 \, {\sqrt{3}} \, \ ( \, \mathrm{m / s^{2} \,} )
$$
C. $$
1 \, {\sqrt{2}} \, \ ( \, \mathrm{m / s^{2} \,} )
$$
D. $$
2 \, {\sqrt{5}} \, \ ( \, \mathrm{m / s^{2} \,} )
$$
E. $$
1 \, {\sqrt{6}} \, \ ( \, \mathrm{m / s^{2} \,} )
$$
F. $$
4 \, {\sqrt{3}} \, \ ( \, \mathrm{m / s^{2} \,} )
$$
G. $$
3 \, {\sqrt{6}} \, \ ( \, \mathrm{m / s^{2} \,} )
$$
H. $$
2 \, {\sqrt{1}} \, \ ( \, \mathrm{m / s^{2} \,} )
$$
I. $$
2 \, {\sqrt{7}} \, \ ( \, \mathrm{m / s^{2} \,} )
$$
J. $$
3 \, {\sqrt{3}} \, \ ( \, \mathrm{m / s^{2} \,} )
$$
Answer: B
A pipe is drawn from a pool of constant water level, consisting of three sections with cross-sectional areas of $A_{1} = 0.05 \, \text{m}^{2}$, $A_{2} = 0.03 \, \text{m}^{2}$, and $A_{3} = 0.04 \, \text{m}^{2}$, respectively. The pipe discharges into the atmosphere at its end. Assuming the pool is very large and the inflow velocity can be neglected, and disregarding head loss in the pipe, find the exit velocity $v_{3}$ and the flow rate $Q$ .

Options:
A. $$
v_{3}=9. \, 1 \, \, \, ( {\mathrm{m / s}} )
$$
$$
Q \!=\! 0. \, 3 5 0 \, \, \, ( \mathrm{m^{3}} / \mathrm{s} )
$$
B. $$
v_{3}=9. \, 0 \, \, \, ( {\mathrm{m / s}} )
$$
$$
Q \!=\! 0. \, 3 5 8 \, \, \, ( \mathrm{m^{3}} / \mathrm{s} )
$$
C. $$
v_{3}=8. \, 7 \, \, \, ( {\mathrm{m / s}} )
$$
$$
Q \!=\! 0. \, 3 4 0 \, \, \, ( \mathrm{m^{3}} / \mathrm{s} )
$$
D. $$
v_{3}=7. \, 2 \, \, \, ( {\mathrm{m / s}} )
$$
$$
Q \!=\! 0. \, 2 7 6 \, \, \, ( \mathrm{m^{3}} / \mathrm{s} )
$$
E. $$
v_{3}=7. \, 5 \, \, \, ( {\mathrm{m / s}} )
$$
$$
Q \!=\! 0. \, 2 8 5 \, \, \, ( \mathrm{m^{3}} / \mathrm{s} )
$$
F. $$
v_{3}=8. \, 9 \, \, \, ( {\mathrm{m / s}} )
$$
$$
Q \!=\! 0. \, 3 4 5 \, \, \, ( \mathrm{m^{3}} / \mathrm{s} )
$$
G. $$
v_{3}=8. \, 4 \, \, \, ( {\mathrm{m / s}} )
$$
$$
Q \!=\! 0. \, 3 2 5 \, \, \, ( \mathrm{m^{3}} / \mathrm{s} )
$$
H. $$
v_{3}=7. \, 0 \, \, \, ( {\mathrm{m / s}} )
$$
$$
Q \!=\! 0. \, 2 7 0 \, \, \, ( \mathrm{m^{3}} / \mathrm{s} )
$$
I. $$
v_{3}=6. \, 8 \, \, \, ( {\mathrm{m / s}} )
$$
$$
Q \!=\! 0. \, 2 5 4 \, \, \, ( \mathrm{m^{3}} / \mathrm{s} )
$$
J. $$
v_{3}=9. \, 9 \, \, \, ( {\mathrm{m / s}} )
$$
$$
Q \!=\! 0. \, 3 9 6 \, \, \, ( \mathrm{m^{3}} / \mathrm{s} )
$$
Answer: J
The radiator is composed of rectangular cross-section water pipes measuring $8 \times 12 \mathrm{mm}$. To ensure turbulent flow within each water pipe to facilitate heat dissipation, knowing that the water temperature is 60°C, what should be the flow rate in the water pipes?

Options:
A. $$
12.991(cm^{3}/s)
$$
B. $$
12.334(cm^{3}/s)
$$
C. $$
9.456(cm^{3}/s)
$$
D. $$
10.788(cm^{3}/s)
$$
E. $$
14.448(cm^{3}/s)
$$
F. $$
11.500(cm^{3}/s)
$$
G. $$
7.600(cm^{3}/s)
$$
H. $$
13.201(cm^{3}/s)
$$
I. $$
8.924(cm^{3}/s)
$$
J. $$
8.812(cm^{3}/s)
$$
Answer: D
A pressure water transmission pipe has a pipe wall roughness of $\Delta\!=\! 0.3 \, \mathrm{mm}$, with a water temperature of 15°C. If the pipe length $L = 5 \, \mathrm{m}$ and the pipe diameter $d = 1.0 \, \mathrm{cm}$, with a flow rate of $0.05 \, \mathrm{L/s}$, what is the head loss?

Options:
A. $$
67.89 (cm)
$$
B. $$
64.61 (cm)
$$
C. $$
53.21 (cm)
$$
D. $$
58.36 (cm)
$$
E. $$
45.83 (cm)
$$
F. $$
55.63 (cm)
$$
G. $$
72.49 (cm)
$$
H. $$
61.47 (cm)
$$
I. $$
49.75 (cm)
$$
J. $$
70.12 (cm)
$$
Answer: B
Given the turbulent flow in a circular pipe, $u_{x}=u_{\operatorname* {max}} \, ( \, y / r_{0} \, )^{n} \,, \, \, \, u_{y}=0$ , where $u_{\mathrm{max}}$, $r_{0}$, and $n$ are constants, determine its flow pattern.

Options:
A. Laminar distribution
B. Parabolic curve
C. Linear gradient
D. Hyperbolic stream
E. Non-viscous wave
F. Circular Vortex
G. Stationary field
H. Rotational motion
I. Uniform velocity
J. Oscillatory drift
Answer: H
The surrounding rock of the underground powerhouse of the hydroelectric station is dolomitic limestone, with a saturated uniaxial compressive strength of 50 MPa, and the rock mass integrity coefficient $K_{\mathrm{v}}=0.50$. The joint surface width is 3 mm, filled with rock debris, and the fracture surfaces are straight and smooth, with a structural plane extension length of $7 \mathbf{m}_{\circ}$. The rock wall has water seepage. The maximum principal stress of the surrounding rock is 8 MPa. According to the "Code for Investigation of Geology in Water Resources and Hydropower Engineering" (GB 50487 2008), which engineering geological category should this powerhouse's surrounding rock fall under?

Options:
A. Category V
B. Category IV
C. Category VI
D. Category I
E. Category II
F. Category III
Answer: B
The foundation of a certain building requires compacted fill soil of $8000 \mathrm{m}^{3}$, with a controlled post-compaction moisture content of $w_{1}=14\%$, a saturation degree of $S_{\mathrm{r}}=90\%$, a unit weight of fill material $\gamma=15.5 \mathrm{kN/m}^{3}$, and a natural moisture content of $w_{0}=10\%$. The relative density is $G_{n}=2.72$. What is the approximate volume of fill material needed?

Options:
A. $10750.8 m^{3}$
B. $10990.3 m^{3}$
C. $10844.6 m^{3}$
D. $11200.7 m^{3}$
E. $11500.4 m^{3}$
F. $10400.0 m^{3}$
G. $10200.1 m^{3}$
H. $10500.2 m^{3}$
I. $11350.9 m^{3}$
J. $11000.5 m^{3}$
Answer: C
For a certain site's foundation, the rock mass has 2 sets of structural planes, with an average spacing of the controlling structural plane being 1.5m. The average value of 9 saturated uniaxial compressive strength tests conducted indoors is 26.5 MPa, with a coefficient of variation of 0.2. According to the "Code for Design of Building Foundation" (GB 50007--2002), the characteristic value of the rock foundation bearing capacity determined by the above data is () MPa.

Options:
A. 40.2MPa
B. 25.1MPa
C. 22.4MPa
D. 11.6MPa
E. 14.3MPa
F. 44.0MPa
G. 29.8MPa
H. 33.5MPa
I. 18.7MPa
J. 37.6MPa
Answer: D
A bridge pier is planned to be constructed on a site with an intensity of 8 degrees, with a foundation depth of 2.0 m. The site is covered by a soil layer of 20 m, all of which is of the geological age $Q_{4}$. Below the surface is a 5.0 m layer of newly deposited non-liquefiable cohesive soil, under which lies 15 m of loose silt. The groundwater depth is $d_{w}=$ 5.0 m. According to the "Seismic Design Code for Highway Engineering" (JTJ004-1989), the expression illustrating the ratio of $\sigma_{0} / \sigma_{e}$ at various points within the 20 m range of soil beneath this site's surface, the following is ().

Options:
A. The ratio between the two below 5m from the ground drastically decreases with depth.
B. The ratio between the two above 5m from the ground significantly decreases with depth.
C. The ratio between the two below 5m from the ground continuously increases with depth.
D. The ratio between the two above 5m from the ground continuously decreases with depth.
E. The ratio between the two below 5m from the ground momentarily decreases with depth.
F. The ratio between the two above 5m from the ground sporadically fluctuates with depth.
G. The ratio between the two below 5m from the ground oscillates with depth.
H. The ratio between the two above 5m from the ground significantly increases with depth.
I. The ratio between the two below 5m from the ground remains constant with depth.
J. The ratio between the two above 5m from the ground remains constant with depth.
Answer: C
Patient, male, 50 years old. 10-year history of chronic nephritis, blood pressure $160 \sim 180 / 85 \sim 95 \mathrm{mmHg}$, significant edema in both lower limbs, denies history of diabetes. The first-choice medication for controlling blood pressure is ( ).

Options:
A. Losartan
B. Hydrochlorothiazide
C. Amlodipine
D. Nifedipine
E. Atenolol
F. Metoprolol
G. Furosemide
H. Clonidine
I. Spironolactone
J. Benazepril
Answer: J
The tensile stress at which an object fractures when subjected to tensile loading is called the ()

Options:
A. Toughness
B. Elasticity
C. Ductility
D. Hardness
E. Compressive strength
F. Rigidity
G. Plasticity
H. Brittleness
I. Tensile strength
J. Flexibility
Answer: C
The cross-sectional area of a circular water pipe at a certain point is $5 \mathrm{cm}^{2}$, with water flowing through the pipe at a velocity of $4 \mathrm{m/s}$. The pressure at this point is greater than atmospheric pressure by $1.5 \times 10^{4} \mathrm{Pa}$. At another point, the cross-sectional area of the water pipe is $10 \mathrm{cm}^{2}$, and the pressure is greater than atmospheric pressure by $3.3 \times 10^{4} \mathrm{Pa}$. What is the difference in height between this point and the original point?

Options:
A. -1.5m
B. 2.9m
C. 0.8m
D. -1.8m
E. -0.7m
F. 2.4m
G. 0.5m
H. 1.1m
I. -1.2m
J. 3.0m
Answer: I
Place the U-shaped tube vertically and inject some water. Assume the inner diameters of the two vertical tubes of the U-shaped tube are $1.0mm$ and $0.10mm$, respectively. What is the height difference between the water levels in the two vertical tubes? (The surface tension coefficient of water is given as $\alpha = 7.0 \times 10^{-2} \mathrm{N/m}$)

Options:
A. 0.413m
B. 0.369m
C. 0.150m
D. 0.200m
E. 0.498m
F. 0.290m
G. 0.314m
H. 0.257m
I. 0.142m
J. 0.181m
Answer: H
Two concentric spherical surfaces have radii of 10.0 cm and 30.0 cm, respectively. The smaller sphere is uniformly charged with a positive charge of $1.0 \times 10^{-8} \mathrm{C}$, while the larger sphere is uniformly charged with a positive charge of $1.5 \times 10^{-8} \mathrm{C}$. The electric potential at distances of 20.0 cm and 50.0 cm from the center of the spheres are (). Given the electric potential in the electric field of uniformly-charged spherical surfaces is distributed as:
$$
V= \begin{cases}\frac{q}{4 \pi \varepsilon_0 R} & (r \leqslant R) \\ \frac{q}{4 \pi \varepsilon_0 r} & (r>R)\end{cases}
$$

Options:
A. $$870V,490V$$
B. $$900V,450V$$
C. $$950V,470V$$
D. $$880V,460V$$
E. $$1000V,600V$$
F. $$800V,500V$$
G. $$890V,440V$$
H. $$920V,430V$$
I. $$910V,480V$$
J. $$930V,420V$$
Answer: B
An ophthalmologist prescribed +2.0D glasses for person A and -4.0D glasses for person B. What are the distances of the far point for the nearsighted eye and the near point for the farsighted eye?

Options:
A. 1.0m,0.5m
B. 0.5m,0.25m
C. 0.4m,0.25m
D. 2.0m,0.5m
E. 2.0m,0.25m
F. 0.5m,0.2m
G. 0.25m,0.4m
H. 0.25m,2.0m
I. 0.4m,0.5m
J. 0.5m,1.0m
Answer: B
The measured velocity of an electron is $200 \mathrm{m/s}$, with an accuracy of 0.1%. What is the uncertainty in determining the position of this electron?

Options:
A. $$
1. 5 9 8 \times1 0^{-3} \mathrm{m}
$$
B. $$
2. 9 5 5 \times1 0^{-3} \mathrm{m}
$$
C. $$
4. 8 7 3 \times1 0^{-3} \mathrm{m}
$$
D. $$
8. 9 8 5 \times1 0^{-3} \mathrm{m}
$$
E. $$
6. 4 4 9 \times1 0^{-3} \mathrm{m}
$$
F. $$
5. 7 2 1 \times1 0^{-3} \mathrm{m}
$$
G. $$
9. 5 6 7 \times1 0^{-3} \mathrm{m}
$$
H. $$
3. 6 3 7 \times1 0^{-3} \mathrm{m}
$$
I. $$
7. 2 3 1 \times1 0^{-3} \mathrm{m}
$$
J. $$
1. 8 2 4 \times1 0^{-3} \mathrm{m}
$$
Answer: H
According to Bohr's theory, the diameter of the electron orbit in the ground state of a hydrogen atom is approximately $1 \times 10^{-10} \mathrm{m}$, and the electron velocity is about $2.18 \times 10^{6} \mathrm{m/s}$. Assuming the uncertainty in the electron's position within the hydrogen atom is $1 \times 10^{-10} \mathrm{m}$, calculate the uncertainty in the electron's velocity.

Options:
A. $$
3. 2 \times1 0^{6} {\mathrm{m / s}}
$$
B. $$
6. 3 \times1 0^{6} {\mathrm{m / s}}
$$
C. $$
2. 9 \times1 0^{6} {\mathrm{m / s}}
$$
D. $$
9. 4 \times1 0^{6} {\mathrm{m / s}}
$$
E. $$
8. 1 \times1 0^{6} {\mathrm{m / s}}
$$
F. $$
5. 7 \times1 0^{6} {\mathrm{m / s}}
$$
G. $$
1. 8 \times1 0^{6} {\mathrm{m / s}}
$$
H. $$
3. 5 \times1 0^{6} {\mathrm{m / s}}
$$
I. $$
4. 0 \times1 0^{6} {\mathrm{m / s}}
$$
J. $$
7. 2 \times1 0^{6} {\mathrm{m / s}}
$$
Answer: J
The atomic mass of $_{9 2}^{2 3 8} \mathrm{U}$ is $238.0486 \mathrm{u}$. Calculate its mass defect, binding energy, and average binding energy.

Options:
A. $$
- 1. 9 1 0 6 \mathrm{u}
$$
$$
1 8 5 3. 3 2 1 0 \mathrm{M e V}
$$
$$
7. 0 9 7 \mathrm{M e V}
$$
B. $$
- 1. 8 2 5 5 \mathrm{u}
$$
$$
1 7 9 2. 9 7 4 7 \mathrm{M e V}
$$
$$
7. 5 1 2 \mathrm{M e V}
$$
C. $$
- 1. 9 8 5 0 \mathrm{u}
$$
$$
1 7 0 4. 4 8 6 3 \mathrm{M e V}
$$
$$
8. 2 4 1 \mathrm{M e V}
$$
D. $$
- 2. 0 1 4 7 \mathrm{u}
$$
$$
1 6 8 0. 3 9 2 5 \mathrm{M e V}
$$
$$
7. 8 6 5 \mathrm{M e V}
$$
E. $$
- 1. 6 9 4 1 \mathrm{u}
$$
$$
1 8 2 6. 1 3 7 2 \mathrm{M e V}
$$
$$
6. 9 8 3 \mathrm{M e V}
$$
F. $$
- 1. 7 5 2 9 \mathrm{u}
$$
$$
1 8 0 2. 6 1 4 5 \mathrm{M e V}
$$
$$
7. 1 2 4 \mathrm{M e V}
$$
G. $$
- 1. 9 2 3 1 \mathrm{u}
$$
$$
1 6 9 5. 2 7 3 8 \mathrm{M e V}
$$
$$
7. 6 8 1 \mathrm{M e V}
$$
H. $$
- 1. 8 8 4 6 \mathrm{u}
$$
$$
1 7 5 5. 5 0 4 9 \mathrm{M e V}
$$
$$
7. 3 7 6 \mathrm{M e V}
$$
I. $$
- 2. 0 0 3 8 \mathrm{u}
$$
$$
1 6 4 3. 5 8 9 3 \mathrm{M e V}
$$
$$
8. 0 0 9 \mathrm{M e V}
$$
J. $$
- 1. 7 3 8 2 \mathrm{u}
$$
$$
1 7 2 2. 5 9 8 4 \mathrm{M e V}
$$
$$
6. 7 5 3 \mathrm{M e V}
$$
Answer: H
For radiation with a wavelength of $0.154nm$, the linear absorption coefficient for aluminum is $132 \, \mathrm{cm}^{-1}$, and for lead, it is $2610 \, \mathrm{cm}^{-1}$. What should be the thickness of the aluminum plate to achieve the same protective effect as a $1mm$ thick lead layer?

Options:
A. 5.89cm
B. 3.12cm
C. 0.92cm
D. 0.78cm
E. 3.67cm
F. 2.54cm
G. 1.45cm
H. 2.13cm
I. 4.20cm
J. 1.98cm
Answer: J
A horizontal turntable with mass $M$ and radius $R$ can rotate around a vertical axis through its center without friction. A person with mass $m$ stands on the edge of the turntable, with both the person and the turntable originally at rest. When the person walks around the edge of the turntable,The angle of rotation of the person and the turntable relative to the ground is _____.

Options:
A. $$
\frac{5 \pi M R^{2}} {m r^{2}+\frac{1} {5} M R^{2}}
$$
B. $$
\frac{3 \pi M r^{2}} {M r^{2}+\frac{1} {6} m R^{2}}
$$
C. $$
\frac{4 \pi m R^{2}} {M r^{2}+\frac{1} {3} m R^{2}}
$$
D. $$
\frac{\pi m r^{2}} {m R^{2}+\frac{1} {8} M r^{2}}
$$
E. $$
\frac{\pi M r^{2}} {m r^{2}+\frac{1} {7} M R^{2}}
$$
F. $$
\frac{3 \pi m r^{2}} {M R^{2}+\frac{1} {4} m r^{2}}
$$
G. $$
\frac{2 \pi M r^{2}} {m R^{2}+\frac{1} {2} M r^{2}}
$$
H. $$
\frac{4 \pi M R^{2}} {M R^{2}+\frac{1} {4} m r^{2}}
$$
I. $$
\frac{\pi m R^{2}} {m R^{2}+\frac{1} {3} M r^{2}}
$$
J. $$
\frac{2 \pi m r^{2}} {m r^{2}+\frac{1} {2} M R^{2}}
$$
Answer: J
What is the amount of energy released when many small water droplets with a radius of $r = 2.0 \times 10^{-6}$ m merge into a large water droplet with a radius of $R = 2.0 \times 10^{-3}$ m?

Options:
A. $$
2. 9 \times1 0^{-4} \ \mathrm{J}
$$
B. $$
1. 3 \times1 0^{-2} \ \mathrm{J}
$$
C. $$
5. 4 \times1 0^{-3} \ \mathrm{J}
$$
D. $$
7. 5 \times1 0^{-4} \ \mathrm{J}
$$
E. $$
4. 8 \times1 0^{-3} \ \mathrm{J}
$$
F. $$
9. 6 \times1 0^{-5} \ \mathrm{J}
$$
G. $$
8. 2 \times1 0^{-3} \ \mathrm{J}
$$
H. $$
2. 4 \times1 0^{-3} \ \mathrm{J}
$$
I. $$
3. 7 \times1 0^{-3} \ \mathrm{J}
$$
J. $$
6. 1 \times1 0^{-5} \ \mathrm{J}
$$
Answer: I
The motion of the piston in the cylinder is simple harmonic, with the equation of motion given by $x=5.0 \cos \left( 2.0 t+{\frac{\pi}{6}} \right) \text{ cm}$, where the unit of $t$ is seconds. Determine the amplitude, period, frequency, and initial phase.

Options:
A. $$
5. 5 \, \mathrm{c m}
$$
$$
\pi s
$$
$$
\frac{1} {2\pi} \mathrm{~ H z}
$$
$$
\frac{\pi} {2}
$$
B. $$
5. 0 \, \mathrm{c m}
$$
$$
\frac{\pi} {2} s
$$
$$
\frac{2} {\pi} \mathrm{~ H z}
$$
$$
\frac{\pi} {4}
$$
C. $$
5. 0 \, \mathrm{c m}
$$
$$
\pi s
$$
$$
\frac{1} {\pi} \mathrm{~ H z}
$$
$$
\frac{\pi} {6}
$$
D. $$
5. 0 \, \mathrm{c m}
$$
$$
3\pi s
$$
$$
\frac{3} {\pi} \mathrm{~ H z}
$$
$$
\frac{\pi} {2}
$$
E. $$
5. 2 \, \mathrm{c m}
$$
$$
2\pi s
$$
$$
\frac{2} {\pi} \mathrm{~ H z}
$$
$$
\frac{\pi} {3}
$$
F. $$
4. 0 \, \mathrm{c m}
$$
$$
2\pi s
$$
$$
\frac{1} {2\pi} \mathrm{~ H z}
$$
$$
\frac{\pi} {3}
$$
G. $$
4. 5 \, \mathrm{c m}
$$
$$
2\pi s
$$
$$
\frac{1} {2} \mathrm{~ H z}
$$
$$
\frac{\pi} {2}
$$
H. $$
5. 0 \, \mathrm{c m}
$$
$$
\pi s
$$
$$
\frac{2} {\pi} \mathrm{~ H z}
$$
$$
\frac{\pi} {3}
$$
I. $$
6. 0 \, \mathrm{c m}
$$
$$
2\pi s
$$
$$
\frac{1} {\pi} \mathrm{~ H z}
$$
$$
\frac{\pi} {3}
$$
J. $$
6. 0 \, \mathrm{c m}
$$
$$
\pi s
$$
$$
\frac{1} {\pi} \mathrm{~ H z}
$$
$$
\frac{\pi} {4}
$$
Answer: C
A spring oscillator performs simple harmonic motion with an amplitude of $12 \text{ cm}$. At a distance of $6 \text{ cm}$ from the equilibrium position, its velocity is $24 \ \text{cm} \cdot \text{s}^{-1}$. Find the displacement when the velocity is $12 \text{ cm} \cdot \text{s}^{-1}$.

Options:
A. $$
\approx\pm5. 2 \, ( \mathrm{c m} )
$$
B. $$
\approx\pm3. 6 \, ( \mathrm{c m} )
$$
C. $$
\approx\pm1. 5 \, ( \mathrm{c m} )
$$
D. $$
\approx\pm2. 9 \, ( \mathrm{c m} )
$$
E. $$
\approx\pm4. 3 \, ( \mathrm{c m} )
$$
F. $$
\approx\pm6. 8 \, ( \mathrm{c m} )
$$
G. $$
\approx\pm7. 1 \, ( \mathrm{c m} )
$$
H. $$
\approx\pm1 0. 8 \, ( \mathrm{c m} )
$$
I. $$
\approx\pm9. 0 \, ( \mathrm{c m} )
$$
J. $$
\approx\pm8. 5 \, ( \mathrm{c m} )
$$
Answer: H
Two polarizers $P_{1}$ and $P_{2}$ are stacked together. The angle between their polarization directions is denoted as $\alpha$. A mixed light beam, composed of natural light and linearly polarized light with equal intensity, is incident perpendicularly on the polarizers. The angle between the vibration direction of the light vector of the linearly polarized light and the polarization direction of $P_{1}$ is $\theta$. Neglecting reflection and absorption, and given that $\alpha=30^{\circ}$ and $\theta=60^{\circ}$, find the ratio of the transmitted light intensity after passing through $P_{1}$ and $P_{2}$ to the incident light intensity.

Options:
A. $$\frac{1}{16}$$
B. $$\frac{2}{9}$$
C. $$\frac{1}{12}$$
D. $$\frac{3}{20}$$
E. $$\frac{3}{14}$$
F. $$\frac{11}{36}$$
G. $$\frac{9}{32}$$
H. $$\frac{7}{24}$$
I. $$\frac{1}{8}$$
J. $$\frac{5}{18}$$
Answer: G
Given $1.2\, \mathrm{kg}$ of ice at $0^{\circ} \mathrm{C}$ absorbs heat and melts to become water at $10^{\circ} \mathrm{C}$, what is the change in entropy? (It is known that the heat of fusion of ice at $0^{\circ} \mathrm{C}$ is $3.34 \times 10^{5} \, \mathrm{J} \cdot \mathrm{kg}^{-1}$, and the specific heat capacity of water is $4.18 \times 10^{3} \, \mathrm{J} \cdot \mathrm{kg}^{-1} \cdot \mathrm{K}^{-1}$.)

Options:
A. $$
5. 8 6 \times1 0^{3} \ \mathrm{J} \cdot\mathrm{K}^{-1}
$$
B. $$
1. 6 5 \times1 0^{3} \ \mathrm{J} \cdot\mathrm{K}^{-1}
$$
C. $$
9. 4 0 \times1 0^{3} \ \mathrm{J} \cdot\mathrm{K}^{-1}
$$
D. $$
7. 2 4 \times1 0^{3} \ \mathrm{J} \cdot\mathrm{K}^{-1}
$$
E. $$
3. 4 2 \times1 0^{3} \ \mathrm{J} \cdot\mathrm{K}^{-1}
$$
F. $$
2. 7 3 \times1 0^{3} \ \mathrm{J} \cdot\mathrm{K}^{-1}
$$
G. $$
8. 1 8 \times1 0^{3} \ \mathrm{J} \cdot\mathrm{K}^{-1}
$$
H. $$
3. 5 9 \times1 0^{3} \ \mathrm{J} \cdot\mathrm{K}^{-1}
$$
I. $$
4. 6 5 \times1 0^{3} \ \mathrm{J} \cdot\mathrm{K}^{-1}
$$
J. $$
6. 3 7 \times1 0^{3} \ \mathrm{J} \cdot\mathrm{K}^{-1}
$$
Answer: B
Archaeologists discovered ancient biological remains and measured the $β^{-}$ radioactivity of their $^{14}{C}$, obtaining a radioactivity level of $133.3 Bq$ per kilogram of the remains. To determine the era in which the organism lived, the $β^{-}$ radioactivity of $^{14}{C}$ in a currently living organism of the same species was measured, yielding $208.3 Bq$ per kilogram of sample. Calculate how many years ago the ancient organism lived?

Options:
A. 4821
B. 2010
C. 1047
D. 3142
E. 3691
F. 1428
G. 2567
H. 5283
I. 6210
J. 3912
Answer: E
At a certain temperature, styrene undergoes anionic polymerization in tetrahydrofuran initiated by n-butyllithium, with an n-butyllithium concentration of $1 \times 10^{-3} \mathrm{mol/L}$ and a styrene concentration of 1.0 mol/L. It is assumed that n-butyllithium dissociates completely and instantaneously, and the reaction system is free of impurities, with $R_{i} {\approx} R_{p}$. Write the functional relationship between $\overline{{{{X_{n}}}}}$ and reaction time. And calculate the $\overline{{{{X_{n}}}}}$ value of the product when the conversion rate reaches 50%.

Options:
A. $$
\overline{{{{X_{n}}}}} \!=\! [ \mathrm{M} ]_{0} \, ( 1 \!-\! \mathrm{e}^{-k_{p} [ \mathrm{C} ] t} ) / [ \mathrm{C} ]
$$
$$
\overline{{{{X_{n}}}}}=1 0 0 0
$$
B. $$
\overline{{{{X_{n}}}}} \!=\! [ \mathrm{M} ]_{0} \, ( 1 \!+\! \mathrm{e}^{-k_{p} [ \mathrm{C} ] t} ) / [ \mathrm{C} ]
$$
$$
\overline{{{{X_{n}}}}}=1 0 0 0
$$
C. $$
\overline{{{{X_{n}}}}} \!=\! [ \mathrm{C} ]_{0} \, ( 1 \!-\! \mathrm{e}^{-k_{p} t} ) / [ \mathrm{M} ]
$$
$$
\overline{{{{X_{n}}}}}=1 0 0 0
$$
D. $$
\overline{{{{X_{n}}}}} \!=\! ( [ \mathrm{M} ]_{0} \, + \mathrm{e}^{k_{p} [ \mathrm{C} ] t} ) / [ \mathrm{C} ]
$$
$$
\overline{{{{X_{n}}}}}=1 0 0 0
$$
E. $$
\overline{{{{X_{n}}}}} \!=\! [ \mathrm{M} ]_{0} \, ( 1 \!-\! \mathrm{e}^{k_{p} t} ) / [ \mathrm{C} ]
$$
$$
\overline{{{{X_{n}}}}}=1 0 0 0
$$
F. $$
\overline{{{{X_{n}}}}} \!=\! [ \mathrm{M} ]_{0} \, ( 1 \!-\! \mathrm{e}^{-k_{p} [ \mathrm{M} ] t} ) / [ \mathrm{C} ]
$$
$$
\overline{{{{X_{n}}}}}=1 0 0 0
$$
G. $$
\overline{{{{X_{n}}}}} \!=\! [ \mathrm{C} ]_{0} \, ( 1 \!-\! \mathrm{e}^{-k_{p} [ \mathrm{M} ] t} ) / [ \mathrm{M} ]
$$
$$
\overline{{{{X_{n}}}}}=1 0 0 0
$$
H. $$
\overline{{{{X_{n}}}}} \!=\! [ \mathrm{M} ]_{0} \, ( \mathrm{e}^{-k_{p} [ \mathrm{C} ] t} ) / [ \mathrm{C} ]
$$
$$
\overline{{{{X_{n}}}}}=1 0 0 0
$$
I. $$
\overline{{{{X_{n}}}}} \!=\! [ \mathrm{C} ]_{0} \, ( 1 \!-\! \mathrm{e}^{-2k_{p} [ \mathrm{C} ] t} ) / [ \mathrm{M} ]
$$
$$
\overline{{{{X_{n}}}}}=1 0 0 0
$$
J. $$
\overline{{{{X_{n}}}}} \!=\! [ \mathrm{M} ]_{0} \, ( 1 \!-\! \mathrm{e}^{-k_{p} [ \mathrm{C} ] t} ) / [ \mathrm{M} ]
$$
$$
\overline{{{{X_{n}}}}}=1 0 0 0
$$
Answer: A
What parameters can characterize the chain flexibility of polymers? For a certain poly-α-olefin with an average degree of polymerization of 500, the root mean square end distance in an unperturbed state is 25 nm. Given that the C-C bond length is 0.154 nm and the bond angle is 109.5°, calculate the rigidity factor characterizing the flexibility of the macromolecular chain.

Options:
A. 7.1
B. 7.9
C. 6.7
D. 4.8
E. 2.9
F. 3.6
G. 8.3
H. 9.5
I. 5.2
J. 1.8
Answer: F
A polymer degrades during processing, and its weight average molecular weight decreases from $1.0 \times 10^{6}$ to $8.0 \times 10^{5}$. What is the ratio of the melt viscosities of the polymer before and after processing?

Options:
A. 2.20
B. 2.50
C. 2.05
D. 1.85
E. 1.95
F. 1.75
G. 2.14
H. 2.00
I. 2.30
J. 1.65
Answer: G
Determine the molecular weight of the polystyrene sample using the dilute solution viscosity method, with a temperature of 30°C and benzene as the solvent. The solution concentration is $2.75 \times 10^{-5} \, \mathrm{g/mL}$. The efflux time for the pure solvent $t$ is 106s, and the efflux time for the solution $t$ is 166s. Under these conditions, the value of $K$ is $0.99 \times 10^{-2}$, and $\alpha$ is 0.74. The sum of the Huggins equation constant $K'$ and the Kraemer equation constant $\beta$ is 1/2. Calculate the viscosity-average molecular weight of this sample.

Options:
A. $$
7. 5 \times1 0^{6}
$$
B. $$
7. 1 \times1 0^{6}
$$
C. $$
1. 2 \times1 0^{7}
$$
D. $$
8. 0 \times1 0^{6}
$$
E. $$
9. 0 \times1 0^{6}
$$
F. $$
9. 3 \times1 0^{6}
$$
G. $$
5. 8 \times1 0^{6}
$$
H. $$
7. 9 \times1 0^{6}
$$
I. $$
8. 7 \times1 0^{6}
$$
J. $$
6. 4 \times1 0^{6}
$$
Answer: I
In a solution polymerization system, the concentration of a certain monomer $c(\mathbf{M}) = 0.2 \, \text{mol/L}$, and the concentration of a certain peroxide initiator $c(1) = 4.0 \times 10^{-3} \, \text{mol/L}$. Free radical polymerization is conducted at 60°C. It is known that $k_{\mathrm{p}} = 1.45 \times 10^{2} \, \text{L/(mol} \cdot \text{s)}$, $k_{\mathrm{t}} = 7.0 \times 10^{7} \, \text{L/(mol} \cdot \text{s)}$, $f = 1$, and the half-life of the initiator $t_{1/2} = 44 \, \text{h}$. The initial polymerization rate $R_{\mathrm{p}}$ is ().

Options:
A. $1. 23\times 10^{- 8}[$mol/ ( L$\cdot s) ]$
B. $9. 11\times 10^{- 9}[$mol/ ( L$\cdot s) ]$
C. $3. 30\times 10^{- 7}[$mol/ ( L$\cdot s) ]$
D. $2. 58\times 10^{- 6}[$mol/ ( L$\cdot s) ]$
E. $2. 95\times 10^{- 7}[$mol/ ( L$\cdot s) ]$
F. $4. 59\times 10^{- 7}[$mol/ ( L$\cdot s) ]$
G. $5. 81\times 10^{- 7}[$mol/ ( L$\cdot s) ]$
H. $6. 44\times 10^{- 7}[$mol/ ( L$\cdot s) ]$
I. $3. 72\times 10^{- 6}[$mol/ ( L$\cdot s) ]$
J. $7. 76\times 10^{- 8}[$mol/ ( L$\cdot s) ]$
Answer: F
The kinetic equation for the polymerization of a certain monomer initiated by dibenzoyl peroxide is $R_{\mathrm{p}} \!=\! k_{\mathrm{p}} \big[ \mathrm{M} \big] ( f k_{\mathrm{d}} / k_{\mathrm{t}} )^{1 / 2} \big[ \mathrm{I} \big]^{1 / 2}$, assuming that the rate constant of the elementary reaction and $f$ are independent of the conversion rate, and $\left[ \mathrm{M} \right]_{0} \!=\! 2 \, \mathrm{mol} \cdot\mathrm{L}^{-1}, \left[ \mathrm{I} \right] \!=\! 0.01 \, \mathrm{mol} \cdot\mathrm{L}^{-1}$, and the limiting conversion rate is 10%. If the polymerization time is kept constant, by how many times should [M] be increased or decreased to increase the final conversion from 10% to 20%?

Options:
A. When the polymerization time is fixed, $C$ is independent of the initial monomer concentration. Therefore, when the polymerization time is constant, changing [M] does not alter the conversion rate.
B. The polymerization process depends solely on the initiator's concentration, thus [M] must remain unchanged for the desired conversion.
C. By increasing the initiator concentration, the conversion rate will directly double, irrespective of changes in monomer concentration.
D. As the initiator concentration is recalibrated, doubling it results in a doubling of the conversion rate, independent of the monomer.
E. The monomer's influence is null as the conversion correlates with an unchanged initiator factor, ensuring stable conversion rates.
F. When the initiator concentration doubles, the conversion rate similarly doubles, with the monomer concentration remaining constant.
G. Changing [M] does not alter conversion as it solely interacts with initiator concentration, leading to the desired conversion increment.
H. Conversion rate relates to the initiator's proportional increase, unaffected by alterations in the monomer's initial concentration.
I. Increasing [M] twofold will triple the conversion percentage, clearly showing direct proportionality between [M] and conversion.
J. Regardless of [M]'s state, conversion aligns with the constant initiator ratio, maintaining consistent conversion through time.
Answer: A
A polymer solution is composed of a solute with a relative molecular mass of $M_{2}=10^{6}$ (degree of polymerization $x=10^{4}$) and a solvent with a relative molecular mass of $M_{1}=10^{2}$, forming a solution with a concentration of 1% (mass fraction). Calculate the mixing entropy $\Delta S_{\mathrm{m}}$ of this polymer solution (macromolecule).

Options:
A. $$
9. 3 4 \times1 0^{-2} ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
B. $$
7. 1 5 \times1 0^{-2} ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
C. $$
3. 9 2 \times1 0^{-2} ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
D. $$
5. 0 4 \times1 0^{-2} ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
E. $$
7. 3 1 \times1 0^{-2} ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
F. $$
2. 5 6 \times1 0^{-2} ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
G. $$
6. 8 9 \times1 0^{-2} ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
H. $$
8. 2 7 \times1 0^{-2} ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
I. $$
1. 2 3 \times1 0^{-2} ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
J. $$
4. 7 8 \times1 0^{-2} ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
Answer: H
Under the $\theta$ solvent condition of PS-cyclohexane at 308 K, with a solution concentration $c \!=\! 7.36 \times 10^{-3} \mathrm{~kg ~\cdot~ dm^{-3} ~}$, its osmotic pressure is measured to be 24.3 Pa. Use the Flory-Huggins solution theory to find the PS's $\ \delta_{2}$ of this solution.

Options:
A. $13.6(\mathrm{J}^{1/2}\cdot\mathrm{cm}^{-3/2})$
B. $14.8(\mathrm{J}^{1/2}\cdot\mathrm{cm}^{-3/2})$
C. $14.0(\mathrm{J}^{1/2}\cdot\mathrm{cm}^{-3/2})$
D. $13.7(\mathrm{J}^{1/2}\cdot\mathrm{cm}^{-3/2})$
E. $13.1(\mathrm{J}^{1/2}\cdot\mathrm{cm}^{-3/2})$
F. $12.0(\mathrm{J}^{1/2}\cdot\mathrm{cm}^{-3/2})$
G. $14.5(\mathrm{J}^{1/2}\cdot\mathrm{cm}^{-3/2})$
H. $12.8(\mathrm{J}^{1/2}\cdot\mathrm{cm}^{-3/2})$
I. $15.0(\mathrm{J}^{1/2}\cdot\mathrm{cm}^{-3/2})$
J. $13.3(\mathrm{J}^{1/2}\cdot\mathrm{cm}^{-3/2})$
Answer: J
Assuming the expansion factor $\alpha = 1.73$ for polystyrene (PS) in benzene solution at 30°C, $\left[ \eta \right] = 147 \mathrm{~cm^{3} ~ \cdot~ g^{-1}}$. Given the Mark-Houwink parameters $K = 0.99 \times 10^{-2}, \, a = 0.74$, find the value of $\Big( \frac{\overline{{{{h_{0}^{2}}}}}} {M} \Big)^{1 / 2}$ is(). $( \phi_{0} = 2.84 \times 10^{23} \mathrm{~mol}^{-1} )$.

Options:
A. $$ 4. 0 6 \times1 0^{-10} \mathrm{~ c m \cdot~ m o l}^{1 / 2} \cdot\mathrm{~ g}^{-1 / 2} $$
B. $$ 9. 5 7 \times1 0^{-8} \mathrm{~ c m \cdot~ m o l}^{1 / 2} \cdot\mathrm{~ g}^{-1 / 2} $$
C. $$ 3. 4 7 \times1 0^{-9} \mathrm{~ c m \cdot~ m o l}^{1 / 2} \cdot\mathrm{~ g}^{-1 / 2} $$
D. $$ 2. 6 8 \times1 0^{-7} \mathrm{~ c m \cdot~ m o l}^{1 / 2} \cdot\mathrm{~ g}^{-1 / 2} $$
E. $$ 5. 2 4 \times1 0^{-9} \mathrm{~ c m \cdot~ m o l}^{1 / 2} \cdot\mathrm{~ g}^{-1 / 2} $$
F. $$ 8. 0 1 \times1 0^{-11} \mathrm{~ c m \cdot~ m o l}^{1 / 2} \cdot\mathrm{~ g}^{-1 / 2} $$
G. $$ 5. 7 9 \times1 0^{-10} \mathrm{~ c m \cdot~ m o l}^{1 / 2} \cdot\mathrm{~ g}^{-1 / 2} $$
H. $$ 1. 8 9 \times1 0^{-7} \mathrm{~ c m \cdot~ m o l}^{1 / 2} \cdot\mathrm{~ g}^{-1 / 2} $$
I. $$ 7. 3 1 \times1 0^{-8} \mathrm{~ c m \cdot~ m o l}^{1 / 2} \cdot\mathrm{~ g}^{-1 / 2} $$
J. $$
6. 1 5 \times1 0^{-9} \mathrm{~ c m \cdot~ m o l}^{1 / 2} \cdot\mathrm{~ g}^{-1 / 2}
$$
Answer: J
The known bandgap of intrinsic silicon material is $E_{\mathrm{g}} = 1.2 \mathrm{eV}$. The intrinsic absorption long-wavelength limit of this semiconductor material is ().

Options:
A. 1.30μm
B. 1.20μm
C. 0.65μm
D. 2.00μm
E. 1.10μm
F. 0.95μm
G. 1.75μm
H. 1.50μm
I. 0.80μm
J. 1.03μm
Answer: J
If the two-phase linear CCD device TCD1206UD has 2,160 pixels and the total transfer efficiency of the device is 0.92, what is the minimum transfer efficiency of each transfer unit?

Options:
A. 0.98732
B. 0.99311
C. 0.94536
D. 0.97645
E. 0.93147
F. 0.96875
G. 0.99996
H. 0.98021
I. 0.92459
J. 0.95023
Answer: G
Inject $50 \mu W$ of optical power into a $500 m$ long optical fiber. If the power received at the end is $38 \mu W$, what is the loss per kilometer of the optical fiber in $dB/km$? If the fiber is 5 km long, what is the output optical power?

Options:
A. 2.38dB/km,3.23μW
B. 1.92dB/km,2.93μW
C. 3.20dB/km,2.71μW
D. 1.75dB/km,3.02μW
E. 1.84dB/km,3.23μW
F. 2.85dB/km,4.05μW
G. 3.30dB/km,3.11μW
H. 2.50dB/km,4.22μW
I. 2.38dB/km,5.12μW
J. 3.12dB/km,3.65μW
Answer: A
What are the argument and principal value of the complex numbers $-1-\mathrm{i}$ and $-1+3\mathrm{i}$?

Options:
A. $${\frac{7 \pi} {4}}+2 k \pi\,, k=0 \,, \pm1 \,, \pm2 \,, \cdots.$$;
$${\operatorname{a r c t a n}} \left( -4 \right)+\left( 2 k \right) \pi\,, \quad k = 0 \,, \pm 1 \,, \pm 2 \,, \cdots.$$
B. $$
-\frac{3 \pi} {4}+2 k \pi\,, k=0 \,, \pm1 \,, \pm2 \,, \cdots.
$$;
$$
\operatorname{a r c t a n} \left( \,-3 \, \right)+\left( \, 2 k \!+\! 1 \, \right) \pi\,, \quad k \!=\! 0 \,, \pm\! 1 \,, \pm\! 2 \,, \cdots.
$$
C. $${\pi \over 2}+2 k \pi\,, k=0 \,, \pm1 \,, \pm2 \,, \cdots.$$;
$${\operatorname{a r c t a n}} \left( 2 \right)+\left( 2 k \right) \pi\,, \quad k = 0 \,, \pm 1 \,, \pm 2 \,, \cdots.$$
D. $${\pi \over 4}+2 k \pi\,, k=0 \,, \pm1 \,, \pm2 \,, \cdots.$$;
$${\operatorname{a r c t a n}} \left( -0.5 \right)+\left( 2 k \right) \pi\,, \quad k = 0 \,, \pm 1 \,, \pm 2 \,, \cdots.$$
E. $${\frac{2 \pi} {3}}+2 k \pi\,, k=0 \,, \pm1 \,, \pm2 \,, \cdots.$$;
$${\operatorname{a r c t a n}} \left( 3 \right)+\left( 2 k \right) \pi\,, \quad k \!=\! 0 \,, \pm\! 1 \,, \pm\! 2 \,, \cdots.$$
F. $${\frac{5 \pi} {6}}+2 k \pi\,, k=0 \,, \pm1 \,, \pm2 \,, \cdots.$$;
$${\operatorname{a r c t a n}} \left( -2 \right)+\left( 2 k \right) \pi\,, \quad k = 0 \,, \pm 1 \,, \pm 2 \,, \cdots.$$
G. $${3 \pi \over 4}+2 k \pi\,, k=0 \,, \pm1 \,, \pm2 \,, \cdots.$$;
$${\operatorname{a r c t a n}} \left( \,3 \, \right)+\left( \, 2 k \!-\! 1 \, \right) \pi\,, \quad k \!=\! 0 \,, \pm\! 1 \,, \pm\! 2 \,, \cdots.$$
H. $${\pi \over 3}+2 k \pi\,, k=0 \,, \pm1 \,, \pm2 \,, \cdots.$$;
$${\operatorname{a r c t a n}} \left( 1 \right)+\left( 2 k \right) \pi\,, \quad k \!=\! 0 \,, \pm\! 1 \,, \pm\! 2 \,, \cdots.$$
I. $${\pi}+2 k \pi\,, k=0 \,, \pm1 \,, \pm2 \,, \cdots.$$;
$${\operatorname{a r c t a n}} \left( -1 \right)+\left( 2 k \right) \pi\,, \quad k = 0 \,, \pm 1 \,, \pm 2 \,, \cdots.$$
J. $${\frac{\pi} {6}}+2 k \pi\,, k=0 \,, \pm1 \,, \pm2 \,, \cdots.$$;
$${\operatorname{a r c t a n}} \left( 0 \right)+\left( 2 k \pi \right)\,, \quad k \!=\! 0 \,, \pm\! 1 \,, \pm\! 2 \,, \cdots.$$
Answer: B
The function value of $\cos(\pi + 5i)$ is ( ).

Options:
A. -cosh5
B. -sinh5
C. sin5i
D. -sin5
E. cos5
F. cosh5i
G. sinh5
H. -cos5
I. cosh5
J. -sin5i
Answer: A
Let $C$ be the upper semicircle of the unit circle. What is the value of$\int_{C} \left( z-1 \right) \mathrm{d} z \,$?

Options:
A. 4
B. -2
C. 3
D. -1
E. 1
F. 0
G. 2
H. -i
I. -1/2
J. i
Answer: G
What is the value of the integral $\oint_{C} \frac{\mathrm{d} z} {( z^{2} \!-\! 4 \, ) \left( z \!-\! \frac{\pi} {2} \right)} \,$? $C : x^{2} \!+\! y^{2}=4 x.$

Options:
A. $$
2\pi\mathrm{i} \bigg( \frac{1} {3 - \pi} \bigg) \;
$$
B. $$
\pi\mathrm{i} \bigg( \frac{2} {3}+\frac{1} {5-\pi} \bigg) \;
$$
C. $$
\mathrm{i} \bigg( \frac{\pi} {4-\pi^{2}} \bigg) \;
$$
D. $$
\frac{4 \pi\mathrm{i}} {\pi^{2} - 8} \;
$$
E. $$
\pi\mathrm{i} \bigg( \frac{2} {\pi^{2}}+\frac{3} {4} \bigg) \;
$$
F. $$
\pi\mathrm{i} \bigg( \frac{6} {\pi^{2}-1 6} \bigg) \;
$$
G. $$
\frac{\pi\mathrm{i}} {4-\pi} + \frac{3} {2} \;
$$
H. $$
\pi \bigg( \frac{\mathrm{i}} {4-\pi} \bigg) \;
$$
I. $$
\pi\mathrm{i} \bigg( \frac{8} {\pi^{2}-1 6}+\frac{1} {4-\pi} \bigg) \;
$$
J. $$
\pi\mathrm{i} \bigg( \frac{4} {\pi - 2} \bigg) \;
$$
Answer: I
What is the radius of convergence for $\sum_{n=1}^{\infty} \, ( -\mathrm{i} \, )^{n-1} \frac{2n-1}{2^{n}} z^{2n-1} \,$?

Options:
A. $$
R=\infty \,
$$
B. $$
R=\frac{1}{2} \,
$$
C. $$
R=\frac{\pi}{2} \,
$$
D. $$
R=\frac{\sqrt{2}}{2} \,
$$
E. $$
R=\sqrt{2} \,
$$
F. $$
R=1 \,
$$
G. $$
R=1+\sqrt{2} \,
$$
H. $$
R=\sqrt{3} \,
$$
I. $$
R=2\pi \,
$$
J. $$
R=2 \,
$$
Answer: E
The power series expansion of $f ( \, z \, )={\frac{4 z^{2} \!+\! 3 0 z \!+\! 6 8} {( \, z \!+\! 4 \, )^{2} ( \, z \!-\! 2 \, )}}$ in terms of $z$ is ().

Options:
A. $$
= \ \sum_{n=0}^{n} \ \left[ \ (-1)^{n+1} \frac{n-2} {5^{n+3}}+\frac{3} {5^{n+1}} \right] z^{n} \,, \ | \ z \ | < 2.
$$
B. $$
= \ \sum_{n=0}^{n} \ \left[ \ (-1)^{n+2} \frac{n} {2^{2 n+4}}-\frac{3} {2^{n+1}} \right] z^{n} \,, \ | \ z \ | < 3.
$$
C. $$
= \ \sum_{n=0}^{n} \ \left[ \ (-1)^{n} \frac{n+3} {2^{3 n+3}}-\frac{3} {4^{n}} \right] z^{n} \,, \ | \ z \ | < 5.
$$
D. $$
= \ \sum_{n=0}^{n} \ \left[ \ (-1)^{n} \frac{n} {3^{2 n+3}}-\frac{2} {3^{n-1}} \right] z^{n} \,, \ | \ z \ | < 3.
$$
E. $$
= \ \sum_{n=0}^{n} \ \left[ \ (-1)^{n+2} \frac{n+4} {2^{n+3}}+\frac{1} {2^{n-2}} \right] z^{n} \,, \ | \ z \ | < 2.
$$
F. $$
= \ \sum_{n=0}^{n} \ \left[ \ (-1)^{n-2} \frac{n+1} {2^{n+4}}-\frac{1} {3^{n}} \right] z^{n} \,, \ | \ z \ | < 4.
$$
G. $$
= \ \sum_{n=0}^{n} \ \left[ \ ( \,-1 \, )^{n+1} \frac{n+1} {2^{2 n+3}}-\frac{1} {2^{n-1}} \right] z^{n} \,, \ | \ z \ | < 2.
$$
H. $$
= \ \sum_{n=0}^{n} \ \left[ \ (-1)^{n+1} \frac{n+2} {4^{2 n+3}}+\frac{2} {2^{n+1}} \right] z^{n} \,, \ | \ z \ | < 2.
$$
I. $$
= \ \sum_{n=0}^{n} \ \left[ \ (-1)^{n} \frac{3n} {3^{3 n+4}}+\frac{2} {3^{n}} \right] z^{n} \,, \ | \ z \ | < 1.
$$
J. $$
= \ \sum_{n=0}^{n} \ \left[ \ (-1)^{n} \frac{n-1} {3^{n+3}}+\frac{2} {3^{n-1}} \right] z^{n} \,, \ | \ z \ | < 2.
$$
Answer: G
What are all the singularities of the function $f(z) = z^{4} / (1 + z^{4})$, and what are their types?

Options:
A. $z=2i$ is a removable singularity of $f(z)$.
B. $z=0$ is a removable singularity of $f(z)$.
C. $z=i$ is a simple pole of $f(z)$.
D. $z=-2i$ is a removable singularity of $f(z)$.
E. $z^{2}=i$ is a simple pole of $f(z)$.
F. $z=\infty$ is a removable singularity of $f(z)$.
G. $z=-i$ is an essential singularity of $f(z)$.
H. $z=1$ is an essential singularity of $f(z)$.
I. $z^{4}=1$ is a branch cut of $f(z)$.
J. $z=-1$ is a branch point of $f(z)$.
Answer: F
The residue of the function $f ( \, z \, )=\operatorname{cot}^{2} z$ at its finite singularities is ().

Options:
A. 0
B. $e^{\pi i}$
C. 1
D. $2\pi i$
E. $\frac{3}{2}$
F. $4i$
G. $\pi$
H. $2i$
I. $-\frac{1}{2}$
J. $\ln(2)$
Answer: A
Let the function $f(z)$ be analytic on the complex plane, where $f(z) = \sum_{n=0}^{∞} a_{n} z^{n}$. For any positive integer $k$, what is the residue of the function $\frac{f(z)}{z^{k}}$ at the point $z=0$, denoted as $\mathrm{Res} \left[ \frac{f(z)}{z^{k}}, 0 \right]$?

Options:
A. $$a_{k}
$$
B. $$a_{k+1}
$$
C. $$a_{k-2}
$$
D. $$0
$$
E. $$a_{0}
$$
F. $$a_{1}
$$
G. $$k \cdot a_{k-1}
$$
H. $$a_{k-1}
$$
I. $$a_{2k-1}
$$
J. $$a_{n}
$$
Answer: H
What is the contour integral $\oint_{C} \frac{1+z} {1-\cos z} \mathrm{d} z$ where $C$ is the positively oriented circle $\mid z \mid=7$?

Options:
A. $$
3 2 \pi\mathrm{i}
$$
B. $$
9 8 \pi\mathrm{i}
$$
C. $$
1 6 \pi\mathrm{i}
$$
D. $$
1 4 \pi\mathrm{i}
$$
E. $$
1 2 \pi\mathrm{i}
$$
F. $$
1 3 \pi\mathrm{i}
$$
G. $$
7 2 \pi\mathrm{i}
$$
H. $$
0 \pi\mathrm{i}
$$
I. $$
5 0 \pi\mathrm{i}
$$
J. $$
1 0 \pi\mathrm{i}
$$
Answer: E