MikaStars39/nano-eval huggingface dataset:
An originally uncharged conductor small sphere makes contact with a large conductor sphere that carries a charge amount of $Q$. After each separation, the small sphere gains a charge amount of $q$. Now, the small sphere is repeatedly brought into contact with the large sphere, and after each separation, the large sphere is replenished with charge to restore its original charge amount. What is the maximum amount of charge the small sphere can acquire?

Options:
A. $$
q_{n}=\frac{q^{2} Q} {Q+q}$$
B. $$
q_{n}=\frac{Q^{2} q} {Q-q}$$
C. $$
q_{n}=\frac{q Q} {Q^{2}-q}$$
D. $$
q_{n}=\frac{Q^{2} q} {Q-q^{2}}$$
E. $$
q_{n}=\frac{Q q^{2}} {Q+q^{2}}$$
F. $$
q_{n}=\frac{q^{2} Q} {Q^{2}-q}$$
G. $$
q_{n}=\frac{q Q} {Q-q}
$$
H. $$
q_{n}=\frac{q Q} {Q^{2}+q}$$
I. $$
q_{n}=\frac{Q q} {Q-q^{2}}$$
J. $$
q_{n}=\frac{q Q^{2}} {Q+q}$$
Answer: G
Two small spheres, identical in material and volume, are charged with equal amounts of the same sign and are suspended from the same point by two equally long insulating threads. When they are placed in kerosene, the angle between the two spheres remains the same as when they are in the air. If the relative dielectric constant of kerosene is $\varepsilon_{r}=2$ and its density is $\rho_{r}=0.8 \times 10^{3} \mathrm{~kg/m}^{3}$, what is the density $\rho$ of the small spheres?

Options:
A. $$
1. 4 \times1 0^{3} \ \mathrm{k g / m}^{3}
$$
B. $$
1. 3 \times1 0^{3} \ \mathrm{k g / m}^{3}
$$
C. $$
1. 8 \times1 0^{3} \ \mathrm{k g / m}^{3}
$$
D. $$
2. 5 \times1 0^{3} \ \mathrm{k g / m}^{3}
$$
E. $$
1. 6 \times1 0^{3} \ \mathrm{k g / m}^{3}
$$
F. $$
2. 0 \times1 0^{3} \ \mathrm{k g / m}^{3}
$$
G. $$
1. 5 \times1 0^{3} \ \mathrm{k g / m}^{3}
$$
H. $$
2. 8 \times1 0^{3} \ \mathrm{k g / m}^{3}
$$
I. $$
1. 2 \times1 0^{3} \ \mathrm{k g / m}^{3}
$$
J. $$
1. 0 \times1 0^{3} \ \mathrm{k g / m}^{3}
$$
Answer: E
If the voltage in the circuit is $U_{1}=120 \mathrm{~V}$, then the water in the electric kettle boils after $t_{1}=20$ minutes. If the voltage in the circuit is $U_{2}=110 \mathrm{~V}$, the same amount of water at the same initial temperature boils after $t_{2}=28$ minutes. For simplicity, assume that the heat lost by the kettle to the surrounding space is proportional to the heating time. How long will it take to boil the same amount of water at the same initial temperature if the voltage in the circuit is $U_{3}=100 \mathrm{~V}$?

Options:
A. $$
4 4 \, \operatorname* {m i n}
$$
B. $$
4 6 \, \operatorname* {m i n}
$$
C. $$
3 6 \, \operatorname* {m i n}
$$
D. $$
5 2 \, \operatorname* {m i n}
$$
E. $$
4 2 \, \operatorname* {m i n}
$$
F. $$
6 0 \, \operatorname* {m i n}
$$
G. $$
5 6 \, \operatorname* {m i n}
$$
H. $$
4 8 \, \operatorname* {m i n}
$$
I. $$
3 8 \, \operatorname* {m i n}
$$
J. $$
5 0 \, \operatorname* {m i n}
$$
Answer: A
The electromotive force of the power supply at the input terminal of the transformer is $E$, with an internal resistance of $r$. At the output terminal, a load with resistance $R$ is connected. What is the transformer turns ratio when the load receives maximum power? (Ignore the transformer's losses.)

Options:
A. $$
K={R^{2}}
$$
B. $$
K={\sqrt{\frac{r} {R}}}
$$
C. $$
K={\frac{r}{R} - 1}
$$
D. $$
K={\frac{R}{r} + 1}
$$
E. $$
K={\frac{2r} {R}}
$$
F. $$
K={\frac{R} {r}}
$$
G. $$
K={\frac{r} {R}}
$$
H. $$
K={r \cdot R}
$$
I. $$
K={R \cdot r}
$$
J. $$
K={\sqrt{\frac{R} {r}}}
$$
Answer: B
Experiments have proven that electromagnetic waves possess momentum, with momentum density (momentum per unit volume) given by $G = \varepsilon_{0} \mu_{0} S$, where $S = E \times H$ is the Poynting vector. It is known that when sunlight is directly incident, the energy received per square centimeter per minute on the ground is $1.94\mathrm{~cal}$, where $1\mathrm{~cal}=4.1868\mathrm{~J}$. Assuming all the sunlight striking the ground is completely absorbed, and given that the Earth's radius is $6.4 \times 10^3 \mathrm{~km}$, what is the force exerted by sunlight on the entire Earth?

Options:
A. $$
6. 7 \times1 0^{8} \mathrm{~N}
$$
B. $$
5. 8 \times1 0^{8} \mathrm{~N}
$$
C. $$
4. 1 \times1 0^{8} \mathrm{~N}
$$
D. $$
7. 3 \times1 0^{9} \mathrm{~N}
$$
E. $$
4. 4 \times1 0^{7} \mathrm{~N}
$$
F. $$
2. 9 \times1 0^{7} \mathrm{~N}
$$
G. $$
8. 5 \times1 0^{9} \mathrm{~N}
$$
H. $$
3. 2 \times1 0^{8} \mathrm{~N}
$$
I. $$
9. 6 \times1 0^{8} \mathrm{~N}
$$
J. $$
1. 5 \times1 0^{8} \mathrm{~N}
$$
Answer: B
A coaxial cable is composed of a long straight conductor with a radius of $a$ and a thin cylindrical conductor that is coaxial with it, with the cylinder having a radius of $b$. Between the conductor and the cylinder, there is a uniform medium with a dielectric constant of $\varepsilon_{r}$ and a relative permeability of $\mu_{\mathrm{r}}$. When the cable is in use, the current is uniformly distributed across the cross-sections of both the conductor and the cylinder. The characteristic impedance of the cable is defined as $Z_{0}=\sqrt{L_{1} / C_{1}}$, where $L_{1}$ is the inductance per unit length and $C_{1}$ is the capacitance per unit length. The magnetic flux inside the conductor is neglected. Many practical cables adopt $Z_{0}=50 \Omega$ (sometimes referred to as 50 ohm cables), assuming the medium is polyethylene with $\varepsilon_{\mathrm{r}}=2.3$ and $\mu_{\mathrm{r}}=1$. What is the value of $b/a$?

Options:
A. $4.3$
B. $5.6$
C. $1.7$
D. $3.5$
E. $3.9$
F. $1.3$
G. $4.6$
H. $2.0$
I. $5.1$
J. $2.8$
Answer: D
When the known resistor $R$, inductance $L$, and capacitance $C$ are connected in series to a constant voltage source, the frequency $\nu$ of this source can be changed. What is the frequency $\nu_{C}$ (expressed in terms of $R, L, C$, etc.) when the voltage across $C$ reaches its maximum?

Options:
A. $$
\frac{1} {2 \pi} \sqrt{\frac{L} {R C}-\frac{R^{2}} {2 L^{2}}}
$$
B. $$
\frac{1} {2 \pi} \sqrt{\frac{1} {L R}-\frac{C^{2}} {2 L^{2}}}
$$
C. $$
\frac{1} {2 \pi} \sqrt{\frac{R} {C L}-\frac{R^{2}} {2 L^{2}}}
$$
D. $$
\frac{1} {2 \pi} \sqrt{\frac{1} {L C}-\frac{R^{2}} {2 L^{2}}}
$$
E. $$
\frac{1} {2 \pi} \sqrt{\frac{1} {C L}-\frac{L^{2}} {2 R^{2}}}
$$
F. $$
\frac{R} {2 \pi} \sqrt{\frac{1} {L C}+\frac{R^{2}} {2 L^{2}}}
$$
G. $$
\frac{1} {2 \pi} \sqrt{\frac{R} {L C}+\frac{R^{2}} {2 L^{2}}}
$$
H. $$
\frac{1} {2 \pi} \sqrt{\frac{1} {2 L C}+\frac{R^{2}} {L^{2}}}
$$
I. $$
\frac{1} {2 \pi} \sqrt{\frac{1} {R C}-\frac{L^{2}} {R^{2}}}
$$
J. $$
\frac{1} {2 \pi} \sqrt{\frac{2} {L C}-\frac{R^{2}} {L^{2}}}
$$
Answer: D
Two coaxial circular coils, each with a radius of $R$, carry identical currents $I$ in both magnitude and direction. The distance between them is equal to the radius $R$ (Helmholtz coils). What is the magnetic energy density at a point on the axis equidistant from both coils?

Options:
A. $$
\frac{1 1} {2 1 1} \, \frac{\mu_{0} \, I^{2}} {R^{4}} $$
B. $$
\frac{3 2} {1 2 5} \, \frac{\mu_{0} \, I^{2}} {R^{2}}
$$
C. $$
\frac{5 4} {2 3 4} \, \frac{{\mu_{0} \, I^{2}}} {R^{3}} $$
D. $$
\frac{2 4} {3 4 6} \, \frac{\mu_{0}^{3} \, I^{2}} {R} $$
E. $$
\frac{3 3} {8 1 1} \, \frac{{\mu_{0} \, I^{2}}} {R^{5}} $$
F. $$
\frac{8 6} {4 6 3} \, \frac{\mu_{0} \, I^{2}} {R^{2}} $$
G. $$
\frac{6 5} {3 1 5} \, \frac{\mu_{0} \, I^{3}} {R^{2}} $$
H. $$
\frac{7 3} {2 9 1} \, \frac{\mu_{0} \, I} {R^{3}} $$
I. $$
\frac{4 1} {1 1 9} \, \frac{{\mu_{0}^{2} \, I^{2}}} {R} $$
J. $$
\frac{2 7} {7 8 9} \, \frac{\mu_{0}^{2} \, I^{3}} {R^{2}} $$
Answer: B
The length of a solenoid is $l = 300 \text{ mm}$, with a cross-sectional diameter of $d = 15 \text{ mm}$, and it is closely wound with a fine, surface-insulated wire for a total of $N = 2500$ turns. When a current of $I = 2.0 \text{ A}$ flows through the wire, what is the value of the magnetic field energy density $\varpi_{m}$ at the center of the solenoid?

Options:
A. $$
7.6 \times 1 0^{3}~\mathrm{J / m^{3}}
$$
B. $$
5.3 \times 1 0^{1}~\mathrm{J / m^{3}}
$$
C. $$
1. 7 \times1 0^{2}~\mathrm{J / m^{3}}
$$
D. $$
4.7 \times 1 0^{5}~\mathrm{J / m^{3}}
$$
E. $$
5.9 \times 1 0^{4}~\mathrm{J / m^{3}}
$$
F. $$
9.8 \times 1 0^{4}~\mathrm{J / m^{3}}
$$
G. $$
8.1 \times 1 0^{0}~\mathrm{J / m^{3}}
$$
H. $$
6.2 \times 1 0^{1}~\mathrm{J / m^{3}}
$$
I. $$
3.4 \times 1 0^{2}~\mathrm{J / m^{3}}
$$
J. $$
2.5 \times 1 0^{3}~\mathrm{J / m^{3}}
$$
Answer: C
A cylindrical tube with a length of 30 cm and a diameter of 3.0 cm has 500 turns of coil wound around it. If an iron core with a relative permeability $\mu_{r}=5000$ is placed inside this coil, what is the inductance $L$ at this time?

Options:
A. $$
3. 7~\mathrm{H}
$$
B. $$
3. 9~\mathrm{H}
$$
C. $$
4. 0~\mathrm{H}
$$
D. $$
3. 5~\mathrm{H}
$$
E. $$
2. 8~\mathrm{H}
$$
F. $$
2. 7~\mathrm{H}
$$
G. $$
4. 1~\mathrm{H}
$$
H. $$
3. 6~\mathrm{H}
$$
I. $$
4. 2~\mathrm{H}
$$
J. $$
2. 9~\mathrm{H}
$$
Answer: A
A ferromagnetic core coil is formed by tightly winding insulated wire around an iron ring, with the central length of the ring being 600 mm and a cross-sectional area of $1000 \, \text{mm}^2$. To produce a magnetic flux density of $B = 1.0 \, \text{T}$ inside the ring, the $BH$ curve for iron indicates that the relative permeability, $\mu_{\text{r}}$, at this point is 795. Calculate the required ampere-turns. If there is a 2.0 mm wide air gap in the iron ring, what is the required ampere-turns?

Options:
A. $$
2. 2 \times1 0^{3}~\mathrm{A·t}
$$
B. $$
1. 5 \times1 0^{3}~\mathrm{A·t}
$$
C. $$
3. 5 \times1 0^{3}~\mathrm{A·t}
$$
D. $$
3. 0 \times1 0^{3}~\mathrm{A·t}
$$
E. $$
4. 0 \times1 0^{3}~\mathrm{A·t}
$$
F. $$
1. 2 \times1 0^{3}~\mathrm{A·t}
$$
G. $$
1. 8 \times1 0^{3}~\mathrm{A·t}
$$
H. $$
2. 8 \times1 0^{3}~\mathrm{A·t}
$$
I. $$
5. 0 \times1 0^{3}~\mathrm{A·t}
$$
J. $$
2. 0 \times1 0^{3}~\mathrm{A·t}
$$
Answer: A
The mass of a deuteron is twice that of a proton, and its charge is the same as that of a proton; the mass of an α particle is four times that of a proton, and its charge is twice that of a proton. When they are accelerated and enter the same uniform magnetic field, they both move in circular paths. It is measured that the radius of the proton's circular path is 10 cm. What are the radii of the paths for the deuteron and the α particle?

Options:
A. $$
1 0 \, \mathrm{c m},~2 0 \, \mathrm{c m}
$$
B. $$
1 5 \, \mathrm{c m},~2 0 \, \mathrm{c m}
$$
C. $$
1 2 \, \mathrm{c m},~1 2 \, \mathrm{c m}
$$
D. $$
1 8 \, \mathrm{c m},~1 8 \, \mathrm{c m}
$$
E. $$
1 5 \, \mathrm{c m},~1 5 \, \mathrm{c m}
$$
F. $$
2 0 \, \mathrm{c m},~2 0 \, \mathrm{c m}
$$
G. $$
2 2 \, \mathrm{c m},~1 0 \, \mathrm{c m}
$$
H. $$
1 4 \, \mathrm{c m},~1 4 \, \mathrm{c m}
$$
I. $$
1 6 \, \mathrm{c m},~1 6 \, \mathrm{c m}
$$
J. $$
1 0 \, \mathrm{c m},~1 5 \, \mathrm{c m}
$$
Answer: H
A parallel plate capacitor has two plates, each with an area of $2.0 \, \mathrm{m}^2$, and they are separated by $5.0 \, \mathrm{mm}$. When the space between the plates is air, a voltage of 10,000 volts is applied, and the power source is then disconnected. Two parallel dielectric layers are inserted between the plates: one layer has a dielectric constant of 5.0 and a thickness of $2.0 \, \mathrm{mm}$; the other layer has a dielectric constant of 2.0 and a thickness of $3.0 \, \mathrm{mm}$. Neglecting edge effects, what is the capacitance $C$ of the plates?

Options:
A. $$
8. 0~\mathrm{n F}
$$
B. $$
9. 4~\mathrm{n F}
$$
C. $$
8. 7~\mathrm{n F}
$$
D. $$
5. 5~\mathrm{n F}
$$
E. $$
7. 0~\mathrm{n F}
$$
F. $$
6. 8~\mathrm{n F}
$$
G. $$
2. 3~\mathrm{n F}
$$
H. $$
6. 2~\mathrm{n F}
$$
I. $$
3. 9~\mathrm{n F}
$$
J. $$
4. 2~\mathrm{n F}
$$
Answer: B
In a single-effect evaporator, a certain aqueous solution is concentrated from a concentration of 0.10 to 0.35 (both mass fractions, the same applies hereafter), with a throughput of 3000 kg of raw material per hour. If the actual amount of water evaporated is 1500 kg/h, what is the concentration of the finished liquid?

Options:
A. 0.6
B. 0.1
C. 0.4
D. 0.05
E. 0.3
F. 0.5
G. 0.45
H. 0.15
I. 0.2
J. 0.25
Answer: I
Stir a solution using a disc-type turbine agitator with a standard baffle-less configuration. Given: a tank diameter of 1.8 m, an impeller diameter of 0.6 m, a rotational speed of 90 r/min; liquid viscosity of 12 cP, density of 1500 kg/m³. What is the power required for the agitator?

Options:
A. 430W
B. 490W
C. 571W
D. 655W
E. 760W
F. 800W
G. 845W
H. 350W
I. 515W
J. 620W
Answer: C
Inject alkali solution with a density of $1200 \text{ kg/m}^3$ from an atmospheric alkali pool to the top of the alkali washing tower using a centrifugal pump. Given: the pressure gauge at the top of the tower reads 59.3 kPa, the flow rate is $30 \text{ m}^3/\text{h}$, the resistance in the suction pipeline is equivalent to a 2-meter column of alkali solution, the resistance in the discharge pipeline is equivalent to a 5-meter column of alkali solution, and the vertical distance from the surface of the alkali pool to the alkali inlet of the washing tower is 12 meters. If the pump's shaft power is 3.6 kW, what is the mechanical efficiency of the pump?

Options:
A. 70.47%
B. 68.90%
C. 60.72%
D. 57.29%
E. 63.58%
F. 62.13%
G. 74.91%
H. 65.44%
I. 66.35%
J. 73.85%
Answer: H
Water at 283K flows through a steel pipe with an inner diameter of 25mm at a speed of 1m/s. Try calculating its $R e$ value is ().

Options:
A. 21047
B. 18326
C. 16789
D. 15268
E. 19151
F. 19487
G. 22691
H. 20534
I. 17459
J. 14263
Answer: E
Assuming that 5 kg of air with an initial pressure of 95 kPa and a temperature of 20°C is compressed isentropically at constant pressure to 40% of its original volume, calculate the change in entropy of the gas after compression.

Options:
A. $$
1 8 5 2 0 0 0 \mathrm{J}
$$
B. $$
1 7 5 0 0 0 0 \mathrm{J}
$$
C. $$
1 8 0 0 0 0 0 \mathrm{J}
$$
D. $$
2 0 0 0 0 0 0 \mathrm{J}
$$
E. $$
1 9 0 0 0 0 0 \mathrm{J}
$$
F. $$
2 0 5 0 0 0 0 \mathrm{J}
$$
G. $$
1 9 7 0 0 0 0 \mathrm{J}
$$
H. $$
1 9 3 0 0 0 0 \mathrm{J}
$$
I. $$
1 9 5 2 0 0 0 \mathrm{J}
$$
J. $$
2 1 0 0 0 0 0 \mathrm{J}
$$
Answer: I
A boiler feed pump rod has a diameter of $\phi = (30 \pm 0.5) \ \ \mathrm{mm}$, with the material's yield strength ranging from $275 \! \sim\! 305 \mathrm{MPa}$. Determine the tensile force that the rod can withstand when it reaches its yield strength.

Options:
A. $$
( 1 8 9 \pm1 1. 9 ) \ \ \mathrm{k N}
$$
B. $$
( 2 2 0 \pm1 5. 2 ) \ \ \mathrm{k N}
$$
C. $$
( 2 1 0 \pm1 4. 1 ) \ \ \mathrm{k N}
$$
D. $$
( 1 9 0 \pm1 0. 8 ) \ \ \mathrm{k N}
$$
E. $$
( 1 9 5 \pm1 3. 4 ) \ \ \mathrm{k N}
$$
F. $$
( 2 3 0 \pm1 3. 3 ) \ \ \mathrm{k N}
$$
G. $$
( 2 1 5 \pm1 6. 5 ) \ \ \mathrm{k N}
$$
H. $$
( 2 0 5 \pm1 2. 6 ) \ \ \mathrm{k N}
$$
I. $$
( 2 0 0 \pm1 5. 0 ) \ \ \mathrm{k N}
$$
J. $$
( 1 8 5 \pm1 4. 7 ) \ \ \mathrm{k N}
$$
Answer: H
A newly established GC method was used to determine the borneol content in the same batch of Compound Danshen Tablets. A standard sample (with a known borneol content of 4.22 mg/tablet) was used to verify this new method. The data obtained from five measurements were: 4.52, 4.29, 4.50, 4.26, and 4.13 mg/tablet. Try to evaluate this new method.

Options:
A. The explanation states that the new method produces readings twice as high as the known standard, indicating inaccuracy.
B. The explanation reveals a consistent deviation in measurements, implying potential systematic errors need addressing.
C. The explanation finds the results of the new method fall below the expected range, questioning its validity.
D. The explanation infers a notable bias in results compared to the standard, indicating a need for further optimization.
E. The explanation concludes that results indicate a higher standard deviation, suggesting modifications to the method are required.
F. The explanation suggests deviations that might undermine the reliability of measuring borneol content accurately.
G. The explanation shows a significant variance in the results making this method less reliable for determining borneol content.
H. The explanation reveals the new method yields significantly lower values, not aligning with the standard content.
I. The explanation points to discrepancies suggesting this method is unsuitable for precise measurement.
J. The explanation indicates that the results of the new method for determination show no significant difference from the known content of the standard sample, suggesting that this method can be used to measure the content of borneol in Compound Danshen Tablets.
Answer: J
The premise for inferring that the analysis results are reliable from good precision is( ).

Options:
A. High variability indicates precision.
B. Precision negates the need for calibration.
C. Standard deviation increases reliability.
D. Systematic errors are small.
E. Observational data are never biased.
F. Random errors are always reduced.
G. Precision and accuracy are identical concepts.
H. Repeatability confirms absolute accuracy.
I. Instrument precision remains consistent.
J. All measurements align exactly.
Answer: D
Determine the relationship between the following two titration jumps ( ).
① Using 0.02 mol/L KMnO₄ solution to titrate 0.1 mol/L $\mathrm{Fe}^{2+}$ solution ② Using 0.002 mol/L KMnO₄ solution to titrate 0.01 mol/L $\mathrm{Fe}^{2+}$ solution.

Options:
A. The concentration is different and cannot be judged
B. The titration reactions are the same and cannot be compared.
C. ①≠②
D. ①=②
E. ①≥②
F. ①$>$②
G. Missing potential value, unable to compare
H. Reaction temperature is missing and cannot be compared
I. ①≤②
J. ①$<$②
Answer: D
Take a 2.00 ml sample solution of chloroethanol ($\mathrm{C_{2}H_{4}ClOH}$) and $\mathrm{HCl}$ in an Erlenmeyer flask, add $\mathrm{NaOH}$ and heat to convert organic chlorine into inorganic $\mathrm{Cl^{-}}$. In this acidic solution, add 30.05 ml of 0.1038 mol/L $\mathrm{AgNO_{3}}$ standard solution. An excess of $\mathrm{AgNO_{3}}$ consumes 9.30 ml of 0.1055 mol/L $\mathrm{NH_{4}SCN}$ solution. Take another 2.00 ml sample solution to determine the inorganic chlorine ($\mathrm{HCl}$), and add 30.00 ml of the aforementioned $\mathrm{AgNO_{3}}$ solution; in the back-titration, 19.20 ml of the above $\mathrm{NH_{4}SCN}$ solution is required. Calculate the content of chloroethanol $(\mathrm{C_{2}H_{4}ClOH})$ (relative density of the sample solution = 1.033).

Options:
A. $$
8 2. 4 \%
$$
B. $$
6 5. 4 \%
$$
C. $$
7 5. 8 \%
$$
D. $$
6 7. 5 \%
$$
E. $$
7 0. 1 \%
$$
F. $$
8 0. 7 \%
$$
G. $$
6 8. 9 \%
$$
H. $$
7 9. 3 \%
$$
I. $$
7 6. 2 \%
$$
J. $$
7 1. 0 \%
$$
Answer: E
Palladium (Pd) reacts with thio-Michler's ketone to form a colored coordination compound in a 1:4 ratio. Using a 1.00 cm absorption cell at 520 nm, the absorbance value for a Pd solution with a concentration of $0.200 \times 10^{-6}$ g/ml is 0.390. What is the $E_{\mathrm{1cm}}^{1 \%}$ of the palladium-thioamichone complex?

Options:
A. $$
7. 5 4 \times1 0^{4}
$$
B. $$
1. 9 5 \times1 0^{4}
$$
C. $$
5. 3 3 \times1 0^{4}
$$
D. $$
8. 8 1 \times1 0^{4}
$$
E. $$
2. 1 8 \times1 0^{4}
$$
F. $$
10. 0 3 \times1 0^{4}
$$
G. $$
3. 7 6 \times1 0^{4}
$$
H. $$
4. 4 2 \times1 0^{4}
$$
I. $$
9. 6 7 \times1 0^{4}
$$
J. $$
6. 2 9 \times1 0^{4}
$$
Answer: B
It is known from measurements with a 60 MHz instrument: $\delta_{\mathrm{a}}=6.72 \,, \delta_{\mathrm{b}}=7.26 \,, J_{\mathrm{ab}}=8.5 \mathrm{Hz}$. What kind of spin system do the two protons belong to?

Options:
A. AX system
B. MQ system
C. BC system
D. ABX system
E. XY system
F. AXZ system
G. AB system
H. AM system
I. AA system
J. AA' system
Answer: G
The retention time of compound A on a certain chromatographic column is 350s, with a half-width of 7.5s. What is the theoretical plate number of this column?

Options:
A. 13000
B. 13500
C. 14500
D. 15000
E. 12064
F. 11000
G. 12500
H. 14000
I. 11500
J. 15500
Answer: E
Using the reversed-phase chromatography method to quantitatively determine a certain drug and its metabolites, the retention times measured with a column length of 15 cm are 4.50 minutes and 5.50 minutes, respectively, with half peak widths of 0.52 minutes and 0.58 minutes, respectively. What is the resolution between the drug and its metabolites?

Options:
A. 0.87
B. 1.37
C. 1.07
D. 1.57
E. 0.67
F. 1.17
G. 0.97
H. 1.47
I. 0.77
J. 1.27
Answer: C
$\mathrm{O i l} \,, \rho=8 5 0 \, \mathrm{k g} / \mathrm{m}^{3} \,, \nu=0. 1 8 \times1 0^{-4} \, \mathrm{m}^{2} / \mathrm{s}$ , moving in a pipe of which diameter $d=0 .1 \mathrm{m}$, at a velocity $v \!=\! 0. 0 6 3 5 \mathrm{m / s}$ and make laminar flow. What is the maximum flow rate at the center of the pipe, the velocity at the distance of $r= 20$ mm from the center of the pipe, the friction head loss coefficient A, the wall shear stress $\tau_{0}$ , respectively?

Options:
A. $$0.127\mathrm{m / s},~0.107\mathrm{m / s},~0.18,~0.077\mathrm{N / m^2}$$
B. $$0.126\mathrm{m / s},~0.109\mathrm{m / s},~0.16,~0.074\mathrm{N / m^2}$$
C. $$0.132\mathrm{m / s},~0.100\mathrm{m / s},~0.19,~0.078\mathrm{N / m^2}$$
D. $$0.120\mathrm{m / s},~0.097\mathrm{m / s},~0.14,~0.070\mathrm{N / m^2}$$
E. $$0.128\mathrm{m / s},~0.119\mathrm{m / s},~0.21,~0.083\mathrm{N / m^2}$$
F. $$0.129\mathrm{m / s},~0.110\mathrm{m / s},~0.17,~0.075\mathrm{N / m^2}$$
G. $$0.140\mathrm{m / s},~0.092\mathrm{m / s},~0.15,~0.072\mathrm{N / m^2}$$
H. $$0.135\mathrm{m / s},~0.105\mathrm{m / s},~0.25,~0.090\mathrm{N / m^2}$$
I. $$0.130\mathrm{m / s},~0.115\mathrm{m / s},~0.22,~0.085\mathrm{N / m^2}$$
J. $$0.125\mathrm{m / s},~0.120\mathrm{m / s},~0.20,~0.080\mathrm{N / m^2}$$
Answer: A
A 10 - bar pressure, 12 cm diameter piston can carry the following load?

Options:
A. 6 tons
B. 250 kg
C. 750 kg
D. 1 ton
E. 1000 kg
F. 4 tons
G. 3 tons
H. 500 kg
I. 2 tons
J. 5 tons
Answer: D
Given that the width of a rectangular thin-plate weir with free surface and without lateral contraction is $b \!=\! 0.50 \mathrm{m}$, the height of the weir is $h_{\mathrm{p}}=0.35 \mathrm{m}$, and the water head in front of the weir is $H = 0.40 \mathrm{m}$, try to calculate the flow rate over the weir $q_{\mathrm{V}}$ is ().

Options:
A. $$
0. 3 1 7 {\mathrm{m}}^{3} / {\mathrm{s}}
$$
B. $$
0. 2 4 3 {\mathrm{m}}^{3} / {\mathrm{s}}
$$
C. $$
0. 2 9 2 {\mathrm{m}}^{3} / {\mathrm{s}}
$$
D. $$
0. 1 7 5 {\mathrm{m}}^{3} / {\mathrm{s}}
$$
E. $$
0. 3 0 1 {\mathrm{m}}^{3} / {\mathrm{s}}
$$
F. $$
0. 2 6 0 {\mathrm{m}}^{3} / {\mathrm{s}}
$$
G. $$
0. 2 6 7 {\mathrm{m}}^{3} / {\mathrm{s}}
$$
H. $$
0. 3 3 4 {\mathrm{m}}^{3} / {\mathrm{s}}
$$
I. $$
0. 3 5 9 {\mathrm{m}}^{3} / {\mathrm{s}}
$$
J. $$
0. 2 8 5 {\mathrm{m}}^{3} / {\mathrm{s}}
$$
Answer: G
The long, straight irrigation canal runs through a section of well-compacted sandy loam. The section is trapezoidal, and the slope ratio is $m=1.5$. The width of trapezoidal groove bottom is $b=7.0m$, and the roughness coefficient of groove wall is $n=0.02$ . According to the terrain, the bottom slope of the passage $i=0.0015$ is used. If the freeboard (the additional height above the design water depth) is 0.25m, what is the design water depth h when the design flow rate $q_V=18 m^3/s$?

Options:
A. 1.18m
B. 1.24m
C. 1.10m
D. 1.12m
E. 1.20m
F. 1.08m
G. 1.14m
H. 1.26m
I. 1.16m
J. 1.22m
Answer: G
Apply Rayleigh's method to analyze the expression for the unit width flow rate $q$ over an overflow weir is ().It is known that $q$ is related to the head $H$ above the weir, the density of water $\rho$, and the gravitational acceleration $g$.

Options:
A. $$
q=k H^{\frac{2} {3}} g^{\frac{3} {2}}
$$
B. $$
q=k H^{\frac{4} {3}} g^{\frac{3} {2}}
$$
C. $$
q=k H^{\frac{3} {2}} g^{\frac{1} {3}}
$$
D. $$
q=k H^{\frac{5} {2}} g^{\frac{1} {2}}
$$
E. $$
q=k H^{\frac{3} {2}} g^{\frac{1} {2}}
$$
F. $$
q=k H^{\frac{1} {2}} g^{\frac{3} {2}}
$$
G. $$
q=k H^{\frac{5} {3}} g^{\frac{1} {2}}
$$
H. $$
q=k H^{\frac{3} {2}} g^{\frac{2} {3}}
$$
I. $$
q=k H^{\frac{3} {4}} g^{\frac{1} {2}}
$$
J. $$
q=k H^{\frac{1} {3}} g^{\frac{3} {2}}
$$
Answer: E
Conduct a breakwater model experiment using a model with a length scale $\lambda_{l}=40$. If the measured wave pressure on the model is $F_{\mathrm{m}}=$ 130N, calculate the wave pressure $F_{\mathrm{p}}$ acting on the prototype breakwater is ().

Options:
A. 23400N
B. 32000N
C. 8320N
D. 16640N
E. 200N
F. 10400N
G. 4950N
H. 1120N
I. 4000N
J. 520N
Answer: C
The rectangular water conduit has a length of 100m, with a cross-section of $1.2 \mathrm{m} \times 2.0 \mathrm{m}$, a roughness coefficient of $n=0.014$, and a flow rate of $q_{\mathrm{V}}= 8.8 \mathrm{m}^3/\mathrm{s}$. Calculate the head loss along the length of the conduit is ().

Options:
A. 1.065m
B. 0.962m
C. 0.988m
D. 0.894m
E. 1.025m
F. 0.781m
G. 0.670m
H. 1.290m
I. 0.743m
J. 1.150m
Answer: B
A hydraulic conductivity with a width of $b = 800 \mathrm{m}$ is located on a horizontal impermeable layer. The hydraulic conductivity is $k = 0.03 \mathrm{cm/s}$. If the hydraulic heads measured in two observation wells, located $l = 1000 \mathrm{m}$ apart in the direction of seepage, are $h_{1} = 8 \mathrm{m}$ and $h_{2} = 6 \mathrm{m}$, calculate the seepage flow rate $q_{\mathrm{V}}$ is ().

Options:
A. 2.95L/s
B. 2.44L/s
C. 1.88L/s
D. 3.78L/s
E. 3.36L/s
F. 4.11L/s
G. 5.60L/s
H. 4.80L/s
I. 4.53L/s
J. 3.02L/s
Answer: E
To determine the permeability coefficient $k$ of the phreatic aquifer soil using the water injection method on-site, it is known that the diameter of the borehole is $d = 30 \, \text{cm}$, reaching down to the impermeable layer. The injection flow rate is $q_{\mathrm{V}} = 400 \, \mathrm{cm}^{3}/\mathrm{s}$, the water depth in the well is $h_{0} = 5 \, \mathrm{m}$, the natural aquifer thickness before water injection is $H = 3.5 \, \mathrm{m}$, and the radius of influence is $R = 150 \, \mathrm{m}$. Calculate the permeability coefficient $k$ is ().

Options:
A. 0.0074cm/s
B. 0.0069cm/s
C. 0.0079cm/s
D. 0.0062cm/s
E. 0.0051cm/s
F. 0.0096cm/s
G. 0.0045cm/s
H. 0.0038cm/s
I. 0.0089cm/s
J. 0.0082cm/s
Answer: B
When the radiation pattern of a certain antenna is independent of the $\varphi$ angle and changes with $\theta$ as follows
$$
\begin{array} {l l} {{F=1}} & {{\quad0^\circ\leq\theta\leqslant30^\circ}} \\ {{F=0.5}} & {{\quad60^\circ\leq\theta\leqslant120^\circ}} \\ {{F=0.707}} & {{\quad150^\circ\leq\theta\leqslant180^\circ}} \\ {{F=0}} & {{\quad30^\circ< \theta< 60^\circ \text{ and}}}\\ \end{array}$$
$120^\circ < \theta< 150^\circ$
Find the antenna directivity coefficient. When $\theta=90^\circ$, what is the directivity coefficient?

Options:
A. $$
\frac{\pi} {10} ( 13-9 \ \sqrt{10} )
$$
$$
4, 2 8
$$
B. $$
\frac{\pi} {5} ( 8-6 \ \sqrt{7} )
$$
$$
1, 3 4
$$
C. $$
\frac{\pi} {8} ( 5-2 \ \sqrt{9} )
$$
$$
0, 4 5
$$
D. $$
\frac{\pi} {6} ( 9-4 \ \sqrt{6} )
$$
$$
3, 1 0
$$
E. $$
\frac{\pi} {11} ( 14-10 \ \sqrt{11} )
$$
$$
6, 1 5
$$
F. $$
\frac{\pi} {9} ( 12-7 \ \sqrt{8} )
$$
$$
5, 0 9
$$
G. $$
\frac{\pi} {3} ( 6-2 \ \sqrt{5} )
$$
$$
0, 2 3
$$
H. $$
\frac{\pi} {2} ( 7-3 \ \sqrt{3} )
$$
$$
1, 1 1
$$
I. $$
\frac{\pi} {4} ( 10-5 \ \sqrt{2} )
$$
$$
2, 0 2
$$
J. $$
\frac{\pi} {7} ( 11-8 \ \sqrt{4} )
$$
$$
2, 1 6
$$
Answer: H
Given the dimensions of the rectangular waveguide are $a \times b = 25 \times 10 \, \text{mm}^2$, and the waveguide is filled with air, determine the following: If the waveguide transmission line operates in a standing wave mode, and it is known that at the midpoint of the wider side, $a/2$, the maximum electric field $|E|_{\operatorname{max}} = 30 \, \text{V}$ and the minimum electric field $|E|_{\operatorname{min}} = 10 \, \text{V}$, calculate the power absorbed by the load.

Options:
A. $$
\approx2 \times1 0^{-1} \mathbf{W}
$$
B. $$
\approx9 \times1 0^{-4} \mathbf{W}
$$
C. $$
\approx3 \times1 0^{-7} \mathbf{W}
$$
D. $$
\approx5 \times1 0^{-4} \mathbf{W}
$$
E. $$
\approx2 \times1 0^{-6} \mathbf{W}
$$
F. $$
\approx6 \times1 0^{-2} \mathbf{W}
$$
G. $$
\approx4 \times1 0^{-5} \mathbf{W}
$$
H. $$
\approx7 \times1 0^{-3} \mathbf{W}
$$
I. $$
\approx1 \times1 0^{-5} \mathbf{W}
$$
J. $$
\approx8 \times1 0^{-8} \mathbf{W}
$$
Answer: G
Given that the electric field at $\theta{=} 300, r {=} 5 \mathrm{km}$ for a current element is $\mathrm{2 mV / m}$, find its radiated power $P_{\mathrm{r}}$.

Options:
A. $$
\mathrm{6 m V / m},5.0W
$$
B. $$
\mathrm{5 m V / m},3.7W
$$
C. $$
\mathrm{9 m V / m},7.4W
$$
D. $$
\mathrm{8 m V / m},6.6W
$$
E. $$
\mathrm{3 m V / m},2.2W
$$
F. $$
\mathrm{12 m V / m},8.8W
$$
G. $$
\mathrm{11 m V / m},3.3W
$$
H. $$
\mathrm{7 m V / m},1.8W
$$
I. $$
\mathrm{4 m V / m},4.4W
$$
J. $$
\mathrm{10 m V / m},2.5W
$$
Answer: I
The normalized direction function of a certain antenna is known to be $F ( \theta)=\left\{\begin{matrix} {{\operatorname{cos}^{2} \! \theta}} & {{| \theta| \leq\frac{\pi} {2}}} \\ {{0}} & {{| \theta| \geq\frac{\pi} {2}}} \\ \end{matrix} \right.$. Try to find its directivity coefficient.

Options:
A. 9
B. 10
C. 13
D. 12
E. 14
F. 11
G. 5
H. 8
I. 15
J. 7
Answer: B
Given that the input power of a certain transmitting antenna is $675 \pi \, \text{(W)}$, with a conversion efficiency of 80% and an effective area of $A_{e}=4 \, \text{m}^{2}, f=3 \, \text{GHz}).$ At point $P$, use a receiving antenna with $D=144$ to align and receive. What are the effective area and received power of the receiving antenna?

Options:
A. $$
{\frac{4 5 \times1 0^{-2}} {\pi}} ( \mathbf{m}^{2} )
$$
$$
3 0 . 4 \ ( \mu\mathbf{W} )
$$
B. $$
{\frac{3 6 \times1 0^{-2}} {\pi}} ( \mathbf{m}^{2} )
$$
$$
2 1. 6 \ ( \mu\mathbf{W} )
$$
C. $$
{\frac{3 5 \times1 0^{-2}} {\pi}} ( \mathbf{m}^{2} )
$$
$$
2 3 . 0 \ ( \mu\mathbf{W} )
$$
D. $$
{\frac{4 2 \times1 0^{-3}} {\pi}} ( \mathbf{m}^{2} )
$$
$$
2 9 . 3 \ ( \mu\mathbf{W} )
$$
E. $$
{\frac{3 3 \times1 0^{-2}} {\pi}} ( \mathbf{m}^{2} )
$$
$$
2 0 . 9 \ ( \mu\mathbf{W} )
$$
F. $$
{\frac{3 8 \times1 0^{-2}} {\pi}} ( \mathbf{m}^{2} )
$$
$$
2 2 . 8 \ ( \mu\mathbf{W} )
$$
G. $$
{\frac{4 7 \times1 0^{-3}} {\pi}} ( \mathbf{m}^{2} )
$$
$$
3 1 . 5 \ ( \mu\mathbf{W} )
$$
H. $$
{\frac{3 0 \times1 0^{-2}} {\pi}} ( \mathbf{m}^{2} )
$$
$$
1 9 . 7 \ ( \mu\mathbf{W} )
$$
I. $$
{\frac{5 1 \times1 0^{-2}} {\pi}} ( \mathbf{m}^{2} )
$$
$$
3 2 . 0 \ ( \mu\mathbf{W} )
$$
J. $$
{\frac{2 9 \times1 0^{-2}} {\pi}} ( \mathbf{m}^{2} )
$$
$$
1 8 . 5 \ ( \mu\mathbf{W} )
$$
Answer: B
The characteristic impedances of the two coaxial segments are respectively $Z_{01} = 75 \Omega$ and $Z_{02} = 50 \Omega$. A 1/4 wavelength transformer section made of a dielectric sleeve is used for matching. Given the operating frequency $f$ is $3\,GHz$ and the inner diameter of the outer conductor $D = 16\,mm$, determine the relative permittivity $\varepsilon_{r}$ of the dielectric and the length $I$ of the transformer section.

Options:
A. 1.2, 1.75(com)
B. 2.0, 3.15(com)
C. 2.1, 3.00(com)
D. 1.7, 2.30(com)
E. 1.4, 2.00(com)
F. 0.9, 2.10(com)
G. 1.6, 2.20(com)
H. 2.2, 2.90(com)
I. 1.8, 2.50(com)
J. 1.5, 2.04(com)
Answer: J
For a lossless transmission line with a characteristic impedance of $75\Omega$, length $l$, and terminated with a load $Z_{L}$, at $400MHz$, the measured $Z_{L}=150-\mathrm{j}90\Omega$, and at $600MHz$, the measured $Z_{L}=150+\mathrm{j}90\Omega$. Determine the line length $l$ that results in the same input impedance at these two frequencies, and what this input impedance value is?

Options:
A. $$
\approx2. 2 5 3 {\mathrm{m}}
$$
$$
\approx2 8. 0+\mathrm{j} 2 2. 7 \Omega
$$
B. $$
\approx0. 3 7 4 9 {\mathrm{m}}
$$
$$
\approx2 6. 8-\mathrm{j} 2 1. 9 \Omega
$$
C. $$
\approx0. 5 6 2 7 {\mathrm{m}}
$$
$$
\approx3 3. 5-\mathrm{j} 1 6. 7 \Omega
$$
D. $$
\approx0. 7 1 8 4 {\mathrm{m}}
$$
$$
\approx3 4. 0+\mathrm{j} 1 7. 6 \Omega
$$
E. $$
\approx0. 8 9 3 5 {\mathrm{m}}
$$
$$
\approx2 9. 2-\mathrm{j} 1 8. 5 \Omega
$$
F. $$
\approx0. 2 5 4 6 {\mathrm{m}}
$$
$$
\approx3 2. 1+\mathrm{j} 1 2. 3 \Omega
$$
G. $$
\approx0. 1 1 8 3 {\mathrm{m}}
$$
$$
\approx2 8. 8-\mathrm{j} 2 2. 4 \Omega
$$
H. $$
\approx1. 0 0 0 {\mathrm{m}}
$$
$$
\approx3 0. 0+\mathrm{j} 2 0. 0 \Omega
$$
I. $$
\approx1. 3 4 7 2 {\mathrm{m}}
$$
$$
\approx2 7. 5+\mathrm{j} 2 5. 4 \Omega
$$
J. $$
\approx0. 0 5 9 1 {\mathrm{m}}
$$
$$
\approx3 1. 0-\mathrm{j} 2 3. 1 \Omega
$$
Answer: G
A rectangular waveguide filled with air has cross-sectional dimensions of $a \times b$, where $b < a < 2b$. Due to significant losses near the cutoff frequency, the lower working frequency is typically set to be 1.25 times the cutoff frequency, and the upper limit is set to 0.80 times the cutoff frequency of the nearest higher order mode. For single-mode operation, the transmitted signal frequency is 4.8-6.0 GHz. Find:
If the waveguide's conductivity is $\sigma=5.8 \times 10^{7} \mathrm{S/m}$ and the average transmitted power is $1kW$, calculate the power dissipated per meter of waveguide when $\lambda=5 \mathrm{cm}$.

Options:
A. $$
6. 9 9 ( \mathbf{W} )
$$
B. $$
8. 1 3 ( \mathbf{W} )
$$
C. $$
5. 2 4 ( \mathbf{W} )
$$
D. $$
4. 5 7 ( \mathbf{W} )
$$
E. $$
1. 2 7 ( \mathbf{W} )
$$
F. $$
6. 2 9 ( \mathbf{W} )
$$
G. $$
2. 9 8 ( \mathbf{W} )
$$
H. $$
7. 6 1 ( \mathbf{W} )
$$
I. $$
9. 8 3 ( \mathbf{W} )
$$
J. $$
3. 4 5 ( \mathbf{W} )
$$
Answer: I
A certain eight-element side-fed linear antenna array has its current distributed according to the Chebyshev polynomial. The element spacing is $d=\lambda/2$, and the elements are half-wave dipoles aligned in a straight line. When the side lobe level is required to be $26dB$ lower than the main lobe, find the radiation impedance for the maximum current.

Options:
A. $$
5 0 3. 2 6+j 2 1 8. 4 5 \ ( \Omega)
$$
B. $$
2 3 8. 9 5+j 2 7 3. 9 4 \ ( \Omega)
$$
C. $$
4 9 5. 5 6+j 3 3 5. 0 2 \ ( \Omega)
$$
D. $$
3 6 2. 5 8+j 4 0 7. 4 6 \ ( \Omega)
$$
E. $$
3 9 7. 8 9+j 2 3 4. 5 1 \ ( \Omega)
$$
F. $$
5 7 6. 4 9+j 2 6 1. 3 8 \ ( \Omega)
$$
G. $$
4 2 1. 7 3+j 2 8 9. 5 6 \ ( \Omega)
$$
H. $$
6 5 4. 1 3+j 4 2 7. 8 3 \ ( \Omega)
$$
I. $$
4 8 5. 6 2+j 1 9 9. 6 7 \ ( \Omega)
$$
J. $$
5 9 4. 6 1+j 3 8 2. 2 0 \ ( \Omega)
$$
Answer: C
A uniform oil flow passes over a 2.5m long thin plate, with a flow velocity $v_{\infty}$ of $4 \mathrm{m} / \mathrm{s}$. The kinematic viscosity of the oil is known to be $\nu=10^{-5} \mathrm{m}^{2} / \mathrm{s}$, and the density is $\rho=850 \mathrm{kg} / \mathrm{m}^{3}$. What is the wall shear stress $\tau_{w}$ at distances of 0.5m, 1.0m, 1.5m, and 2.0m from the leading edge of the plate?

Options:
A. $$
5.60 \mathrm{N / m^{2}},\ 22.10 \mathrm{N / m^{2}},\ 20.54 \mathrm{N / m^{2}}
$$
B. $$
6.50 \mathrm{N / m^{2}},\ 24.21 \mathrm{N / m^{2}},\ 23.75 \mathrm{N / m^{2}}
$$
C. $$
4.85 \mathrm{N / m^{2}},\ 19.98 \mathrm{N / m^{2}},\ 18.33 \mathrm{N / m^{2}}
$$
D. $$
8.10 \mathrm{N / m^{2}},\ 30.45 \mathrm{N / m^{2}},\ 29.89 \mathrm{N / m^{2}}
$$
E. $$
11.90 \mathrm{N / m^{2}},\ 32.65 \mathrm{N / m^{2}},\ 30.50 \mathrm{N / m^{2}}
$$
F. $$
5.10 \mathrm{N / m^{2}},\ 24.95 \mathrm{N / m^{2}},\ 22.79 \mathrm{N / m^{2}}
$$
G. $$
9.00 \mathrm{N / m^{2}},\ 31.05 \mathrm{N / m^{2}},\ 27.33 \mathrm{N / m^{2}}
$$
H. $$
10.50 \mathrm{N / m^{2}},\ 35.20 \mathrm{N / m^{2}},\ 28.89 \mathrm{N / m^{2}}
$$
I. $$
6.95 \mathrm{N / m^{2}},\ 27.34 \mathrm{N / m^{2}},\ 26.12 \mathrm{N / m^{2}}
$$
J. $$
7.85 \mathrm{N / m^{2}},\ 28.23 \mathrm{N / m^{2}},\ 26.65 \mathrm{N / m^{2}}
$$
Answer: J
In the float procession of a flower parade, there is a float with a front emblem shaped approximately like a disk with a diameter of $d = 2.0$ m. The float moves at a speed of 12.6 km/h against a headwind of 3 m/s. The local atmospheric temperature is $t= 20^{\circ} \mathrm{C}$. What is the power consumed to overcome the resistance acting on the emblem?

Options:
A. $$
3 2 2. 6 \mathbf{W}
$$
B. $$
3 7 5. 9 \mathbf{W}
$$
C. $$
4 5 9. 2 \mathbf{W}
$$
D. $$
1 8 3. 0 \mathbf{W}
$$
E. $$
3 3 4. 5 \mathbf{W}
$$
F. $$
1 6 9. 1 \mathbf{W}
$$
G. $$
2 6 5. 5 \mathbf{W}
$$
H. $$
4 0 4. 4 \mathbf{W}
$$
I. $$
2 8 8. 7 \mathbf{W}
$$
J. $$
2 1 7. 8 \mathbf{W}
$$
Answer: E
The main pipeline between $\mathbf{A}$ and $\mathbf{B}$ is a parallel pipeline composed of two branch pipes. The lengths and diameters of the two branch pipes are $l_{1}=1800 \mathrm{m}, \ d_{1}=0.15 \mathrm{m}, \ l_{2}=3000 \mathrm{m}, \ d_{2}=0.20 \mathrm{m},$ respectively. The friction loss coefficient for both pipes is $\lambda=0.03$. The measured flow rate in the main pipeline is $q_{V}=0.03 \mathrm{m}^{3} / \mathrm{s}$. What are the hydraulic head losses between $\mathbf{A}$ and $\mathrm{B}$, and the flow rates in each pipe?

Options:
A. $$
0. 0 1 9 6 7 {\bf m}^{3} / {\bf s},\ 0. 0 1 2 0 4 {\bf m}^{3} / {\bf s},\ 8.2345 {\bf m}
$$
B. $$
0. 0 1 7 3 5 {\bf m}^{3} / {\bf s},\ 0. 0 1 1 2 1 {\bf m}^{3} / {\bf s},\ 9.6552 {\bf m}
$$
C. $$
0. 0 2 0 8 1 {\bf m}^{3} / {\bf s},\ 0. 0 1 0 9 6 {\bf m}^{3} / {\bf s},\ 7.1118 {\bf m}
$$
D. $$
0. 0 1 8 4 2 {\bf m}^{3} / {\bf s},\ 0. 0 1 158 {\bf m}^{3} / {\bf s},\ 7.8823 {\bf m}
$$
E. $$
0. 0 2 3 8 9 {\bf m}^{3} / {\bf s},\ 0. 0 0 9 6 3 {\bf m}^{3} / {\bf s},\ 6.6543 {\bf m}
$$
F. $$
0. 0 1 6 5 9 {\bf m}^{3} / {\bf s},\ 0. 0 1 4 7 3 {\bf m}^{3} / {\bf s},\ 7.7830 {\bf m}
$$
G. $$
0. 0 3 0 1 2 {\bf m}^{3} / {\bf s},\ 0. 0 0 8 5 9 {\bf m}^{3} / {\bf s},\ 5.7681 {\bf m}
$$
H. $$
0. 0 1 3 2 4 {\bf m}^{3} / {\bf s},\ 0. 0 1 3 4 8 {\bf m}^{3} / {\bf s},\ 12.5423 {\bf m}
$$
I. $$
0. 0 2 1 1 4 {\bf m}^{3} / {\bf s},\ 0. 0 1 0 7 2 {\bf m}^{3} / {\bf s},\ 6.9926 {\bf m}
$$
J. $$
0. 0 1 4 9 0 {\bf m}^{3} / {\bf s},\ 0. 0 1 2 5 0 {\bf m}^{3} / {\bf s},\ 10.4315 {\bf m}
$$
Answer: D
The Mach number of the supersonic airflow before the normal shock wave is $Ma_{1}=3$. The total pressure and total temperature are $p_{01}=6 \times10^{5} \mathrm{Pa}$ and $T_{01}=333 \mathrm{K}$, respectively. What are the speed $V_{2}$ behind the wave?

Options:
A. $$
1 9 5. 0 5 {\mathrm{m / s}}
$$
B. $$
1 6 0. 0 4 {\mathrm{m / s}}
$$
C. $$
1 5 5. 0 7 {\mathrm{m / s}}
$$
D. $$
1 6 5. 0 0 {\mathrm{m / s}}
$$
E. $$
1 9 0. 0 8 {\mathrm{m / s}}
$$
F. $$
1 6 8. 0 9 {\mathrm{m / s}}
$$
G. $$
1 7 5. 0 1 {\mathrm{m / s}}
$$
H. $$
1 8 5. 0 3 {\mathrm{m / s}}
$$
I. $$
1 7 0. 0 2 {\mathrm{m / s}}
$$
J. $$
1 4 5. 0 6 {\mathrm{m / s}}
$$
Answer: I
Considering the binomial model of stock price fluctuations, if the current stock price is $S$, then after one unit of time, it becomes $uS$ with probability $p$, and $dS$ with probability $1-p$. Assuming the price fluctuations in each time period are independent, try to calculate the probability that the stock price rises by at least 30% after 1000 units of time, where $u = 1.02$, $d = 0.980$, and $p = 0.52$.

Options:
A. 0.8121
B. 0.8467
C. 0.9978
D. 0.7214
E. 0.6893
F. 0.8796
G. 0.9125
H. 0.7588
I. 0.9542
J. 0.6453
Answer: C
It is known that the number of calls received by the paging station within the time interval $[ 0, t )$ $\{N(t), t \geq 0 \}$ follows a Poisson process, with an average of 2 calls received per minute. Given that 5 calls are received in the time interval $[ 0, 3 )$, find the probability of receiving 3 calls in the time interval $[ 0, 2 )$ is ().

Options:
A. $$
\frac{7 2} {2 4 9}
$$
B. $$
\frac{5 4} {2 3 3}
$$
C. $$
\frac{8 0} {2 4 3}
$$
D. $$
\frac{4 7} {2 5 3}
$$
E. $$
\frac{9 1} {2 4 1}
$$
F. $$
\frac{6 8} {2 4 5}
$$
G. $$
\frac{2 3} {2 4 7}
$$
H. $$
\frac{1 2} {2 5 3}
$$
I. $$
\frac{8 9} {2 2 3}
$$
J. $$
\frac{3 5} {4 4 3}
$$
Answer: C
Considering the issue of electron emission in vacuum tubes, let the number of electrons arriving at the anode per unit time, denoted as $N$, follow a Poisson distribution $$P\{N=k\}=\frac{\lambda^{k}}{k!}\mathrm{e}^{-\lambda}.$$ The energy carried by each electron forms a sequence of random variables $X_1, X_2, \cdots, X_k, \cdots$. It is known that $\{X_k\}$ is statistically independent of $N$, and $\{X_k\}$ are uncorrelated with each other, all having the same mean and variance $$E\langle X_k\rangle=\eta,\quad D(X_k)=\sigma^2.$$ The energy received by the anode per unit time is $S=\sum_{k=1}^{N}X_k$. Find variance $D(S)$ of $S$ is ().

Options:
A. $$ \begin{aligned} {{D ( S )}} & {{} {{}=\lambda \cdot \sigma}} \\ \end{aligned} $$
B. $$ \begin{aligned} {{D ( S )}} & {{} {{}=\lambda^{2} \cdot \sigma}} \\ \end{aligned} $$
C. $$
\begin{aligned} {{D ( S )}} & {{} {{}=\lambda( \sigma^{2}+\eta^{2} )}} \\ \end{aligned}
$$
D. $$ \begin{aligned} {{D ( S )}} & {{} {{}=\sigma \cdot \eta^{2}}} \\ \end{aligned} $$
E. $$ \begin{aligned} {{D ( S )}} & {{} {{}=\eta^{2} \cdot \lambda}} \\ \end{aligned} $$
F. $$ \begin{aligned} {{D ( S )}} & {{} {{}=\sigma^{2}+\eta}} \\ \end{aligned} $$
G. $$ \begin{aligned} {{D ( S )}} & {{} {{}=\lambda \cdot \sigma^{2}}} \\ \end{aligned} $$
H. $$ \begin{aligned} {{D ( S )}} & {{} {{}=\lambda + \eta^{2}}} \\ \end{aligned} $$
I. $$ \begin{aligned} {{D ( S )}} & {{} {{}=\lambda \cdot \eta}} \\ \end{aligned} $$
J. $$ \begin{aligned} {{D ( S )}} & {{} {{}=\sigma^{2} + \eta^{2}}} \\ \end{aligned} $$
Answer: C
Consider a process of continuously flipping a coin. Let $Y_n$ denote the number of heads that have appeared by the $n$-th flip. Find the one-step transition probabilities of the sequence $\{Y_{n}, n \geq 0\}$ is ().

Options:
A. $$ p_{i j}=\left\{\begin{cases} {{{{\frac{1}{6}},}}} & {{{j=i}}} \\ {{{{\frac{5}{6}},}}} & {{{j=i+1}}} \\ {{{0}}} & {{{others}}} \\ \end{cases} \right. $$
B. $$ p_{i j}=\left\{\begin{cases} {{{{\frac{1}{4}},}}} & {{{j=i}}} \\ {{{{\frac{3}{4}},}}} & {{{j=i+1}}} \\ {{{0}}} & {{{others}}} \\ \end{cases} \right. $$
C. $$ p_{i j}=\left\{\begin{cases} {{{{1},}}} & {{{j=i}}} \\ {{{0}}} & {{{j=i+1}}} \\ {{{{{0}}}}} & {{{others}}} \\ \end{cases} \right. $$
D. $$
p_{i j}=\left\{\begin{cases} {{{{\frac{1} {2}},}}} & {{{j=i}}} \\ {{{{\frac{1} {2}},}}} & {{{j=i+1}}} \\ {{{0}}} & {{{others}}} \\ \end{cases} \right.
$$
E. $$ p_{i j}=\left\{\begin{cases} {{{{\frac{3}{4}},}}} & {{{j=i}}} \\ {{{{\frac{1}{4}},}}} & {{{j=i+1}}} \\ {{{0}}} & {{{others}}} \\ \end{cases} \right. $$
F. $$ p_{i j}=\left\{\begin{cases} {{{{\frac{1}{5}},}}} & {{{j=i}}} \\ {{{{\frac{4}{5}},}}} & {{{j=i+1}}} \\ {{{0}}} & {{{others}}} \\ \end{cases} \right. $$
G. $$ p_{i j}=\left\{\begin{cases} {{{{\frac{3}{5}},}}} & {{{j=i}}} \\ {{{{\frac{2}{5}},}}} & {{{j=i+1}}} \\ {{{0}}} & {{{others}}} \\ \end{cases} \right. $$
H. $$ p_{i j}=\left\{\begin{cases} {{{{0},}}} & {{{j=i}}} \\ {{{{1},}}} & {{{j=i+1}}} \\ {{{0}}} & {{{others}}} \\ \end{cases} \right. $$
I. $$ p_{i j}=\left\{\begin{cases} {{{{\frac{1}{3}},}}} & {{{j=i}}} \\ {{{{\frac{1}{3}},}}} & {{{j=i+1}}} \\ {{{{\frac{1}{3}}}}} & {{{others}}} \\ \end{cases} \right. $$
J. $$ p_{i j}=\left\{\begin{cases} {{{{\frac{2}{3}},}}} & {{{j=i}}} \\ {{{{\frac{1}{3}},}}} & {{{j=i+1}}} \\ {{{0}}} & {{{others}}} \\ \end{cases} \right. $$
Answer: D
When the power supply voltage for the resistance spot welding of reinforcing steel decreases by 6%, one should _____.

Options:
A. Modify the Electrode Tip Shape
B. Substitute the Electrode Alloy Type
C. Improve the Welding Transformer Stages
D. Enhance the Electrode Cooling System
E. Adjust the Electrode Force Calibration
F. Reduce the Welding Pulse Frequency
G. Reconfigure the Weld Time Duration
H. Increase the Electrode Contact Pressure
I. Change the Welding Cable Length
J. Decrease the Welding Current Intensity
Answer: C
A construction company is responsible for the construction of a shaft, which is 500 meters deep. According to the contract, the project cost is 30 million yuan, including a total of 20.10 million yuan for labor, materials, and machinery costs, a planned profit of 1.5 million yuan, taxes of 1.2 million yuan, contingency expenses of 2.1 million yuan, regulatory fees of 2.1 million yuan, corporate management fees of 3 million yuan, and a construction period of 15 months. If the variation in project volume is within ±5%, only the labor, materials, and machinery costs are to be adjusted. The billing during construction downtime is the same as during normal operations. The construction company's equipment and capacity can meet the requirements for a shaft depth of 600 meters. During construction, the following events occurred: the client requested to deepen the shaft by $20 \mathrm{m}$, requiring an additional material cost of 180,000 yuan, a labor cost of 100,000 yuan, and a machinery usage cost of 100,000 yuan, extending the construction period by 0.2 months. The project volume changes occurred; how should the costs be handled?

Options:
A. The cost of materials is 155,000 yuan, labor costs are 90,000 yuan, and the machinery usage fee is 105,000 yuan. Party A will settle these, causing a false adjustment of 350,000 yuan.
B. The cost of materials is 140,000 yuan, labor costs are 105,000 yuan, and the machinery usage fee is 75,000 yuan. Party A will account for these, resulting in a mistaken adjustment of 320,000 yuan.
C. The cost of materials is 165,000 yuan, labor costs are 85,000 yuan, and the machinery usage fee is 115,000 yuan. Party A will manage these, resulting in a wrong adjustment of 365,000 yuan.
D. The cost of materials is 175,000 yuan, labor costs are 125,000 yuan, and the machinery usage fee is 95,000 yuan. Party A will correct these, resulting in a faulty adjustment of 395,000 yuan.
E. The cost of materials is 180,000 yuan, labor costs are 100,000 yuan, and the construction machinery usage fee is 100,000 yuan. Party A will provide compensation for these, resulting in an adjusted increase of 380,000 yuan.
F. The cost of materials is 170,000 yuan, labor costs are 95,000 yuan, and the machinery usage fee is 85,000 yuan. Party A will handle these, causing a false adjustment of 350,000 yuan.
G. The cost of materials is 200,000 yuan, labor costs are 120,000 yuan, and the machinery usage fee is 90,000 yuan. Party A will cover these, resulting in a wrong adjustment of 410,000 yuan.
H. The cost of materials is 190,000 yuan, labor costs are 115,000 yuan, and the machinery usage fee is 110,000 yuan. Party A will rectify these, making an inaccurate adjustment of 415,000 yuan.
I. The cost of materials is 160,000 yuan, labor costs are 110,000 yuan, and the machinery usage fee is 95,000 yuan. Party A will adjust these, leading to an errant adjustment of 365,000 yuan.
J. The cost of materials is 150,000 yuan, labor costs are 80,000 yuan, and the machinery usage fee is 80,000 yuan. Party A will reimburse these, resulting in an incorrect adjustment of 310,000 yuan.
Answer: E
Crystalline polyethylene belongs to a body-centered orthorhombic structure with lattice constants: $$a = 0.740\ \text{nm},\ b = 0.493\ \text{nm},\ c = 0.253\ \text{nm}.$$ Two molecular chains pass through one unit cell.Given the density of amorphous polyethylene as $$\rho_a = 0.854\ \text{g/cm}^3,$$ and the density of commercial low-density polyethylene as $$\rho = 0.920\ \text{g/cm}^3,$$ determine the crystalline region's volume fraction $$\phi_c$$ and mass fraction $$w_c$$.

Options:
A. $$
\approx{46.2} \%
$$
$$
\approx{43.7} \%
$$
B. $$
\approx{43.5} \%
$$
$$
\approx{49.2} \%
$$
C. $$
\approx{41.2} \%
$$
$$
\approx{48.3} \%
$$
D. $$
\approx{39.3} \%
$$
$$
\approx{48.7} \%
$$
E. $$
\approx{44.1} \%
$$
$$
\approx{47.9} \%
$$
F. $$
\approx{40.7} \%
$$
$$
\approx{46.0} \%
$$
G. $$
\approx{38.8} \%
$$
$$
\approx{47.1} \%
$$
H. $$
\approx{39.9} \%
$$
$$
\approx{44.4} \%
$$
I. $$
\approx{42.3} \%
$$
$$
\approx{46.6} \%
$$
J. $$
\approx{45.6} \%
$$
$$
\approx{45.8} \%
$$
Answer: I
Given a face-centered cubic crystal with a stacking fault energy $\gamma = 0.01 \, \mathrm{J/m^{2}}$, shear modulus $G = 7 \times 10^{10} \, \mathrm{Pa}$, and lattice constant $a = 0.3 \, \mathrm{nm}$, determine the equilibrium distance between the two partial dislocations $\frac{a}{6} [1 1 \bar{2}]$ and $\frac{a}{6} [2 \bar{1} \bar{1}]$ is ().

Options:
A. $$
8. 8 9 \ \mu\mathrm{m}
$$
B. $$
8. 3 6 \ \mu\mathrm{m}
$$
C. $$
8. 6 1 \ \mu\mathrm{m}
$$
D. $$
9. 1 2 \ \mu\mathrm{m}
$$
E. $$
7. 6 8 \ \mu\mathrm{m}
$$
F. $$
8. 0 2 \ \mu\mathrm{m}
$$
G. $$
7. 9 7 \ \mu\mathrm{m}
$$
H. $$
9. 3 4 \ \mu\mathrm{m}
$$
I. $$
7. 4 5 \ \mu\mathrm{m}
$$
J. $$
9. 0 5 \ \mu\mathrm{m}
$$
Answer: B
For a copper single crystal under tension, with the tensile axis in the $[001]$ direction and $\sigma=10^6 \, \mathrm{Pa}$, calculate the force on an edge dislocation line lying on the (111) plane with Burgers vector $b=\frac{a}{2}[\overline{1}01]$, where $a_\mathrm{Cu}=0.36 \, \mathrm{nm}$.

Options:
A. $$
\approx1. 0 4 \times1 0^{-4} \mathrm{~ N / m}
$$
B. $$
\approx0. 5 2 \times1 0^{-4} \mathrm{~ N / m}
$$
C. $$
\approx2. 0 8 \times1 0^{-4} \mathrm{~ N / m}
$$
D. $$
\approx4. 7 0 \times1 0^{-4} \mathrm{~ N / m}
$$
E. $$
\approx0. 7 6 \times1 0^{-4} \mathrm{~ N / m}
$$
F. $$
\approx3. 5 6 \times1 0^{-4} \mathrm{~ N / m}
$$
G. $$
\approx8. 3 8 \times1 0^{-4} \mathrm{~ N / m}
$$
H. $$
\approx9. 1 0 \times1 0^{-4} \mathrm{~ N / m}
$$
I. $$
\approx6. 9 2 \times1 0^{-4} \mathrm{~ N / m}
$$
J. $$
\approx5. 4 8 \times1 0^{-4} \mathrm{~ N / m}
$$
Answer: A
Carburize the steel with a carbon mass fraction of 0.1%, keeping the carbon mass fraction on the surface of the steel at 1.2% during the carburization process. It is required that the carbon mass fraction be 0.45% at 2 mm below the surface. Given $D=2 \times 10^{-11} \mathrm{m^{2}/s}$, calculate the time required for carburization.

Options:
A. 35.7h
B. 29.6h
C. 34.5h
D. 36.3h
E. 27.3h
F. 31.5h
G. 28.4h
H. 33.9h
I. 32.2h
J. 30.1h
Answer: G