MikaStars39/nano-eval huggingface dataset:
For an ideal gas mixture composed of $\mathrm{N_{2}}$ and Ar, the entropy at $300 \mathrm{~K}, 0.1 \mathrm{~MPa}$ is equal to the entropy at $560 \mathrm{~K, ~0.7 ~MPa}$. Please determine its mole fraction. Known data: for nitrogen gas, $R_{\mathrm{g1}}=296 \, \mathrm{J} / ( \mathrm{kg} \cdot \mathrm{K} )$, $c_{p1}=1038 \, \mathrm{J / ( kg \cdot K )}$; for argon gas, $R_{\mathrm{g2}}=208 \, \mathrm{J / ( kg \cdot K )}$, $c_{p2}=523 \, \mathrm{J / ( kg \cdot K )}$.

Options:
A. 0.402
B. 0.417
C. 0.392
D. 0.376
E. 0.385
F. 0.429
G. 0.355
H. 0.368
I. 0.350
J. 0.439
Answer: C
The volumetric expansion coefficient of water at 27°C is $\alpha_{\nu}=\frac{1} {v} \left( \frac{\partial v} {\partial T} \right)_{\nu}=1.3 \times 10^{-4} \mathrm{~ K}^{-1}$. Assuming the process of water sinking is adiabatic, determine the change in temperature as the water flows from the surface to a depth of 1 km at the bottom.

Options:
A. $$0.098K$$
B. $$0.097K$$
C. $$0.093K$$
D. $$0.088K$$
E. $$0.095K$$
F. $$0.089K$$
G. $$0.091K$$
H. $$0.086K$$
I. $$0.100K$$
J. $$0.085K$$
Answer: G
Air at a pressure of 100 kPa and a temperature of 300 K enters the diffuser with an inlet cross-sectional area of $A_{1}=100 \ \mathrm{mm}^{2}$ at a velocity of $200 \ \mathrm{m/s}$. If the diffuser has an outlet cross-sectional area of $A_{2}=860 \ \mathrm{mm}^{2}$ and an outlet velocity of $c_{12}=20 \ \mathrm{m/s}$, determine the temperature and pressure of the air at the outlet cross-section.

Options:
A. $$18.0^{\circ} \ \mathrm{C}$$
$$
1 2 3. 5 \ \mathrm{k P a}
$$
B. $$18.7^{\circ} \ \mathrm{C}$$
$$
1 2 3. 0 \ \mathrm{k P a}
$$
C. $$20.9^{\circ} \ \mathrm{C}$$
$$
1 2 2. 5 \ \mathrm{k P a}
$$
D. $$23.5^{\circ} \ \mathrm{C}$$
$$
1 2 0. 0 \ \mathrm{k P a}
$$
E. $$20.1^{\circ} \ \mathrm{C}$$
$$
1 2 5. 0 \ \mathrm{k P a}
$$
F. $$21.3^{\circ} \ \mathrm{C}$$
$$
1 2 2. 0 \ \mathrm{k P a}
$$
G. $$19.4^{\circ} \ \mathrm{C}$$
$$
1 2 6. 0 \ \mathrm{k P a}
$$
H. $$19.7^{\circ} \ \mathrm{C}$$
$$
1 2 4. 0 \ \mathrm{k P a}
$$
I. $$22.1^{\circ} \ \mathrm{C}$$
$$
1 2 1. 5 \ \mathrm{k P a}
$$
J. $$17.9^{\circ} \ \mathrm{C}$$
$$
1 2 4. 6 \ \mathrm{k P a}
$$
Answer: H
A certain air conditioning system's heat exchanger cools air at a constant pressure with an initial pressure of \( $p_1 = 101 \, \text{kPa}$ \), initial temperature of \( $t_1 = 35 \, \degree \text{C}$ \), and flow rate of \( $q_{m1} = 0.5 \, \text{kg/s}$ \). This air is then mixed in the duct with another airflow that has a flow rate of \( $q_{m3} = 0.25 \, \text{kg/s}$ \), temperature \( $t_3 = 20 \, \degree \text{C}$ \), and the same pressure of $101 kPa$. Given that the heat dissipation rate of the heat exchanger is 15.1 kW, find the airflow temperature \( $t_4 \, \degree \text{C}$ \) inside the duct. It is known that the enthalpy of the air is given by \( $h = c_p \, T_{\degree}$ \).

Options:
A. 19 °C
B. 15 °C
C. 7 °C
D. 18 °C
E. 9 °C
F. 14 °C
G. 20 °C
H. 10 °C
I. 12 °C
J. 11 °C
Answer: H
Vinyl acetate undergoes bulk polymerization at 60 °C, using azobisisobutyronitrile as an initiator. The concentration of the initiator is $[\mathrm{I}]=0.206\times10^{-3} \ \mathrm{mol} \cdot\mathrm{L}^{-1}$, and the efficiency factor is $f=0.8$, assuming no chain transfer reactions and complete disproportionation termination. What is the degree of polymerization of the polymer product ? (The following data may be used: $k_{d}=1.16 \times10^{-5} \ \mathrm{s}^{-1}$, $k_{p}=3.7 \times10^{3} \ \mathrm{L \cdot mol}^{-1} \cdot \mathrm{s}^{-1}$, $k_{t}=7.4 \times10^{7} \ \mathrm{L \cdot mol}^{-1} \cdot \mathrm{s}^{-1}$, with $\left[ \mathrm{M} \right] = 10.86 \ \mathrm{mol} \cdot\mathrm{L}^{-1}$.)

Options:
A. $$
5. 8 \times1 0^{3}
$$
B. $$
8. 4 \times1 0^{4}
$$
C. $$
5. 3 \times1 0^{4}
$$
D. $$
9. 6 \times1 0^{5}
$$
E. $$
2. 5 \times1 0^{4}
$$
F. $$
3. 9 \times1 0^{4}
$$
G. $$
7. 2 \times1 0^{3}
$$
H. $$
1. 2 \times1 0^{3}
$$
I. $$
4. 7 \times1 0^{3}
$$
J. $$
6. 4 \times1 0^{4}
$$
Answer: C
In the styrene polymerization reaction, $k_{p} = 145 \, \mathrm{L \cdot mol^{-1} \cdot s^{-1}}$, $k_{t} = 2.9 \times 10^{7} \, \mathrm{L \cdot mol^{-1} \cdot s^{-1}}$, and the density of styrene is $0.8 \, \mathrm{g \cdot cm^{-3}}$. Using BPO as the initiator, with a half-life of 44 hours at the polymerization reaction temperature, and a usage amount of 0.5% (mass fraction) of styrene, assuming the initiation efficiency is 0.5, what is the number-average relative molecular mass of polystyrene?

Options:
A. $$
6. 7 \times 1 0^{3}
$$
B. $$
4. 5 \times 1 0^{3}
$$
C. $$
2. 8 \times 1 0^{3}
$$
D. $$
8. 9 \times 1 0^{3}
$$
E. $$
3. 2 \times 1 0^{3}
$$
F. $$
7. 0 \times 1 0^{3}
$$
G. $$
1. 1 \times1 0^{3}
$$
H. $$
9. 6 \times 1 0^{3}
$$
I. $$
0. 3 \times 1 0^{3}
$$
J. $$
5. 4 \times1 0^{3}
$$
Answer: G
In the calculations, the following data are used: $[ I ]=0.04 \, \mathrm{mol} \cdot\mathrm{L}^{-1}$, $f=0.8$, $k_{d}=2.0 \times 10^{-6} \, \mathrm{s}^{-1}$, $k_{p}=176 \, \mathrm{L} \cdot\mathrm{mol}^{-1} \cdot \mathrm{s}^{-1}$, $k_{1} = 3.6 \times10^{7} \mathrm{L} \cdot\mathrm{mol}^{-1} \cdot s^{-1}$, $\rho\ (60^{\circ} \mathrm{C}) = 0.887 \, \mathrm{g} \cdot\mathrm{cm}^{-3}$, $C_{1} = 0.05$, $C_{\mathrm{M}} = 0.85 \times 10^{-4}$. Using benzoyl peroxide as the initiator, with styrene undergoing bulk polymerization at 60 °C, what percentage does each of the three parts of monomer transfer occupy in the inverse degree of polymerization?

Options:
A. $8.1\%$
B. $5.8\%$
C. $5.1\%$
D. $6.4\%$
E. $2.6\%$
F. $7.2\%$
G. $9.3\%$
H. $4.9\%$
I. $7.5\%$
J. $3.7\%$
Answer: D
Given: The total volume of the polymer in the reactor is 1L, with a density of 0.878 g/mL. The mass of the monomer is 300 g, and the amount of initiator used is 0.6% of the monomer. The rate constants are: $k_d = 2.0 \times 10^{-6} \, \text{s}^{-1}$, $k_p = 367 \, \text{L} \cdot \text{mol}^{-1} \cdot \text{s}^{-1}$, $k_t = 0.93 \times 10^7 \, \text{L} \cdot \text{mol}^{-1} \cdot \text{s}^{-1}$, $k_2 = 1 \, \text{s}^{-1}$. The initiator efficiency (f) is 0.8, and the concentrations are: $C_I = 0.02$, $C_M = 0.18 \times 10^{-4}$, $C_S = 0.46 \times 10^{-6}$. The kinetic chain termination is primarily through disproportionation, accounting for approximately 85%. What is the number average degree of polymerization when the reaction stops at low conversion rates?

Options:
A. $$
1. 7 4 \times1 0^{3}
$$
B. $$
2. 8 7 \times1 0^{3}
$$
C. $$
1. 9 9 \times1 0^{3}
$$
D. $$
2. 4 9 \times1 0^{3}
$$
E. $$
3. 2 4 \times1 0^{3}
$$
F. $$
4. 1 5 \times1 0^{3}
$$
G. $$
2. 6 1 \times1 0^{3}
$$
H. $$
3. 0 2 \times1 0^{3}
$$
I. $$
4. 5 8 \times1 0^{3}
$$
J. $$
2. 3 3 \times1 0^{3}
$$
Answer: B
Latex particle number $= 1.0 \times 10^{15}$ molecules·mL$^{-1}$, $[M] = 5.0 \, \text{mol} \cdot \text{L}^{-1}$, $\rho = 5.0 \times 10^{12}$ molecules·mL$^{-1} \cdot \text{s}^{-1}$. The rate constants for the two systems are the same: $k_{p} = 176 \, \text{L} \cdot \text{mol}^{-1} \cdot \text{s}^{-1}$, $k_{1} = 3.6 \times 10^{7} \, \text{L} \cdot \text{mol}^{-1} \cdot \text{s}^{-1}$. What are the rate and degree of polymerization of the latex polymerization of Styrene at 60 °C ?

Options:
A. $$
3. 3 \times1 0^{-4} \, ( \mathrm{m o l} \cdot\mathrm{L}^{-1} \cdot\mathrm{s}^{-1} ),\ 7. 8 9 \times1 0^{5}
$$
B. $$
8. 2 \times1 0^{-3} \, ( \mathrm{m o l} \cdot\mathrm{L}^{-1} \cdot\mathrm{s}^{-1} ),\ 1. 0 0 \times1 0^{4}
$$
C. $$
7. 3 \times1 0^{-2} \, ( \mathrm{m o l} \cdot\mathrm{L}^{-1} \cdot\mathrm{s}^{-1} ),\ 1. 7 6 \times1 0^{3}
$$
D. $$
5. 9 \times1 0^{-5} \, ( \mathrm{m o l} \cdot\mathrm{L}^{-1} \cdot\mathrm{s}^{-1} ),\ 9. 3 2 \times1 0^{5}
$$
E. $$
4. 4 \times1 0^{-4} \, ( \mathrm{m o l} \cdot\mathrm{L}^{-1} \cdot\mathrm{s}^{-1} ),\ 5. 6 7 \times1 0^{3}
$$
F. $$
9. 4 \times1 0^{-4} \, ( \mathrm{m o l} \cdot\mathrm{L}^{-1} \cdot\mathrm{s}^{-1} ),\ 8. 1 0 \times1 0^{4}
$$
G. $$
1. 1 \times1 0^{-4} \, ( \mathrm{m o l} \cdot\mathrm{L}^{-1} \cdot\mathrm{s}^{-1} ),\ 2. 3 4 \times1 0^{6}
$$
H. $$
7. 3 \times1 0^{-4} \, ( \mathrm{m o l} \cdot\mathrm{L}^{-1} \cdot\mathrm{s}^{-1} ),\ 1. 7 6 \times1 0^{5}
$$
I. $$
6. 5 \times1 0^{-4} \, ( \mathrm{m o l} \cdot\mathrm{L}^{-1} \cdot\mathrm{s}^{-1} ),\ 1. 2 0 \times1 0^{6}
$$
J. $$
4. 9 \times1 0^{-4} \, ( \mathrm{m o l} \cdot\mathrm{L}^{-1} \cdot\mathrm{s}^{-1} ),\ 2. 7 1 \times1 0^{5}
$$
Answer: H
Monomers $\mathbf{M}_{1}$ and $\mathbf{M}_{2}$ undergo copolymerization. At 50 °C, $r_{1} = 4.4$ and $r_{2} = 0.12$. Initially, the mole fractions of the copolymer formed by $\mathbf{M}_{1}$ and $\mathbf{M}_{2}$ each account for 50%. Assuming that the copolymer composition remains constant within every 10% conversion range, what is the composition of the copolymer when the total monomer conversion reaches 20%?

Options:
A. $0.278$
B. $0.271$
C. $0.451$
D. $0.492$
E. $0.385$
F. $0.467$
G. $0.346$
H. $0.213$
I. $0.329$
J. $0.302$
Answer: J
Styrene $( \mathbf{M}_{1} )$ and acrylonitrile $( \mathbf{M}_{2} )$ are copolymerized, with $r_{1}=0.4$ and $r_{2}=0.04$. What should be the initial monomer mixture ratio (mass ratio) and feeding method if the desired copolymer composition contains a 70% mass fraction of styrene monomer units?

Options:
A. 80/20, continuous feed process
B. 72/28, rapid mixing technique
C. 90/10, alternating monomer feed
D. 76/24, single batch feeding
E. 82/18, semi-batch operation method
F. 74/26, variable reactant flow
G. 70/30, multi-stage addition method
H. 78/22, controlled pressure system
I. 85/15, constant temperature process
J. 60/40, reflux with catalyst
Answer: D
The known Q values of styrene and methyl methacrylate are 1.00 and 0.74, respectively, and the $e$ values are -0.80 and 0.40, respectively. What are the reactivity ratios when these two monomers undergo copolymerization? Also, describe the type of copolymerization.

Options:
A. $1.05,\ 0.55$, random copolymerization
B. $0.95,\ 0.52$, homopolymerization
C. $0.98,\ 0.46$, alternating copolymerization
D. $1.10,\ 0.44$, sequential copolymerization
E. $1.08,\ 0.53$, branched copolymerization
F. $1.00,\ 0.49$, isotactic copolymerization
G. $0.92,\ 0.50$, gradient copolymerization
H. $0.85,\ 0.43$, segmented copolymerization
I. $0.93,\ 0.39$, syndiotactic copolymerization
J. $1.12,\ 0.47$, block copolymerization
Answer: C
Using BuLi as the initiator and cyclohexane as the solvent, synthesize the linear triblock copolymer SBS. The total amount of monomers is 150 g. The concentration of the BuLi cyclohexane solution is $0.4 \ \mathrm{mol} \cdot \mathrm{L}^{-1}$. The conversion rate of the monomers is 100%. If the system contains $1.8 \times 10^{-2} \, \mathrm{mL}$ of water that was not removed before the reaction, what is the actual relative molecular weight of the resulting polymer in this system?

Options:
A. $$
3 \times1 0^{5}
$$
B. $$
4 \times1 0^{5}
$$
C. $$
1 \times1 0^{5}
$$
D. $$
2 \times1 0^{5}
$$
E. $$
1.5 \times1 0^{5}
$$
F. $$
8 \times1 0^{5}
$$
G. $$
6 \times1 0^{5}
$$
H. $$
7 \times1 0^{5}
$$
I. $$
9 \times1 0^{5}
$$
J. $$
5 \times1 0^{5}
$$
Answer: A
Upon hydrogenation, the cis-1,4 and trans-1,4 isomers of polybutadiene become linear carbon chains, while the 1,2 addition isomers become carbon chains with ethyl side groups. The microstructure composition of a polybutadiene sample with a relative molecular mass of 168,000 is as follows: 47.2% cis-1,4 units, 44.9% trans-1,4 units, and 7.9% 1,2 addition units. What is the average number of carbon atoms between the ethyl groups in the hydrogenated molecular chain?

Options:
A. $50.5$
B. $51.2$
C. $48.3$
D. $49.7$
E. $48.0$
F. $44.8$
G. $46.9$
H. $47.6$
I. $45.3$
J. $52.1$
Answer: H
If polyethylene is regarded as a freely rotating chain, the end-to-end distance follows a Gaussian distribution function, and it is given that the C-C bond length $l = 0.154 \, \text{nm}$, and the bond angle $\alpha = 109.5^{\circ}$. What is the probability that the end-to-end distance is within ±1 nm and ±10 nm, respectively? ( The unit is $nm^{-1}$. )

Options:
A. $$
3. 5 9 \times1 0^{-5},\ 3. 5 8 \times1 0^{-3}
$$
B. $$
3. 6 0 \times1 0^{-5},\ 3. 6 5 \times1 0^{-3}
$$
C. $$
3. 5 7 \times1 0^{-5},\ 3. 5 9 \times1 0^{-3}
$$
D. $$
3. 5 5 \times1 0^{-5},\ 3. 5 3 \times1 0^{-3}
$$
E. $$
3. 6 1 \times1 0^{-5},\ 3. 6 2 \times1 0^{-3}
$$
F. $$
3. 5 0 \times1 0^{-5},\ 3. 5 0 \times1 0^{-3}
$$
G. $$
3. 5 3 \times1 0^{-5},\ 3. 5 5 \times1 0^{-3}
$$
H. $$
3. 4 8 \times1 0^{-5},\ 3. 5 6 \times1 0^{-3}
$$
I. $$
3. 4 9 \times1 0^{-5},\ 3. 5 2 \times1 0^{-3}
$$
J. $$
3. 6 2 \times1 0^{-5},\ 3. 6 7 \times1 0^{-3}
$$
Answer: A
During the development of computers, how was multiplication and division typically implemented in 8-bit microcomputers?

Options:
A. Firmware
B. Software
C. Parallel buses
D. Algorithms
E. Logic gates
F. Transistors
G. Hardware
H. Registers
I. Circuitry
J. ROM chips
Answer: B
What method should be chosen to transfer data between devices with different speeds?

Options:
A. Incremental Bandwidth Synchronization
B. Cross-Platform Interference Control
C. Dynamic Frequency Adjustment
D. Asymmetric Speed Matching Protocol
E. Bi-directional Rate Limiting
F. Adaptive Timing Negotiation
G. Intermediary Signal Bridging
H. Variable Data Compression Algorithms
I. Synchronous and Asynchronous Methods
J. Sequential Channel Switching
Answer: I
What is the Hamming code corresponding to 1100?

Options:
A. 1101010
B. 1100111
C. 1011100
D. 0110110
E. 1011110
F. 1001011
G. 0110011
H. 1110100
I. 1010011
J. 1001100
Answer: H
A certain computer's cache consists of 16 blocks, using 2-way set associative mapping (i.e., each set contains 2 blocks). Each main memory block is 32 bytes in size and is addressed by bytes. Which cache set should the main memory block containing main memory unit 129 be loaded into?

Options:
A. 7
B. 6
C. 9
D. 2
E. 12
F. 8
G. 5
H. 3
I. 10
J. 11
Answer: H
A certain computer system has a word length of 32 bits, includes two selection channels and one multiplexer channel. Each selection channel is connected to two disk drives and two tape drives, and the multiplexer channel is connected to two line printers, two card readers, and 10 terminals. Assuming the transfer rates of each device are as follows: disk drive 800KB/s, tape drive 200KB/s, line printer 6.6KB/s, card reader 1.2KB/s, and terminal 1KB/s, what is the maximum I/O data transfer rate of this computer system?

Options:
A. $$
1 6 8 9. 8 \mathrm{K B / s}
$$
B. $$
1 6 5 7. 4 \mathrm{K B / s}
$$
C. $$
1 7 2 3. 2 \mathrm{K B / s}
$$
D. $$
1 6 3 1. 0 \mathrm{K B / s}
$$
E. $$
1 5 9 6. 4 \mathrm{K B / s}
$$
F. $$
1 5 8 2. 2 \mathrm{K B / s}
$$
G. $$
1 7 0 0. 0 \mathrm{K B / s}
$$
H. $$
1 6 2 5. 6 \mathrm{K B / s}
$$
I. $$
1 6 4 0. 0 \mathrm{K B / s}
$$
J. $$
1 6 0 0. 8 \mathrm{K B / s}
$$
Answer: H
The value of an 8-bit register is known to be 11001010. What is the result after a small circular left shift by one bit?

Options:
A. 10011011
B. 01110010
C. 11001001
D. 01011001
E. 00110101
F. 11011000
G. 01101001
H. 10101001
I. 10010101
J. 11002010
Answer: I
A certain machine has a total of 7 instructions, with usage frequencies of 30%, 20%, 20%, 10%, 10%, 5%, and 5% respectively. What is the average opcode length when using Huffman coding?

Options:
A. 2.5
B. 1.5
C. 3.5
D. 1.2
E. 4.0
F. 2.6
G. 3.0
H. 2.0
I. 2.1
J. 2.9
Answer: A
Identification by chemical methods: Cyclohexene, tertiary Butanol, benzyl chloride, benzene. 1-pentyne, cyclohexyl chloride, and cyclohexanol. When treated with $\mathrm{AgNO_3-C_2H_5OH}$: immediate formation of a white precipitate is ____. After heating, the formation of a white precipitate is ____. Others ____.

Options:
A. Benzene, 1-pentyne, does not meet the criteria.
B. Benzyl chloride, tert-butyl alcohol, different from this
C. 1-Pentyne and cyclohexanol show no reaction
D. 1-Pentyne, cyclohexene, no precipitation occurs
E. Cyclohexene and benzene show no significant changes.
F. Tert-butyl alcohol, cyclohexanol, no reaction
G. Benzene, benzyl chloride, and others differ
H. Cyclohexyl chloride, benzene, does not precipitate.
I. Tertiary butanol, cyclohexene, this phenomenon does not occur.
J. Benzyl chloride , cyclohexyl chloride, do not exhibit this reaction.
Answer: J
Add an appropriate amount of water to the mixture, then adjust the pH to 5 with NaOAc under thorough stirring, and separate the organic phase. To the aqueous phase, add an excess of hydrochloric acid until $pH = 1\sim2$, precipitating ____. In the residual organic phase, add an appropriate amount of dilute NaOH solution, stir well, and separate the organic phase. To the aqueous phase, add an excess of acetic acid, precipitating the ____ layer. After separation, wash the organic phase with a small amount of saturated $\mathrm{NaHCO}_{3}$ and $\mathrm{H}_{2} \mathrm{O}$ sequentially before drying to obtain phenol. The residual organic phase contains ____ and ____ (as well as a small amount of residual impurities), which have a very large difference in polarity. Therefore, there is a significant difference in boiling points.

Options:
A. With tartaric acid, thymol, cumene, nitromethane
B. Regarding terephthalic acid, phenol, toluene, nitrobenzene
C. Including formic acid, anisole, ethylbenzene, pyrrole
D. Associating malonic acid, phenacetin, benzene, indene
E. Considering lauric acid, resorcinol, styrene, acetone
F. Regarding citric acid, chlorobenzene, paraxylene, benzaldehyde
G. Involving oxalic acid, catechol, cyclohexane, nitrotoluene
H. About butyric acid, carbolic acid, cyclopentane, hydrazine
I. With benzoic acid, benzene, xylene, cumene
J. Pertaining to acetic acid, m-cresol, ethylbenzene, aniline
Answer: B
In mice, allele A causes yellow fur, and is not lethal when homozygous; allele R can independently cause black fur; when A and R are together, they cause gray fur; when $a$ and $r$ are together, they cause white fur. A gray male mouse and a yellow female mouse were mated, resulting in the following F1 phenotypes and ratios: 3/8 yellow mice, 3/8 gray mice, 1/8 black mice, and 1/8 white mice. Please write out the genotypes of the parents is().

Options:
A. aaRr (black male mouse) × AaRR (gray female mouse)
B. AaRR (white male mouse) × aaRr (yellow female mouse)
C. AaRr (gray male mouse) × AaRr (yellow female mouse)
D. Aarr (black male mouse) × AaRr (white female mouse)
E. AaRR (gray male mouse) × aaRR (yellow female mouse)
F. aaRr (gray male mouse) × AaRR (yellow female mouse)
G. AaRr (yellow male mouse) × aaRr (gray female mouse)
H. aaRR (yellow male mouse) × Aarr (gray female mouse)
I. Aarr (gray male mouse) × Aarr (yellow female mouse)
J. AaRr (black male mouse) × AaRR (yellow female mouse)
Answer: C
A pure line of disc-shaped pumpkin is crossed with a pure line of elongated pumpkin, resulting in F, obtaining disc-shaped pumpkin, F. The new spherical fruit trait emerges, with the phenotype and quantity as follows: 270 disc-shaped fruits, 178 spherical fruits, and 32 elongated fruits. The genotype of the $\mathbf{F}_{2}$ parent generation is ().

Options:
A. 9/16 aabb elongated fruit
3/16 A_bb spherical fruit
3/16 A_B_ spherical fruit
1/16 aaB_ disc-shaped fruit
B. 9/16 A_B_ disc-shaped fruit
3/16 A_bb disc-shaped fruit
3/16 aaB_ elongated fruit
1/16 aabb spherical fruit
C. 9/16 A_bb elongated fruit
3/16 A_B_ disc-shaped fruit
3/16 aaB_ spherical fruit
1/16 aabb disc-shaped fruit
D. 9/16 aabb spherical fruit
3/16 A_B_ elongated fruit
3/16 aaB_ disc-shaped fruit
1/16 A_bb disc-shaped fruit
E. 9/16 aaB_ elongated fruit
3/16 A_bb disc-shaped fruit
3/16 aabb elongated fruit
1/16 A_B_ spherical fruit
F. 9/16 aaB_ disc-shaped fruit
3/16 aabb spherical fruit
3/16 A_bb disc-shaped fruit
1/16 A_B_ elongated fruit
G. 9/16 aabb disc-shaped fruit
3/16 A_B_ spherical fruit
3/16 aaB_ elongated fruit
1/16 A_bb elongated fruit
H. 9/16 A_bb disc-shaped fruit
3/16 A_B_ elongated fruit
3/16 aaB_ elongated fruit
1/16 aabb spherical fruit
I. 9/16 A_B_ disc-shaped fruit
3/16 aaB_ spherical fruit
3/16 A_bb spherical fruit
1/16 aabb elongated fruit
J. 9/16 A_B_ spherical fruit
3/16 aabb disc-shaped fruit
3/16 A_bb elongated fruit
1/16 aaB_ disc-shaped fruit
Answer: I
The crossing of pumpkins with white fruit and pumpkins with yellow fruit produces offspring with approximately half having white fruit and half having yellow fruit. Let allele W determine white fruit in pumpkins and $w$ determine yellow fruit, with W being completely dominant over $w$. What are the genotypes of the two parents?

Options:
A. \(WW\) and \(WW\)
B. \(WW\) and \(Ww\)
C. \(ww\) and \(Ww\)
D. \(WW\) and \(ww\)
E. \(Ww\) and \(WW\)
F. \(Ww\) and \(ww\)
G. \(Ww\) and \(Ww\)
H. \(ww\) and \(ww\)
I. \(ww\) and \(WW\)
Answer: F
In self-pollinated kidney beans, colored flowers are dominant over white flowers. Suppose a colored flower plant, genotype Cc, exists on an island where no other kidney bean plants are present. Moreover, this is an annual plant, so there won't be any crossbreeding between plants of different generations. What will be the phenotypes and their ratios of the flower colors in the third generation population of this colored flower after self-pollination?

Options:
A. 6:4
B. 8:6
C. 9:8
D. 3:1
E. 9:7
F. 5:3
G. 4:2
H. 8:8
I. 7:7
J. 7:5
Answer: E
In Arabidopsis thaliana, the gene locus that determines pod length (L for long pods, l for short pods) and the gene locus that determines fruit hairiness (H for hairy, h for smooth) are located on the same chromosome, 16 map units (cM) apart. The F1 generation from the cross $LLHH × llhh$ and $LLhh × llHH$ are crossed with each other. What proportion of the expected offspring will be $Llhh$?

Options:
A. 0.202
B. 0.132
C. 0.152
D. 0.228
E. 0.238
F. 0.118
G. 0.182
H. 0.162
I. 0.142
J. 0.218
Answer: G
Phage transduction from a bacterial strain that cannot synthesize isoleucine $( i l e^{-} )$ was performed to a bacterial strain that cannot synthesize methionine $( m e t^{-} )$. The broth medium used for conjugation was diluted and spread on a minimal medium supplemented with isoleucine. An equal amount of diluted broth medium was also spread on a minimal medium without supplementation. A total of 18 colonies grew on the minimal medium, while 360 colonies grew on the minimal medium supplemented with isoleucine. Calculate the normalized recombination ratio.

Options:
A. ${25} \%$
B. ${20} \%$
C. ${5} \%$
D. ${15} \%$
E. ${40} \%$
F. ${45} \%$
G. ${10} \%$
H. ${50} \%$
I. ${30} \%$
J. ${35} \%$
Answer: B
The two types of wheat mature in 14 days and 28 days respectively. After they are crossbred, the F1 generation is obtained, and through self-pollination of F1, 6,200,000 F2 plants are produced. Among these, 100 plants mature within 14 days (including 14 days). How many genes are involved in controlling the maturation time of wheat?

Options:
A. 12
B. 9
C. 5
D. 3
E. 10
F. 11
G. 6
H. 7
I. 8
J. 4
Answer: I
The known speed of the plane when it makes contact with the water surface is 160 km/h, and after the plane taxis 400 m on the water, the speed decreases to 32 km/h. If the deceleration is proportional to the square of the plane's taxiing speed on the water, i.e., \( a = -k v^{2} \), find the value of the parameter \( k \) that represents the shape and size of the propeller?

Options:
A. $$
0. 0 3 8 \quad( l/ \mathrm{m} )
$$
B. $$
0. 0 1 6 \quad( l/ \mathrm{m} )
$$
C. $$
0. 0 0 3 \quad( l/ \mathrm{m} )
$$
D. $$
0. 0 0 5 \quad( l/ \mathrm{m} )
$$
E. $$
0. 0 5 2 \quad( l/ \mathrm{m} )
$$
F. $$
0. 0 2 7 \quad( l/ \mathrm{m} )
$$
G. $$
0. 0 2 1 \quad( l/ \mathrm{m} )
$$
H. $$
0. 0 0 6 \quad( l/ \mathrm{m} )
$$
I. $$
0. 0 0 4 \quad( l/ \mathrm{m} )
$$
J. $$
0. 0 1 0 \quad( l/ \mathrm{m} )
$$
Answer: I
When the third-stage rocket separates at point $A$, its speed is $u = 15,000$ km/h, then it flies to point $B$ without propulsion. After reaching point $B$, the engine is ignited, at which point the angle between the orbit and the horizontal line is 20°. During the interval from $A$ to $B$, the magnitude and direction of gravitational acceleration can be considered constant, and it can be taken as $g = 9$ m/s². Calculate the time $t$ it takes for the rocket to travel from A to B and determine the change in altitude h during this process.

Options:
A. 195s, $\text{430km}$
B. 214s, $\text{410km}$
C. 205s, $\text{435km}$
D. 215s, $\text{415km}$
E. 250s, $\text{425km}$
F. 202s, $\text{408km}$
G. 208s, $\text{418km}$
H. 198s, $\text{420km}$
I. 185s, $\text{412km}$
J. 220s, $\text{405km}$
Answer: G
To measure the density of meteoric dust, a space probe was launched vertically above the North Pole. When the altitude is $160km$ above the North Pole, the probe's upward velocity is $16000km/h$. Given that the Earth's polar radius is $6357km$ and the gravitational acceleration at the poles is $9.833m/s^{2}$, find the maximum altitude $h$ the probe can reach.

Options:
A. $1420\mathbf{km}$
B. $1700\mathbf{km}$
C. $1500\mathbf{km}$
D. $1200\mathbf{km}$
E. $1300\mathbf{km}$
F. $1800\mathbf{km}$
G. $1350\mathbf{km}$
H. $1600\mathbf{km}$
I. $1550\mathbf{km}$
J. $1450\mathbf{km}$
Answer: A
The roof of a certain building has a hyperbolic paraboloid shape, and the equation for this hyperbolic paraboloid is $z=\frac{x y}{10}$, where the lengths are measured in meters. A small ball rolls on the roof, and its equations of motion are $x=10-20t$, $y=10-20t^{2}$, where $t$ is measured in seconds. Find the speed and acceleration of the ball when it reaches the $x=0$ boundary, and determine the tangential acceleration and radius of curvature at that instant.

Options:
A. $25m/s,85.3m/s^{2}, 35m/s^{2},10.75m$
B. $29m/s,88.4m/s^{2}, 39m/s^{2},11.55m$
C. $31m/s,91.2m/s^{2}, 41m/s^{2},12.05m$
D. $30m/s,89.4m/s^{2}, 40m/s^{2},11.25m$
E. $32m/s,87.1m/s^{2}, 43m/s^{2},10.85m$
F. $27m/s,86.9m/s^{2}, 37m/s^{2},11.95m$
G. $33m/s,90.7m/s^{2}, 42m/s^{2},10.95m$
H. $35m/s,89.9m/s^{2}, 45m/s^{2},12.65m$
I. $26m/s,93.1m/s^{2}, 34m/s^{2},11.15m$
J. $28m/s,92.6m/s^{2}, 38m/s^{2},12.35m$
Answer: D
The plane takes off along the flight deck of the aircraft carrier, with the runway being $160m$ long and forming an $18°$ angle with the ship's hull. The carrier's cruising speed is $v_{o}=50\mathrm{km/h}$, and the wind is blowing in the opposite direction of the ship's heading at a speed of $v_{w}=35\mathrm{km/h}$. The relative headwind speed when the plane takes off is $v_{ra}=260\mathrm{km/h}$. What should be the minimum acceleration $a_{r}$ of the plane relative to the deck to ensure that it can take off before reaching the end of the deck?

Options:
A. $$
5. 8 4 \, \mathrm{m} / {\mathrm{s}}^{2}
$$
B. $$
8. 8 6 \, \mathrm{m} / {\mathrm{s}}^{2}
$$
C. $$
7. 7 4 \, \mathrm{m} / {\mathrm{s}}^{2}
$$
D. $$
9. 2 1 \, \mathrm{m} / {\mathrm{s}}^{2}
$$
E. $$
8. 0 4 \, \mathrm{m} / {\mathrm{s}}^{2}
$$
F. $$
8. 3 9 \, \mathrm{m} / {\mathrm{s}}^{2}
$$
G. $$
7. 1 2 \, \mathrm{m} / {\mathrm{s}}^{2}
$$
H. $$
9. 5 8 \, \mathrm{m} / {\mathrm{s}}^{2}
$$
I. $$
6. 5 2 \, \mathrm{m} / {\mathrm{s}}^{2}
$$
J. $$
6. 9 7 \, \mathrm{m} / {\mathrm{s}}^{2}
$$
Answer: C
Find the volume of the solid formed by rotating the ellipse $\frac{x^{2}} {a^{2}}+\frac{y^{2}} {b^{2}}=1$ around the line $x=2a$.

Options:
A. $$
V=8 \pi^{2} a b^{2}
$$
B. $$
V=2 \pi a^{2} b
$$
C. $$
V=4 \pi a^{2} b
$$
D. $$
V=12 \pi^{2} a^{3} b
$$
E. $$
V=4 \pi a^{3} b
$$
F. $$
V=4 \pi^{2} a b^{3}
$$
G. $$
V=4 \pi^{2} a b
$$
H. $$
V=6 \pi a b^{2}
$$
I. $$
V=10 \pi a^{2} b
$$
J. $$
V=4 \pi^{2} a^{2} b
$$
Answer: J
The thermal efficiency of the car engine is $35%$, and the coefficient of performance for the car's air conditioner is $3$. Calculate the energy consumed from the fuel for every $1 kJ$ of heat removed from the car interior.

Options:
A. $$
1.133 \mathrm{kJ}
$$
B. $$
0.842 \mathrm{kJ}
$$
C. $$
0.765 \mathrm{kJ}
$$
D. $$
0.889 \mathrm{kJ}
$$
E. $$
1.052 \mathrm{kJ}
$$
F. $$
1.025 \mathrm{kJ}
$$
G. $$
0.952 \mathrm{kJ}
$$
H. $$
1.201 \mathrm{kJ}
$$
I. $$
0.902 \mathrm{kJ}
$$
J. $$
1.317 \mathrm{kJ}
$$
Answer: G
There is a rubber ball, which is in a free state when the pressure of the gas inside it is the same as the atmospheric pressure, at 0.1 MPa, and the volume is $0.3 \mathrm{m}^{3}$. The balloon is heated by a flame, causing its volume to double and the pressure to increase to 0.15 MPa, assuming the pressure inside the balloon is proportional to the volume. Find the work done by the gas during this process.

Options:
A. $$
0.580kg
$$
B. $$
0.275kg
$$
C. $$
0.400kg
$$
D. $$
0.470kg
$$
E. $$
0.330kg
$$
F. $$
0.360kg
$$
G. $$
0.590kg
$$
H. $$
0.210kg
$$
I. $$
0.520kg
$$
J. $$
0.490kg
$$
Answer: F
A pump is used to pump well water from a depth of 6 meters to a water tower 30 meters above ground level, with a water flow rate of $25 \, \text{m}^3/\text{h}$, and the pump's power consumption is 12 kW. In winter, the temperature of the well water is 3.5°C, and to prevent freezing in winter, the temperature of the water entering the water tower should not be lower than $4^{\circ} \text{C}$. The entire system and pipelines are insulated with a certain thickness of insulation material. Is it necessary to install a heater in the pipeline? If necessary, how much heat needs to be added? Assume that the difference in kinetic energy of the water at the inlet and outlet of the pipeline can be neglected. The specific heat capacity of the water is $c_{p}=4.187 \, \text{kJ}/(\text{kg} \cdot \text{K})$, and the enthalpy difference of the water $\Delta h \cong c_{p} \Delta t$, with the density of water taken as 1000 kg/m³.

Options:
A. $$
1.6 {\times} 10^{4} \, \mathrm{kJ/h}
$$
B. $$
1.5 {\times} 10^{4} \, \mathrm{kJ/h}
$$
C. $$
1.7 {\times} 10^{4} \, \mathrm{kJ/h}
$$
D. $$
1.9 {\times} 10^{4} \, \mathrm{kJ/h}
$$
E. $$
2.0 {\times} 10^{4} \, \mathrm{kJ/h}
$$
F. $$
2.2 {\times} 10^{4} \, \mathrm{kJ/h}
$$
G. $$
1.2 {\times} 10^{4} \, \mathrm{kJ/h}
$$
H. $$
2.5 {\times} 10^{4} \, \mathrm{kJ/h}
$$
I. $$
1.8 {\times} 10^{4} \, \mathrm{kJ/h}
$$
J. $$
2.1 {\times} 10^{4} \, \mathrm{kJ/h}
$$
Answer: I
The pressure gauge measures the pressure of propane $\mathbf{C}_{3} \mathbf{H}_{8}$ in the storage tank as 4.4 MPa, and the temperature of the propane is $120 \mathrm{~C}$. What is the specific volume at this time? If 1000 kg of propane in this state is to be stored, what volume does the storage tank need to have?

Options:
A. $$
21.08 \mathrm{m}^{3}
$$
B. $$
18.25 \mathrm{m}^{3}
$$
C. $$
19.36 \mathrm{m}^{3}
$$
D. $$
15.72 \mathrm{m}^{3}
$$
E. $$
14.33 \mathrm{m}^{3}
$$
F. $$
13.84 \mathrm{m}^{3}
$$
G. $$
16.88 \mathrm{m}^{3}
$$
H. $$
17.45 \mathrm{m}^{3}
$$
I. $$
12.50 \mathrm{m}^{3}
$$
J. $$
20.10 \mathrm{m}^{3}
$$
Answer: G
The initial state of the $5_{\mathrm{g}}$ argon gas is $p_{1}=0.6 \mathrm{MPa}$, $T_{1}=600 \ K$. It undergoes an isentropic process expanding to a volume $V_{2}=3 V_{1}$. Argon can be considered an ideal gas, and its heat capacity can be treated as constant. Find the final temperature $T_{z}$, final pressure $p_{2}$, and the total change in entropy $\Delta S$.

Options:
A. $$
5.67 {\times} 10^{-4} \mathbf{kJ} / \mathbf{K}
$$
B. $$
1.30 {\times} 10^{-3} \mathbf{kJ} / \mathbf{K}
$$
C. $$
1.50 {\times} 10^{-3} \mathbf{kJ} / \mathbf{K}
$$
D. $$
1.14 {\times} 10^{-3} \mathbf{kJ} / \mathbf{K}
$$
E. $$
1.14 {\times} 10^{-2} \mathbf{kJ} / \mathbf{K}
$$
F. $$
1.08 {\times} 10^{-3} \mathbf{kJ} / \mathbf{K}
$$
G. $$
7.54 {\times} 10^{-3} \mathbf{kJ} / \mathbf{K}
$$
H. $$
9.87 {\times} 10^{-4} \mathbf{kJ} / \mathbf{K}
$$
I. $$
1.22 {\times} 10^{-3} \mathbf{kJ} / \mathbf{K}
$$
J. $$
1.00 {\times} 10^{-3} \mathbf{kJ} / \mathbf{K}
$$
Answer: D
In a certain nuclear power plant in southern China, the pressure of the new steam generated within the steam generator is $6.53 \ \mathrm{MPa}$, with a dryness fraction of $0.9956$. The steam flow rate is 608.47 kg/s. Assuming that the flow velocity within the main steam pipe of the steam generator does not exceed 20 m/s, determine the enthalpy of the new steam and the inner diameter of the main steam pipe of the steam generator.

Options:
A. $$
0.89 \mathrm{m}
$$
B. $$
1.18 \mathrm{m}
$$
C. $$
0.98 \mathrm{m}
$$
D. $$
1.15 \mathrm{m}
$$
E. $$
1.41 \mathrm{m}
$$
F. $$
1.33 \mathrm{m}
$$
G. $$
0.67 \mathrm{m}
$$
H. $$
1.07 \mathrm{m}
$$
I. $$
1.25 \mathrm{m}
$$
J. $$
0.75 \mathrm{m}
$$
Answer: H
The initial state of methane $\mathrm{CH_{4}}$ is given as $p_{1}=0.47 \mathrm{MPa}$, $T_{1}=393 \mathrm{K}$. It undergoes reversible isobaric cooling, releasing heat to the surroundings amounting to 4110.76 J/mol. Determine its final temperature and the change in thermodynamic energy $\Delta U_{\mathrm{m}}$ and the change in enthalpy $\Delta H_{m}$ for $1 \mathrm{mol\ CH}_{4}$. Assume the specific heat capacity of methane is approximately constant, $c_{p}=2.3298 \mathrm{kJ} / (\mathrm{kg} \cdot \mathrm{K})$.

Options:
A. $$
-3720.90 \mathrm{J / m o l}
$$
B. $$
-3910.68 \mathrm{J / m o l}
$$
C. $$
-3890.20 \mathrm{J / m o l}
$$
D. $$
-3000.34 \mathrm{J / m o l}
$$
E. $$
-4700.50 \mathrm{J / m o l}
$$
F. $$
-4110.76 \mathrm{J / m o l}
$$
G. $$
-4200.25 \mathrm{J / m o l}
$$
H. $$
-4300.12 \mathrm{J / m o l}
$$
I. $$
-4500.76 \mathrm{J / m o l}
$$
J. $$
-5000.15 \mathrm{J / m o l}
$$
Answer: F
Using a reverse Carnot engine as a heat pump to supply heat to the room, with the outside temperature at $-5^{\circ} \mathrm{C}$ and maintaining the indoor temperature at 20°C, it is required to supply $2.5 \times 10^{4} \mathrm{kJ}$ of heat per hour to the interior. How much heat is absorbed from outside per hour?

Options:
A. $$
2.501 \times10^{4} \, \mathrm{k J / h}
$$
B. $$
2.410 \times10^{4} \, \mathrm{k J / h}
$$
C. $$
3.051 \times10^{4} \, \mathrm{k J / h}
$$
D. $$
2.150 \times10^{4} \, \mathrm{k J / h}
$$
E. $$
2.735 \times10^{4} \, \mathrm{k J / h}
$$
F. $$
1.850 \times10^{4} \, \mathrm{k J / h}
$$
G. $$
1.654 \times10^{4} \, \mathrm{k J / h}
$$
H. $$
1.980 \times10^{4} \, \mathrm{k J / h}
$$
I. $$
3.120 \times10^{4} \, \mathrm{k J / h}
$$
J. $$
2.287 \times10^{4} \, \mathrm{k J / h}
$$
Answer: J
Pressure of the gas $\mathrm{NH}$ is $p=10.13 \ \mathrm{MPa}$, temperature $T=633 \mathrm{~K}$. Try to find its density using the generalized compressibility chart and compare it with the density calculated from the ideal gas equation of state.

Options:
A. $$ 29.1\mathrm{kg/m}^{3},0.976 $$
B. $$ 40.2\mathrm{kg/m}^{3},1.054 $$
C. $$
34.9\mathrm{kg/m}^{3},1.064
$$
D. $$ 32.8\mathrm{kg/m}^{3},0.999 $$
E. $$ 45.3\mathrm{kg/m}^{3},1.025 $$
F. $$ 36.7\mathrm{kg/m}^{3},1.082 $$
G. $$ 37.1\mathrm{kg/m}^{3},1.118 $$
H. $$ 38.5\mathrm{kg/m}^{3},1.092 $$
I. $$ 28.4\mathrm{kg/m}^{3},1.032 $$
J. $$ 25.7\mathrm{kg/m}^{3},0.987 $$
Answer: C
Air at pressure $p_{1}=0.3 \text{MPa}$ and temperature $t_{1}=24^{\circ} \text{C}$ is injected through a nozzle into a space with a pressure of 0.157 MPa. What type of nozzle should be used? If the air mass flow rate is $q_{m}=4 \text{kg/s}$, what should be the minimum cross-sectional area of the nozzle?

Options:
A. $$
60.72 \times 10^{-4} {\mathrm{m}}^{2}
$$
B. $$
48.28 \times 10^{-4} {\mathrm{m}}^{2}
$$
C. $$
55.19 \times 10^{-4} {\mathrm{m}}^{2}
$$
D. $$
61.83 \times 10^{-4} {\mathrm{m}}^{2}
$$
E. $$
57.43 \times1 0^{-4} {\mathrm{m}}^{2}
$$
F. $$
53.91 \times 10^{-4} {\mathrm{m}}^{2}
$$
G. $$
45.87 \times 10^{-4} {\mathrm{m}}^{2}
$$
H. $$
62.15 \times 10^{-4} {\mathrm{m}}^{2}
$$
I. $$
50.34 \times 10^{-4} {\mathrm{m}}^{2}
$$
J. $$
59.46 \times 10^{-4} {\mathrm{m}}^{2}
$$
Answer: E
An example of data from an axial flow compressor is as follows: At the compressor inlet, the air pressure is $p_{1}=0.1 \mathrm{M Pa}$, and the temperature is $t_{1}=17^{\circ} \mathrm{C}$. At the outlet, the temperature is $t_{2}=207^{\circ} \mathrm{C}$, and the pressure is $p_{2}=0.4 \mathrm{M Pa}$. The gas flow rate is $60 \mathrm{kg} / \operatorname{min}$; the power consumption is 185kW. If the compression process is adiabatic, calculate the percentage error.

Options:
A. $$
1.9 \%
$$
B. $$
4.2 \%
$$
C. $$
6.3 \%
$$
D. $$
5.5 \%
$$
E. $$
7.4 \%
$$
F. $$
8.6 \%
$$
G. $$
2.7 \%
$$
H. $$
3.1 \%
$$
I. $$
9.1 \%
$$
J. $$
0.8 \%
$$
Answer: H
A double-layer flat wall furnace composed of a 100mm thick layer of firebrick and a 100mm thick layer of regular brick has thermal conductivities of 0.9 W·m⁻¹·K⁻¹ and 0.7 W·m⁻¹·K⁻¹ for each layer, respectively. When in steady operation, the measured temperature of the inner surface of the furnace wall is 700°C.And the outer surface temperature is 130°C. To reduce heat loss from the furnace, an additional 40mm thick layer of insulation material with a thermal conductivity of 0.06 W·m⁻¹·K⁻¹ is added to the outside of the regular brick. After achieving steady operation once more, the inner surface temperature rises to 740°C, and the outermost surface temperature is recorded at 90°C, with all other conditions unchanged. Calculate the percentage reduction in heat loss from the furnace wall after adding the insulation layer compared to the original state.

Options:
A. 60.4%
B. 70.6%
C. 68.5%
D. 72.3%
E. 76.2%
F. 64.1%
G. 65.9%
H. 67.2%
I. 73.8%
J. 58.7%
Answer: C
The continuous distillation column separates a certain binary mixture. With bubble point feed, its concentration is 0.35 (mole fraction, the same hereinafter). The column top uses a total condenser, ultimately achieving a top product concentration of $x_{\mathrm{D}}=0.96$, and a bottom product concentration of$x_{\mathrm{W}}=0.025$. What is the recovery rate of the top product $D/F$?

Options:
A. 0.15
B. 0.45
C. 0.60
D. 0.55
E. 0.40
F. 0.35
G. 0.30
H. 0.25
I. 0.20
J. 0.50
Answer: F
The air enters the dryer with a temperature of 60°C, a pressure of 99.3 kPa, and a relative humidity of 10%, at a flow rate of 1500 cubic meters per hour. The moisture evaporation rate inside the dryer is 25 kilograms per hour. The air leaving the dryer has a temperature of 35°C and a pressure of 98.9 kPa. What is the relative humidity of the air leaving the dryer?

Options:
A. 48%
B. 84%
C. 95%
D. 25%
E. 62%
F. 33%
G. 90%
H. 55%
I. 78%
J. 80%
Answer: I
Two tractors move at a constant speed along a straight riverbank, pulling a barge with two cables. The tension in the two cables is 0.8 kN and 0.96 kN respectively, and the angle between the cables is 60°. Assuming the barge moves parallel to the riverbank, what are the resistance $P$ exerted by the water on the barge and the angles $\alpha$ and $\beta$ between the cables and the riverbank ?

Options:
A. $$
1. 5 8 \ \mathrm{kN}, 3 8^{\circ}, 2 4^{\circ}
$$
B. $$
1. 6 0 \ \mathrm{kN}, 2 5^{\circ}, 3 5^{\circ}
$$
C. $$
1. 5 3 \ \mathrm{kN}, 3 3^{\circ}, 2 7^{\circ}
$$
D. $$
1. 4 5 \ \mathrm{kN}, 4 5^{\circ}, 1 5^{\circ}
$$
E. $$
1. 4 2 \ \mathrm{kN}, 4 7^{\circ}, 1 3^{\circ}
$$
F. $$
1. 3 9 \ \mathrm{kN}, 4 1^{\circ}, 1 9^{\circ}
$$
G. $$
1. 6 2 \ \mathrm{kN}, 3 0^{\circ}, 3 0^{\circ}
$$
H. $$
1. 4 9 \ \mathrm{kN}, 3 9^{\circ}, 2 1^{\circ}
$$
I. $$
1. 4 7 \ \mathrm{kN}, 4 3^{\circ}, 1 7^{\circ}
$$
J. $$
1. 5 1 \ \mathrm{kN}, 3 6^{\circ}, 2 2^{\circ}
$$
Answer: C
A wind turbine has four blades, and the angle between each blade and the vertical plane of the rotation axis is $\alpha = 15^{\circ} = \operatorname{arcsin} \ 0.259$. The wind pressure acts along the normal lines of each blade's surface, and the resultant wind pressure on each blade is 1 kN, all acting at a distance of 3 m from the rotation axis. What is the rotational moment of force ?

Options:
A. $$
5 2. 4 ~ \mathrm{k N} \cdot\mathrm{m}
$$
B. $$
1 5. 3 ~ \mathrm{k N} \cdot\mathrm{m}
$$
C. $$
0 9. 7 ~ \mathrm{k N} \cdot\mathrm{m}
$$
D. $$
2 7. 8 ~ \mathrm{k N} \cdot\mathrm{m}
$$
E. $$
2 5. 5 ~ \mathrm{k N} \cdot\mathrm{m}
$$
F. $$
4 3. 6 ~ \mathrm{k N} \cdot\mathrm{m}
$$
G. $$
6 4. 2 ~ \mathrm{k N} \cdot\mathrm{m}
$$
H. $$
1 8. 9 ~ \mathrm{k N} \cdot\mathrm{m}
$$
I. $$
3 1. 1 ~ \mathrm{k N} \cdot\mathrm{m}
$$
J. $$
4 9. 4 ~ \mathrm{k N} \cdot\mathrm{m}
$$
Answer: I
An object oscillates around a fixed axis, with its angle represented by the equation
$$
\varphi = 20^\circ \sin \psi
$$
where $\psi = 2t$ (with $\psi$ in degrees and $t$ in seconds). What are the angular velocity of this object at $t = 0$, and the first two moments $t_{1}, t_{2}$ when the direction of rotation changes, as well as the period of oscillation $T$ ?

Options:
A. $${\frac{\pi^{2}} {8 6 0}} \ \mathrm{r a d / s}, 4 9 \ \mathrm{s},1 2 9 \ \mathrm{s}, \,2 0 5 \ \mathrm{s}$$
B. $${\frac{\pi^{2}} {1 5 1 0}} \ \mathrm{r a d / s}, 6 5 \ \mathrm{s},1 0 5 \ \mathrm{s}, \,1 7 0 \ \mathrm{s}$$
C. $${\frac{\pi^{2}} {9 1 5}} \ \mathrm{r a d / s}, 4 7 \ \mathrm{s},1 4 7 \ \mathrm{s}, \,1 8 2 \ \mathrm{s}$$
D. $${\frac{\pi^{2}} {7 1 0}} \ \mathrm{r a d / s}, 5 0 \ \mathrm{s},1 4 0 \ \mathrm{s}, \,1 7 5 \ \mathrm{s}$$
E. $${\frac{\pi^{2}} {8 1 0}} \ \mathrm{r a d / s}, 4 5 \ \mathrm{s},1 3 5 \ \mathrm{s}, \,1 8 0 \ \mathrm{s}$$
F. $${\frac{\pi^{2}} {9 1 0}} \ \mathrm{r a d / s}, 4 8 \ \mathrm{s},1 2 8 \ \mathrm{s}, \,1 9 5 \ \mathrm{s}$$
G. $${\frac{\pi^{2}} {7 9 0}} \ \mathrm{r a d / s}, 3 9 \ \mathrm{s},1 3 1 \ \mathrm{s}, \,1 9 2 \ \mathrm{s}$$
H. $${\frac{\pi^{2}} {1 0 1 0}} \ \mathrm{r a d / s}, 3 5 \ \mathrm{s},1 2 5 \ \mathrm{s}, \,2 0 0 \ \mathrm{s}$$
I. $${\frac{\pi^{2}} {8 2 0}} \ \mathrm{r a d / s}, 4 0 \ \mathrm{s},1 3 3 \ \mathrm{s}, \,1 8 5 \ \mathrm{s}$$
J. $${\frac{\pi^{2}} {1 2 1 0}} \ \mathrm{r a d / s}, 5 5 \ \mathrm{s},1 5 5 \ \mathrm{s}, \,1 9 0 \ \mathrm{s}$$
Answer: E
The trolley travels on a horizontal straight track at a speed of $v=5 \mathrm{~m/s}$, while simultaneously vibrating on a spring with an amplitude of $a=0.008 \mathrm{~m}$ and a period of $T=0.5$ s. It is known that the average distance from the center of mass of the trolley to the road surface is $h=1.5 \mathrm{~m}$. At $t=0$, the center of mass is at its average position, and the vibration velocity is upward. What is the trajectory equation of the center of mass? ( The $Ox$ axis runs along the horizontal track and points in the direction of travel, while the $Oy$ axis passes through the instantaneous position of the center of mass at $t=0$ and points vertically upward. )

Options:
A. $$1.5+0.0008\sin0.8\pi t$$
B. $$1.5+0.0008\sin0.8\pi \omega t$$
C. $$1.5+0.0004\sin0.8\pi x$$
D. $$1.5+0.0008\cos1.6\pi t$$
E. $$1.5+0.0008\sin1.6\pi x$$
F. $$1.5+0.0008\sin0.4\pi x$$
G. $$1.5+0.0016\sin0.8\pi x$$
H. $$1.5+0.0008\cos0.8\pi x$$
I. $$1.5+0.0008\sin0.8\pi y$$
J. $$1.5+0.0008\sin0.8\pi x$$
Answer: J
A military train with a mass of 200 tons is traveling along a horizontal straight track with an acceleration of 0.2 m/s². The resistance due to axle friction is 0.01 times the weight of the train, independent of speed. Assuming the initial speed of the train is 18 m/s, what is the locomotive's power at $t = 10$ s ?

Options:
A. $$1180kW$$
B. $$1355kW$$
C. $$1105kW$$
D. $$1320kW$$
E. $$1250kW$$
F. $$1140kW$$
G. $$1400kW$$
H. $$1155kW$$
I. $$1225kW$$
J. $$1192kW$$
Answer: J
The mass of the vertical engine is $M = 10^4 \, \mathrm{kg}$, with a base area of $S = 100 \, \mathrm{m}^2$, and the specific stiffness of the soil under the base is $\lambda = 490 \, \mathrm{kN/m^3}$. The length of the engine's crank is $r = 30 \, \mathrm{cm}$, the length of the connecting rod is $l = 180 \, \mathrm{cm}$, and the angular velocity of the shaft is $\omega = 8 \pi \, \mathrm{rad/s}$. The mass of the piston and the unbalanced portion involved in reciprocating motion is $m = 250 \, \mathrm{kg}$, and the crank is considered balanced with counterweights. The mass of the connecting rod is neglected. To ensure that the amplitude of vertical forced vibration of the base does not exceed 0.25 mm, the weight $G$ of the base is ().

Options:
A. $$4050.0kg$$
B. $$3630.4kg$$
C. $$4478.5kg$$
D. $$3741.6kg$$
E. $$3219.3kg$$
F. $$3592.7kg$$
G. $$3985.9kg$$
H. $$4260.8kg$$
I. $$3152.5kg$$
J. $$3389.1kg$$
Answer: F
Given the stream function $\psi = x^{2} + xy - y^{2}$ of an irrotational flow that is known to be incompressible, its velocity potential $\phi$ is ().

Options:
A. $$
\varphi=\frac{1} {4} \left( y^{2}+x^{2} \right)+2 y x+\mathrm{c o n s t}
$$
B. $$
\varphi=\frac{1} {2} \left( 2y-x^{2} \right)+y^{2}+\mathrm{c o n s t}
$$
C. $$
\varphi=\left( x^{2}-2 y^{2} \right)+y x+\mathrm{c o n s t}
$$
D. $$
\varphi=x y+\frac{3} {2} \left( y^{2}-x^{2} \right)+\mathrm{c o n s t}
$$
E. $$
\varphi=\frac{1} {2} \left( x y+y^{2} \right)-x^{2}+\mathrm{c o n s t}
$$
F. $$
\varphi=-\frac{1} {2} \left( y^{2}-x^{2} \right)+x y+\mathrm{c o n s t}
$$
G. $$
\varphi=\left( xy-y^{2} \right)+2 x^{2}+\mathrm{c o n s t}
$$
H. $$
\varphi=\frac{1} {2} \left( y^{2}+x^{2} \right)-3 y x+\mathrm{c o n s t}
$$
I. $$
\varphi=\frac{1} {2} \left( x^{2}-y^{2} \right)-2 x y+\mathrm{c o n s t}
$$
J. $$
\varphi=\frac{1} {3} x^{2}+y^{2}-2 y x+\mathrm{c o n s t}
$$
Answer: I
In the air, there is a spherical water droplet with a radius of $a$, and the densities of water and air are $\rho_{1}$ and $\rho$, respectively. Find the acceleration of the falling water droplet, assuming the flow is ideal, incompressible, and irrotational is ().

Options:
A. $$
\dot{V}_{0}=\frac{2 \left( \rho_{1}\cdot\dot{\rho} \right)} {\rho+ \rho_{1}} g
$$
B. $$
\dot{V}_{0}=\frac{2 \left( \rho_{1}-\dot{\rho} \right)} {\rho-\rho_{1}} g
$$
C. $$
\dot{V}_{0}=\frac{\left( \rho_{1}-\dot{\rho} \right)} {\rho+\rho_{1}} g
$$
D. $$
\dot{V}_{0}=\frac{\left( 2\rho_{1}-\dot{\rho} \right)} {2\rho+ \rho_{1}} g
$$
E. $$
\dot{V}_{0}=\frac{\left( \rho_{1}-2\dot{\rho} \right)} {\rho+2 \rho_{1}} g
$$
F. $$
\dot{V}_{0}=\frac{2 \left( \rho_{1}-\dot{\rho} \right)} {2\rho+ \rho_{1}} g
$$
G. $$
\dot{V}_{0}=\frac{3 \left( \rho_{1}+\dot{\rho} \right)} {\rho+2 \rho_{1}} g
$$
H. $$
\dot{V}_{0}=\frac{2 \left( \rho_{1}+\dot{\rho} \right)} {\rho+\dot{\rho}} g
$$
I. $$
\dot{V}_{0}=\frac{4 \left( \rho_{1}-2\dot{\rho} \right)} {\rho+2 \rho_{1}} g
$$
J. $$
\dot{V}_{0}=\frac{2 \left( \rho_{1}-\dot{\rho} \right)} {\rho+2 \rho_{1}} g
$$
Answer: J
The normal shock wave propagates toward a wall at $D=514.5 \mathrm{m/s}$ in still air at 20°C. If the wall is stationary, what is the propagation speed $D^{\prime}$ of the reflected wave?

Options:
A. 273.4m/s
B. 521.7m/s
C. 412.6m/s
D. 238.2m/s
E. 525.9m/s
F. 446.1m/s
G. 289.9m/s
H. 498.3m/s
I. 260.7m/s
J. 378.5m/s
Answer: D
A newly cast iron pipe placed horizontally, 120 meters long, with a diameter of 0.1 meters, has oil flowing through it with a kinematic viscosity of $\boldsymbol{v}=1 \times 10^{-5} \mathbf{m^{2}} / \mathbf{s}$. The pressure loss is equivalent to a 5-meter oil column height. the flow rate is ().

Options:
A. 16.1l/s
B. 10.5l/s
C. 11.6l/s
D. 9.4l/s
E. 12.6l/s
F. 14.2l/s
G. 18.0l/s
H. 13.6l/s
I. 15.5l/s
J. 20.3l/s
Answer: E
A hydrofoil with a water depth of $h$ and circulation $\varGamma$ moves horizontally to the left at a constant speed $V_\infty$. Assuming it can be considered as a point vortex moving underwater with infinite water depth, the wave energy $W_{1}$ transferred across the vertical cross-section per unit time is ().

Options:
A. $$
W_{1}=\frac{\Gamma \rho g} {V_{\infty} h} \mathrm{e x p} \Big(-\frac{1} {F_{r}^{2}} \Big)
$$
B. $$
W_{1}=\frac{\Gamma \rho g} {V_{\infty}} \mathrm{e x p} \Big(-\frac{2} {F_{r}^{3}} \Big)
$$
C. $$
W_{1}=\frac{\Gamma^{3} \rho} {V_{\infty}} \mathrm{e x p} \Big(-\frac{3} {F_{r}^{2}} \Big)
$$
D. $$
W_{1}=\frac{\Gamma^{2} \rho g h} {V_{\infty}^{2}} \mathrm{e x p} \Big(-\frac{1} {F_{r}^{2}} \Big)
$$
E. $$
W_{1}=\frac{\Gamma^{2} \rho g} {h} \mathrm{e x p} \Big(-\frac{2} {F_{r}} \Big)
$$
F. $$
W_{1}=\frac{\Gamma^{2} \rho g} {V_{\infty}} \mathrm{e x p} \Big(-\frac{2} {F_{r}^{2}} \Big)
$$
G. $$
W_{1}=\frac{\Gamma^{2} g} {V_{\infty}} \mathrm{e x p} \Big(-\frac{2} {F_{r}^{2}} \Big)
$$
H. $$
W_{1}=\frac{\Gamma^{2} \rho} {V_{\infty} h} \mathrm{e x p} \Big(-\frac{3} {F_{r}} \Big)
$$
I. $$
W_{1}=\frac{\Gamma^{2} \rho} {V_{\infty}} \mathrm{e x p} \Big(-\frac{2} {F_{r}^{3}} \Big)
$$
J. $$
W_{1}=\frac{\Gamma \rho g h} {V_{\infty}} \mathrm{e x p} \Big(-\frac{1} {F_{r}^{2}} \Big)
$$
Answer: F
The total weight of the oil barrel is 300 kg, with a barrel diameter of 0.6 m and a height of 1.2 m. What is the density of the machine oil ?

Options:
A. $$
\rho=8 4 4 \mathrm{k g} / \mathrm{m}^{3}
$$
B. $$
\rho=8 5 0 \mathrm{k g} / \mathrm{m}^{3}
$$
C. $$
\rho=8 9 0 \mathrm{k g} / \mathrm{m}^{3}
$$
D. $$
\rho=7 6 0 \mathrm{k g} / \mathrm{m}^{3}
$$
E. $$
\rho=9 5 0 \mathrm{k g} / \mathrm{m}^{3}
$$
F. $$
\rho=9 1 0 \mathrm{k g} / \mathrm{m}^{3}
$$
G. $$
\rho=8 2 0 \mathrm{k g} / \mathrm{m}^{3}
$$
H. $$
\rho=8 0 0 \mathrm{k g} / \mathrm{m}^{3}
$$
I. $$
\rho=7 8 5 \mathrm{k g} / \mathrm{m}^{3}
$$
J. $$
\rho=9 3 5 \mathrm{k g} / \mathrm{m}^{3}
$$
Answer: A
Nozzle diameter d = 75mm, water pipe diameter D = 150mm, water gun tilt angle $\theta = 30°$, pressure gauge reading h = 3m water column. The jet diameter $d^{\prime}$ at the highest point is ().

Options:
A. 95mm
B. 73mm
C. 67mm
D. 54mm
E. 85mm
F. 81mm
G. 90mm
H. 79mm
I. 77mm
J. 82mm
Answer: F