MikaStars39/nano-eval huggingface dataset:
At the input terminal of a certain amplifier circuit, the measured peak-to-peak values of the input sinusoidal signal current and voltage are 5 $\mu A$ and 5 $\mathrm{mV}$, respectively. With a 2 k$\Omega$ load connected at the output terminal, the peak-to-peak value of the measured sinusoidal voltage signal is 1 $\mathbf{V}_{\circ}$. Try to calculate the voltage gain $A_{\mathrm{F}}$, current gain $A_{i}$, and power gain $A_{P}$ of this amplifier circuit, and convert each into dB.

Options:
A. $$
=4 5 0
$$
$$
\approx\! 5 4 \mathrm{~ d B}
$$
$$
=1 6 0
$$
$$
3 8 dB
$$
$$
=19000
$$
$$
\approx4 5 \, \, \, \mathrm{d B}
$$
B. $$
=1 5 0
$$
$$
\approx\! 4 2 \mathrm{~ d B}
$$
$$
=1 1 0
$$
$$
3 9 dB
$$
$$
=18000
$$
$$
\approx4 0 \, \, \, \mathrm{d B}
$$
C. $$
=2 0 0
$$
$$
\approx\! 4 6 \mathrm{~ d B}
$$
$$
=1 0 0
$$
$$
=40 dB
$$
$$
=20000
$$
$$
\approx4 3 \, \, \, \mathrm{d B}
$$
D. $$
=3 0 0
$$
$$
\approx\! 5 0 \mathrm{~ d B}
$$
$$
=1 5 0
$$
$$
3 5 dB
$$
$$
=15000
$$
$$
\approx4 5 \, \, \, \mathrm{d B}
$$
E. $$
=5 0 0
$$
$$
\approx\! 5 5 \mathrm{~ d B}
$$
$$
=1 8 0
$$
$$
3 7 dB
$$
$$
=25000
$$
$$
\approx4 6 \, \, \, \mathrm{d B}
$$
F. $$
=1 0 0
$$
$$
\approx\! 3 6 \mathrm{~ d B}
$$
$$
=1 9 0
$$
$$
3 6 dB
$$
$$
=22000
$$
$$
\approx4 4 \, \, \, \mathrm{d B}
$$
G. $$
=3 5 0
$$
$$
\approx\! 4 9 \mathrm{~ d B}
$$
$$
=1 4 0
$$
$$
4 0 dB
$$
$$
=24000
$$
$$
\approx3 9 \, \, \, \mathrm{d B}
$$
H. $$
=3 2 0
$$
$$
\approx\! 5 1 \mathrm{~ d B}
$$
$$
=1 7 0
$$
$$
3 6 dB
$$
$$
=26000
$$
$$
\approx4 7 \, \, \, \mathrm{d B}
$$
I. $$
=2 5 0
$$
$$
\approx\! 4 8 \mathrm{~ d B}
$$
$$
=1 2 0
$$
$$
3 8 dB
$$
$$
=21000
$$
$$
\approx4 2 \, \, \, \mathrm{d B}
$$
J. $$
=4 0 0
$$
$$
\approx\! 5 2 \mathrm{~ d B}
$$
$$
=1 3 0
$$
$$
4 1 dB
$$
$$
=23000
$$
$$
\approx4 1 \, \, \, \mathrm{d B}
$$
Answer: C
Under room temperature (300 K), if the reverse saturation current of a diode is 1 nA, what voltage should be applied for its forward current to be 0.5 mA? Assume the exponential model of the diode is $i_{\mathrm{D}} = I_{\mathrm{S}} ( \, \mathrm{e}^{v_{\mathrm{D}} / \mathrm{n} V_{\mathrm{T}}} - 1 \, )$, where $n=1$.

Options:
A. $$
\approx0. 5 0 \mathrm{~ V}
$$
B. $$
\approx1. 5 4 \mathrm{~ V}
$$
C. $$
\approx1. 0 2 \mathrm{~ V}
$$
D. $$
\approx0. 6 9 \mathrm{~ V}
$$
E. $$
\approx0. 4 6 \mathrm{~ V}
$$
F. $$
\approx0. 8 3 \mathrm{~ V}
$$
G. $$
\approx2. 3 1 \mathrm{~ V}
$$
H. $$
\approx0. 3 4 \mathrm{~ V}
$$
I. $$
\approx0. 2 8 \mathrm{~ V}
$$
J. $$
\approx0. 1 7 \mathrm{~ V}
$$
Answer: H
Solve the following problem: Given an NMOS transistor with $W / L=10$, $I_{\mathrm{n Q}}=0.1 \, \mathrm{mA}$, $V_{\mathrm{T N}}=0.5 \, \mathrm{V}$, and $K_{\mathrm{n}}^{\prime}=387 \, \mu\mathrm{A} / \mathrm{V}^{2}$, with the channel length modulation effect being negligible. Find the value of $V_{\mathrm{c s q}}$.

Options:
A. $$
{\approx0. 6 9 ~ V}
$$
B. $$
{\approx0. 7 9 ~ V}
$$
C. $$
{\approx0. 7 0 ~ V}
$$
D. $$
{\approx0. 6 5 ~ V}
$$
E. $$
{\approx0. 8 5 ~ V}
$$
F. $$
{\approx0. 7 8 ~ V}
$$
G. $$
{\approx0. 7 3 ~ V}
$$
H. $$
{\approx0. 8 2 ~ V}
$$
I. $$
{\approx0. 9 0 ~ V}
$$
J. $$
{\approx0. 5 8 ~ V}
$$
Answer: G
Suppose the open-loop gain of a certain direct-coupled amplifier circuit is $\dot{A}=\frac{300}{1+\mathrm{j} \omega/ (2 \pi \times 10^{4})}$ . If a voltage series negative feedback with a feedback factor $F=0.3$ is introduced into this circuit, what is the mid-frequency gain of the circuit after introducing this feedback? What is the bandwidth?

Options:
A. $$
\approx3. 3
$$
$$
9 1 0 \ \mathrm{k H z}
$$
B. $$
\approx2. 8
$$
$$
7 5 0 \ \mathrm{k H z}
$$
C. $$
\approx3. 9
$$
$$
9 8 0 \ \mathrm{k H z}
$$
D. $$
\approx4. 0
$$
$$
8 5 0 \ \mathrm{k H z}
$$
E. $$
\approx4. 5
$$
$$
1 1 0 0 \ \mathrm{k H z}
$$
F. $$
\approx2. 5
$$
$$
8 0 0 \ \mathrm{k H z}
$$
G. $$
\approx4. 2
$$
$$
1 0 0 0 \ \mathrm{k H z}
$$
H. $$
\approx5. 6
$$
$$
1 2 0 \ \mathrm{k H z}
$$
I. $$
\approx3. 7
$$
$$
8 9 0 \ \mathrm{k H z}
$$
J. $$
\approx3. 1
$$
$$
9 5 0 \ \mathrm{k H z}
$$
Answer: A
A radio frequency coil has the following parameters: at 3 MHz, the self-inductance is 20 μH, the self-capacitance is 8 pF, and the resistance is 1.2 Ω. The equivalent series inductance and resistance values at 3 MHz as well as the coil's own resonant frequency are ().

Options:
A. $$
2 1. 9 0 \mu\mathbf{H}, \; \; 1. 7 5 9 \Omega, \; \; 1 1. 4 5 \mathbf{M} \mathbf{H} \mathbf{z}
$$
B. $$
2 2. 4 8 \mu\mathbf{H}, \; \; 1. 1 1 0 \Omega, \; \; 1 3. 9 2 \mathbf{M} \mathbf{H} \mathbf{z}
$$
C. $$
2 3. 9 9 \mu\mathbf{H}, \; \; 1. 5 5 5 \Omega, \; \; 1 5. 0 4 \mathbf{M} \mathbf{H} \mathbf{z}
$$
D. $$
1 9. 7 3 \mu\mathbf{H}, \; \; 1. 3 0 2 \Omega, \; \; 6. 5 0 \mathbf{M} \mathbf{H} \mathbf{z}
$$
E. $$
1 8. 2 2 \mu\mathbf{H}, \; \; 1. 6 2 3 \Omega, \; \; 9. 9 8 \mathbf{M} \mathbf{H} \mathbf{z}
$$
F. $$
2 0. 3 3 \mu\mathbf{H}, \; \; 1. 8 8 8 \Omega, \; \; 1 5. 2 0 \mathbf{M} \mathbf{H} \mathbf{z}
$$
G. $$
2 0. 8 5 \mu\mathbf{H}, \; \; 1. 4 8 9 \Omega, \; \; 1 1. 7 3 \mathbf{M} \mathbf{H} \mathbf{z}
$$
H. $$
1 7. 5 5 \mu\mathbf{H}, \; \; 1. 9 9 9 \Omega, \; \; 8. 0 8 \mathbf{M} \mathbf{H} \mathbf{z}
$$
I. $$
2 0. 5 0 \mu\mathbf{H}, \; \; 1. 0 0 1 \Omega, \; \; 1 0. 3 7 \mathbf{M} \mathbf{H} \mathbf{z}
$$
J. $$
2 1. 2 1 \mu\mathbf{H}, \; \; 1. 2 5 6 \Omega, \; \; 1 2. 5 8 \mathbf{M} \mathbf{H} \mathbf{z}
$$
Answer: J
Transmit a sinusoidal signal with a frequency of $f$, resulting in a narrowband frequency modulation system with a carrier frequency deviation of $0.1 f_{\mathbf{M}}$. The relative amplitude of the effective sideband pairs is ().

Options:
A. 0.00125
B. 0.00200
C. 0.00300
D. 0.00050
E. 0.00250
F. 0.00400
G. 0.00375
H. 0.00100
I. 0.00075
J. 0.00525
Answer: A
The frequency-modulated current output of a sensor is $\boldsymbol{i}=I_{m} \mathbf{s i n} \left( \omega_{\epsilon} t+K \, \mathbf{c o s} \, \omega_{m} t \right)$. If this current passes through an inductor $L$, determine the modulation depth is ().

Options:
A. $$
L \omega_{m} / K
$$
B. $$
K \omega_{M} L
$$
C. $$
\omega_\epsilon / K \omega_{M}
$$
D. $$
K \omega_{M} / \omega_\epsilon
$$
E. $$
\omega_{m} L / \omega_{M}
$$
F. $$
K \omega_m / L
$$
G. $$
L K / \omega_{m}
$$
H. $$
K \omega_\epsilon / \omega_{M}
$$
I. $$
K L / \omega_\epsilon
$$
J. $$
K L \omega_{M} / \omega_{m}
$$
Answer: D
A first-class RF pulse train has a radio frequency of 10 GHz, with a duty cycle of 1:1000 and a pulse repetition frequency of 10 kHz. The estimated bandwidth required to transmit these signals is ().

Options:
A. 0.5MHz
B. 3MHz
C. 6MHz
D. 7MHz
E. 4MHz
F. 5MHz
G. 1.5MHz
H. 2MHz
I. 10MHz
J. 8MHz
Answer: H
There are 960 signals, each with a bandwidth limit of 4 kHz, sampled at the minimum rate and then subjected to time-division multiplexing to determine the sampling frequency. If the expanded sampled pulse forms a pulse with a duration of $\tau$, thereby achieving a 50% duty cycle (the pulse occupies half of the time slot allocated to each sample), the value of $\tau$ is ().

Options:
A. $$Sampling\ frequency = 13\ kHz,
\tau = \frac{1} {2} \times (160 / 960) = 0.083 \mu s
$$
B. $$Sampling\ frequency = 8\ kHz,
\tau = \frac{1} {2} \times (125 / 960) = 0.065 \mu s
$$
C. $$Sampling\ frequency = 5\ kHz,
\tau = \frac{1} {2} \times (70 / 960) = 0.036 \mu s
$$
D. $$Sampling\ frequency = 6\ kHz,
\tau = \frac{1} {2} \times (80 / 960) = 0.041 \mu s
$$
E. $$Sampling\ frequency = 11\ kHz,
\tau = \frac{1} {2} \times (140 / 960) = 0.073 \mu s
$$
F. $$Sampling\ frequency = 9\ kHz,
\tau = \frac{1} {2} \times (110 / 960) = 0.057 \mu s
$$
G. $$Sampling\ frequency = 7\ kHz,
\tau = \frac{1} {2} \times (90 / 960) = 0.047 \mu s
$$
H. $$Sampling\ frequency = 10\ kHz,
\tau = \frac{1} {2} \times (130 / 960) = 0.068 \mu s
$$
I. $$Sampling\ frequency = 12\ kHz,
\tau = \frac{1} {2} \times (150 / 960) = 0.078 \mu s
$$
J. $$Sampling\ frequency = 4\ kHz,
\tau = \frac{1} {2} \times (60 / 960) = 0.031 \mu s
$$
Answer: B
A PPM signal with a bandwidth limited to 5 kHz consists of equal-amplitude pulses with a duration of 1 μs. The pulse duration can be delayed by 2 μs to 5 μs relative to the sampling time. What is the maximum number of such signals that can be time-division multiplexed?

Options:
A. 20
B. 35
C. 10
D. 45
E. 50
F. 25
G. 30
H. 40
I. 15
J. 55
Answer: F
The dimensions of a waveguide are 72.14 × 34.04 $mm^{2}$, operating at a frequency of 3GHz with the $\mathbf{H}_{1 0}$ mode, transmitting a pulse of 100kW peak power to a matched load. What is the maximum electric field strength within the waveguide during transmission? If the waveguide is used to feed an antenna, which produces a Voltage Standing Wave Ratio (VSWR) of 1.08 in the waveguide, what are the maximum and minimum values of the electric field amplitude in the feed line, and compute the peak reflected power?

Options:
A. $1 9 5. 4 \mathrm{k V / m}, E_{\mathrm{m a x}}=2 0 1. 1 \mathrm{k V / m},E_{\mathrm{min}}=1 8 8.2 \mathrm{k V / m}$ , $1 4 0. 0 \mathbf{W}$
B. $1 9 1. 8 \mathrm{k V / m}, E_{\mathrm{m a x}}=1 9 8. 0 \mathrm{k V / m},E_{\mathrm{min}}=1 8 1.5 \mathrm{k V / m}$ , $1 4 9. 2 \mathbf{W}$
C. $1 9 0. 5 \mathrm{k V / m}, E_{\mathrm{m a x}}=1 9 7. 8 \mathrm{k V / m},E_{\mathrm{min}}=1 8 3.2 \mathrm{k V / m}$ , $1 4 7. 9 \mathbf{W}$
D. $1 8 5. 0 \mathrm{k V / m}, E_{\mathrm{m a x}}=1 9 5. 4 \mathrm{k V / m},E_{\mathrm{min}}=1 7 9.1 \mathrm{k V / m}$ , $1 4 8. 5 \mathbf{W}$
E. $1 9 3. 2 \mathrm{k V / m}, E_{\mathrm{m a x}}=1 9 9. 6 \mathrm{k V / m},E_{\mathrm{min}}=1 7 5.0 \mathrm{k V / m}$ , $1 2 3. 4 \mathbf{W}$
F. $1 8 9. 1 \mathrm{k V / m}, E_{\mathrm{m a x}}=1 9 6. 5 \mathrm{k V / m},E_{\mathrm{min}}=1 7 6.4 \mathrm{k V / m}$ , $1 3 5. 8 \mathbf{W}$
G. $1 8 8. 9 \mathrm{k V / m}, E_{\mathrm{m a x}}=1 9 8. 2 \mathrm{k V / m},E_{\mathrm{min}}=1 8 0.3 \mathrm{k V / m}$ , $1 5 1. 7 \mathbf{W}$
H. $1 9 2. 7 \mathrm{k V / m}, E_{\mathrm{m a x}}=2 0 0. 8 \mathrm{k V / m},E_{\mathrm{min}}=1 8 2.9 \mathrm{k V / m}$ , $1 5 5. 3 \mathbf{W}$
I. $2 0 0. 3 \mathrm{k V / m}, E_{\mathrm{m a x}}=2 0 4. 6 \mathrm{k V / m},E_{\mathrm{min}}=1 8 5.1 \mathrm{k V / m}$ , $1 5 0. 0 \mathbf{W}$
J. $1 8 2. 3 \mathrm{k V / m}, E_{\mathrm{m a x}}=1 9 1. 5 \mathrm{k V / m},E_{\mathrm{min}}=1 7 2.0 \mathrm{k V / m}$ , $1 2 0. 2 \mathbf{W}$
Answer: C
An antenna array consists of three vertical and parallel half-wave dipoles, all centered on a horizontal line. They are spaced at $\lambda/4$, fed with currents of the same amplitude, but with a progressive phase difference of δ radians between sequential dipoles. What is the value of δ when the gain is maximum in the horizontal plane in the direction of $\phi = 45^{\circ}$?

Options:
A. 0.222rad
B. 3.555rad
C. 1.111rad
D. 5.999rad
E. 0.999rad
F. 1.666rad
G. 4.888rad
H. 0.333rad
I. 2.444rad
J. 0.777rad
Answer: C
A three-phase asynchronous motor is given with $P_{\mathrm{N}}=2 \, \mathrm{kW}$, $n_{\mathrm{N}}=2,840 \, \mathrm{r/min}$, $\lambda_{\mathrm{m}}=2$, $U_{\mathrm{N}}=380 \, \mathrm{V}$, $f_{N}=50 \, \mathrm{Hz}$. Find the expression for its characteristic torque.

Options:
A. $${\frac{2 7. 0} {{\frac{0. 1 7 5} {S}}+{\frac{S} {0. 2 3 0}}}}
$$
B. $${\frac{2 8. 7} {{\frac{0. 2 0 5} {S}}+{\frac{S} {0. 1 9 5}}}}
$$
C. $${\frac{2 9. 8} {{\frac{0. 1 9 0} {S}}+{\frac{S} {0. 2 2 0}}}}
$$
D. $${\frac{2 5. 4} {{\frac{0. 1 9 5} {S}}+{\frac{S} {0. 2 1 0}}}}
$$
E. $${\frac{3 0. 9} {{\frac{0. 2 2 4} {S}}+{\frac{S} {0. 2 2 4}}}}
$$
F. $${\frac{2 7. 9} {{\frac{0. 1 8 5} {S}}+{\frac{S} {0. 2 0 1}}}}
$$
G. $${\frac{2 6. 5} {{\frac{0. 2 1 0} {S}}+{\frac{S} {0. 1 9 0}}}}
$$
H. $${\frac{3 0. 0} {{\frac{0. 2 0 0} {S}}+{\frac{S} {0. 1 8 0}}}}
$$
I. $${\frac{2 6. 8} {{\frac{0. 1 9 8} {S}}+{\frac{S} {0. 1 9 8}}}}
$$
J. $${\frac{2 6. 3} {{\frac{0. 2 2 0} {S}}+{\frac{S} {0. 1 8 2}}}}
$$
Answer: I
The valve spring of a certain diesel engine has a mean spring radius $R=59.5\mathrm{mm}$, a spring wire cross-sectional diameter $d=14\mathrm{mm}$, and an effective number of coils $n=5$. The material has an allowable shear stress $\left[\tau\right]=350\mathrm{MPa}$ and a shear modulus $G=80\mathrm{GPa}$. When the spring is in operation, it withstands a force $F=2500\mathrm{N}$. Calculate the maximum shear stress on the cross-section of the spring wire and determine its compression deformation.

Options:
A. $$
\approx3. 2 1 \times1 0^{8} \mathrm{~ P a}
$$
$$
5 5. 7 \mathrm{~ m m}
$$
B. $$
\approx2. 9 5 \times1 0^{8} \mathrm{~ P a}
$$
$$
5 4. 0 \mathrm{~ m m}
$$
C. $$
\approx3. 9 0 \times1 0^{8} \mathrm{~ P a}
$$
$$
5 4. 5 \mathrm{~ m m}
$$
D. $$
\approx3. 4 5 \times1 0^{8} \mathrm{~ P a}
$$
$$
5 2. 6 \mathrm{~ m m}
$$
E. $$
\approx3. 0 7 \times1 0^{8} \mathrm{~ P a}
$$
$$
5 6. 2 \mathrm{~ m m}
$$
F. $$
\approx4. 1 8 \times1 0^{8} \mathrm{~ P a}
$$
$$
5 0. 8 \mathrm{~ m m}
$$
G. $$
\approx3. 1 2 \times1 0^{8} \mathrm{~ P a}
$$
$$
5 6. 9 \mathrm{~ m m}
$$
H. $$
\approx3. 5 0 \times1 0^{8} \mathrm{~ P a}
$$
$$
5 3. 9 \mathrm{~ m m}
$$
I. $$
\approx2. 8 2 \times1 0^{8} \mathrm{~ P a}
$$
$$
5 8. 8 \mathrm{~ m m}
$$
J. $$
\approx2. 7 4 \times1 0^{8} \mathrm{~ P a}
$$
$$
5 7. 3 \mathrm{~ m m}
$$
Answer: A
The traffic volume of a certain city's road is 280 vehicles per hour, with a road width of 15 meters and an average pedestrian speed of 1.2 meters per second. What is the number of times and the duration pedestrians are allowed to cross the road within an hour is ().

Options:
A. 111 times,46′18.2″
B. 113 times,47′05.4″
C. 92 times,39′55.0″
D. 89 times,35′22.7″
E. 106 times,44′45.3″
F. 120 times,52′10.5″
G. 95 times,40′30.8″
H. 101 times,42′15.6″
I. 98 times,38′20.1″
J. 107 times,44′10.7″
Answer: E
A Liberation brand heavy-duty truck, loaded with $4t$ of cargo, has a wheelbase of 1740mm and a center of gravity height of 1060mm. It is traveling on a road with a curve radius of 30m. At what speed can the truck travel safely and steadily?

Options:
A. 67.4km/h
B. 51.2km/h
C. 48.6km/h
D. 58.5km/h
E. 61.3km/h
F. 64.9km/h
G. 70.2km/h
H. 65.7km/h
I. 59.9km/h
J. 54.8km/h
Answer: J
A certain highway needs to be widened and reconstructed. After investigation and prediction, it is estimated that the average daily traffic volume during the planning period will be 50,000 cars per day. The design hourly factor is $\mathsf{K}=1.786 \mathsf{X}^{-1.3}-0.082$, where $\mathsf{X}$ is the design hourly position. Assuming the design capacity of one lane is 1,500 cars per hour, how many lanes does the highway need to have?

Options:
A. Three-lane coastal route
B. Nine-lane commuter highway
C. Six-lane dual carriageway
D. Four-lane rural expressway
E. Two-lane scenic drive
F. Eleven-lane city boulevard
G. Ten-lane urban freeway
H. Eight-lane suburban avenue
I. Five-lane mountain road
J. Seven-lane industrial bypass
Answer: C
The traffic volume of a certain traffic flow is 600 vehicles per hour and follows a Poisson distribution. What is the probability of one vehicle arriving within 6 seconds?

Options:
A. 0.8145
B. 0.2817
C. 0.5738
D. 0.6890
E. 0.6324
F. 0.2456
G. 0.7192
H. 0.3679
I. 0.5123
J. 0.4521
Answer: H
Suppose the volume is incompressible, the displacements $u_{1} ( x_{1}, x_{2} )$ and $u_{2} ( x_{1}, x_{2} )$ are very small, and $u_{3} \equiv 0$. Within a certain region, it is known that $u_{1}=\left( 1-x_{2}^{2} \right) \left( a+b x_{1}+c x_{1}^{2} \right)$, where $a, b, c$ are constants. Find $u_{2} ( x_{1}, x_{2} )$ is ().

Options:
A. $$
u_{2}=\int_{x_{1 0}}^{x_{1}} \varepsilon_{2 3} \mathrm{d} x_{1}=( b+2 b x_{1} ) \left[ \left( \frac{1} {2} x_{2}^{3}-x_{2} \right)-\left( \frac{1} {2} x_{2 0}^{3}-x_{2 0} \right) \right]
$$
B. $$
u_{2}=\int_{x_{1 0}}^{x_{1}} \varepsilon_{2 2} \mathrm{d} x_{1}=( a+3 c x_{1} ) \left[ \left( \frac{1} {3} x_{2}^{3}-x_{2} \right)-\left( \frac{1} {3} x_{2 0}^{3}-x_{2 0} \right) \right]
$$
C. $$
u_{2}=\int_{x_{2 0}}^{x_{2}} \varepsilon_{2 1} \mathrm{d} x_{2}=( c+2 a x_{1} ) \left[ \left( \frac{2} {3} x_{2}^{3}-x_{2} \right)-\left( \frac{2} {3} x_{2 0}^{3}-x_{2 0} \right) \right]
$$
D. $$
u_{2}=\int_{x_{2 0}}^{x_{2}} \varepsilon_{1 3} \mathrm{d} x_{2}=( a+2 b x_{1} ) \left[ \left( \frac{1} {4} x_{2}^{3}-x_{2} \right)-\left( \frac{1} {4} x_{2 0}^{3}-x_{2 0} \right) \right]
$$
E. $$
u_{2}=\int_{x_{2 0}}^{x_{2}} \varepsilon_{2 2} \mathrm{d} x_{2}=( b+2 c x_{1} ) \left[ \left( \frac{1} {3} x_{2}^{3}-x_{2} \right)-\left( \frac{1} {3} x_{2 0}^{3}-x_{2 0} \right) \right]
$$
F. $$
u_{2}=\int_{x_{2 0}}^{x_{2}} \varepsilon_{1 2} \mathrm{d} x_{2}=( b+2 a x_{1} ) \left[ \left( \frac{1} {3} x_{2}^{3}-x_{2} \right)-\left( \frac{1} {3} x_{2 0}^{3}-x_{2 0} \right) \right]
$$
G. $$
u_{2}=\int_{x_{1 0}}^{x_{1}} \varepsilon_{2 2} \mathrm{d} x_{1}=( c+2 b x_{1} ) \left[ \left( \frac{3} {3} x_{2}^{3}-x_{2} \right)-\left( \frac{3} {3} x_{2 0}^{3}-x_{2 0} \right) \right]
$$
H. $$
u_{2}=\int_{x_{2 0}}^{x_{2}} \varepsilon_{3 3} \mathrm{d} x_{2}=( a+2 c x_{1} ) \left[ \left( \frac{1} {3} x_{2}^{4}-x_{2} \right)-\left( \frac{1} {3} x_{2 0}^{4}-x_{2 0} \right) \right]
$$
I. $$
u_{2}=\int_{x_{2 0}}^{x_{2}} \varepsilon_{3 2} \mathrm{d} x_{2}=( b+2 c x_{1} ) \left[ \left( \frac{1} {3} x_{2}^{3}+x_{2} \right)-\left( \frac{1} {3} x_{2 0}^{3}+x_{2 0} \right) \right]
$$
J. $$
u_{2}=\int_{x_{2 0}}^{x_{2}} \varepsilon_{1 1} \mathrm{d} x_{2}=( b+3 c x_{1} ) \left[ \left( \frac{1} {3} x_{2}^{2}-x_{2} \right)-\left( \frac{1} {3} x_{2 0}^{2}-x_{2 0} \right) \right]
$$
Answer: E
Assume the design value for the compressive strength of the grouted block masonry is $f_{\mathrm{g}}=5.0 \text{ MPa}$, the total cross-sectional area of the vertical reinforcement is $2412 \text{ mm}^2$, and the design value for the compressive strength of the reinforcement is 360 MPa. Horizontal distribution reinforcement is provided within the wall, and the calculated height of the wall is $H_{0}=3600 \text{ mm}$. What is the design value of the axial compressive load-bearing capacity of this wall (in kN) ?(which of the following values is it closest to?)

Options:
A. 2450
B. 2550
C. 2350
D. 2650
E. 2250
F. 2150
G. 2850
H. 3050
I. 2750
J. 2950
Answer: B
Assuming the basic wind pressure value is $w_{0}=0.40 \mathrm{kN/m}^{2}$ for a 10-year recurrence period; for a 50-year period, the basic wind pressure value is $w_{0}=0.65 \mathrm{kN/m}^{2}$; and for a 100-year period, the basic wind pressure value is $w_{0}=0.75 \mathrm{kN/m}^{2}$. The fundamental period of the structure is $T_{1}=2.9s$. In the design for load-bearing capacity, try to determine which of the following values is closest to the resonant component factor of the building's fluctuating wind load?

Options:
A. 1.40
B. 1.10
C. 2.60
D. 1.80
E. 2.00
F. 1.30
G. 2.40
H. 1.20
I. 2.20
J. 1.60
Answer: F
A certain highway mid-span bridge is a prestressed concrete box girder structure of uniform height, with a design safety level classified as Grade II. The standard value for the self-weight shear force at a certain section of this beam is $V_{g}$, and the standard value for the shear force induced by vehicles is $V_{\mathrm{k}}$. When calculating the ultimate limit state of load-bearing capacity for this bridge, which of the following represents the basic combination of effect actions?

Options:
A. $0.8 \ \ (1.3 V_{\mathrm{g}} + 1.2 V_{\mathrm{k}})$
B. $1.1 \ \ (0.9 V_{\mathrm{g}} + 1.4 V_{\mathrm{k}})$
C. $1.3 \ \ (1.4 V_{\mathrm{g}} + 1.3 V_{\mathrm{k}})$
D. $0.9 \ \ (1.1 V_{\mathrm{g}} + 1.3 V_{\mathrm{k}})$
E. $1.2 \ \ (1.2 V_{\mathrm{g}} + 1.5 V_{\mathrm{k}})$
F. $0.9 \ \ (1.5 V_{\mathrm{g}} + 1.0 V_{\mathrm{k}})$
G. $1.0 \ \ (1.5 V_{\mathrm{g}} + 1.2 V_{\mathrm{k}})$
H. $1.0 \ \ (1.2 V_{\mathrm{g}} + 1.4 V_{\mathrm{k}})$
I. $0.7 \ \ (1.1 V_{\mathrm{g}} + 1.6 V_{\mathrm{k}})$
J. $1.1 \ \ (1.3 V_{\mathrm{g}} + 1.5 V_{\mathrm{k}})$
Answer: H
Given that the total pressure of moist air is 100 kPa, the temperature is 60°C, and the relative humidity is 40%, try to calculate the density of the moist air.

Options:
A. $$
1. 3 0 1 \mathrm{k g} / \mathrm{m}^{3}
$$
B. $$
1. 1 4 0 \mathrm{k g} / \mathrm{m}^{3}
$$
C. $$
0. 8 7 6 \mathrm{k g} / \mathrm{m}^{3}
$$
D. $$
0. 1 2 9 \mathrm{k g} / \mathrm{m}^{3}
$$
E. $$
0. 9 8 5 \mathrm{k g} / \mathrm{m}^{3}
$$
F. $$
1. 2 0 5 \mathrm{k g} / \mathrm{m}^{3}
$$
G. $$
1. 0 0 4 \mathrm{k g} / \mathrm{m}^{3}
$$
H. $$
1. 5 6 7 \mathrm{k g} / \mathrm{m}^{3}
$$
I. $$
1. 0 1 6 \mathrm{k g} / \mathrm{m}^{3}
$$
J. $$
1. 1 1 9 \mathrm{k g} / \mathrm{m}^{3}
$$
Answer: I
Try to use the mass transfer rate equation and the diffusion flux equation to convert the following mass transfer coefficients, transforming $k_{n}$ into $k_{L}^{o}$.

Options:
A. $k_{\mathrm{L}}^{\circ}=c_{\mathrm{a v}} k_{\mathrm{a}} x_{\mathrm{B M}}$
B. $k_{\mathrm{L}}^{\circ}=k_{\mathrm{a}} x_{\mathrm{B M}} / c_{\mathrm{a v}}$
C. $k_{\mathrm{L}}^{\circ}=k_{\mathrm{a}} x_{\mathrm{B M}} / c_{\mathrm{a v}}^2$
D. $k_{\mathrm{L}}^{\circ}=k_{\mathrm{n}} x_{\mathrm{M}} / a_{\mathrm{v}}$
E. $k_{\mathrm{L}}^{\circ}=k_{\mathrm{a}} x_{\mathrm{B M}} c_{\mathrm{a v}}$
F. $k_{\mathrm{L}}^{\circ}=k_{\mathrm{a}} / x_{\mathrm{B M}} c_{\mathrm{a v}}$
G. $k_{\mathrm{L}}^{\circ}=k_{\mathrm{m}} x_{\mathrm{B M}}^2 / c_{\mathrm{a v}}$
H. $k_{\mathrm{L}}^{\circ}=k_{\mathrm{a}} + x_{\mathrm{B M}} / c_{\mathrm{a v}}$
I. $k_{\mathrm{L}}^{\circ}=x_{\mathrm{B M}} / k_{\mathrm{a}} c_{\mathrm{a v}}$
J. $k_{\mathrm{L}}^{\circ}=k_{\mathrm{a}}^2 x_{\mathrm{B M}} / c_{\mathrm{a v}}$
Answer: B
Under the conditions of 25°C and a total pressure of 101.3 kPa, the phase equilibrium relationship of the ammonia-water solution is $p_{e}=93.90x \text{ kPa}$. Determine the phase equilibrium constant $m$.

Options:
A. 0.8952
B. 1.0896
C. 0.9269
D. 1.1345
E. 0.7428
F. 1.2510
G. 0.8391
H. 1.3468
I. 1.0299
J. 0.8717
Answer: C
Under the conditions of 101.3 kPa and 25°C, water is used in a packing tower to counter currently absorb hydrogen sulfide from a mixed gas. The compositions of the mixed gas entering and exiting the tower are $y_{1}=0.03$ and $y_{2}=0.001$, respectively. The equilibrium relation of the system under operating conditions is given by $p_{\mathrm{e}}=5.52 \times 10^{4} x$ kPa. During the operation, the amount of absorbent used is 1.5 times the minimum required amount. Determine the composition of the absorbing liquid, $x_{1}$.

Options:
A. $3.670×10^{-6}$
B. $3.970×10^{-5}$
C. $5.670×10^{-5}$
D. $3.670×10^{-4}$
E. $0.670×10^{-5}$
F. $2.670×10^{-5}$
G. $3.270×10^{-5}$
H. $1.670×10^{-5}$
I. $4.670×10^{-5}$
J. $3.670×10^{-5}$
Answer: J
For a certain earth fill project, the fill volume is $V = 30,000 \, \mathrm{m}^{3}$, and the required compacted dry density is not less than $\rho_{\mathrm{d}} = 1.70 \, \mathrm{t/m}^{3}$. The optimal moisture content during compaction is $\omega_{\mathrm{op}} = 18\%$. The natural moisture content of the soil material on site is $w = 15\%$, and the natural density is $\rho = 1.64 \, \mathrm{t/m}^{3}$. How much water needs to be added to the soil material before compaction to achieve the optimal moisture content?

Options:
A. $$
1 5 5 5 \mathrm{t}
$$
B. $$
1 6 2 0 \mathrm{t}
$$
C. $$
1 6 0 5 \mathrm{t}
$$
D. $$
1 4 8 0 \mathrm{t}
$$
E. $$
1 7 0 0 \mathrm{t}
$$
F. $$
1 3 5 0 \mathrm{t}
$$
G. $$
1 2 9 0 \mathrm{t}
$$
H. $$
1 5 3 0 \mathrm{t}
$$
I. $$
1 8 2 0 \mathrm{t}
$$
J. $$
1 1 5 0 \mathrm{t}
$$
Answer: H
The cohesion of a certain cohesive soil is 20 kPa, and the internal friction angle is 25°. What is the maximum vertical pressure it can withstand during a uniaxial test?

Options:
A. $$
9 0. 1 2 \mathbf{k P a}
$$
B. $$
7 3. 5 8 \mathbf{k P a}
$$
C. $$
8 1. 4 3 \mathbf{k P a}
$$
D. $$
5 8. 2 6 \mathbf{k P a}
$$
E. $$
6 2. 7 8 \mathbf{k P a}
$$
F. $$
4 7. 8 5 \mathbf{k P a}
$$
G. $$
6 5. 6 4 \mathbf{k P a}
$$
H. $$
5 4. 9 9 \mathbf{k P a}
$$
I. $$
7 7. 3 1 \mathbf{k P a}
$$
J. $$
8 2. 5 9 \mathbf{k P a}
$$
Answer: E
On a cohesive soil foundation with $c=15 \mathrm{kPa}, \ \ \varphi=0$, a $5 \mathrm{m}$ high earth embankment is quickly constructed. The unit weight of the embankment fill is $\gamma=17 ~ \mathrm{kN/m}^{3}$. It is required that the safety factor of the embankment reaches 1.2. Currently, counterweight berms are used on both sides of the embankment to ensure safety. Determine the minimum height of the counterweight berms is__.

Options:
A. 1.2m
B. 2.0m
C. 2.5m
D. 1.0m
E. 1.8m
F. 1.3m
G. 1.5m
H. 1.7m
I. 2.8m
J. 2.3m
Answer: G
In the farmland on a certain alluvial plain, the soil texture within the depth of 1 meter is loam, with a porosity of 47%. The maximum water content held by capillary action is 30%, and the wilting point is 9.5% (all values are percentages of the total soil volume). The soil bulk density is 1.40 t/m³, and the groundwater level is 7 meters below the surface. The planned thickness of the soil moisture layer is set to 0.8 meters.
Based on the given information, convert the water content to percentages by dry bulk density and express it using the percentage of the volume of the voids is().

Options:
A. ${60.3} \%$, ${22.7} \%$,
B. ${59.8} \%$, ${23.5} \%$,
C. ${65.0} \%$, ${20.7} \%$,
D. ${64.2} \%$, ${19.9} \%$,
E. ${61.7} \%$, ${18.4} \%$,
F. ${66.3} \%$, ${17.6} \%$,
G. ${62.5} \%$, ${21.0} \%$,
H. ${58.6} \%$, ${24.1} \%$,
I. ${63.8} \%$,
${20.2} \%$,
J. ${67.1} \%$, ${19.5} \%$,
Answer: I
On October 12, 2005, the Shenzhou 6 spacecraft was successfully launched. At around 16:33 on the 13th, astronaut Fei Junlong was playing a "somersault" game inside the cabin. According to reports, "it is said that Sun Wukong can travel 108,000 li in one somersault, while Fei Junlong completed 4 somersaults in 3 minutes, with each somersault covering 351 km." Based on this report, what is the ratio of the altitude of Shenzhou 6 in its predetermined orbit in space to the radius of the Earth? (It is known that the Earth's radius is 6400 km, and $g$ is taken as $10 m/s^{2}$. Retain two significant figures in the result.)

Options:
A. 4.08
B. 5.67
C. 3.25
D. 0.48
E. 1.50
F. 0.27
G. 2.15
H. 0.05
I. 0.03
J. 6.73
Answer: I
When two solid small iron spheres of the same size are in contact, the gravitational force between them is $F$. If two solid large spheres with a radius twice that of the solid small spheres are in contact, then the gravitational force between them is ().

Options:
A. 8F
B. 64F
C. 1F
D. 4F
E. 0.25F
F. 0.5F
G. 10F
H. 2F
I. 32F
J. 16F
Answer: J
The radius of the Earth is $R$, and there is a geostationary satellite at a height of $h$ from the Earth's center. Another planet has a radius of $3R$, and there is also a geostationary satellite at a height of $3h$ from the planet's center. Its orbital period is 72 hours. The ratio of the average density of this planet to the average density of the Earth is__.

Options:
A. 2:3
B. 1:2
C. 1:3
D. 4:1
E. 9:1
F. 3:2
G. 1:9
H. 1:4
I. 5:1
J. 2:1
Answer: G
In the HERA collider, a head-on collision occurs between an electron with an energy of 28 GeV and a quark carrying 20% of the energy of a proton with an energy of 800 GeV. What is the maximum value of the momentum transfer squared $q^{2}$? (In units of $(\mathrm{GeV}/c)^{2}$)

Options:
A. $$
1. 5 1 \times1 0^{4} \mathrm{~ G e V}^{2}
$$
B. $$
2. 5 6 \times1 0^{3} \mathrm{~ G e V}^{2}
$$
C. $$
2. 3 6 \times1 0^{4} \mathrm{~ G e V}^{2}
$$
D. $$
1. 8 7 \times1 0^{3} \mathrm{~ G e V}^{2}
$$
E. $$
1. 2 4 \times1 0^{5} \mathrm{~ G e V}^{2}
$$
F. $$
1. 9 2 \times1 0^{3} \mathrm{~ G e V}^{2}
$$
G. $$
2. 0 1 \times1 0^{5} \mathrm{~ G e V}^{2}
$$
H. $$
1. 4 9 \times1 0^{4} \mathrm{~ G e V}^{2}
$$
I. $$
1. 7 9 \times1 0^{4} \mathrm{~ G e V}^{2}
$$
J. $$
1. 6 8 \times1 0^{4} \mathrm{~ G e V}^{2}
$$
Answer: I
Assuming the white dwarf has a mass equal to the mass of the Sun while its radius is only 1% of the Sun's radius, its maximum rotational frequency is ().

Options:
A. $$
0. 5 9 \ \mathrm{r a d} \cdot\mathrm{s}^{-1}
$$
B. $$
0. 7 2 \ \mathrm{r a d} \cdot\mathrm{s}^{-1}
$$
C. $$
0. 9 9 \ \mathrm{r a d} \cdot\mathrm{s}^{-1}
$$
D. $$
0. 4 8 \ \mathrm{r a d} \cdot\mathrm{s}^{-1}
$$
E. $$
2. 0 0 \ \mathrm{r a d} \cdot\mathrm{s}^{-1}
$$
F. $$
4. 8 3 \ \mathrm{r a d} \cdot\mathrm{s}^{-1}
$$
G. $$
0. 6 3 \ \mathrm{r a d} \cdot\mathrm{s}^{-1}
$$
H. $$
1. 8 6 \ \mathrm{r a d} \cdot\mathrm{s}^{-1}
$$
I. $$
3. 5 7 \ \mathrm{r a d} \cdot\mathrm{s}^{-1}
$$
J. $$
1. 1 5 \ \mathrm{r a d} \cdot\mathrm{s}^{-1}
$$
Answer: G
Estimate the mass and radius of black holes whose lifetime is equal to the age of the universe.

Options:
A. $$
5.30 \times 10^{25} \ \mathrm{kg}
$$
$$
5.8 \times 10^{-12} \ \mathrm{m}
$$
B. $$
3.75 \times 10^{18} \ \mathrm{kg}
$$
$$
9.0 \times 10^{-14} \ \mathrm{m}
$$
C. $$
2.41 \times 10^{11} \ \mathrm{kg}
$$
$$
7.4 \times 10^{-16} \ \mathrm{m}
$$
D. $$
6.15 \times 10^{20} \ \mathrm{kg}
$$
$$
2.4 \times 10^{-10} \ \mathrm{m}
$$
E. $$
7.25 \times 10^{19} \ \mathrm{kg}
$$
$$
4.0 \times 10^{-15} \ \mathrm{m}
$$
F. $$
4.00 \times 10^{23} \ \mathrm{kg}
$$
$$
1.5 \times 10^{-9} \ \mathrm{m}
$$
G. $$
8.60 \times 10^{14} \ \mathrm{kg}
$$
$$
7.5 \times 10^{-13} \ \mathrm{m}
$$
H. $$
9.00 \times 10^{16} \ \mathrm{kg}
$$
$$
6.4 \times 10^{-11} \ \mathrm{m}
$$
I. $$
1.20 \times 10^{15} \ \mathrm{kg}
$$
$$
3.2 \times 10^{-13} \ \mathrm{m}
$$
J. $$
3.50 \times 10^{13} \ \mathrm{kg}
$$
$$
5.2 \times 10^{-08} \ \mathrm{m}
$$
Answer: C
The escape velocity of a typical galaxy and a typical galaxy cluster is ().

Options:
A. $$
v_{\mathrm{galaxy}} \sim 2.5 \times 10^5 m \cdot s^{-1}
$$
$$
v_{\mathrm{cluster}} \sim 4 \times 10^5 m \cdot s^{-1}
$$
B. $$
v_{\mathrm{galaxy}} \sim 2.9 \times 10^5 m \cdot s^{-1}
$$
$$
v_{\mathrm{cluster}} \sim 3.9 \times 10^5 m \cdot s^{-1}
$$
C. $$
v_{\mathrm{galaxy}} \sim 1.8 \times 10^5 m \cdot s^{-1}
$$
$$
v_{\mathrm{cluster}} \sim 3.3 \times 10^5 m \cdot s^{-1}
$$
D. $$
v_{\mathrm{galaxy}} \sim 4.0 \times 10^5 m \cdot s^{-1}
$$
$$
v_{\mathrm{cluster}} \sim 6.5 \times 10^5 m \cdot s^{-1}
$$
E. $$
v_{\mathrm{galaxy}} \sim 3.1 \times 10^5 m \cdot s^{-1}
$$
$$
v_{\mathrm{cluster}} \sim 5.2 \times 10^5 m \cdot s^{-1}
$$
F. $$
v_{\mathrm{galaxy}} \sim 2.2 \times 10^5 m \cdot s^{-1}
$$
$$
v_{\mathrm{cluster}} \sim 5.5 \times 10^5 m \cdot s^{-1}
$$
G. $$
v_{\mathrm{galaxy}} \sim 3.2 \times 10^5 m \cdot s^{-1}
$$
$$
v_{\mathrm{cluster}} \sim 4.6 \times 10^5 m \cdot s^{-1}
$$
H. $$
v_{\mathrm{galaxy}} \sim 2.0 \times 10^5 m \cdot s^{-1}
$$
$$
v_{\mathrm{cluster}} \sim 4.7 \times 10^5 m \cdot s^{-1}
$$
I. $$
v_{\mathrm{galaxy}} \sim 3.5 \times 10^5 m \cdot s^{-1}
$$
$$
v_{\mathrm{cluster}} \sim 2.8 \times 10^5 m \cdot s^{-1}
$$
J. $$
v_{\mathrm{galaxy}} \sim 1.9 \times 10^5 m \cdot s^{-1}
$$
$$
v_{\mathrm{cluster}} \sim 3.7 \times 10^5 m \cdot s^{-1}
$$
Answer: A
The mean free path for primary cosmic ray protons interacting in the atmosphere is $\lambda \sim 100 \ \mathrm{g} \ \mathrm{cm}^{-2}$. They produce relativistic charged $\pi$ mesons with energy $E$ that propagate vertically downward. These $\pi$ mesons subsequently decay in flight or undergo nuclear interactions, with the mean free path also being equal to $\lambda$. Assuming the atmosphere is of an exponential type with a scale height $H$, and $E_{0}=m_{\pi} \, c^{2} \, H / (c \, \tau_{\pi})$, what is the total probability for a $\pi$ meson to undergo decay rather than a nuclear reaction? (Express the probability in terms of $E$ and $E_0$.)

Options:
A. $$ P=(E_{0}-E) / (E_{0}+E) $$
B. $$ P=(E \times E_{0}) / (E_{0}+E) $$
C. $$ P=E_{0} / (E_{0}-E) $$
D. $$ P=E / (E_{0}+E) $$
E. $$ P=(E+E_{0}) / E $$
F. $$ P=E_{0} / (E_{0}+E) $$
G. $$ P=(E_{0}+E) / E_{0} $$
H. $$ P=E_{0} / (E-E_{0}) $$
I. $$ P=(E_{0} \times E) / (E_{0}+E) $$
J. $$ P=1 / (E_{0} \times E) $$
Answer: F
A uniform rectangular thin plate weighing 50 N is suspended and can freely rotate around a horizontal edge. A steady wind causes the plate to maintain an angle of 18° with the vertical plane.What is the pressure exerted by the wind perpendicular to the plate ?

Options:
A. 13.1 $\mathbf{N}$
B. 9.7 $\mathbf{N}$
C. 19.2 $\mathbf{N}$
D. 15.5 $\mathbf{N}$
E. 12.3 $\mathbf{N}$
F. 17.0 $\mathbf{N}$
G. 21.4 $\mathbf{N}$
H. 18.6 $\mathbf{N}$
I. 14.8 $\mathbf{N}$
J. 16.9 $\mathbf{N}$
Answer: D
A particle moves under the central attractive force $F(r) = -\frac{\alpha m}{r^{5}}$ in a circular orbit. If the particle moves with the same angular momentum as the circular orbit, and when $r = 2a, \, \theta = 0$, $\dot{r} = -\frac{3v}{4\sqrt{2}}$.What is the trajectory equation of the particle under these conditions ?

Options:
A. $$r=\frac{a(1+3\cos(\sqrt{2}\theta))}{3\cos(\sqrt{2}\theta)-1}$$
B. $$r=\frac{a(1+3\mathrm{e}^{\sqrt{2}\theta})}{1-3\mathrm{e}^{\sqrt{2}\theta}}$$
C. $$r=\frac{a(1+3\mathrm{e}^{\sqrt{2}\theta})}{3\mathrm{e}^{\sqrt{2}\theta}-1}$$
D. $$r=\frac{a(1+3\mathrm{e}^{\theta})}{3\mathrm{e}^{\theta}-1}$$
E. $$r=\frac{a(1+2\mathrm{e}^{\sqrt{2}\theta})}{2\mathrm{e}^{\sqrt{2}\theta}-1}$$
F. $$r=\frac{a(1+3\mathrm{e}^{-\sqrt{2}\theta})}{3\mathrm{e}^{\sqrt{2}\theta}-1}$$
G. $$r=\frac{a(1+3\mathrm{e}^{2\theta})}{3\mathrm{e}^{2\theta}-1}$$
H. $$r=\frac{a(1-3\mathrm{e}^{\sqrt{2}\theta})}{3\mathrm{e}^{\sqrt{2}\theta}-1}$$
I. $$r=\frac{a(2+3\mathrm{e}^{\sqrt{2}\theta})}{3\mathrm{e}^{\sqrt{2}\theta}-1}$$
J. $$r=\frac{a(1+3\mathrm{e}^{\theta/2})}{3\mathrm{e}^{\theta/2}-1}$$
Answer: C
In the turnover mechanism used in rice threshing machines, the tie rod OA and the wheel $I$ with a radius of $r_{1}$ are loosely fitted on the axis $O$. The wheel $II$'s axis $O_{1}$ is fixedly installed on the tie rod. The wheel $III$ with a radius of $r_{3}$ can freely rotate around the axis $O$. Given that the angular velocity of the tie rod OA is $\omega_{0}$ and the wheel $III$ has a reverse angular velocity $\omega_{3}$.What is the angular velocity $\omega_{1}$ of the wheel $I$?

Options:
A. $$
\omega_{1}=\omega_{0} \left( 1-\frac{r_{3}} {r_{1}} \right)+\frac{r_{3}} {r_{1}} | \omega_{3} |.
$$
B. $$
\omega_{1}=\omega_{0} \left( 1+\frac{r_{3}} {r_{1}} \right)+\frac{r_{3}} {r_{1}} | \omega_{3} |.
$$
C. $$
\omega_{1}= \omega_{3} + \frac{r_{3}} {r_{2}} \omega_{0}.
$$
D. $$
\omega_{1}=\omega_{0} + \frac{r_{3}}{r_{1}} (\omega_{3})^2.
$$
E. $$
\omega_{1}=\frac{r_{3}} {r_{1}} | \omega_{0}-\omega_{3} |.
$$
F. $$
\omega_{1}=\omega_{0} \cdot \left( 1+\frac{r_{2}} {r_{1}} \right)-\frac{r_{3}} {r_{1}} | \omega_{3} |.
$$
G. $$
\omega_{1}=\frac{r_{3}} {r_{1}} \cdot \omega_{0} + \omega_{3}.
$$
H. $$
\omega_{1}=\omega_{0} \times \left( 1+\frac{r_{3}} {r_{1}} \right)+\omega_{3}.
$$
I. $$
\omega_{1}=\omega_{0} \left( 1-\frac{r_{3}} {r_{2}} \right)+\frac{r_{3}} {r_{1}} | \omega_{3} |.
$$
J. $$
\omega_{1}=\omega_{0} \left( 1+\frac{r_{3}} {r_{2}} \right)+\frac{r_{3}} {r_{1}} | \omega_{3} |.
$$
Answer: B
A particle with mass $m$ begins to move from a stationary state at position $x_{0}=a$, under the influence of both gravitational and repulsive forces. The gravitational force is proportional to the distance of the particle from the origin: $F_{x}=-c_{1} m x$, and the repulsive force is proportional to the cube of the distance: $Q_{x}=c_{2} m x^{3}$.What is the relationship among $c_{1}$, $c_{2}$ and $a$ to ensure that the particle reaches the origin and comes to a stop ?

Options:
A. $$
c_{1}=2 c_{2} a^{3}.
$$
B. $$
c_{1}=c_{2} a^{2}.
$$
C. $$
c_{1}=\frac{3} {2} c_{2} a^{2}.
$$
D. $$
c_{1}=\frac{1} {3} c_{2} a^{2}.
$$
E. $$
c_{1}=c_{2} a^{3}.
$$
F. $$
c_{1}=c_{2} a^{4}.
$$
G. $$
c_{1}=\frac{1} {4} c_{2} a^{3}.
$$
H. $$
c_{1}=\frac{2} {3} c_{2} a^{2}.
$$
I. $$
c_{1}=\frac{1} {2} c_{2} a^{2}.
$$
J. $$
c_{1}=2 c_{2} a^{2}.
$$
Answer: I
A weight with a mass of 20 $\mathbf{kg}$ is hung on a spring, performing oscillations. It is observed that after 10 oscillations, the maximum displacement is reduced to half, and the time required for these 10 oscillations is 9 seconds. The damping coefficient $\alpha$ (where the resistance of the medium is proportional to velocity). What is the stiffness coefficient $c$ ?

Options:
A. $$
\alpha=3. 2 1 \ \mathrm{N} \cdot\mathrm{s} / \mathrm{m}, c=1 2 0 0. 7 \ \mathrm{N} / \mathrm{m}.
$$
B. $$
\alpha=2. 7 1 \ \mathrm{N} \cdot\mathrm{s} / \mathrm{m}, c=1 0 1 0. 5 \ \mathrm{N} / \mathrm{m}.
$$
C. $$
\alpha=4. 8 3 \ \mathrm{N} \cdot\mathrm{s} / \mathrm{m}, c=9 7 1. 6 \ \mathrm{N} / \mathrm{m}.
$$
D. $$
\alpha=4. 5 6 \ \mathrm{N} \cdot\mathrm{s} / \mathrm{m}, c=8 5 0. 3 \ \mathrm{N} / \mathrm{m}.
$$
E. $$
\alpha=2. 5 7 \ \mathrm{N} \cdot\mathrm{s} / \mathrm{m}, c=1 1 0 2. 4 \ \mathrm{N} / \mathrm{m}.
$$
F. $$
\alpha=3. 6 6 \ \mathrm{N} \cdot\mathrm{s} / \mathrm{m}, c=9 9 5. 2 \ \mathrm{N} / \mathrm{m}.
$$
G. $$
\alpha=3. 0 8 \ \mathrm{N} \cdot\mathrm{s} / \mathrm{m}, c=9 7 4. 8 \ \mathrm{N} / \mathrm{m}.
$$
H. $$
\alpha=3. 9 4 \ \mathrm{N} \cdot\mathrm{s} / \mathrm{m}, c=9 0 0. 0 \ \mathrm{N} / \mathrm{m}.
$$
I. $$
\alpha=3. 1 9 \ \mathrm{N} \cdot\mathrm{s} / \mathrm{m}, c=8 4 6. 9 \ \mathrm{N} / \mathrm{m}.
$$
J. $$
\alpha=4. 0 8 \ \mathrm{N} \cdot\mathrm{s} / \mathrm{m}, c=7 9 2. 5 \ \mathrm{N} / \mathrm{m}.
$$
Answer: G
Under the influence of thermal neutrons, a $U^{235}$ nucleus undergoes fission, resulting in two fragments with mass numbers 95 and 139, while also emitting two neutrons. Calculate the total energy released during the fission process.

Options:
A. ~175 MeV (Mega-electron volts).
B. ~230 MeV (Mega-electron volts).
C. ~220 MeV (Mega-electron volts).
D. ~150 MeV (Mega-electron volts).
E. ~190 MeV (Mega-electron volts).
F. ~140 MeV (Mega-electron volts).
G. ~210 MeV (Mega-electron volts).
H. ~200 MeV (Mega-electron volts).
I. ~180 MeV (Mega-electron volts).
J. ~160 MeV (Mega-electron volts).
Answer: H
Cosmic rays at sea level can generate about 2 pairs of ions per second in 1 cubic centimeter of air. At higher altitudes, the intensity of cosmic rays is related to the latitude of the region. Generally speaking, at an altitude of 3 kilometers above sea level, about 10 pairs of ions are generated per second in 1 cubic centimeter of air, and at 12 kilometers, about 200 pairs are formed. Calculate the dose received per day at each of the above altitudes due to the effect of cosmic rays, expressed in Roentgens.

Options:
A. $$
7.5 \times 10^{-6}; \quad 3.82 \times 10^{-4}; \quad 9.0 \times 10^{-8}
$$
Lun.
B. $$
8.5 \cdot 10^{-6}; \quad 4.63 \cdot 10^{-4}; \quad 7.9 \cdot 10^{-8}
$$
Lun.
C. $$
9. 1 \cdot 10^{-6}; \quad 3. 14 \cdot 10^{-4}; \quad 7. 2 \cdot 10^{-8}
$$
Lun.
D. $$
8. 1 \cdot1 0^{-6} ; \quad4. 4 9 \cdot1 0^{-4} ; \quad9. 2 \cdot1 0^{-8}
$$
Lun.
E. $$
7.9 \cdot 10^{-6} ; \quad 4.05 \cdot 10^{-4} ; \quad 8.7 \cdot 10^{-8}
$$
Lun.
F. $$
9. 3 \times 10^{-6} ; \quad3. 2 5 \times 10^{-4} ; \quad6. 8 \times 10^{-8}
$$
Lun.
G. $$
8.8 \times 10^{-6}; \quad 3.98 \times 10^{-4}; \quad 8.5 \times 10^{-8}
$$
Lun.
H. $$
6.2 \times 10^{-6}; \quad 2.91 \times 10^{-4}; \quad 9.4 \times 10^{-8}
$$
Lun.
I. $$
7.8 \times 10^{-6}; \quad 5.15 \times 10^{-4}; \quad 9.3 \times 10^{-8}
$$
Lun.
J. $$
8.3 \times 10^{-6}; \quad 4.15 \times 10^{-4}; \quad 8.3 \times 10^{-8}
$$
Lun.
Answer: J
Using a Geiger-Müller counter to measure
$$
\mathrm{Ra^{223}}
$$
and an unknown radioactive isotope, the readings show 9000 counts per minute. Measurements taken five and ten days later show 4517 counts per minute and 2509 counts per minute, respectively. Determine what the unknown radioactive isotope in the mixture?

Options:
A. $$
\mathrm{C s}^{137}
$$
B. $$
\mathrm{P o}^{210}
$$
C. $$
\mathrm{A m}^{241}
$$
D. $$
\mathrm{T h}^{227}
$$
E. $$
\mathrm{C o}^{60}
$$
F. $$
\mathrm{U}^{233}
$$
G. $$
\mathrm{R a}^{224}
$$
H. $$
\mathrm{R a}^{221}
$$
I. $$
\mathrm{P u}^{239}
$$
J. $$
\mathrm{I}^{131}
$$
Answer: G
Bombard a carbon target with a density of $2$ using deuterons with an energy of 3.0 MeV. If the bombardment lasts for 10 minutes with a deuteron beam current of 200 microamperes, and the effective cross-section of the reaction is 0.01 bar, with a target area of 12 cm$^{2}$ and a target thickness of 0.003 cm, calculate the radioactivity (in Curies) of the produced $\mathbf{N}^{13}$.

Options:
A. 1.2 Curie
B. 0.7 Curie
C. 0.6 Curie
D. 0.2 Curie
E. 0.3 Curie
F. 1.0 Curie
G. 1.5 Curie
H. 0.8 Curie
I. 0.4 Curie
J. 0.9 Curie
Answer: C
To reduce the energy of a neutron from $E_{0}$ = 2 MeV to $E_{k}$ = 0.025 eV, it passes sequentially through $H_{2}$O, $D_{2}$O, Be, and C, where the energy lost in a single collision corresponds to 0.92, 0.51, 0.2, and 0.16, respectively. Determine the average number of collisions in each material and compare the efficiency of the above substances as moderators.

Options:
A. 20;33;95;111
B. 24;32;93;117
C. 22;30;96;119
D. 20;36;91;115
E. 18;35;89;110
F. 25;31;94;118
G. 22;37;90;112
H. 19;38;88;113
I. 23;39;87;116
J. 21;34;92;114
Answer: D
What is the probability that a ground-state tritium atom becomes ground-state $\mathrm{He}^{+}$ instantly after undergoing beta decay?

Options:
A. $$
{\frac{5 0 8} {7 4 6}}
$$
B. $$
{\frac{6 2 1} {7 0 3}}
$$
C. $$
{\frac{6 0 1} {7 3 5}}
$$
D. $$
{\frac{5 4 7} {7 6 1}}
$$
E. $$
{\frac{5 5 2} {9 1 2}}
$$
F. $$
{\frac{4 9 3} {8 4 1}}
$$
G. $$
{\frac{3 8 2} {5 8 4}}
$$
H. $$
{\frac{5 1 2} {7 2 9}}
$$
I. $$
{\frac{4 4 4} {7 8 8}}
$$
J. $$
{\frac{5 2 9} {6 9 4}}
$$
Answer: H
The distance between the two hydrogen nuclei in a hydrogen molecule is approximately is____.

Options:
A. $$
1. 2 \ \mathrm{n m}
$$
B. $$
1. 5 \ \mathrm{n m}
$$
C. $$
1. 0 \ \mathrm{n m}
$$
D. $$
0. 7 \ \mathrm{n m}
$$
E. $$
0. 5 \ \mathrm{n m}
$$
F. $$
0. 3 \ \mathrm{n m}
$$
G. $$
0. 8 \ \mathrm{n m}
$$
H. $$
0. 9 \ \mathrm{n m}
$$
I. $$
0. 6 \ \mathrm{n m}
$$
J. $$
0. 1 \ \mathrm{n m}
$$
Answer: J
Given that the wavenumber of the incident light is $200000 \, \mathrm{cm}^{-1}$, try to calculate the possible wavenumbers of the scattered lines produced during Raman scattering in the HCl molecule. It is known that the vibrational frequency of the HCl molecule is $9 \times 10^{13} \, \mathrm{Hz}$, and the rotational constant $B$ is $10.59 \, \mathrm{cm}^{-1}$ is___.

Options:
A. $$
\left[ 1 8 0 0 0 \pm( 8 \,+\, 2 n ) \, \times\, 1 0. 5 9 \right] \mathrm{c m}^{-1}
$$
$$
[ 1 5 0 0 0 \pm\, ( 5 \,+\, 6 n ) \, \times\, 1 0. 5 9 ] \mathrm{c m}^{-1}
$$
$$
[ 2 4 0 0 0 \pm( 9+3 n ) \times1 0. 5 9 ] \mathrm{c m}^{-1}
$$
B. $$
\left[ 2 1 5 0 0 \pm( 7 \,+\, 4 n ) \, \times\, 1 0. 5 9 \right] \mathrm{c m}^{-1}
$$
$$
[ 2 6 0 0 0 \pm\, ( 8 \,+\, 2 n ) \, \times\, 1 0. 5 9 ] \mathrm{c m}^{-1}
$$
$$
[ 1 9 0 0 0 \pm( 6+5 n ) \times1 0. 5 9 ] \mathrm{c m}^{-1}
$$
C. $$
\left[ 1 9 8 0 0 \pm( 5 \,+\, 8 n ) \, \times\, 1 0. 5 9 \right] \mathrm{c m}^{-1}
$$
$$
[ 2 0 7 0 0 \pm\, ( 9 \,+\, 2 n ) \, \times\, 1 0. 5 9 ] \mathrm{c m}^{-1}
$$
$$
[ 1 8 5 0 0 \pm( 6+3 n ) \times1 0. 5 9 ] \mathrm{c m}^{-1}
$$
D. $$
\left[ 2 5 0 0 0 \pm( 9 \,+\, 2 n ) \, \times\, 1 0. 5 9 \right] \mathrm{c m}^{-1}
$$
$$
[ 1 7 5 0 0 \pm\, ( 6 \,+\, 3 n ) \, \times\, 1 0. 5 9 ] \mathrm{c m}^{-1}
$$
$$
[ 2 1 0 0 0 \pm( 7+4 n ) \times1 0. 5 9 ] \mathrm{c m}^{-1}
$$
E. $$
\left[ 2 0 5 0 0 \pm( 5 \,+\, 2 n ) \, \times\, 1 0. 5 9 \right] \mathrm{c m}^{-1}
$$
$$
[ 1 9 0 0 0 \pm\, ( 7 \,+\, 3 n ) \, \times\, 1 0. 5 9 ] \mathrm{c m}^{-1}
$$
$$
[ 1 8 0 0 0 \pm( 8+3 n ) \times1 0. 5 9 ] \mathrm{c m}^{-1}
$$
F. $$
\left[ 2 1 8 0 0 \pm( 6 \,+\, 3 n ) \, \times\, 1 0. 5 9 \right] \mathrm{c m}^{-1}
$$
$$
[ 2 4 5 0 0 \pm\, ( 7 \,+\, 3 n ) \, \times\, 1 0. 5 9 ] \mathrm{c m}^{-1}
$$
$$
[ 1 5 8 0 0 \pm( 5+6 n ) \times1 0. 5 9 ] \mathrm{c m}^{-1}
$$
G. $$
\left[ 2 3 5 0 0 \pm( 5 \,+\, 7 n ) \, \times\, 1 0. 5 9 \right] \mathrm{c m}^{-1}
$$
$$
[ 2 0 8 0 0 \pm\, ( 6 \,+\, 5 n ) \, \times\, 1 0. 5 9 ] \mathrm{c m}^{-1}
$$
$$
[ 1 6 0 0 0 \pm( 9+2 n ) \times1 0. 5 9 ] \mathrm{c m}^{-1}
$$
H. $$
\left[ 2 0 0 0 0 \pm( 6 \,+\, 4 n ) \, \times\, 1 0. 5 9 \right] \mathrm{c m}^{-1}
$$
$$
[ 2 3 0 0 0 \pm\, ( 6 \,+\, 4 n ) \, \times\, 1 0. 5 9 ] \mathrm{c m}^{-1}
$$
$$
[ 1 7 0 0 0 \pm( 6+4 n ) \times1 0. 5 9 ] \mathrm{c m}^{-1}
$$
I. $$
\left[ 2 2 0 0 0 \pm( 8 \,+\, 5 n ) \, \times\, 1 0. 5 9 \right] \mathrm{c m}^{-1}
$$
$$
[ 2 2 5 0 0 \pm\, ( 5 \,+\, 4 n ) \, \times\, 1 0. 5 9 ] \mathrm{c m}^{-1}
$$
$$
[ 1 7 5 0 0 \pm( 7+2 n ) \times1 0. 5 9 ] \mathrm{c m}^{-1}
$$
J. $$
\left[ 1 9 5 0 0 \pm( 6 \,+\, 3 n ) \, \times\, 1 0. 5 9 \right] \mathrm{c m}^{-1}
$$
$$
[ 2 1 0 0 0 \pm\, ( 7 \,+\, 2 n ) \, \times\, 1 0. 5 9 ] \mathrm{c m}^{-1}
$$
$$
[ 1 6 5 0 0 \pm( 5+4 n ) \times1 0. 5 9 ] \mathrm{c m}^{-1}
$$
Answer: H
Calculate the binding energy and average binding energy of the nuclides $^{4}$He, $^{40}$Ca, and $^{56}$Fe. The atomic masses of these nuclides are 4.002603u, 39.962590u, and 55.934934u respectively. The mass of a hydrogen atom is 1.007825u, and the neutron mass is $m_{\mathrm{n}}=$ 1.008665u.

Options:
A. $$
1 9. 2 5 6 \mathrm{~ M e V} \,,
7. 4 4 1 \mathrm{M e V}
$$ ;
$$
3 3 1. 8 \ \mathrm{M e V} \,,
8. 6 2 \mathbf{M e V}
$$;
$$
4 7 0. 1 9 \ \mathrm{M e V} \,,
8. 9 0 \mathrm{M e V}
$$.
B. $$
1 8. 7 8 4 \mathrm{~ M e V} \,,
7. 5 3 2 \mathrm{M e V}
$$ ;
$$
3 3 9. 1 \ \mathrm{M e V} \,,
8. 7 2 \mathbf{M e V}
$$;
$$
4 6 5. 0 5 \ \mathrm{M e V} \,,
8. 8 8 \mathrm{M e V}
$$.
C. $$
2 6. 4 8 0 \mathrm{~ M e V} \,,
7. 1 9 7 \mathrm{M e V}
$$ ;
$$
3 4 7. 6 \ \mathrm{M e V} \,,
8. 4 5 \mathbf{M e V}
$$;
$$
4 9 4. 3 4 \ \mathrm{M e V} \,,
8. 9 2 \mathrm{M e V}
$$.
D. $$
2 4. 8 9 4 \mathrm{~ M e V} \,,
7. 2 2 9 \mathrm{M e V}
$$ ;
$$
3 4 0. 3 \ \mathrm{M e V} \,,
8. 6 8 \mathbf{M e V}
$$;
$$
4 8 8. 2 9 \ \mathrm{M e V} \,,
9. 0 6 \mathrm{M e V}
$$.
E. $$
2 9. 0 1 7 \mathrm{~ M e V} \,,
6. 9 8 3 \mathrm{M e V}
$$ ;
$$
3 5 3. 7 \ \mathrm{M e V} \,,
8. 4 9 \mathbf{M e V}
$$;
$$
5 1 1. 4 2 \ \mathrm{M e V} \,,
8. 6 3 \mathrm{M e V}
$$.
F. $$
2 3. 1 4 8 \mathrm{~ M e V} \,,
6. 8 9 3 \mathrm{M e V}
$$ ;
$$
3 5 0. 2 \ \mathrm{M e V} \,,
8. 4 3 \mathbf{M e V}
$$;
$$
4 9 0. 4 6 \ \mathrm{M e V} \,,
8. 6 9 \mathrm{M e V}
$$.
G. $$
2 5. 3 7 0 \mathrm{~ M e V} \,,
7. 3 6 4 \mathrm{M e V}
$$ ;
$$
3 4 4. 8 \ \mathrm{M e V} \,,
8. 6 7 \mathbf{M e V}
$$;
$$
4 7 9. 8 9 \ \mathrm{M e V} \,,
9. 1 0 \mathrm{M e V}
$$.
H. $$
3 0. 1 5 9 \mathrm{~ M e V} \,,
6. 7 5 0 \mathrm{M e V}
$$ ;
$$
3 6 2. 4 \ \mathrm{M e V} \,,
8. 3 7 \mathbf{M e V}
$$;
$$
5 0 5. 7 2 \ \mathrm{M e V} \,,
8. 8 3 \mathrm{M e V}
$$.
I. $$
2 8. 2 9 6 \mathrm{~ M e V} \,,
7. 0 7 4 \mathrm{M e V}
$$ ;
$$
3 4 2. 1 \ \mathrm{M e V} \,,
8. 5 5 \mathbf{M e V}
$$;
$$
4 9 2. 3 1 \ \mathrm{M e V} \,,
8. 7 9 \mathrm{M e V}
$$.
J. $$
2 7. 1 6 2 \mathrm{~ M e V} \,,
7. 0 2 8 \mathrm{M e V}
$$ ;
$$
3 4 5. 9 \ \mathrm{M e V} \,,
8. 8 0 \mathbf{M e V}
$$;
$$
4 9 8. 5 3 \ \mathrm{M e V} \,,
9. 2 7 \mathrm{M e V}
$$.
Answer: I
The far-infrared spectrum of HBr consists of a series of spectral lines spaced $17cm^{-1}$ apart. What is the internuclear distance of HBr?

Options:
A. $$
4. 9 \times1 0^{-8} \mathrm{c m}
$$
B. $$
9. 6 \times1 0^{-8} \mathrm{c m}
$$
C. $$
3. 1 \times1 0^{-8} \mathrm{c m}
$$
D. $$
1. 0 \times1 0^{-8} \mathrm{c m}
$$
E. $$
4. 7 \times1 0^{-8} \mathrm{c m}
$$
F. $$
3. 3 \times1 0^{-8} \mathrm{c m}
$$
G. $$
1. 8 \times1 0^{-8} \mathrm{c m}
$$
H. $$
2. 5 \times1 0^{-8} \mathrm{c m}
$$
I. $$
2. 0 \times1 0^{-8} \mathrm{c m}
$$
J. $$
1. 4 \times1 0^{-8} \mathrm{c m}
$$
Answer: J
An atom initially located at a specific position in a one-dimensional lattice with lattice constant $a$ jumps to the nearest neighboring position every $\tau$ seconds. The probability of jumping to the right is $p$, and the probability of jumping to the left is $q = 1 - p$.
(1) What is the average position $\overline{{{x}}}$ of the atom at time $t = N \tau$ ? ( $N \gg 1$ )
(2) What is the mean square deviation from the average position at time $t$ ?

Options:
A. $$
N a ( p-q )
$$
$$
4 N a^{2} p q
$$
B. $$
N a (p+q)
$$
$$
N^{2} a^{2} (p-q)
$$
C. $$
N^{2} a p (q)
$$
$$
5 N a^{2} p q
$$
D. $$
N^{2} a q (1 - p)
$$
$$
(2 N a p)^{2}
$$
E. $$
q N a (p-q)
$$
$$
N a^{2} (1-p)(1-q)
$$
F. $$
p^{2} a N (q-p)
$$
$$
N a^{2} (p + q)
$$
G. $$
a N (p + q)
$$
$$
N p q a^{2}
$$
H. $$
(1 - p) N q a
$$
$$
4 a N^{2} p q
$$
I. $$
q N a (1 + p)
$$
$$
3 N a^{2} p q
$$
J. $$
N a p (1 - q)
$$
$$
2 N a^{2} q (1-p)
$$
Answer: A