MikaStars39/nano-eval huggingface dataset:
The patient, a female, was admitted to the hospital with comminuted fractures of the femur and fibula due to a car accident. She was diagnosed with breast cancer six months ago. After admission, symptomatic and supportive treatment was provided. Two days later, the patient's vital signs were stable, and her general condition was good. At 6 p.m., she suddenly experienced difficulty breathing, lost consciousness, and died swiftly. The cause of death may have been ( ).

Options:
A. Pulmonary embolism
B. Septic shock
C. Air embolism
D. Hemorrhagic shock
E. Cardiac arrest
F. Pulmonary edema
G. Stroke embolism
H. Hypovolemic shock
I. Myocardial infarction
J. Fat embolism
Answer: J
The patient, a 28-day-old female, was found to have a large low-density mass with irregular enhanced margins in the left lobe of the liver on CT, accompanied by abnormal liver function. Surgery revealed an $8cm\times8cm\times8cm$ mass with unclear boundaries and no capsule. Pathological examination showed a purple-red cut surface of the mass, and microscopy revealed numerous dilated thin-walled blood vessels filled with blood, with flat endothelial cells lining the lumens. What is the possible diagnosis?

Options:
A. Hepatic cyst
B. Bile duct hamartoma
C. Cholangiocarcinoma
D. Focal nodular hyperplasia
E. Hepatic hemangioma
F. Cavernous hemangioma
G. Fibrolamellar carcinoma
H. Liver adenoma
I. Metastatic colon cancer
J. Hepatocellular carcinoma
Answer: F
A word consisting of the letters A, B, C, D is encoded using binary pulses for transmission, with 00 representing A, 01 representing B, 10 representing C, and 1 representing D. Each pulse has a width of 5ms. When different letters appear with equal probability, calculate the average information transmission rate.

Options:
A. $$
R_{b}=R_{\mathrm{B}} \times G ( x )=1 7 5 \mathrm{b i t} / \mathrm{s}
$$
B. $$
R_{b}=R_{\mathrm{B}} \times H ( y )=1 5 0 \mathrm{b i t} / \mathrm{s}
$$
C. $$
R_{a}=R_{\mathrm{B}} \times H ( x )=2 7 5 \mathrm{b i t} / \mathrm{s}
$$
D. $$
R_{b}=R_{\mathrm{C}} \times H ( x )=3 0 0 \mathrm{b i t} / \mathrm{s}
$$
E. $$
R_{x}=R_{\mathrm{B}} \times H ( x )=1 2 5 \mathrm{b i t} / \mathrm{s}
$$
F. $$
R_{b}=R_{\mathrm{B}} \times H ( x )=2 0 0 \mathrm{b i t} / \mathrm{s}
$$
G. $$
R_{b}=R_{\mathrm{C}} \times H ( z )=3 5 0 \mathrm{b i t} / \mathrm{s}
$$
H. $$
R_{b}=R_{\mathrm{B}} \times H ( x )=2 5 0 \mathrm{b i t} / \mathrm{s}
$$
I. $$
R_{c}=R_{\mathrm{B}} \times H ( x )=1 0 0 \mathrm{b i t} / \mathrm{s}
$$
J. $$
R_{d}=R_{\mathrm{B}} \times H ( x )=5 0 0 \mathrm{b i t} / \mathrm{s}
$$
Answer: F
Let $\eta(t) = \xi(t) \cos(\omega_{c} t + \theta)$, where $\xi(t)$ and $\theta$ are statistically independent. $\xi(t)$ is a zero-mean stationary random process, with an autocorrelation function and power spectral density given by $R_{\ell}(\tau)$ and $P_{\ell}(\omega)$, respectively. If $\theta$ is uniformly distributed over $(0, 2\pi)$, determine the mean, autocorrelation function, and power spectral density of $\eta(t)$.

Options:
A. The mean $a_{\eta} = 0$, the autocorrelation function $R_{\eta} (\tau) = \frac{1}{2} R_{\xi} (\tau) \cos \omega_{0} \tau$, and the power spectral density $P_{\eta} (\omega)$
$$
= \frac{P_{\xi} (\omega+\omega_{0})+P_{\xi} (\omega-\omega_{0})}{4}
$$
B. The mean $a_{\eta} = \omega_{c}$, the autocorrelation function $R_{\eta} (\tau) = \frac{1}{2} R_{\xi} (\tau) \cdot \cos \omega_{c} \tau$, and the power spectral density $P_{\eta} (\omega)$
$$
= P_{\xi} (\omega+\omega_{0}) - P_{\xi} (\omega-\omega_{0})
$$
C. The mean $a_{\eta} = \omega_{0}$, the autocorrelation function $R_{\eta} (\tau) = \frac{1}{2} R_{\xi} (\tau) \cos \theta \tau$, and the power spectral density $P_{\eta} (\omega)$
$$
= \frac{P_{\xi} (\omega+\omega_{0})}{4} + \frac{P_{\xi} (\omega-\omega_{0})}{4}
$$
D. The mean $a_{\eta} = 0$, the autocorrelation function $R_{\eta} (\tau) = \frac{1}{3} R_{\xi} (\tau) \cos \omega_{0} \tau$, and the power spectral density $P_{\eta} (\omega)$
$$
= \frac{P_{\xi} (\omega+\omega_{c})+P_{\xi} (\omega-\omega_{c})}{2}
$$
E. The mean $a_{\eta} = \theta$, the autocorrelation function $R_{\eta} (\tau) = R_{\xi} (\tau)$, and the power spectral density $P_{\eta} (\omega)$
$$
= P_{\xi} (\omega+\omega_{0}) + P_{\xi} (\omega-\omega_{0})
$$
F. The mean $a_{\eta} = 1$, the autocorrelation function $R_{\eta} (\tau) = \frac{1}{2} R_{\xi} (\tau) \sin \omega_{0} \tau$, and the power spectral density $P_{\eta} (\omega)$
$$
= \frac{2P_{\xi} (\omega+\omega_{0})}{4} + \frac{2P_{\xi} (\omega-\omega_{0})}{4}
$$
G. The mean $a_{\eta} = 0$, the autocorrelation function $R_{\eta} (\tau) = \frac{1}{2} R_{\xi} (\tau) + \cos \omega_{0} \tau$, and the power spectral density $P_{\eta} (\omega)$
$$
= \frac{P_{\xi} (\omega+\omega_{c}) \cdot P_{\xi} (\omega-\omega_{c})}{4}
$$
H. The mean $a_{\eta} = \sin \theta$, the autocorrelation function $R_{\eta} (\tau) = R_{\xi} (\tau) \cdot \cos \omega_{0} \tau$, and the power spectral density $P_{\eta} (\omega)$
$$
= \frac{P_{\xi} (\omega+\omega_{c})-P_{\xi} (\omega-\omega_{c})}{4}
$$
I. The mean $a_{\eta} = \cos \theta$, the autocorrelation function $R_{\eta} (\tau) = R_{\xi} (\tau) + 1$, and the power spectral density $P_{\eta} (\omega)$
$$
= \frac{2P_{\xi} (\omega+\omega_{0})}{4} - \frac{2P_{\xi} (\omega-\omega_{0})}{4}
$$
J. The mean $a_{\eta} = 0$, the autocorrelation function $R_{\eta} (\tau) = \frac{2}{3} R_{\xi} (\tau) \cos \omega_{c} \tau$, and the power spectral density $P_{\eta} (\omega)$
$$
= P_{\xi} (\omega+\omega_{0}) \cdot P_{\xi} (\omega-\omega_{0})
$$
Answer: A
Given a 100% single-tone modulated AM signal and an SSB signal, they are demodulated using an envelope detector and a coherent demodulator, respectively. If the power of the SSB signal at the input of the demodulator is 5 mW, what should be the input power of the AM signal to ensure that the output signal power is the same?

Options:
A. $1.875mW$
B. $3.000mW$
C. $4.000mW$
D. $5.000mW$
E. $2.500mW$
F. $4.500mW$
G. $2.000mW$
H. $2.250mW$
I. $3.350mW$
J. $3.750mW$
Answer: A
Given the signal \( $m(t) = 10 \cos 20 \pi t \cos 200 \pi t$\), assuming the sampling rate is \( $f_{s}$ \), perform ideal sampling on the signal to obtain the sampled signal \( $m_{s}(t)$ \). After passing \( $m_{s}(t)$ \) through an ideal low-pass filter with a cutoff frequency of \( $f_{c}$ \), the output is still \( m(t) \). Determine the range of values for \( $f_{c}$ \) .

Options:
A. $90Hz$
B. $180Hz$
C. $100Hz$
D. $170Hz$
E. $160Hz$
F. $120Hz$
G. $140Hz$
H. $150Hz$
I. $130Hz$
J. $110Hz$
Answer: J
The maximum and minimum quantization intervals in the thirteen-segment quantization of $A$ differ by _ times.

Options:
A. 52
B. 48
C. 36
D. 60
E. 58
F. 50
G. 44
H. 56
I. 62
J. 64
Answer: J
Given that a 12-channel carrier telephone occupies the frequency range of $60 \sim 108 \mathrm{Hz}$, determine its minimum sampling frequency $f_{\operatorname* {min}}$.

Options:
A. $$
f_{\mathrm{s m i n}}=1 2 0 \mathrm{k H z}
$$
B. $$
f_{\mathrm{s m i n}}=9 6 \mathrm{k H z}
$$
C. $$
f_{\mathrm{s m i n}}=7 8 \mathrm{k H z}
$$
D. $$
f_{\mathrm{s m i n}}=1 4 0 \mathrm{k H z}
$$
E. $$
f_{\mathrm{s m i n}}=8 0 \mathrm{k H z}
$$
F. $$
f_{\mathrm{s m i n}}=1 0 0 \mathrm{k H z}
$$
G. $$
f_{\mathrm{s m i n}}=1 0 8 \mathrm{k H z}
$$
H. $$
f_{\mathrm{s m i n}}=9 0 \mathrm{k H z}
$$
I. $$
f_{\mathrm{s m i n}}=6 6 \mathrm{k H z}
$$
J. $$
f_{\mathrm{s m i n}}=1 1 0 \mathrm{k H z}
$$
Answer: G
Given that $n(t)$ is the output of a narrowband filter with a center frequency of $f_{\mathrm{c}}$, applied to white noise $n_{\mathrm{w}}(t)$, and the power of $n(t)$ is $P_{1 \circ}$, if $n(t)$ is coherently demodulated with the carrier $2 \cos 2 \pi f_{\mathrm{e}} t$, what is the noise power at the output of the demodulator?

Options:
A. $$
P_{2.5}
$$
B. $$
P_{3}
$$
C. $$
P_{1}
$$
D. $$
P_{6.5}
$$
E. $$
P_{5}
$$
F. $$
P_{7}
$$
G. $$
P_{2}
$$
H. $$
P_{0}
$$
I. $$
P_{1.5}
$$
J. $$
P_{4}
$$
Answer: C
Given that the transmission rate of the octal number signal is 1000B, determine its transmission rate. If the code rate remains unchanged and the system is changed to binary transmission, what would the transmission rate be then?

Options:
A. $$
R_{b}=1 0 0 0 \times\operatorname{l o g}_{3} 2=1 5 2 0 \mathrm{b p s}_{\circ}
$$
B. $$
R_{b}=1 0 0 0 \times\operatorname{l o g}_{1 0} 2=2 3 1 0 \mathrm{b p s}_{\circ}
$$
C. $$
R_{b}=1 0 0 0 \times\operatorname{l o g}_{6} 2=8 0 0 \mathrm{b p s}_{\circ}
$$
D. $$
R_{b}=1 0 0 0 \times\operatorname{l o g}_{2} 1=0 \mathrm{b p s}_{\circ}
$$
E. $$
R_{b}=1 0 0 0 \times\operatorname{l o g}_{8} 2=5 0 0 \mathrm{b p s}_{\circ}
$$
F. $$
R_{b}=1 0 0 0 \times\operatorname{l o g}_{4} 8=1 5 0 0 \mathrm{b p s}_{\circ}
$$
G. $$
R_{b}=1 0 0 0 \times\operatorname{l o g}_{2} 8=3 0 0 0 \mathrm{b p s}_{\circ}
$$
H. $$
R_{b}=1 0 0 0 \times\operatorname{l o g}_{2} 2=1 0 0 0 \mathrm{b p s}_{\circ}
$$
I. $$
R_{b}=1 0 0 0 \times\operatorname{l o g}_{1} 2=undefined \mathrm{b p s}_{\circ}
$$
J. $$
R_{b}=1 0 0 0 \times\operatorname{l o g}_{2} 5=1 6 2 0 \mathrm{b p s}_{\circ}
$$
Answer: H
A 250V DC motor with a power rating of 5kW is powered by a three-phase bridge fully controlled rectifier circuit. The armature resistance is $R_{a}=5 \Omega$, the inductance $L_{\mathrm{B}}=1 \, \mathrm{mH}$, and the firing angle $\alpha=60^{\circ}$. Assuming the smoothing reactor is sufficiently large, find the output voltage $U_{2}$ and the back electromotive force $E$.

Options:
A. $$
U_{2}=2 0 5. 4 \mathrm{V}
$$
$$
E=1 4 8 \mathrm{V}
$$
B. $$
U_{2}=2 4 5. 6 \mathrm{V}
$$
$$
E=1 3 0 \mathrm{V}
$$
C. $$
U_{2}=2 0 0. 0 \mathrm{V}
$$
$$
E=1 4 0 \mathrm{V}
$$
D. $$
U_{2}=2 3 0. 5 \mathrm{V}
$$
$$
E=1 6 0 \mathrm{V}
$$
E. $$
U_{2}=2 2 5. 0 \mathrm{V}
$$
$$
E=1 5 5 \mathrm{V}
$$
F. $$
U_{2}=2 1 0. 0 \mathrm{V}
$$
$$
E=1 3 5 \mathrm{V}
$$
G. $$
U_{2}=2 5 0. 8 \mathrm{V}
$$
$$
E=1 4 5 \mathrm{V}
$$
H. $$
U_{2}=2 1 8. 8 \mathrm{V}
$$
$$
E=1 5 0 \mathrm{V}
$$
I. $$
U_{2}=2 4 0. 0 \mathrm{V}
$$
$$
E=1 6 5 \mathrm{V}
$$
J. $$
U_{2}=2 1 5. 0 \mathrm{V}
$$
$$
E=1 5 2 \mathrm{V}
$$
Answer: H
There are two thyristors with equivalent resistances in the blocking state of $1M\Omega$ and $2M\Omega$, respectively. When these two thyristors are connected in series into a circuit with a voltage of $1kV$, calculate the voltage each thyristor bears. If parallel equalizing resistors are used to make the voltage error between the two devices less than 10%, find the value of the equalizing resistors.

Options:
A. $$
R_{p}=2 0 0 \mathbf{k} \Omega
$$
B. $$
R_{p}=3 0 0 \mathbf{k} \Omega
$$
C. $$
R_{p}=1 5 0 \mathbf{k} \Omega
$$
D. $$
R_{p}=2 7 5 \mathbf{k} \Omega
$$
E. $$
R_{p}=4 0 0 \mathbf{k} \Omega
$$
F. $$
R_{p}=3 5 0 \mathbf{k} \Omega
$$
G. $$
R_{p}=1 0 0 \mathbf{k} \Omega
$$
H. $$
R_{p}=5 0 0 \mathbf{k} \Omega
$$
I. $$
R_{p}=2 5 0 \mathbf{k} \Omega
$$
J. $$
R_{p}=2 2 5 \mathbf{k} \Omega
$$
Answer: I
An ideal Boost-Buck conversion circuit, with a chopping frequency of 25kHz; if $U_{S}$ varies from 8V to 36V, and the aim is to maintain $U_O$ = 15V with continuous current, try to calculate the range of the duty cycle $\rho$.

Options:
A. $$
0. 5 1 4 < \rho< 0. 6 2 8
$$
B. $$
0. 1 4 6 < \rho< 0. 2 4 0
$$
C. $$
0. 6 5 2 < \rho< 0. 7 1 4
$$
D. $$
0. 9 0 5 < \rho< 0. 9 8 3
$$
E. $$
0. 2 9 8 < \rho< 0. 3 6 7
$$
F. $$
0. 4 7 5 < \rho< 0. 5 8 9
$$
G. $$
0. 3 3 1 < \rho< 0. 4 0 7
$$
H. $$
0. 6 9 1 < \rho< 0. 7 5 3
$$
I. $$
0. 7 5 9 < \rho< 0. 8 2 1
$$
J. $$
0. 8 4 2 < \rho< 0. 9 1 6
$$
Answer: C
A step-down chopper circuit aims to control and maintain a constant output voltage of $U_{O} = 8V$ through the duty cycle $\rho$, and desires output power $P_{O} \geq 8W$. With a chopping frequency of 20kHz, calculate the minimum inductance $L_{m}$ required to keep the converter operating in continuous conduction mode, with the power supply voltage $U_{s}$ ranging from 16V to 48V.

Options:
A. $$
8 0 0 ( \mu\mathrm{H} )
$$
B. $$
7 5 ( \mu\mathrm{H} )
$$
C. $$
2 0 0 ( \mu\mathrm{H} )
$$
D. $$
1 0 0 ( \mu\mathrm{H} )
$$
E. $$
5 0 ( \mu\mathrm{H} )
$$
F. $$
3 5 0 ( \mu\mathrm{H} )
$$
G. $$
1 5 ( \mu\mathrm{H} )
$$
H. $$
6 5 0 ( \mu\mathrm{H} )
$$
I. $$
4 5 0 ( \mu\mathrm{H} )
$$
J. $$
1 2 5 ( \mu\mathrm{H} )
$$
Answer: D
Single-phase fully-controlled bridge rectifier circuit with back electromotive force and resistive-inductive load, $U_{2}=100 \text{V}$, $R=1\Omega$, the inductance L is extremely large, $E_{\mathrm{M}}=40\text{V}$, $L_{\mathrm{B}}=0.5\text{mH}$, calculate the values of $U_{\mathrm{d}}$, $I_{\mathrm{d}}$, and $\gamma$ when $\alpha=60^{\circ}$.

Options:
A. $$
I_{\mathrm{d}} \approx5. 1 0 \mathrm{A}
$$
$$
U_{\mathrm{d}} \approx5 0. 0 0 \mathrm{V}
$$
$$
\lambda\approx0. 8 8^{\circ}
$$
B. $$
I_{\mathrm{d}} \approx4. 6 5 \mathrm{A}
$$
$$
U_{\mathrm{d}} \approx4 5. 5 0 \mathrm{V}
$$
$$
\lambda\approx0. 9 5^{\circ}
$$
C. $$
I_{\mathrm{d}} \approx4. 9 5 \mathrm{A}
$$
$$
U_{\mathrm{d}} \approx4 8. 5 5 \mathrm{V}
$$
$$
\lambda\approx0. 9 8^{\circ}
$$
D. $$
I_{\mathrm{d}} \approx5. 2 0 \mathrm{A}
$$
$$
U_{\mathrm{d}} \approx4 9. 0 0 \mathrm{V}
$$
$$
\lambda\approx0. 7 0^{\circ}
$$
E. $$
I_{\mathrm{d}} \approx4. 3 5 \mathrm{A}
$$
$$
U_{\mathrm{d}} \approx4 3. 5 0 \mathrm{V}
$$
$$
\lambda\approx1. 1 0^{\circ}
$$
F. $$
I_{\mathrm{d}} \approx4. 8 0 \mathrm{A}
$$
$$
U_{\mathrm{d}} \approx4 7. 0 0 \mathrm{V}
$$
$$
\lambda\approx1. 0 5^{\circ}
$$
G. $$
I_{\mathrm{d}} \approx4. 5 5 \mathrm{A}
$$
$$
U_{\mathrm{d}} \approx4 4. 5 5 \mathrm{V}
$$
$$
\lambda\approx0. 8 3^{\circ}
$$
H. $$
I_{\mathrm{d}} \approx5. 0 5 \mathrm{A}
$$
$$
U_{\mathrm{d}} \approx5 0. 5 5 \mathrm{V}
$$
$$
\lambda\approx0. 9 0^{\circ}
$$
I. $$
I_{\mathrm{d}} \approx4. 7 5 \mathrm{A}
$$
$$
U_{\mathrm{d}} \approx4 6. 5 0 \mathrm{V}
$$
$$
\lambda\approx1. 0 0^{\circ}
$$
J. $$
I_{\mathrm{d}} \approx4. 4 5 \mathrm{A}
$$
$$
U_{\mathrm{d}} \approx4 4. 0 0 \mathrm{V}
$$
$$
\lambda\approx1. 2 5^{\circ}
$$
Answer: G
Three-phase bridge converter circuit, given $U_{2 L}=230 \mathrm{V}$, with back electromotive force and inductive-resistive load, main circuit resistance $R=0.8 \Omega$, $L=\infty$. Assuming continuous and smooth current, when $E_{\mathrm{M}}=-290 \mathrm{V}$ and $\beta=30^{\circ}$, calculate the average output current and the effective value of the output current (neglecting harmonics).

Options:
A. $$
I_{d} \approx3 0 ( \mathrm{A} ),
$$
$$
I \approx3 0 ( \mathrm{A} )
$$
B. $$
I_{d}\approx9 9 ( \mathrm{A} ),
$$
$$
I \approx9 9 ( \mathrm{A} )
$$
C. $$
I_{d}\approx1 8 ( \mathrm{A} ),
$$
$$
I \approx1 8 ( \mathrm{A} )
$$
D. $$
I_{d}\approx5 0 ( \mathrm{A} ),
$$
$$
I \approx5 0 ( \mathrm{A} )
$$
E. $$
I_{d}\approx4 2 ( \mathrm{A} ),
$$
$$
I \approx4 2 ( \mathrm{A} )
$$
F. $$
I_{d}\approx2 6 ( \mathrm{A} ),
$$
$$
I \approx2 6 ( \mathrm{A} )
$$
G. $$
I_{d}\approx1 2 ( \mathrm{A} ),
$$
$$
I \approx1 2 ( \mathrm{A} )
$$
H. $$
I_{d}\approx1 0 ( \mathrm{A} ),
$$
$$
I \approx1 0 ( \mathrm{A} )
$$
I. $$
I_{d}\approx2 2 ( \mathrm{A} ),
$$
$$
I \approx2 2 ( \mathrm{A} )
$$
J. $$
I_{d}\approx3 5 ( \mathrm{A} ),
$$
$$
I \approx3 5 ( \mathrm{A} )
$$
Answer: F
Traffic is flowing smoothly on a six-lane highway at a speed of 80 km/h. There's a four-lane bridge on the road, with a lane capacity of 1,940 vehicles per hour. During peak hours, the traffic flow is 4,200 vehicles per hour (one-way). In the transition section, the speed drops to 22 km/h. This situation lasted for 1.69 hours, after which the traffic flow reduced to 1,956 vehicles per hour (one-way).
Try to estimate the average queue length of vehicles in front of the bridge during the 1.69 hours and the total blocking time for the entire process is().

Options:
A. 1.99(km),2.12(h)
B. 3.01(km),1.68(h)
C. 3.15(km),2.10(h)
D. 2.30(km),1.65(h)
E. 2.50(km),1.60(h)
F. 2.25(km),1.75(h)
G. 1.85(km),1.90(h)
H. 2.02(km),2.05(h)
I. 2.18(km),1.97(h)
J. 1.87(km),1.92(h)
Answer: I
The Basal Metabolic Rate may vary from person to person but it is closely related to a person's amount of ().

Options:
A. Mental State
B. Water Consumption
C. Physical Activity
D. Lean issue
E. Muscular energy
F. Food Tolerance
G. Daily Nutrition
H. Weight of body
I. Living Environment
J. Emotional Stress
Answer: C
Mr. A met with an accident and his right femur broke at 3 different places, The cut was a cllean break and the four pleces were put back together in their ariginal place, what kind of fracture did he have?

Options:
A. Multiple Fragment
B. Triple Dislocation
C. Fragmented Split
D. Muliple Fracture
E. Segmented Rupture
F. Complete Fractured
G. Quadruple Cracke
H. Triple Shattered
I. Multi-Split Fracture
J. Plural Rupture
Answer: A
The ammonia synthesis reaction generally takes place at $773 \mathrm{~K}$. Without a catalyst, the activation energy of the reaction is approximately $326 \mathrm{~kJ \cdot mol}^{-1}$. When reduced iron powder is used as a catalyst, the activation energy decreases to $175 \mathrm{~kJ \cdot mol}^{-1}$. After the catalyst is added, by how many times does the reaction rate increase compared to the original rate?

Options:
A. $$
2. 1 \times1 0^{6}
$$
B. $$
5. 0 \times1 0^{8}
$$
C. $$
2. 4 \times1 0^{9}
$$
D. $$
3. 5 \times1 0^{7}
$$
E. $$
8. 3 \times1 0^{8}
$$
F. $$
4. 8 \times1 0^{9}
$$
G. $$
1. 6 \times1 0^{1 0}
$$
H. $$
9. 9 \times1 0^{9}
$$
I. $$
1. 1 \times1 0^{7}
$$
J. $$
3. 2 \times1 0^{8}
$$
Answer: G
In a solution of a weak monoprotic acid HA, the concentration of hydrogen ions $c \left( \mathrm{~ H^{+} ~} \right)=a \mathrm{~ mol ~} \cdot\mathrm{dm}^{-3}$. When an excess of a sparingly soluble salt $\mathrm{MA}$ is added to the solution, achieving precipitation and dissolution equilibrium, the concentration of hydrogen ions $c \left( \mathrm{~ H^{+} ~} \right)=b \mathrm{~ mol ~} \cdot\mathrm{dm}^{-3}$. Assuming the acid concentration satisfies the conditions for approximate calculation of dissociation equilibrium, what is the solubility product constant $K_{\mathrm{sp}}^{\ominus}$ of $\mathrm{MA}$?

Options:
A. $$
\frac{a b^{3}-b^{2}} {a^{3}}
$$
B. $$
\frac{a b^{2}-a^{4}} {b^{3}}
$$
C. $$
\frac{a^{2} b-a c^{2}} {b c}
$$
D. $$
\frac{a^{3}-b^{3}} {a b^{2}}
$$
E. $$
\frac{b^{4}+a^{2} b} {a b^{2}}
$$
F. $$
\frac{a^{3}+b^{3} c} {a b}
$$
G. $$
\frac{b^{4}-a^{4}} {a^{2}}
$$
H. $$
\frac{a^{4}-a^{2} b^{2}} {b^{2}}
$$
I. $$
\frac{a^{4}+b^{4}} {a^{2} b^{2}}
$$
J. $$
\frac{a^{2} b^{2}+b^{4}} {a b}
$$
Answer: H
A certain amount of ammonium chloride decomposes upon heating according to the following reaction:
$$
\mathrm{NH_4Cl (s)} \rightleftharpoons \mathrm{NH_3 (g)} + \mathrm{HCl (g)}
$$
The enthalpy change of the reaction is known to be $\Delta_{r} H_{m}^{\ominus} = 161$ kJ $\mathrm{mol}^{-1}$ and the entropy change is $\Delta_{r} S_{m}^{\ominus} = 250$ J $\mathrm{mol}^{-1} \cdot \mathrm{K}^{-1}$. What is the total pressure of the system at equilibrium at $700 \, \mathrm{K}$?

Options:
A. $$
7. 6 {\times} 1 0^{4} \mathrm{~ k P a}
$$
B. $$
3. 9 {\times} 1 0^{2} \mathrm{~ k P a}
$$
C. $$
4. 4 {\times} 1 0^{3} \mathrm{~ k P a}
$$
D. $$
9. 8 {\times} 1 0^{2} \mathrm{~ k P a}
$$
E. $$
2. 3 {\times} 1 0^{3} \mathrm{~ k P a}
$$
F. $$
8. 5 {\times} 1 0^{2} \mathrm{~ k P a}
$$
G. $$
7. 1 {\times} 1 0^{3} \mathrm{~ k P a}
$$
H. $$
6. 6 {\times} 1 0^{2} \mathrm{~ k P a}
$$
I. $$
5. 0 {\times} 1 0^{2} \mathrm{~ k P a}
$$
J. $$
1. 2 {\times} 1 0^{4} \mathrm{~ k P a}
$$
Answer: H
Given that $\mathrm{Cu^{2+} + 2e^{-} = Cu}$ has $E^{\ominus} = 0.34 \mathrm{~V}$, and $\mathrm{Cu(NH_{3})_{4}}^{2+}$ has $K_{Steady state}^{\ominus} = 2.1 \times 10^{13}$, what is the $E^{\ominus}$ value for the electrochemical couple [$\mathrm{Cu(NH_{3})_{4}}]^{2+} / \mathrm{Cu}$?

Options:
A. $$
0. 1 5 6 \ \mathrm{V}
$$
B. $$
0. 1 0 2 \ \mathrm{V}
$$
C. $$
- 0. 0 8 2 \ \mathrm{V}
$$
D. $$
0. 0 7 9 \ \mathrm{V}
$$
E. $$
- 0. 2 1 5 \ \mathrm{V}
$$
F. $$
0. 2 3 4 \ \mathrm{V}
$$
G. $$
0. 0 4 5 \ \mathrm{V}
$$
H. $$
- 0. 3 0 8 \ \mathrm{V}
$$
I. $$
- 0. 1 1 7 \ \mathrm{V}
$$
J. $$
- 0. 0 5 3 \ \mathrm{V}
$$
Answer: J
It is known that the $K_{\mathrm{sp}}^\ominus$ of $\mathrm{SrF}_2$ is $4.3 \times 10^{-9}$, and the $K_{\mathrm{Steady state}}^\Theta$ of hydrofluoric acid is $6.3 \times 10^{-4}$. What is the solubility of $\mathrm{SrF}_2$ when the system's $\mathrm{pH}$ is maintained at 3.0?

Options:
A. $$
8. 3 \times1 0^{-1} \mathrm{~ m o l ~ \cdot~ d m^{-3} ~}
$$
B. $$
5. 2 \times1 0^{-7} \mathrm{~ m o l ~ \cdot~ d m^{-3} ~}
$$
C. $$
1. 9 \times1 0^{-3} \mathrm{~ m o l ~ \cdot~ d m^{-3} ~}
$$
D. $$
9. 6 \times1 0^{-9} \mathrm{~ m o l ~ \cdot~ d m^{-3} ~}
$$
E. $$
1. 2 \times1 0^{-10} \mathrm{~ m o l ~ \cdot~ d m^{-3} ~}
$$
F. $$
4. 4 \times1 0^{-8} \mathrm{~ m o l ~ \cdot~ d m^{-3} ~}
$$
G. $$
2. 5 \times1 0^{-4} \mathrm{~ m o l ~ \cdot~ d m^{-3} ~}
$$
H. $$
6. 7 \times1 0^{-6} \mathrm{~ m o l ~ \cdot~ d m^{-3} ~}
$$
I. $$
3. 8 \times1 0^{-5} \mathrm{~ m o l ~ \cdot~ d m^{-3} ~}
$$
J. $$
7. 1 \times1 0^{-2} \mathrm{~ m o l ~ \cdot~ d m^{-3} ~}
$$
Answer: C
1 g of acetylene $\mathrm{C_{2}H_{2}(g)}$ when completely combusted at constant volume at 298 $\mathrm{K}$ releases 50.1 kJ of heat. Determine the standard molar enthalpy of combustion $\Delta_{c}H_{m}^{\ominus}$ of $\mathrm{C_{2}H_{2}(g)}$ at this temperature. Given that the standard molar enthalpies of combustion for $\mathrm{H_{2}(g)}$ and graphite (C) are -286 kJ·mol$^{-1}$ and -394 kJ·mol$^{-1}$ respectively, what is the standard molar enthalpy of formation of $\mathrm{C_{2}H_{2}(g)}$?

Options:
A. $$
2 5 0. 4 \ \mathrm{k J} \cdot\mathrm{m o l}^{-1}
$$
B. $$
1 9 2. 8 \ \mathrm{k J} \cdot\mathrm{m o l}^{-1}
$$
C. $$
2 8 5. 1 \ \mathrm{k J} \cdot\mathrm{m o l}^{-1}
$$
D. $$
1 7 5. 4 \ \mathrm{k J} \cdot\mathrm{m o l}^{-1}
$$
E. $$
2 1 0. 6 \ \mathrm{k J} \cdot\mathrm{m o l}^{-1}
$$
F. $$
2 4 4. 7 \ \mathrm{k J} \cdot\mathrm{m o l}^{-1}
$$
G. $$
3 1 5. 7 \ \mathrm{k J} \cdot\mathrm{m o l}^{-1}
$$
H. $$
2 6 5. 9 \ \mathrm{k J} \cdot\mathrm{m o l}^{-1}
$$
I. $$
2 3 2. 3 \ \mathrm{k J} \cdot\mathrm{m o l}^{-1}
$$
J. $$
3 0 0. 0 \ \mathrm{k J} \cdot\mathrm{m o l}^{-1}
$$
Answer: I
Female, 30 years old. She has pulsatile tinnitus accompanied by hearing loss for six months, with examination revealing a blue eardrum. CT showed a round soft tissue mass in the tympanic cavity, with enhanced CT showing significant enhancement of the mass, with maximal enhancement timing earlier than the jugular vein but later than the carotid artery. This patient most likely has ().

Options:
A. Meniere's Disease
B. Labyrinthitis
C. Conductive Hearing Loss
D. Glomus Tympanicum Tumor
E. Otosclerosis
F. Cholesteatoma
G. Temporal Bone Fracture
H. Mastoiditis
I. Acoustic Neuroma
J. Eustachian Tube Dysfunction
Answer: D
Chronic purulent sinusitis is characteristically shown on a CT as ().

Options:
A. Obstruction and swelling of the Eustachian tubes.
B. Erosion and perforation of the nasal septum.
C. Calcification and degeneration of the nasal septum.
D. Softening and dislocation of the nasal cartilage.
E. Thickening and sclerosis of the cortical bone.
F. Expansion and distortion of the maxillary sinus walls.
G. Infarction and necrosis of the nasal mucosa.
H. Enlargement and congestion of the nasal turbinates.
I. Hyperintensity and liquefaction of the nasal cavity.
J. Retraction and desiccation of the nasal conchae.
Answer: E
What are the imaging characteristics of round atelectasis?

Options:
A. Subvertical dense line near the lung base
B. Subhorizontal faint line near the lung base
C. Vertical dense streak near the lung base
D. Subhorizontal dense streak near the lung base
E. Subhorizontal dense streak near the lung center
F. Horizontal dense streak near the lung apex
G. Diagonal dense streak near the lung apex
H. Subhorizontal dense spot near the lung base
I. Subhorizontal dense streak near the upper lung
J. Vertical dense line near the lung apex
Answer: D
Within 1 to 2 weeks of tuberculosis onset, what clinical symptoms are evident while the X-ray findings are negative?

Options:
A. Non-Hodgkin's Lymphoma
B. Acute Bacterial Pneumonia
C. Primary Lung Carcinoma
D. Allergic Bronchopulmonary Aspergillosis
E. Viral Upper Respiratory Infection
F. Lobar Bacterial Bronchopneumonia
G. Pulmonary Fibrosis Idiopathic
H. Hematogenous Disseminated Pulmonary Tuberculosis
I. Sarcoidosis Granulomatous Disease
J. Chronic Obstructive Pulmonary Disease
Answer: H
Female, 57 years old. Right-sided chest pain accompanied by difficulty breathing for 20 days, 10 years post left breast cancer radical surgery. CT shows mild collapse of the right thoracic cage, nodular thickening of the pleura on the chest wall and mediastinum with enhancement, accompanied by a small amount of pleural effusion. Its diagnosis should be ().

Options:
A. Bronchial constriction zone
B. Pneumothorax compartment
C. Localized empyema
D. Paramalignant effusion
E. Pleural adhesion band
F. Pulmonary thromboembolism
G. Benign pleural tumor
H. Pulmonary embolism syndrome
I. Post-surgical fibrosis
J. Pleural metastasis tumor
Answer: J
X-rays show increased pulmonary blood flow, and clinical manifestations include cyanosis ().

Options:
A. Atrial Septal Defect
B. Mitral Valve Prolapse
C. Patent Ductus Arteriosus
D. Tetralogy of Fallot
E. Eisenmenger Syndrome
F. Ventricular Septal Defect
G. Tricuspid Atresia
H. Marfan Syndrome
I. Aortic Coarctation
J. Pulmonary Valve Stenosis
Answer: E
A 37-year-old male with a known history of chronic hepatitis presented for imaging evaluation. Ultrasonographic examination demonstrated marked splenomegaly with hepatic parenchymal heterogeneity and surface nodularity, consistent with cirrhotic changes. Within the right hepatic lobe, there was a well-circumscribed, round lesion measuring 3.0 cm in diameter, characterized by a peripheral hypoechoic halo and homogeneous central hypoechogenicity. The most likely diagnosis is ().

Options:
A. HCC with metastasis to kidneys
B. Liver abscess with no malignancy
C. Fatty liver disease with splenomegaly
D. Hepatic hemangioma with cirrhosis
E. Splenic hemangioma with no cirrhosis
F. Portal hypertension without cirrhosis
G. Chronic hepatitis without neoplasm
H. Liver fibrosis with benign lesion
I. Hepatic cyst with smooth surface
J. Cirrhosis with liver tumor
Answer: J
A young woman has experienced low-grade fever, fatigue, and left side back pain for over 3 months. CT shows enlargement of the left kidney shadow, with uneven density at the upper pole of the left kidney and speckled calcification. Enhanced scans reveal multiple cystic cavities at the upper pole of the left kidney, with ring-like, moderate intensity enhancement of the cyst walls. The adjacent renal parenchyma is compressed and thinned, and there is mild dilation of the renal calyces. The primary consideration should be a lesion at the upper pole of the left kidney ().

Options:
A. Angiomyolipoma of the upper pole of the left kidney
B. Nephrocalcinosis of the upper pole of the left kidney
C. Renal cell carcinoma of the upper pole of the left kidney
D. Tuberculosis of the upper pole of the left kidney
E. Pyelonephritis of the upper pole of the left kidney
F. Xanthogranulomatous pyelonephritis of the upper pole
G. Renal abscess of the upper pole of the left kidney
H. Cystic nephroma of the upper pole of the left kidney
I. Hydronephrosis of the upper pole of the left kidney
J. Polycystic kidney disease of the upper pole of the left kidney
Answer: D
When a uniform plane wave is perpendicularly incident from free space onto a certain medium plane at $( z=0 )$, a standing wave is formed in the free space. It is known that the standing wave ratio is 2.7 and a node appears on the medium plane. Find the dielectric constant of the medium.

Options:
A. $\varepsilon_{2}=2. 8^{2} \varepsilon_{0} \approx7. 8 \varepsilon_{0} ($ or $\approx6. 8 4 \times1 0^{-1 1} ) \quad\mathrm{F / m}$
B. $\varepsilon_{2}=2. 2^{2} \varepsilon_{0} \approx5. 4 \varepsilon_{0} ($ or $\approx4. 9 0 \times1 0^{-1 1} ) \quad\mathrm{F / m}$
C. $\varepsilon_{2}=1. 9^{2} \varepsilon_{0} \approx4. 9 \varepsilon_{0} ($ or $\approx4. 3 2 \times1 0^{-1 1} ) \quad\mathrm{F / m}$
D. $\varepsilon_{2}=3. 0^{2} \varepsilon_{0} \approx9. 0 \varepsilon_{0} ($ or $\approx8. 1 0 \times1 0^{-1 1} ) \quad\mathrm{F / m}$
E. $\varepsilon_{2}=1. 6^{2} \varepsilon_{0} \approx4. 2 \varepsilon_{0} ($ or $\approx3. 8 5 \times1 0^{-1 1} ) \quad\mathrm{F / m}$
F. $\varepsilon_{2}=3. 2^{2} \varepsilon_{0} \approx8. 4 \varepsilon_{0} ($ or $\approx7. 0 2 \times1 0^{-1 1} ) \quad\mathrm{F / m}$
G. $\varepsilon_{2}=2. 7^{2} \varepsilon_{0} \approx7. 3 \varepsilon_{0} ($ or $\approx6. 4 7 \times1 0^{-1 1} ) \quad\mathrm{F / m}$
H. $\varepsilon_{2}=4. 5^{2} \varepsilon_{0} \approx9. 0 \varepsilon_{0} ($ or $\approx8. 1 0 \times1 0^{-1 1} ) \quad\mathrm{F / m}$
I. $\varepsilon_{2}=3. 6^{2} \varepsilon_{0} \approx9. 6 \varepsilon_{0} ($ or $\approx8. 6 5 \times1 0^{-1 1} ) \quad\mathrm{F / m}$
J. $\varepsilon_{2}=2. 3^{2} \varepsilon_{0} \approx5. 7 \varepsilon_{0} ($ or $\approx5. 1 2 \times1 0^{-1 1} ) \quad\mathrm{F / m}$
Answer: G
Given that the normalized $\mathbf{E}$-plane pattern functions for two antennas are as follows: ① $$\left| F(\theta) \right| = \left| \cos \left( \frac{\pi}{4} \cos \theta - \frac{\pi}{4} \right) \right|$$; ② $$\left| F(\theta) \right| = \left| \cos \left( \theta - \frac{\pi}{4} \right) \right|,$$
what is their half-power beamwidth?

Options:
A. $$
2 \theta_{0. 5}=2 (\theta_{0. 5}^{\prime}-2\, \theta_{\mathrm{m a x}} )=9 0^{\circ}
$$
B. $$
2 \theta_{0. 5}=2 (2 \, \theta_{0. 5}^{\prime}-\theta_{\mathrm{m a x}} )=1 1 0^{\circ}
$$
C. $$
2 \theta_{0. 5}=2 ( \theta_{0. 5}^{\prime}+\theta_{\mathrm{m a x}} )=1 0 0^{\circ}
$$
D. $$
2 \theta_{0. 5}=2 ( \theta_{0. 5}^{\prime}-\theta_{\mathrm{m a x}} )=9 0^{\circ}
$$
E. $$
2 \theta_{0. 5}=2 ( \theta_{0. 5}^{\prime}/\theta_{\mathrm{m a x}} )=8 5^{\circ}
$$
F. $$
2 \theta_{0. 5}=2 ( \theta_{0. 5}^{\prime}-0.5 \, \theta_{\mathrm{m a x}} )=6 5^{\circ}
$$
G. $$
2 \theta_{0. 5}=2 ( \theta_{0. 5}^{\prime}-\theta_{\mathrm{m a x}}+5)=9 5^{\circ}
$$
H. $$
2 \theta_{0. 5}=2 (\theta_{0. 5}^{\prime}+\theta_{\mathrm{m a x}}/2)=1 2 0^{\circ}
$$
I. $$
2 \theta_{0. 5}=2 ( \theta_{0. 5}^{\prime}-\theta_{\mathrm{m a x}} )=7 5^{\circ}
$$
J. $$
2 \theta_{0. 5}=2 ( \theta_{0. 5}^{\prime}\times\theta_{\mathrm{m a x}} )=8 0^{\circ}
$$
Answer: D
A circular waveguide with radius $R=5 \; \mathrm{cm}$ is used for a new microwave oven model, with an operating frequency of $f={\sqrt{3}} ( f_{c} )_{\mathrm{TE}_{01}}$. Calculate the guided wavelength, phase shift constant, and wave impedance for the $TE_{01}$ mode.

Options:
A. $$5.2cm,$$
$$1. 08 rad/cm,$$
$$
4 5 1. 7 5 \ \Omega
$$
B. $$5.6cm,$$
$$1. 30 rad/cm,$$
$$
4 6 1. 9 0 \ \Omega
$$
C. $$6.0cm,$$
$$1. 08 rad/cm,$$
$$
4 3 1. 7 5 \ \Omega
$$
D. $$4.8cm,$$
$$1. 08 rad/cm,$$
$$
4 6 1. 5 5 \ \Omega
$$
E. $$5.6cm,$$
$$1. 20 rad/cm,$$
$$
4 8 1. 7 5 \ \Omega
$$
F. $$5.6cm,$$
$$1. 15 rad/cm,$$
$$
4 6 1. 0 5 \ \Omega
$$
G. $$6.0cm,$$
$$1. 25 rad/cm,$$
$$
4 6 1. 7 5 \ \Omega
$$
H. $$5.6cm,$$
$$1. 08 rad/cm,$$
$$
4 6 1. 7 5 \ \Omega
$$
I. $$5.6cm,$$
$$1. 10 rad/cm,$$
$$
4 7 1. 7 5 \ \Omega
$$
J. $$5.0cm,$$
$$1. 08 rad/cm,$$
$$
4 6 1. 4 5 \ \Omega
$$
Answer: H
The resonant wavelength of a rectangular brass resonator cavity filled with air is known to be $\lambda_{0}=2.5 \text{ cm}$. If the cavity is filled with a polytetrafluoroethylene medium \(\left(\mathbf{e}_{t}=2.1, \text{tan} \delta = 4 \times 10^{-4}\right)\), what is the resonant frequency of this cavity and what is the total quality factor of the cavity?

Options:
A. 1450
B. 1398
C. 1355
D. 1340
E. 1323
F. 1287
G. 1382
H. 1412
I. 1476
J. 1308
Answer: E
There is an air-filled coaxial line with a characteristic impedance of 100 Ω, used to construct a $\lambda_{0} / 4$ type coaxial resonant cavity, with one end having a capacitance of $C=1 \times 10^{-12}/2\pi$ F, and the other end of the cavity being tuned with a short-circuit piston. When the cavity length is adjusted to $l=0.22\lambda_{0}$ and it resonates, find the resonant frequency $f_{0}$.

Options:
A. $$
f_{0}=2. 1 0 \mathrm{~ G H z}_{\circ}
$$
B. $$
f_{0}=1. 8 7 \mathrm{~ G H z}_{\circ}
$$
C. $$
f_{0}=1. 9 3 \mathrm{~ G H z}_{\circ}
$$
D. $$
f_{0}=1. 9 5 \mathrm{~ G H z}_{\circ}
$$
E. $$
f_{0}=1. 9 1 \mathrm{~ G H z}_{\circ}
$$
F. $$
f_{0}=1. 9 0 \mathrm{~ G H z}_{\circ}
$$
G. $$
f_{0}=2. 0 5 \mathrm{~ G H z}_{\circ}
$$
H. $$
f_{0}=1. 8 9 \mathrm{~ G H z}_{\circ}
$$
I. $$
f_{0}=2. 0 1 \mathrm{~ G H z}_{\circ}
$$
J. $$
f_{\circ}=2. 2 0 \mathrm{~ G H z}_{\circ}
$$
Answer: E
In a microwave cutoff attenuator, the waveguide radius of the air-filled circular waveguide section is $R=2 \ \text{cm}$, and we want the guided wave at the operating frequency $f=3 \ \text{GHz}$ to be attenuated by 30 dB. Find the length $l$ of this circular waveguide section.

Options:
A. $$
l=\frac{3 0} {8. 6 8 6_{\alpha}}=0. 0 5 1 \mathrm{m}
$$
B. $$
l=\frac{3 6} {8. 6 8 6_{\alpha}}=0. 0 6 2 \mathrm{m}
$$
C. $$
l=\frac{3 0} {8. 9 1 0_{\alpha}}=0. 0 5 5 \mathrm{m}
$$
D. $$
l=\frac{3 0} {7. 8 4 3_{\alpha}}=0. 0 5 3 \mathrm{m}
$$
E. $$
l=\frac{2 8} {8. 6 8 6_{\alpha}}=0. 0 4 7 \mathrm{m}
$$
F. $$
l=\frac{3 3} {8. 6 8 6_{\alpha}}=0. 0 5 8 \mathrm{m}
$$
G. $$
l=\frac{4 2} {8. 6 8 6_{\alpha}}=0. 0 6 3 \mathrm{m}
$$
H. $$
l=\frac{3 0} {9 . 7 5 2_{\alpha}}=0. 0 4 9 \mathrm{m}
$$
I. $$
l=\frac{3 0} {8. 2 3 1_{\alpha}}=0. 0 5 2 \mathrm{m}
$$
J. $$
l=\frac{3 0} {7. 5 6 3_{\alpha}}=0. 0 5 8 \mathrm{m}
$$
Answer: A
Given a helical antenna with a number of turns $N$ radiating a circularly polarized wave in the normal direction, and the diameter $d$ of the helix and the pitch $h$ are much smaller than $\lambda/N$. Find: the expression for the radiation resistance of this helical antenna.

Options:
A. $$
R_{\mathrm{r}}=\frac{2 P_{\mathrm{r}}} {\mid\stackrel{\bf} {\dot{I}} \mid^{2}}=55 \Big( \frac{\pi h} {N \lambda} \Big)^{2} \Omega
$$
B. $$
R_{\mathrm{r}}=\frac{2 P_{\mathrm{r}}} {\mid\stackrel{\bf} {\dot{I}} \mid^{2}}=95 \Big( \frac{N \pi h} {d} \Big)^{2} \Omega
$$
C. $$
R_{\mathrm{r}}=\frac{2 P_{\mathrm{r}}} {\mid\stackrel{\bf} {\dot{I}} \mid^{2}}=85 \Big( \frac{N \lambda} {\pi h} \Big)^{2} \Omega
$$
D. $$
R_{\mathrm{r}}=\frac{2 P_{\mathrm{r}}} {\mid\stackrel{\bf} {\dot{I}} \mid^{2}}=60 \Big( \frac{N \lambda} {\pi h} \Big)^{2} \Omega
$$
E. $$
R_{\mathrm{r}}=\frac{2 P_{\mathrm{r}}} {\mid\stackrel{\bf} {\dot{I}} \mid^{2}}=8 0 \Big( \frac{N \pi h} {\lambda} \Big)^{2} \Omega
$$
F. $$
R_{\mathrm{r}}=\frac{2 P_{\mathrm{r}}} {\mid\stackrel{\bf} {\dot{I}} \mid^{2}}=100 \Big( \frac{N \pi h} {d} \Big)^{2} \Omega
$$
G. $$
R_{\mathrm{r}}=\frac{2 P_{\mathrm{r}}} {\mid\stackrel{\bf} {\dot{I}} \mid^{2}}=70 \Big( \frac{N h} {\lambda \pi} \Big)^{2} \Omega
$$
H. $$
R_{\mathrm{r}}=\frac{2 P_{\mathrm{r}}} {\mid\stackrel{\bf} {\dot{I}} \mid^{2}}=90 \Big( \frac{N \pi} {\lambda} \Big)^{2} \Omega
$$
I. $$
R_{\mathrm{r}}=\frac{2 P_{\mathrm{r}}} {\mid\stackrel{\bf} {\dot{I}} \mid^{2}}=80 \Big( \frac{h} {N \lambda \pi} \Big)^{2} \Omega
$$
J. $$
R_{\mathrm{r}}=\frac{2 P_{\mathrm{r}}} {\mid\stackrel{\bf} {\dot{I}} \mid^{2}}=50 \Big( \frac{N \pi d} {\lambda} \Big)^{2} \Omega
$$
Answer: E
There is a Cassegrain antenna with a primary reflector focal length of 2m. If the eccentricity of the secondary reflector is chosen as $e=2.4$, what is the focal length of the equivalent parabolic reflector?

Options:
A. $$
f_{e}=4. 2 4 \mathrm{~ m}
$$
B. $$
f_{e}=4. 5 4 \mathrm{~ m}
$$
C. $$
f_{e}=3. 7 9 \mathrm{~ m}
$$
D. $$
f_{e}=6. 3 0 \mathrm{~ m}
$$
E. $$
f_{e}=5. 6 3 \mathrm{~ m}
$$
F. $$
f_{e}=5. 92 \mathrm{~ m}
$$
G. $$
f_{e}=4. 8 6 \mathrm{~ m}
$$
H. $$
f_{e}=3. 9 8 \mathrm{~ m}
$$
I. $$
f_{e}=6. 1 2 \mathrm{~ m}
$$
J. $$
f_{e}=5. 0 1 \mathrm{~ m}
$$
Answer: G
In a homogeneous medium with a permittivity of \( e\) and permeability of $\mu$, there is a monochromatic plane electromagnetic wave propagating along the $x$. It is known that its electric field intensity is $E = E_0 \cos(kx - \omega t)$, and $\omega$ are independent of \( x, y, z, t \). Find its magnetic field intensity $\mathbf{H}$.

Options:
A. $H = \frac{k}{\epsilon} E \times x$
B. $H = \frac{1}{k \omega \mu} z \times E$
C. $H = \frac{\mu}{\omega} x \times E$
D. $H = \frac{E_0}{\epsilon \mu} \times E$
E. $H = \frac{\omega}{\mu k} z \times E$
F. $H = \frac{k \times E}{\epsilon \omega}$
G. $H = \frac{1}{\omega \mu} k \times E$
H. $H = \frac{\omega k}{\epsilon} \times E$
I. $H = \frac{x \times E}{\omega \epsilon}$
J. $H = \frac{E_0}{k \omega} y \times E$
Answer: G
Using Lorentz transformation, attempt to determine the particle in a uniform electric field $E \overrightarrow{e}_{x}$ that is perpendicular to each other.

Options:
A. $x = e^{\left( \frac{eE}{\gamma_u mc} t \right)} - 1$, y = 0, z = ut,
where,
$$
u = \frac{c^2}{EB^2}, \gamma_u = \sqrt{1 - \frac{u^2}{c^2}},
$$
and
$$
x = e^{\left( \frac{eE}{\gamma_u mc} t \right)} - 1, y = 0, z = ut.
$$
B. $x = \ln \left( 1 + \frac{eE}{\gamma_p mc} t \right)$, y = 0, z = pt,
where,
$$
p = \frac{c^3}{EB}, \gamma_p = \sqrt{1 - \frac{p^2}{c^2}},
$$
and
$$
x = \ln \left( 1 + \frac{eE}{\gamma_p mc} t \right), y = 0, z = pt.
$$
C. $x = \frac{mc^2 \gamma_w}{eE} \sin \left( \frac{eE}{\gamma_w mc} t \right)$, y = 0, z = wt,
where,
$$
w = \frac{c^2}{EB^2}, \gamma_w = \sqrt{1 - \frac{w^2}{c^2}},
$$
and
$$
x = \frac{mc^2 \gamma_w}{eE} \sin \left( \frac{eE}{\gamma_w mc} t \right), y = 0, z = wt.
$$
D. $$
x = \frac{mc^2 \gamma_s}{eE} \cosh \left( \frac{eE}{\gamma_s mc} t \right), y = 0, z = st,
$$
where,
$$
s = \frac{c}{EB^3}, \gamma_s = \sqrt{1 - \frac{s^2}{c^2}},
$$
and
$$
x = \frac{mc^2 \gamma_s}{eE} \cosh \left( \frac{eE}{\gamma_s mc} t \right), y = 0, z = st.
$$
E. $x = \frac{mc^2 \gamma_r}{eE} \left[ 1 - \cos \left( \frac{eE}{\gamma_r mc} t \right) \right]$, y = 0, z = rt,
where,
$$
r = \frac{2c^2}{EB}, \gamma_r = \sqrt{1 - \frac{r^2}{c^2}},
$$
and
$$
x = \frac{mc^2 \gamma_r}{eE} \left[ 1 - \cos \left( \frac{eE}{\gamma_r mc} t \right) \right], y = 0, z = rt.
$$
F. $x = \frac{mc^2 \gamma_u}{eE} \left[ \sqrt{1 + \left( \frac{eE}{\gamma_u mc} t \right)^2 } - 1 \right]$, y = 0, z = ut,
where,
$$
u = \frac{c^2}{EB}, \gamma_u = \sqrt{1 - \frac{u^2}{c^2}},
$$
and
$$
x = \frac{mc^2 \gamma_u}{eE} \left[ \sqrt{1 + \left( \frac{eE}{\gamma_u mc} t \right)^2 } - 1 \right], y = 0, z = ut.
$$
G. $x = \frac{mc^2 \gamma_q}{eE} \tan \left( \frac{eE}{\gamma_q mc} t \right)$, y = 0, z = qt,
where,
$$
q = \frac{c}{EB^2}, \gamma_q = \sqrt{1 - \frac{q^2}{c^2}},
$$
and
$$
x = \frac{mc^2 \gamma_q}{eE} \tan \left( \frac{eE}{\gamma_q mc} t \right), y = 0, z = qt.
$$
H. $x = \frac{mc^2 \gamma_t}{eE^2} \left[ \sqrt{1 + \left( \frac{eE}{\gamma_t mc} t \right)^3 } - 1 \right]$, $y = 0$, $z = tt$,
where,
$$
t = \frac{c^2}{E^2 B}, \gamma_t = \sqrt{1 - \frac{t^2}{c^2}},
$$
and
$$
x = \frac{mc^2 \gamma_t}{eE^2} \left[ \sqrt{1 + \left( \frac{eE}{\gamma_t mc} t \right)^3 } - 1 \right], y = 0, z = tt.
$$
I. $x = \frac{mc^2 \gamma_v}{eE} \left[ 1 - \frac{1}{\left(1 + \left( \frac{eE}{\gamma_v mc} t \right)\right)} \right]$, y = 0, z = vt,
where,
$$
v = \frac{c}{EB^2}, \gamma_v = \sqrt{1 - \frac{v^2}{c^2}},
$$
and
$$
x = \frac{mc^2 \gamma_v}{eE} \left[ 1 - \frac{1}{\left(1 + \left( \frac{eE}{\gamma_v mc} t \right)\right)} \right], y = 0, z = vt.
$$
J. $x = \frac{mc^3 \gamma_v}{eE} \left[ \sqrt{1 + \left( \frac{eE}{\gamma_v mc} t \right)^2 } - 1 \right]$, y = 0, z = vt,
where
$$
v = \frac{c}{EB}, \gamma_v = \sqrt{1 - \frac{v^2}{c^2}},
$$
and
$$
x = \frac{mc^3 \gamma_v}{eE} \left[ \sqrt{1 + \left( \frac{eE}{\gamma_v mc} t \right)^2 } - 1 \right], y = 0, z = vt.
$$
Answer: F
A cosmic ray proton with an energy of $1.0 \times 10^{15} \ \mathrm{eV}$ arrives at the ground and enters a magnetic field of $B = 1.0 \times 10^{-5} \ \mathrm{T}$, with its velocity $v$ perpendicular to $\mathbf{B}$. What is the magnitude of the electric field experienced by this proton?

Options:
A. $E'_z = 5.6 \times 10^8 \, (\text{V/m})$
B. $E'_z = 3.0 \times 10^7 \, (\text{V/m})$
C. $E'_z = 3.2 \times 10^9 \, (\text{V/m})$
D. $E'_z = 1.2 \times 10^9 \, (\text{V/m})$
E. $E'_z = 4.1 \times 10^9 \, (\text{V/m})$
F. $E'_z = 2.5 \times 10^8 \, (\text{V/m})$
G. $E'_z = 7.4 \times 10^8 \, (\text{V/m})$
H. $E'_z = 1.7 \times 10^9 \, (\text{V/m})$
I. $E'_z = 9.7 \times 10^8 \, (\text{V/m})$
J. $E'_z = 6.8 \times 10^9 \, (\text{V/m})$
Answer: C
A sample of $n_{1}=n_{2}=250$ independent random samples is extracted from each of the two populations. The sample proportion from population 1 is $p_{1}=0.409$, while from population 2 it is $p_{2}=0.3000$. Requirement: What is the 90% confidence interval for $\pi_{1}-\pi_{2}$?

Options:
A. $$
1 0 \% \pm7. 5 9 \%
$$
B. $$
1 0 \% \pm5. 9 8 \%
$$
C. $$
1 0 \% \pm9. 4 7 \%
$$
D. $$
2 0 \% \pm6. 9 8 \%
$$
E. $$
1 5 \% \pm7. 3 8 \%
$$
F. $$
3 0 \% \pm6. 9 8 \%
$$
G. $$
7 0 \% \pm6. 9 8 \%
$$
H. $$
1 0 \% \pm6. 9 8 \%
$$
I. $$
1 0 \% \pm3. 9 3 \%
$$
J. $$
5 0 \% \pm8. 2 3 \%
$$
Answer: H
The first box contains 5 red balls and 4 white balls; the second box contains 4 red balls and 5 white balls. First, draw 2 balls at random from the first box and place them into the second box, then draw one ball at random from the second box. What is the probability of drawing a white ball?

Options:
A. $$
{\frac{6 3} {9 7}}
$$
B. $$
{\frac{5 3} {9 9}}
$$
C. $$
{\frac{6 1} {9 9}}
$$
D. $$
{\frac{4 5} {9 9}}
$$
E. $$
{\frac{3 4} {8 9}}
$$
F. $$
{\frac{6 2} {9 8}}
$$
G. $$
{\frac{5 2} {8 9}}
$$
H. $$
{\frac{5 4} {8 8}}
$$
I. $$
{\frac{4 6} {8 9}}
$$
J. $$
{\frac{4 4} {9 7}}
$$
Answer: B
Suppose a system is composed of two independently functioning binary components in series (binary components have only two states: functioning normally or failing). Components 1 and 2 have reliabilities of $p_{1}$ and $p_{2}$, respectively, both of which are unknown. Randomly select $N$ systems for testing. The system fails when at least one component in the system fails. The following test data is obtained: $n_{1}$ is the number of systems where only component 1 fails; $n_{2}$ is the number of systems where only component 2 fails; $n_{12}$ is the number of systems where at least one of components 1 or 2 fails; $s$ is the number of systems that do not fail. The equation $n_{1}+n_{2}+n_{12}+s=N$ holds true. Here, $n_{12}$ represents hidden data, meaning that it is only known that the system has failed, without knowing if the failure was caused by component 1 alone, component 2 alone, or neither component. Assume the hidden data is independent of the actual cause of system failure. Given system lifetime test data with $N = 20$, $n_{1} = 5$, $n_{2} = 3$, $n_{12} = 1$, and $s = 11$, determine the maximum likelihood estimates for $p_{1}$ and $p_{2}$ .

Options:
A. $$
\hat{p}_{1} \!=\! 0. 7 4 8 \ 0, \quad\hat{p}_{2} \!=\! 0. 8 0 5 \ 0.
$$
B. $$
\hat{p}_{1} \!=\! 0. 6 7 2 \ 0, \quad\hat{p}_{2} \!=\! 0. 8 5 1 \ 0.
$$
C. $$
\hat{p}_{1} \!=\! 0. 6 8 3 \ 0, \quad\hat{p}_{2} \!=\! 0. 7 9 4 \ 0.
$$
D. $$
\hat{p}_{1} \!=\! 0. 6 9 9 \ 0, \quad\hat{p}_{2} \!=\! 0. 8 4 0 \ 0.
$$
E. $$
\hat{p}_{1} \!=\! 0. 7 1 5 \ 0, \quad\hat{p}_{2} \!=\! 0. 8 2 9 \ 0.
$$
F. $$
\hat{p}_{1} \!=\! 0. 7 2 3 \ 0, \quad\hat{p}_{2} \!=\! 0. 8 8 6 \ 0.
$$
G. $$
\hat{p}_{1} \!=\! 0. 6 6 7 \ 0, \quad\hat{p}_{2} \!=\! 0. 8 7 9 \ 0.
$$
H. $$
\hat{p}_{1} \!=\! 0. 7 5 5 \ 0, \quad\hat{p}_{2} \!=\! 0. 8 1 7 \ 0.
$$
I. $$
\hat{p}_{1} \!=\! 0. 7 0 2 \ 0, \quad\hat{p}_{2} \!=\! 0. 8 6 3 \ 0.
$$
J. $$
\hat{p}_{1} \!=\! 0. 7 9 1 \ 0, \quad\hat{p}_{2} \!=\! 0. 8 3 5 \ 0.
$$
Answer: E
A mixture of 32 cm³ of gases CH₄, H₂, and N₂ is exploded with 61 cm³ of O₂. The volume of the residual gas is 34.5 cm³, of which 24.1 cm³ is absorbed by caustic soda solution. Determine the volume fractions of CH₄, H₂, and N₂ in the mixed gas.

Options:
A. $$
8 0. 0 \%,17.0\%,3.0\%
$$
B. $$
7 0. 2 \%,22.2\%,4.6\%
$$
C. $$
7 7. 5 \%,15.0\%,7.5\%
$$
D. $$
4 0. 6 \%,25.0\%,9.7\%
$$
E. $$
8 1. 7 \%,18.3\%,0.0\%
$$
F. $$
6 8. 4 \%,19.9\%,4.6\%
$$
G. $$
7 3. 9 \%,20.4\%,2.2\%
$$
H. $$
7 5. 3 \%,21.5\%,3.2\%
$$
I. $$
5 9. 8 \%,23.0\%,7.2\%
$$
J. $$
6 2. 0 \%,24.0\%,9.5\%
$$
Answer: H
An ideal Carnot engine operates between two heat sources with a temperature difference of 100 K. If the engine efficiency is 25%, calculate \( T_{1}, T_{2} \), and the work done. It is known that in each cycle, the heat source \( T_{1} \) absorbs 1000 J of heat. Assuming the work \( W \) completely dissipates as frictional heat into the heat source \( T_{2} \), find the entropy change of the engine and the entropy change of the environment after each cycle.

Options:
A. $$
1 \ 3 8 0 \ \mathrm{J}
$$
$$
0. 8 9 \mathrm{~ J} \cdot\mathrm{~ K}^{-1}
$$
B. $$
1 \ 2 8 8 \ \mathrm{J}
$$
$$
0. 7 5 \mathrm{~ J} \cdot\mathrm{~ K}^{-1}
$$
C. $$
1 \ 2 2 2 \ \mathrm{J}
$$
$$
0. 7 1 \mathrm{~ J} \cdot\mathrm{~ K}^{-1}
$$
D. $$
1 \ 2 5 0 \ \mathrm{J}
$$
$$
0. 7 8 \mathrm{~ J} \cdot\mathrm{~ K}^{-1}
$$
E. $$
1 \ 5 5 5 \ \mathrm{J}
$$
$$
1. 0 2 \mathrm{~ J} \cdot\mathrm{~ K}^{-1}
$$
F. $$
1 \ 1 1 1 \ \mathrm{J}
$$
$$
0. 6 5 \mathrm{~ J} \cdot\mathrm{~ K}^{-1}
$$
G. $$
1 \ 4 4 4 \ \mathrm{J}
$$
$$
0. 9 2 \mathrm{~ J} \cdot\mathrm{~ K}^{-1}
$$
H. $$
1 \ 4 2 0 \ \mathrm{J}
$$
$$
0. 9 7 \mathrm{~ J} \cdot\mathrm{~ K}^{-1}
$$
I. $$
1 \ 3 3 3 \ \mathrm{J}
$$
$$
0. 8 3 \mathrm{~ J} \cdot\mathrm{~ K}^{-1}
$$
J. $$
1 \ 6 6 6 \ \mathrm{J}
$$
$$
1. 1 5 \mathrm{~ J} \cdot\mathrm{~ K}^{-1}
$$
Answer: I
At 298 K and standard atmospheric pressure, the density of an aqueous solution with a mole fraction $x_{\mathrm{B}}$ of methanol (B) of 0.458 is 0.8946 $\mathrm{kg} \cdot \mathrm{dm}^{-3}$. The partial molar volume of methanol $V_{\mathrm{CH_{3}OH}} = 39.80 \, \mathrm{cm}^{3} \cdot \mathrm{mol}^{-1}$. Calculate the partial molar volume of water $V_{\mathrm{H_2O}}$ in this solution.

Options:
A. $$
2 2. 1 1 \, \mathrm{\ c m}^{3} \cdot\mathrm{\ m o l}^{-1}
$$
B. $$
1 8. 3 9 \, \mathrm{\ c m}^{3} \cdot\mathrm{\ m o l}^{-1}
$$
C. $$
3 0. 4 5 \, \mathrm{\ c m}^{3} \cdot\mathrm{\ m o l}^{-1}
$$
D. $$
2 4. 9 9 \, \mathrm{\ c m}^{3} \cdot\mathrm{\ m o l}^{-1}
$$
E. $$
1 0. 5 6 \, \mathrm{\ c m}^{3} \cdot\mathrm{\ m o l}^{-1}
$$
F. $$
3 5. 2 3 \, \mathrm{\ c m}^{3} \cdot\mathrm{\ m o l}^{-1}
$$
G. $$
1 2. 6 7 \, \mathrm{\ c m}^{3} \cdot\mathrm{\ m o l}^{-1}
$$
H. $$
1 6. 7 2 \, \mathrm{\ c m}^{3} \cdot\mathrm{\ m o l}^{-1}
$$
I. $$
1 9. 8 4 \, \mathrm{\ c m}^{3} \cdot\mathrm{\ m o l}^{-1}
$$
J. $$
2 7. 8 2 \, \mathrm{\ c m}^{3} \cdot\mathrm{\ m o l}^{-1}
$$
Answer: H
In air with an external pressure of $101.3 \text{ kPa}$, water vapor is introduced into a mixture of solid iodine I(s) and water for steam distillation. The distillate vapor is collected at $371.6 \text{ K}$ and condensed. Analysis of the distillate composition shows that every 100 $g$ of water contains $81.9 \text{ g}$ of iodine. Calculate the vapor pressure of iodine at $371.6 \text{ K}$.

Options:
A. $$
6 8 2 4 \, \mathrm{~ P a}
$$
B. $$
3 6 4 7 \, \mathrm{~ P a}
$$
C. $$
5 5 6 3 \, \mathrm{~ P a}
$$
D. $$
7 0 8 9 \, \mathrm{~ P a}
$$
E. $$
6 0 0 5 \, \mathrm{~ P a}
$$
F. $$
7 3 0 2 \, \mathrm{~ P a}
$$
G. $$
4 4 2 0 \, \mathrm{~ P a}
$$
H. $$
2 9 1 8 \, \mathrm{~ P a}
$$
I. $$
9 1 5 2 \, \mathrm{~ P a}
$$
J. $$
5 3 7 1 \, \mathrm{~ P a}
$$
Answer: C
At 298K, when measuring the transference number using the moving boundary method in a migration tube, a solution of GdCl with a concentration of $3.327 \times 10^{-2} \, \text{mol} \cdot \text{dm}^{-3}$ is first injected. Then, a LiCl solution with a concentration of $7.30 \times 10^{-2} \, \text{mol} \cdot \text{dm}^{-3}$ is carefully added above it, forming a clear boundary. Using a current of 5.594 mA for 3,976 seconds, the boundary moves downwards a distance equivalent to the length occupied by $1.002 \times 10^{-3} \, \text{dm}^{3}$ of solution in the tube. Calculate the transference numbers of $\text{Gd}^{3+}$ and $\text{Cl}^{-}$.

Options:
A. 0.410,0.590
B. 0.495,0.505
C. 0.455,0.545
D. 0.500,0.500
E. 0.375,0.625
F. 0.420,0.580
G. 0.434,0.566
H. 0.467,0.533
I. 0.480,0.520
J. 0.390,0.610
Answer: G
The choice of standard state affects which of the following sets of physical quantities?

Options:
A. $$
\rho \,, n^{\Theta} \,, \Delta_{T} S_{m}^{\Theta}
$$
B. $$
V \,, P^{\Theta} \,, \Delta_{\theta} H_{m}^{\Theta}
$$
C. $$
d \,, \eta^{\Theta} \,, \Delta_{\phi} A_{m}^{\Theta}
$$
D. $$
z \,, k^{\Theta} \,, \Delta_{\chi} B_{m}^{\Theta}
$$
E. $$
c \,, \gamma^{\Theta} \,, \Delta_{P} E_{m}^{\Theta}
$$
F. $$
u \,, \lambda^{\Theta} \,, \Delta_{\omega} C_{m}^{\Theta}
$$
G. $$
p \,, \alpha^{\Theta} \,, \Delta_{\delta} F_{m}^{\Theta}
$$
H. $$
x \,, \zeta^{\Theta} \,, \Delta_{\nu} U_{m}^{\Theta}
$$
I. $$
y \,, \beta^{\Theta} \,, \Delta_{\psi} Q_{m}^{\Theta}
$$
J. $$
a \,, \mu^{\Theta} \,, \Delta_{\tau} G_{m}^{\Theta}
$$
Answer: J