MikaStars39/nano-eval huggingface dataset:
The vacancy formation energy for copper is $1.7 \times 10^{-19} \mathrm{J}$. Try calculating the number of vacancies in $1cm^{3}$ of copper at 1000°C. (The density of copper is $8.9 \mathrm{g/cm}^{3}$, the relative atomic mass is 63.5, and the Boltzmann constant $K=1.38 \times 10^{-23} \mathrm{J/K}$.)

Options:
A. $$
\approx6. 0 5 \times 1 0^{1 8}
$$
B. $$
\approx5. 2 7 \times1 0^{1 8}
$$
C. $$
\approx3. 1 2 \times 1 0^{1 6}
$$
D. $$
\approx5. 3 5 \times 1 0^{1 8}
$$
E. $$
\approx4. 9 8 \times 1 0^{1 8}
$$
F. $$
\approx8. 2 9 \times 1 0^{1 7}
$$
G. $$
\approx4. 6 7 \times 1 0^{1 8}
$$
H. $$
\approx4. 7 1 \times 1 0^{1 7}
$$
I. $$
\approx2. 8 4 \times 1 0^{2 0}
$$
J. $$
\approx6. 3 9 \times 1 0^{1 9}
$$
Answer: B
Copper single crystal's exterior surface is parallel to {001}. When tensile force is applied, the force axis is in the [001] direction. It is measured that $\tau_{c}=0.7$ $\mathrm{MPa}$. Calculate the stress at which the material yields.

Options:
A. $$
1 . 2 5 0 \mathrm{ ~ M P a}
$$
B. $$
1 . 5 5 0 \mathrm{ ~ M P a}
$$
C. $$
2 . 3 4 5 \mathrm{ ~ M P a}
$$
D. $$
0 . 9 2 5 \mathrm{ ~ M P a}
$$
E. $$
4 . 1 0 5 \mathrm{ ~ M P a}
$$
F. $$
9 . 0 5 5 \mathrm{ ~ M P a}
$$
G. $$
3 . 8 4 0 \mathrm{ ~ M P a}
$$
H. $$
1. 7 1 5 \mathrm{~ M P a}
$$
I. $$
1 . 3 6 5 \mathrm{ ~ M P a}
$$
J. $$
0 . 6 0 5 \mathrm{ ~ M P a}
$$
Answer: H
A $PN$ junction is formed by a $P$-type germanium with a resistivity of 1 $\Omega$cm and an N-type germanium with a resistivity of 0.1 $\Omega$cm. It is known that at the aforementioned resistivity, the mobility of holes in the $P$ region $\mu_{p} = 1650 \, \mathrm{cm}^{2} / \mathbf{V} \cdot \mathbf{s}$, and the mobility of electrons in the $N$ region $\mu_{n} = 30000 \, \mathrm{cm}^{2} / \mathbf{V} \cdot \mathbf{s}$. Try calculating the built-in potential difference $V_{D}$ at room temperature $300^{\circ} \mathbf{K}$.

Options:
A. $$
=306 mV
$$
B. $$ =398 mV $$
C. $$ =369 mV $$
D. $$ =127 mV $$
E. $$ =302 mV $$
F. $$ =517 mV $$
G. $$ =215 mV $$
H. $$ =289 mV $$
I. $$ =458 mV $$
J. $$ =263 mV $$
Answer: A
The center frequency of the single-tuned resonant amplifier is $f_{0}=10.7$ MHz. The semiconductor transistor has $I_{e} = 1 \mathrm{~ m} \mathbf{A}, U_{ce} = 6 \mathrm{~V}$. At the operating frequency, the measured $\mathbf{Y}$ parameters are: $\mathbf{y}_{ie} = (2.8+j3.5) \mathbf{m} \mathbf{S}, \mathbf{y}_{re} = (0.08-j0.3) \mathbf{m} \mathbf{S}, \mathbf{y}_{fe} = (36-j17) \mathrm{mS}, \mathbf{y}_{oe} = (0.2+j1.4) \mathrm{m} \mathbf{S}$. Assuming the unloaded quality factor of the circuit is $Q_{0}=60$ and the loaded quality factor is $Q_{e}=30$, calculate the power gain when matched

Options:
A. $$
= 1 0 3. 2
$$
B. $$
= 6 5 4. 1
$$
C. $$
= 2 1 9. 6
$$
D. $$
= 8 9 0. 4
$$
E. $$
= 4 8 3. 3
$$
F. $$
= 7 3 8. 5
$$
G. $$
= 1 7 6. 9
$$
H. $$
= 3 4 2. 8
$$
I. $$
= 5 7 1. 0
$$
J. $$
= 9 2 5. 7
$$
Answer: G
There is a resonant power amplifier, with $E_{c} = 12 \mathrm{V}$, a loop resonant impedance of $R_{e} = 130 \Omega$, collector efficiency $\eta = 74.5\%$, and output power $P_{o} = 500 \mathrm{mW}$. Now, in order to increase $\eta$, under the condition that $E_{e_{'}} R_{e_{'}} P_{o}$ remains unchanged, the conduction angle is reduced to 60°, making the amplifier operate in a critical state. Calculate the efficiency when $\theta = 60°$.

Options:
A. $$
= 8 5. 5 \%
$$
B. $$
= 8 0. 2 \%
$$
C. $$
= 8 9. 0 \%
$$
D. $$
= 9 0. 1 \%
$$
E. $$
= 6 7. 7 \%
$$
F. $$
= 7 2. 3 \%
$$
G. $$
= 7 8. 4 \%
$$
H. $$
= 8 7. 6 \%
$$
I. $$
= 6 9. 8 \%
$$
J. $$
= 9 2. 5 \%
$$
Answer: A
In a certain amplifier circuit, the input resistance is $R_{i}=10 \ \ \mathrm{k} \Omega$. If it is driven by a 1 μA current source (with an internal resistance of $\infty$), the short-circuit output current of the amplifier circuit is 10 mA, and the open-circuit output voltage is 10 $\mathrm{V_{o}}$. Calculate the voltage gain $A_{F}$, current gain $A_{i}$, and power gain $A_{P}$ of the amplifier circuit when a 4 kΩ load resistor is connected, and convert each into decibels (dB).

Options:
A. $$
\approx6 5 \mathrm{~ d B}
$$
$$
\approx7 2 \mathrm{~ d B}
$$
$$
\approx6 5 \mathrm{~ d B}
$$
B. $$
\approx5 8 \mathrm{~ d B}
$$
$$
\approx6 6 \mathrm{~ d B}
$$
$$
\approx6 2 \mathrm{~ d B}
$$
C. $$
\approx5 7 \mathrm{~ d B}
$$
$$
\approx6 8 \mathrm{~ d B}
$$
$$
\approx6 3 \mathrm{~ d B}
$$
D. $$
\approx6 0 \mathrm{~ d B}
$$
$$
\approx7 0 \mathrm{~ d B}
$$
$$
\approx5 9 \mathrm{~ d B}
$$
E. $$
\approx5 5 \mathrm{~ d B}
$$
$$
\approx6 5 \mathrm{~ d B}
$$
$$
\approx6 0 \mathrm{~ d B}
$$
F. $$
\approx6 1 \mathrm{~ d B}
$$
$$
\approx6 9 \mathrm{~ d B}
$$
$$
\approx6 2 \mathrm{~ d B}
$$
G. $$
\approx5 9 \mathrm{~ d B}
$$
$$
\approx6 4 \mathrm{~ d B}
$$
$$
\approx6 6 \mathrm{~ d B}
$$
H. $$
\approx5 3 \mathrm{~ d B}
$$
$$
\approx6 2 \mathrm{~ d B}
$$
$$
\approx6 4 \mathrm{~ d B}
$$
I. $$
\approx5 6 \mathrm{~ d B}
$$
$$
\approx6 7 \mathrm{~ d B}
$$
$$
\approx5 8 \mathrm{~ d B}
$$
J. $$
\approx5 4 \mathrm{~ d B}
$$
$$
\approx6 3 \mathrm{~ d B}
$$
$$
\approx6 1 \mathrm{~ d B}
$$
Answer: B
At room temperature (300 K), if a diode is supplied with a forward voltage of 0.7 V, the resulting forward current is 1 $\mathrm{mA}$. When the forward current of the diode increases by a factor of 10, what should the voltage be? Assume the diode still uses the exponential model, with $n=1$.

Options:
A. $$
\approx0. 7 1 \mathrm{~ V}
$$
B. $$
\approx0. 7 8 \mathrm{~ V}
$$
C. $$
\approx0. 8 2 \mathrm{~ V}
$$
D. $$
\approx0. 7 5 \mathrm{~ V}
$$
E. $$
\approx0. 9 0 \mathrm{~ V}
$$
F. $$
\approx0. 7 0 \mathrm{~ V}
$$
G. $$
\approx0. 5 6 \mathrm{~ V}
$$
H. $$
\approx0. 6 9 \mathrm{~ V}
$$
I. $$
\approx0. 8 0 \mathrm{~ V}
$$
J. $$
\approx0. 7 6 \mathrm{~ V}
$$
Answer: J
Under the condition of $T=259 \mathrm{C}$, for a resistor $R=100 \ \Omega$ and $10 \ \mathrm{k\Omega}$, respectively calculate its voltage spectral density $V_{n} / {\sqrt{B}}$.

Options:
A. $$
3. 3 5 \, {\frac{\mathrm{n V}} {\sqrt{\mathrm{H z}}}}
$$
$$
6 . 2 \, \mathrm{n V} / \sqrt{\mathrm{H z}}
$$
B. $$
2. 4 9 \, {\frac{\mathrm{n V}} {\sqrt{\mathrm{H z}}}}
$$
$$
7 . 3 \, \mathrm{n V} / \sqrt{\mathrm{H z}}
$$
C. $$
4. 8 3 \, {\frac{\mathrm{n V}} {\sqrt{\mathrm{H z}}}}
$$
$$
3 . 4 \, \mathrm{n V} / \sqrt{\mathrm{H z}}
$$
D. $$
5. 0 2 \, {\frac{\mathrm{n V}} {\sqrt{\mathrm{H z}}}}
$$
$$
6 . 8 \, \mathrm{n V} / \sqrt{\mathrm{H z}}
$$
E. $$
3. 9 4 \, {\frac{\mathrm{n V}} {\sqrt{\mathrm{H z}}}}
$$
$$
5 . 6 \, \mathrm{n V} / \sqrt{\mathrm{H z}}
$$
F. $$
2. 5 7 \, {\frac{\mathrm{n V}} {\sqrt{\mathrm{H z}}}}
$$
$$
1 3. 5 \, \mathrm{n V} / \sqrt{\mathrm{H z}}
$$
G. $$
1. 5 4 \, {\frac{\mathrm{n V}} {\sqrt{\mathrm{H z}}}}
$$
$$
8 . 4 \, \mathrm{n V} / \sqrt{\mathrm{H z}}
$$
H. $$
3. 7 8 \, {\frac{\mathrm{n V}} {\sqrt{\mathrm{H z}}}}
$$
$$
9 . 0 \, \mathrm{n V} / \sqrt{\mathrm{H z}}
$$
I. $$
4. 3 8 \, {\frac{\mathrm{n V}} {\sqrt{\mathrm{H z}}}}
$$
$$
2 . 7 \, \mathrm{n V} / \sqrt{\mathrm{H z}}
$$
J. $$
1. 2 6 \, {\frac{\mathrm{n V}} {\sqrt{\mathrm{H z}}}}
$$
$$
1 2. 6 \, \mathrm{n V} / \sqrt{\mathrm{H z}}
$$
Answer: J
The transfer function of a certain active filter circuit is given by
$$
A(s) = \frac{V_{\circ}(s)}{V_{\text{in}}(s)} = \frac{-s^{2}}{s^{2} + \frac{3}{R_{1} \, C} \, s + \frac{1}{R_{1} \, R_{2} \, C^{2}}}
$$
Find the passband gain $A_{0}$, the characteristic angular frequency $\omega_{c}$, and the equivalent quality factor $Q$.

Options:
A. $$
-2
$$
$$
\frac{R_1}{C\sqrt{R_2}}
$$
$$
\frac{2} {3} \sqrt{\frac{R_{2}} {R_{1}}}
$$
B. $$
1
$$
$$
\frac{1}{R_2\sqrt{R_1C}}
$$
$$
\frac{1} {2} \sqrt{\frac{R_{1}} {R_{2}}}
$$
C. $$
-1
$$
$$
\frac{1}{C\sqrt{R_1R_2}}
$$
$$
\frac{1} {3} \sqrt{\frac{R_{1}} {R_{2}}}
$$
D. $$
0
$$
$$
\frac{1}{C^2\sqrt{R_1R_2}}
$$
$$
\frac{3} {4} \sqrt{\frac{R_{2}} {R_{1}}}
$$
E. $$
1
$$
$$
\frac{R_1}{R_2\sqrt{C}}
$$
$$
\frac{4} {3} \sqrt{\frac{R_{1}} {R_{2}}}
$$
F. $$
-3
$$
$$
\frac{1}{C\sqrt{R_{1}}}
$$
$$
\frac{5} {2} \sqrt{\frac{R_{2}} {R_{1}}}
$$
G. $$
0
$$
$$
\frac{1}{R_1\sqrt{R_2C}}
$$
$$
\frac{1} {4} \sqrt{\frac{R_{2}} {R_{1}}}
$$
H. $$
2
$$
$$
\frac{1}{R_{1}C\sqrt{R_{2}}}
$$
$$
\frac{1} {5} \sqrt{\frac{R_{2}} {R_{1}}}
$$
I. $$
0
$$
$$
\frac{R_2}{C\sqrt{R_1}}
$$
$$
\frac{3} {2} \sqrt{\frac{R_{1}} {R_{2}}}
$$
J. $$
0
$$
$$
\frac{1}{R_1C^2\sqrt{R_2}}
$$
$$
\frac{2} {5} \sqrt{\frac{R_{2}} {R_{1}}}
$$
Answer: C
Two high $Q$ value parallel tuning networks $L_{1} C_{1}$ and $L_{2} C_{2 1}$ each resonate at the same frequency $f_{0}$, with quality factors of $Q_1$ and $Q_{2}$ respectively. The networks are inductively coupled, with a coupling coefficient $k > 1/\sqrt{Q_1Q_2}$. Suppose $Q_{1} = Q_{2} = 50$, $L_{1} = L_{2} = 50$ μH, and $C_{1} = C_{2} = 32$ pF. The value of $k$ when the frequency between the double peaks of the $U_2$ curve is 240 kHz is ___.

Options:
A. 0.0545
B. 0.0795
C. 0.0485
D. 0.0515
E. 0.0765
F. 0.0635
G. 0.0675
H. 0.0595
I. 0.0725
J. 0.0705
Answer: F
Added a local carrier $3A \cos \omega_\epsilon t$ to demodulate a single-sideband signal $A \cos (\omega_\epsilon + \omega_{M} ) t$, and then passed the combined signal through an envelope detector. This envelope detector provides an output voltage proportional to the amplitude of the input signal but does not reflect frequency changes on the carrier or nearby frequencies.The amplitude of the second harmonic $2 \omega_{N}$ content of the demodulator and the ratio of the fundamental to the second harmonic content expressed in decibels are ().

Options:
A. 0.0523A,25.4dB
B. 0.0674A,22.2dB
C. 0.0755A,21.8dB
D. 0.0887A,19.7dB
E. 0.0692A,24.3dB
F. 0.0711A,22.5dB
G. 0.0629A,23.1dB
H. 0.0578A,26.1dB
I. 0.0733A,23.8dB
J. 0.0814A,20.9dB
Answer: F
In FM radio broadcasting, with a frequency deviation of 75 kHz, the highest transmitted audio frequency is 15 kHz. In the situation where the modulating signal is 15 kHz, what is the percentage of power contained within the 150 kHz bandwidth near the carrier frequency?

Options:
A. 87.5%
B. 89.8%
C. 94.5%
D. 90.1%
E. 95.9%
F. 88.4%
G. 91.2%
H. 89.3%
I. 92.7%
J. 93.6%
Answer: E
What is the estimated the required bandwidth when there are 24 telephone voice channels, each with a signal bandwidth limited to between 0.3 and 3.4 kHz, an effective guard bandwidth of 0.9 kHz, using single-sideband modulation and frequency-division multiplexing?

Options:
A. 102kHz
B. 84kHz
C. 90kHz
D. 96kHz
E. 108kHz
F. 120kHz
G. 72kHz
H. 66kHz
I. 78kHz
J. 114kHz
Answer: D
The signal $u(t) = \cos \omega_{0} t + \cos 3 \omega_{0} t$ is sampled by an electrical transducer, with the sampling time effectively considered as instantaneous. What is the minimum bandwidth of the bandpass filter that can be used to recover this signal?

Options:
A. 8f
B. 2f
C. 3f
D. 10f
E. 5f
F. 9f
G. 11f
H. 6f
I. 4f
J. 7f
Answer: I
The effective values of the current and voltage measured on the matched lossless coaxial line are 500 mA and 20 V, respectively. The dielectric constant of the medium between the inner and outer conductors is $\varepsilon_{r}=2.25$. The amplitude of the electric field and the magnetic field at any point on the line $(r \cdot \phi \cdot z)$ are ().

Options:
A. $$
\frac{0. 0 8 3 9} {r} \quad\mathrm{A / m},
$$
$$
\frac{2 9 .7 8} {r} \quad\mathrm{V / m}
$$
B. $$
\frac{0. 1 0 5 8} {r} \quad\mathrm{A / m},
$$
$$
\frac{2 5 .6 1} {r} \quad\mathrm{V / m}
$$
C. $$
\frac{0. 1 1 2 5} {r} \quad\mathrm{A / m},
$$
$$
\frac{2 8 .2 7} {r} \quad\mathrm{V / m}
$$
D. $$
\frac{0. 1 3 7 2} {r} \quad\mathrm{A / m},
$$
$$
\frac{2 6 .3 4} {r} \quad\mathrm{V / m}
$$
E. $$
\frac{0. 1 6 1 7} {r} \quad\mathrm{A / m},
$$
$$
\frac{3 0 .8 3} {r} \quad\mathrm{V / m}
$$
F. $$
\frac{0. 1 3 1 4} {r} \quad\mathrm{A / m},
$$
$$
\frac{2 3 .7 9} {r} \quad\mathrm{V / m}
$$
G. $$
\frac{0. 1 4 8 3} {r} \quad\mathrm{A / m},
$$
$$
\frac{3 2 .1 5} {r} \quad\mathrm{V / m}
$$
H. $$
\frac{0. 1 5 4 3} {r} \quad\mathrm{A / m},
$$
$$
\frac{3 1 .4 9} {r} \quad\mathrm{V / m}
$$
I. $$
\frac{0. 1 2 9 0} {r} \quad\mathrm{A / m},
$$
$$
\frac{2 4 .9 6} {r} \quad\mathrm{V / m}
$$
J. $$
\frac{0. 0 9 8 6} {r} \quad\mathrm{A / m},
$$
$$
\frac{2 7 .5 2} {r} \quad\mathrm{V / m}
$$
Answer: C
The radiation resistance of a certain antenna is 70Ω, fed by a sinusoidal current with an effective value of 4A. The transmission power in the direction of maximum radiation is 1.6 times that of an omnidirectional antenna that radiates the same total power. An identical antenna is placed at this location and oriented towards the transmitter. If the effective length of each antenna is 2m, the maximum power that the receiver connected to this antenna can obtain, and the total transmission loss are ().

Options:
A. 0.195μW,99.03dB
B. 0.230μW,87.68dB
C. 0.120μW,82.45dB
D. 0.300μW,90.50dB
E. 0.215μW,95.62dB
F. 0.250μW,93.15dB
G. 0.198μW,98.74dB
H. 0.110μW,85.37dB
I. 0.213μW,97.21dB
J. 0.280μW,96.89dB
Answer: I
Constant current excited motor, with a rated power of $P_{\mathrm{N}}=40 \mathrm{~kW}$, rated voltage $U_{\mathrm{N}}=220 \mathrm{~V}$, rated current $I_{\mathrm{N}}=203.3 \mathrm{~A}$, rated speed $n_{\mathrm{N}}=1500 \ \mathrm{r/min}$, armature winding resistance $R_{\mathrm{a}}=0.06 \ \Omega$, system flywheel inertia $GD^{2}=15 \ \mathrm{N} \cdot \mathrm{m}^{2}$, and load torque $T_{\mathrm{L}}$ is 0.6 times the rated electromagnetic torque $T_{\mathrm{N}}$. If the motor starts under the condition of double the rated current, determine: $I_{a}(t)$ and $n(t)$ during the startup process is_____.

Options:
A. $$ 115.7+310.6 \mathrm{e}^{-t / \tau_{\mathrm{m}}} $$
$$ 1115 ( 1-\mathrm{e}^{-t /\tau_{m}} ) $$
B. $$ 118.2+290.2 \mathrm{e}^{-t / \tau_{\mathrm{m}}} $$
$$ 1120 ( 1-\mathrm{e}^{-t /\tau_{m}} ) $$
C. $$ 137.6+245.1 \mathrm{e}^{-t / \tau_{\mathrm{m}}} $$
$$ 1135 ( 1-\mathrm{e}^{-t /\tau_{m}} ) $$
D. $$
122.1+284.5 \mathrm{e}^{-t / \tau_{\mathrm{m}}}
$$
$$
1108 ( 1-\mathrm{e}^{-t /\tau_{m}} )
$$
E. $$ 128.3+270.8 \mathrm{e}^{-t / \tau_{\mathrm{m}}} $$
$$ 1160 ( 1-\mathrm{e}^{-t /\tau_{m}} ) $$
F. $$ 126.8+250.7 \mathrm{e}^{-t / \tau_{\mathrm{m}}} $$
$$ 1050 ( 1-\mathrm{e}^{-t /\tau_{m}} ) $$
G. $$ 120.5+300.3 \mathrm{e}^{-t / \tau_{\mathrm{m}}} $$
$$ 1185 ( 1-\mathrm{e}^{-t /\tau_{m}} ) $$
H. $$ 145.3+300.1 \mathrm{e}^{-t / \tau_{\mathrm{m}}} $$
$$ 1200 ( 1-\mathrm{e}^{-t /\tau_{m}} ) $$
I. $$ 131.9+276.4 \mathrm{e}^{-t / \tau_{\mathrm{m}}} $$
$$ 1150 ( 1-\mathrm{e}^{-t /\tau_{m}} ) $$
J. $$ 135.0+260.9 \mathrm{e}^{-t / \tau_{\mathrm{m}}} $$
$$ 1090 ( 1-\mathrm{e}^{-t /\tau_{m}} ) $$
Answer: D
The automobile drive shaft $AB$ made from seamless steel pipe, with an outer diameter $D=90 \, \mathrm{mm}$ and a wall thickness $t=2.5 \, \mathrm{mm}$, is composed of 45 steel, with an allowable shear stress $\left[ \begin{matrix} \tau \\ \end{matrix} \right]=60 \, \mathrm{MPa}$. The maximum torque during operation is $T=1.5 \, \mathrm{kN} \cdot \mathrm{m}$.
Convert shaft $AB$ to a solid shaft and determine the diameter of the solid shaft under the same conditions is _____.

Options:
A. $$52.0mm$$
B. $$53.2mm$$
C. $$55.8mm$$
D. $$51.5mm$$
E. $$57.1mm$$
F. $$54.9mm$$
G. $$58.4mm$$
H. $$50.6mm$$
I. $$59.3mm$$
J. $$56.7mm$$
Answer: B
At a certain intersection, the signal cycle of a certain intersection is 90 seconds, and the effective green time for a certain phase is 45 seconds. During the effective green time, queued vehicles pass through the intersection at a flow rate of 1200 vehicles per hour. Assuming that the arrival rate of upstream vehicles at the signalized intersection is 400 vehicles per hour and follows a Poisson distribution, find the probability that the number of arriving vehicles does not exceed 10 within one cycle, and the probability that the arriving vehicles do not queue up twice is ().

Options:
A. 0.6000,0.9400
B. 0.5200,0.9900
C. 0.5600,0.9300
D. 0.5300,0.9800
E. 0.5700,0.9000
F. 0.5800,0.9200
G. 0.5900,0.9100
H. 0.5400,0.9700
I. 0.5500,0.9600
J. 0.5830,0.9513
Answer: J
A two-lane rural road is designed with a speed limit of $97 \ \mathrm{km/h}$, a lane width of 3.35 m, and a shoulder width of 0.61 m. In mountainous terrain, the no-overtaking zone covers 80% of the road, with a length of 1.609 km. The peak hour traffic volume is 180 vehicles per hour, consisting of 15% trucks, 5% buses, and 80% passenger cars, with a directional distribution of 60/40. Attempt to determine the level of service of this road during peak hours is ().

Options:
A. Lower than Class A and Class B
B. Higher than Class D and Class E
C. Between Class D and Class E
D. Between Class F and Class G
E. Lower than Class C and Class D
F. Between Class B and Class C
G. Between Class C and Class D
H. Higher than Class C and Class D
I. Between Class A and Class B
J. Between Class C and Class E
Answer: G
At a certain intersection, there is an entry lane with a width of 7.0 meters, handling traffic volumes of 450 cars per hour, 94 trucks per hour, and 55 buses per hour. The cycle times are set at 40 seconds, 60 seconds, and 80 seconds, respectively. The effective green light time of the entrance lane is the cycle time minus 30% of the total loss time of 12s within the cycle. Try calculating the delay time at the intersection for a cycle time of 80 seconds for traffic signal control is ().

Options:
A. 29.763 seconds per sedan
B. 33.491 seconds per van
C. 26.981 seconds per bike
D. 32.472 seconds per vehicle
E. 27.193 seconds per bus
F. 35.612 seconds per car
G. 36.459 seconds per pickup
H. 28.244 seconds per truck
I. 31.248 seconds per SUV
J. 30.351 seconds per car
Answer: J
At an approach of a certain traffic light intersection, the traffic flow follows a V-K linear model. The saturated headway is 2 seconds, and the head-to-head spacing of queued vehicles is 8 meters. The arrival flow rate is 720 vehicles per hour, the red light duration is 48.1 seconds, and the green light is sufficiently long. What is the maximum distance the queue of stopped vehicles can extend?

Options:
A. 108m
B. 95m
C. 112m
D. 116m
E. 130m
F. 105m
G. 114m
H. 99m
I. 120m
J. 123m
Answer: C
What is the probability that there are no vehicles on any 600-meter section of a 6-kilometer road if 50 cars are randomly distributed along it?

Options:
A. 0.0067
B. 0.0070
C. 0.0069
D. 0.0061
E. 0.0053
F. 0.0072
G. 0.0075
H. 0.0063
I. 0.0078
J. 0.0059
Answer: A
Insert a steel screw of length $L$ into a copper tube, assuming the cross-sectional area ratio between the screw and the tube is $S_{1} / S_{2} = 1 / 2$. The longitudinal elastic modulus of the steel screw is $E_{1} = 2 \times 10^{6} \mathrm{kg/cm^{2}}$, and its thermal expansion coefficient is $\alpha_{1} = 1.1 \times 10^{-5} / \mathbf{°C}$. The longitudinal elastic modulus of the copper tube is $E_{2} = 10^{6} \mathrm{kg/cm^{2}}$, and its thermal expansion coefficient is $\alpha_{2} = 1.65 \times 10^{-5} / \mathbf{°C}$. Calculate the thermal stress when the temperature rises from 20°C to 220°C is ().

Options:
A. The thermal stress in the steel screws is $\sigma_{1}=950 \mathrm{kg/cm^{2}}$, and the thermal stress in the copper pipe is $\sigma_{2}=-400 \mathrm{kg/cm^{2}}$.
B. The thermal stress in the steel screws is $\sigma_{1}=1100 \mathrm{kg/cm^{2}}$, and the thermal stress in the copper pipe is $\sigma_{2}=-550 \mathrm{kg/cm^{2}}$.
C. The thermal stress in the steel screws is $\sigma_{1}=1025 \mathrm{kg/cm^{2}}$, and the thermal stress in the copper pipe is $\sigma_{2}=-500 \mathrm{kg/cm^{2}}$.
D. The thermal stress in the steel screws is $\sigma_{1}=1050 \mathrm{kg/cm^{2}}$, and the thermal stress in the copper pipe is $\sigma_{2}=-525 \mathrm{kg/cm^{2}}$.
E. The thermal stress in the steel screws is $\sigma_{1}=1200 \mathrm{kg/cm^{2}}$, and the thermal stress in the copper pipe is $\sigma_{2}=-600 \mathrm{kg/cm^{2}}$.
F. The thermal stress in the steel screws is $\sigma_{1}=1125 \mathrm{kg/cm^{2}}$, and the thermal stress in the copper pipe is $\sigma_{2}=-590 \mathrm{kg/cm^{2}}$.
G. The thermal stress in the steel screws is $\sigma_{1}=975 \mathrm{kg/cm^{2}}$, and the thermal stress in the copper pipe is $\sigma_{2}=-450 \mathrm{kg/cm^{2}}$.
H. The thermal stress in the steel screws is $\sigma_{1}=990 \mathrm{kg/cm^{2}}$, and the thermal stress in the copper pipe is $\sigma_{2}=-470 \mathrm{kg/cm^{2}}$.
I. The thermal stress in the steel screws is $\sigma_{1}=1150 \mathrm{kg/cm^{2}}$, and the thermal stress in the copper pipe is $\sigma_{2}=-575 \mathrm{kg/cm^{2}}$.
J. The thermal stress in the steel screws is $\sigma_{1}=1250 \mathrm{kg/cm^{2}}$, and the thermal stress in the copper pipe is $\sigma_{2}=-650 \mathrm{kg/cm^{2}}$.
Answer: B
Conditions: The self-weight of a work platform in a certain factory is $5.4kN/m^{2}$, the live load is $2.0kN/m^{2}$, and the design service life is 50 years. The design value of the load combination is ().

Options:
A. $15.18kN/m^{2}$
B. $9.28kN/m^{2}$
C. $14.00kN/m^{2}$
D. $12.43kN/m^{2}$
E. $10.32kN/m^{2}$
F. $11.56kN/m^{2}$
G. $6.67kN/m^{2}$
H. $13.21kN/m^{2}$
I. $8.75kN/m^{2}$
J. $7.89kN/m^{2}$
Answer: B
A ramp bridge on a certain interchange bridge is a single-span simply supported beam bridge with a span of $30 \mathrm{m}$ and a clear width of 8.0m on the bridge deck, designed for two lanes of traffic in the same direction, and accommodates Highway-I level loads; it uses chloroprene rubber pad bearings. The question is, which of the following values is closest to the standard value of the braking force (kN) borne by each abutment of this bridge?
Hint: 1. The standard value of the uniformly distributed load for the lane load is $q_{\mathrm{k}}=10.5 \mathrm{kN/m}$, and the standard value of the concentrated load is $P_{\mathrm{k}}=280 \mathrm{kN}$.
2. Assume that the braking force is equally distributed between the two abutments.

Options:
A. 85
B. 89
C. 74
D. 81
E. 72
F. 76
G. 78
H. 83
I. 67
J. 91
Answer: H
Distillation separation of a benzene-toluene mixture containing 0.5 mole fraction of benzene is performed under normal pressure, with a feed processing quantity of 100 kmol. The system's average relative volatility is 2.5, and the vaporization rate is 0.4. Calculate the distillate amount in simple distillation and its average composition.

Options:
A. 50kmol,0.5800
B. 66kmol,0.7200
C. 62kmol,0.6800
D. 57kmol,0.6300
E. 55kmol,0.6000
F. 58kmol,0.6400
G. 65kmol,0.7100
H. 53kmol,0.6100
I. 70kmol,0.7500
J. 60kmol,0.6695
Answer: J
In an atmospheric concurrent-flow dryer, hot air is used to dry a certain material from an initial moisture content of $X_{1} = 1 \mathrm{kg} / \mathrm{kg}$ (dry basis) to a final moisture content of $X_{2} = 0.1 \mathrm{kg} / \mathrm{kg}$ (dry basis). The air enters the dryer at a temperature of 135°C and a humidity of 0.01 kg/kg (dry air); the air exits the dryer at a temperature of $60^{\circ} \mathrm{C}$. The air undergoes an isothermal process in the dryer. From experiments, the drying rate expression for the first drying stage is $-\frac{\mathrm{d} X}{\mathrm{d} \tau} = 30(H_{s}^{\prime} - H)$, where $\frac{\mathrm{d} X}{\mathrm{d} \tau}$ is the drying rate, kg/[kg (dry basis)·h]. The drying rate expression for the second drying stage is $-\frac{\mathrm{d} X}{\mathrm{d} \tau} = 1.2X$. Try calculating the drying time required to complete the aforementioned drying task.

Options:
A. 0.995h
B. 1.758h
C. 0.876h
D. 1.678h
E. 1.926h
F. 2.007h
G. 2.269h
H. 2.518h
I. 2.035h
J. 1.432h
Answer: E
Use wash oil to absorb aromatic hydrocarbons from coke oven gas. It is known that the molar fraction of aromatic hydrocarbons in the inlet coke oven gas is 0.02. The aromatic hydrocarbon recovery rate is required to be no less than 95% (recovery rate $\phi_{\Lambda} \!=\! {\frac{Y_{1}-Y_{2}} {Y_{1}}} \! \times\! 1 0 0 \ \%$). Try to calculate the molar ratio of aromatic hydrocarbons $Y_{2}$ in the coke oven gas in the tower.

Options:
A. $9.72×10^{-4}$
B. $8.14×10^{-4}$
C. $7.63×10^{-4}$
D. $2.56×10^{-3}$
E. $1.58×10^{-3}$
F. $1.02×10^{-3}$
G. $4.87×10^{-4}$
H. $3.09×10^{-3}$
I. $1.95×10^{-3}$
J. $2.31×10^{-3}$
Answer: F
Under a total pressure of 101.3 kPa and a temperature of 20°C, the solubility of ammonia in water is $2.5g(NH_3)/100g(H_2O)$. If the vapor-liquid equilibrium of ammonia solution follows Henry's Law with an equilibrium constant of 0.76, calculate the gas phase composition expressed as $y$ and $\mathbf{Y}$.

Options:
A. y=0.0205,Y=0.0210
B. y=0.0230,Y=0.0240
C. y=0.0168,Y=0.0170
D. y=0.0180,Y=0.0185
E. y=0.0150,Y=0.0155
F. y=0.0250,Y=0.0260
G. y=0.0210,Y=0.0220
H. y=0.0196,Y=0.0200
I. y=0.0190,Y=0.0195
J. y=0.0175,Y=0.0180
Answer: H
Given that the Henry's law constant for $\mathrm{CO_2}$ in water at 30°C is $1.88 \times 10^5 \, \mathrm{kPa}$, a packed column is currently used with countercurrent flow to absorb $\mathrm{CO_2}$ mixed in air using pure water. The volume fraction of $\mathrm{CO_2}$ in the air is 0.08. The operating conditions are 30°C and 506.6 kPa, and the composition of $\mathrm{CO_2}$ in the absorbing liquid is $x_1 = 1.5 \times 10^{-4}$. Try to determine the total absorption driving forces at the bottom of the column: $\Delta y$, $\Delta x$, $\Delta p_G$, $\Delta c_{L}$, $\Delta X$, and $\Delta Y$.

Options:
A. $\Delta y=0.02433,\Delta x=6.560\times10^{-5},\Delta p_{\mathrm{G}}=12.53\mathbf{kPa},\Delta c_{L}=0.003532\mathbf{kmol/m^{3}},\Delta X\approx\Delta x=6.460$
$\times 10^{- 5}$ , $\Delta Y= 0. 03001$
B. $\Delta y=0.02313,\Delta x=5.550\times10^{-5},\Delta p_{\mathrm{G}}=11.33\mathbf{kPa},\Delta c_{L}=0.003732\mathbf{kmol/m^{3}},\Delta X\approx\Delta x=5.550$
$\times 10^{- 5}$ , $\Delta Y= 0. 02761$
C. $\Delta y=0.02333,\Delta x=6.460\times10^{-5},\Delta p_{\mathrm{G}}=12.83\mathbf{kPa},\Delta c_{L}=0.003732\mathbf{kmol/m^{3}},\Delta X\approx\Delta x=6.760$
$\times 10^{- 5}$ , $\Delta Y= 0. 02941$
D. $\Delta y=0.02403,\Delta x=6.360\times10^{-5},\Delta p_{\mathrm{G}}=12.23\mathbf{kPa},\Delta c_{L}=0.003532\mathbf{kmol/m^{3}},\Delta X\approx\Delta x=6.360$
$\times 10^{- 5}$ , $\Delta Y= 0. 02791$
E. $\Delta y=0.02453,\Delta x=6.860\times10^{-5},\Delta p_{\mathrm{G}}=13.33\mathbf{kPa},\Delta c_{L}=0.003432\mathbf{kmol/m^{3}},\Delta X\approx\Delta x=6.860$
$\times 10^{- 5}$ , $\Delta Y= 0. 02781$
F. $\Delta y=0.02563,\Delta x=6.960\times10^{-5},\Delta p_{\mathrm{G}}=11.33\mathbf{kPa},\Delta c_{L}=0.003432\mathbf{kmol/m^{3}},\Delta X\approx\Delta x=6.960$
$\times 10^{- 5}$ , $\Delta Y= 0. 02821$
G. $\Delta y=0.02473,\Delta x=7.060\times10^{-5},\Delta p_{\mathrm{G}}=12.13\mathbf{kPa},\Delta c_{L}=0.003832\mathbf{kmol/m^{3}},\Delta X\approx\Delta x=7.060$
$\times 10^{- 5}$ , $\Delta Y= 0. 02751$
H. $\Delta y=0.02233,\Delta x=6.160\times10^{-5},\Delta p_{\mathrm{G}}=12.63\mathbf{kPa},\Delta c_{L}=0.003932\mathbf{kmol/m^{3}},\Delta X\approx\Delta x=6.560$
$\times 10^{- 5}$ , $\Delta Y= 0. 02861$
I. $\Delta y=0.02543,\Delta x=7.560\times10^{-5},\Delta p_{\mathrm{G}}=10.33\mathbf{kPa},\Delta c_{L}=0.002632\mathbf{kmol/m^{3}},\Delta X\approx\Delta x=7.560$
$\times 10^{- 5}$ , $\Delta Y= 0. 02901$
J. $\Delta y=0.02433,\Delta x=6.560\times10^{-5},\Delta p_{\mathrm{G}}=12.33\mathbf{kPa},\Delta c_{L}=0.003632\mathbf{kmol/m^{3}},\Delta X\approx\Delta x=6.560$
$\times 10^{- 5}$ , $\Delta Y= 0. 02801$
Answer: J
The density of a dry sand sample is $1.66\mathbf{g} / \mathbf{c m}^{3}$, and the relative density of the soil particles is 2.70. If this dry sand sample is placed in the rain and its volume remains unchanged, with the saturation degree increasing to 0.60, calculate the density and water content of the wet sand at this time.

Options:
A. $$
2. 5 0 \mathbf{g} / \mathbf{c m}^{3} \,, \ 5 0. 0 \%
$$
B. $$
1. 5 0 \mathbf{g} / \mathbf{c m}^{3} \,, \ 1 8. 0 \%
$$
C. $$
1. 7 0 \mathbf{g} / \mathbf{c m}^{3} \,, \ 1 0. 0 \%
$$
D. $$
1. 8 9 \mathbf{g} / \mathbf{c m}^{3} \,, \ 1 3. 9 \%
$$
E. $$
1. 9 0 \mathbf{g} / \mathbf{c m}^{3} \,, \ 2 9. 0 \%
$$
F. $$
1. 9 5 \mathbf{g} / \mathbf{c m}^{3} \,, \ 2 0. 0 \%
$$
G. $$
1. 6 5 \mathbf{g} / \mathbf{c m}^{3} \,, \ 1 5. 0 \%
$$
H. $$
2. 1 0 \mathbf{g} / \mathbf{c m}^{3} \,, \ 3 0. 5 \%
$$
I. $$
2. 0 0 \mathbf{g} / \mathbf{c m}^{3} \,, \ 2 5. 0 \%
$$
J. $$
1. 6 0 \mathbf{g} / \mathbf{c m}^{3} \,, \ 8. 0 \%
$$
Answer: D
A clay sample with relatively low moisture content was subjected to a uniaxial compression test. When the pressure reached 90 kPa, the soil sample began to fail and developed a failure plane, which formed a 35° angle with the vertical line. Determine the internal friction angle $\varphi$ and the cohesion $c$.

Options:
A. $$
3 0^{\circ}
$$
$$
2 0. 0 \mathbf{k P a}
$$
B. $$
2 1^{\circ}
$$
$$
3 0. 5 \mathbf{k P a}
$$
C. $$
2 5^{\circ}
$$
$$
2 9. 0 \mathbf{k P a}
$$
D. $$
2 2^{\circ}
$$
$$
1 8. 5 \mathbf{k P a}
$$
E. $$
2 0^{\circ}
$$
$$
3 1. 5 \mathbf{k P a}
$$
F. $$
1 7^{\circ}
$$
$$
2 8. 0 \mathbf{k P a}
$$
G. $$
2 3^{\circ}
$$
$$
1 7. 5 \mathbf{k P a}
$$
H. $$
1 8^{\circ}
$$
$$
3 4. 0 \mathbf{k P a}
$$
I. $$
1 9^{\circ}
$$
$$
2 5. 5 \mathbf{k P a}
$$
J. $$
2 4^{\circ}
$$
$$
1 6. 0 \mathbf{k P a}
$$
Answer: E
An unconfined compression test was conducted on a certain clay sample, and the unconfined compressive strength $q_{\mathrm{u}} = 200 \mathrm{kPa}$ was measured. At failure, the angle between the failure plane and the horizontal plane was 57°. Determine the cohesive strength $c$ for the clay.

Options:
A. $$
8 5 \mathbf{k P a}
$$
B. $$
5 5 \mathbf{k P a}
$$
C. $$
6 0 \mathbf{k P a}
$$
D. $$
5 0 \mathbf{k P a}
$$
E. $$
9 5 \mathbf{k P a}
$$
F. $$
4 5 \mathbf{k P a}
$$
G. $$
7 0 \mathbf{k P a}
$$
H. $$
7 5 \mathbf{k P a}
$$
I. $$
8 0 \mathbf{k P a}
$$
J. $$
6 5 \mathbf{k P a}
$$
Answer: J
Below a sand layer at a certain foundation site, there is a clay layer with a thickness of $6 \mathrm{m}$, beneath which lies an impermeable bedrock. A large area (infinitely distributed) load is applied to the ground surface. It is known from laboratory tests that the initial void ratio of the clay layer is $e_{1}=0.815$, and the void ratio after compression stabilization under the pressure equal to the large area load is $e_{2}=0.795$. The consolidation coefficient is $C_{\mathrm{v}}\!=\!4.6\times10^{-3}\,\mathrm{cm}^{2}/\mathrm{s}$. When the degree of consolidation $U_{t}=$ 60%, the time factor $T_{\mathrm{v}}=0.287$. Estimate the time required to achieve 60% consolidation.

Options:
A. $$
2 9 8. 8 7\ \mathrm{days}
$$
B. $$
2 6 6. 2 4\ \mathrm{days}
$$
C. $$
3 2 7. 5 1\ \mathrm{days}
$$
D. $$
3 4 6. 7 5\ \mathrm{days}
$$
E. $$
2 5 0. 4 9\ \mathrm{days}
$$
F. $$
2 8 3. 1 0\ \mathrm{days}
$$
G. $$
2 7 5. 3 8\ \mathrm{days}
$$
H. $$
3 1 0. 6 2\ \mathrm{days}
$$
I. $$
2 5 9. 9 6\ \mathrm{days}
$$
J. $$
2 3 1. 4 5\ \mathrm{days}
$$
Answer: I
For a specific irrigation district, the total water requirement for winter wheat throughout its entire growth period is $\mathrm{E=380 \, m^{3}/}$ mu. The designed rainfall is $\mathrm{P=150 \, mm}$, with an effective rainfall utilization coefficient of $\sigma=0.8$. The groundwater recharge during the full growth period is $\mathrm{K=30 \, m^{3}/}$ mu. At the initial growth stage, the planned depth of the moist soil layer is $0.3 \, \mathrm{m}$, while at the later growth stage, it is set at $0.8 \, \mathrm{m}$. The soil porosity is $\mathrm{n=48\%}$ (as a proportion of soil volume), and the field capacity is $70\%$ (as a proportion of pore volume). Before sowing the winter wheat, irrigation is conducted to ensure that the water content within the maximum planned moist layer of the soil reaches field capacity. By the time of harvest, the soil water content may decrease to $80\%$ of the field capacity.
Estimate the irrigation quota during the full growth period of winter wheat $\mathrm{M^{2}}$.

Options:
A. $198.45123 \text{ m}^3/\text{mu}$
B. $245.67210 \text{ m}^3/\text{mu}$
C. $259.34212 \text{ m}^3/\text{mu}$
D. $240.68975 \text{ m}^3/\text{mu}$
E. $252.81347 \text{ m}^3/\text{mu}$
F. $267.58056 \text{ m}^3/\text{mu}$
G. $220.35808 \text{ m}^3/\text{mu}$
H. $212.39418 \text{ m}^3/\text{mu}$
I. $223.45698 \text{ m}^3/\text{mu}$
J. $234.14208 \text{ m}^3/\text{mu}$
Answer: J
The semi-major axis of Earth's orbit around the Sun is $1.50 \times 10^{11} \mathrm{m}$, with a period of 365 days; the semi-major axis of the Moon's orbit around Earth is $3.8 \times 10^{8}$ m, with a period of 27.3 days. Therefore, the value of $R^{3} / T^{2}$ for a planet orbiting the Sun is ________$m^{3} / s^{2}$; for a satellite orbiting Earth, the value of $R^{3} / T^{2}$ is ________$m^{3} / s^{2}$.

Options:
A. $$
5. 0 {\times} 1 0^{1 8} \ \ 2. 0 {\times} 1 0^{1 3}
$$
B. $$
4. 5 {\times} 1 0^{1 8} \ \ 2. 8 {\times} 1 0^{1 3}
$$
C. $$
3. 4 {\times} 1 0^{1 8} \ \ 1. 0 {\times} 1 0^{1 3}
$$
D. $$
4. 1 {\times} 1 0^{1 8} \ \ 1. 5 {\times} 1 0^{1 3}
$$
E. $$
7. 8 {\times} 1 0^{1 8} \ \ 1. 9 {\times} 1 0^{1 3}
$$
F. $$
3. 0 {\times} 1 0^{1 8} \ \ 5. 6 {\times} 1 0^{1 3}
$$
G. $$
3. 2 {\times} 1 0^{1 8} \ \ 8. 0 {\times} 1 0^{1 3}
$$
H. $$
6. 3 {\times} 1 0^{1 8} \ \ 3. 0 {\times} 1 0^{1 3}
$$
I. $$
2. 7 {\times} 1 0^{1 8} \ \ 9. 5 {\times} 1 0^{1 3}
$$
J. $$
1. 9 {\times} 1 0^{1 8} \ \ 1. 2 {\times} 1 0^{1 3}
$$
Answer: C
The average angular velocity of the Earth's orbit around the Sun is approximately 1 degree per day. The average distance from the Earth to the Sun is about $1.5\times10^{8}km$. The mass of the Sun is ().

Options:
A. $$
1. 8 2 \times1 0^{3 0} \mathrm{k g}
$$
B. $$
2. 3 4 \times1 0^{3 0} \mathrm{k g}
$$
C. $$
1. 6 0 \times1 0^{3 0} \mathrm{k g}
$$
D. $$
2. 4 0 \times1 0^{3 0} \mathrm{k g}
$$
E. $$
2. 0 6 \times1 0^{3 0} \mathrm{k g}
$$
F. $$
1. 9 8 \times1 0^{3 0} \mathrm{k g}
$$
G. $$
2. 5 9 \times1 0^{3 0} \mathrm{k g}
$$
H. $$
1. 7 5 \times1 0^{3 0} \mathrm{k g}
$$
I. $$
2. 7 1 \times1 0^{3 0} \mathrm{k g}
$$
J. $$
2. 1 1 \times1 0^{3 0} \mathrm{k g}
$$
Answer: E
The artificial satellite performs uniform circular motion around the Earth. If the orbital height from the ground is equal to 1.5 times the radius of the Earth, and the Earth's radius is 6. $4 \times 10^{4} \text{m}$, with the gravitational acceleration near the ground $g_{0}={\frac{\pi^{2} m} {S^{2}}}$, the period of this artificial Earth satellite is __.

Options:
A. $$
2. 0 \times1 0^{4} s
$$
B. $$
1. 5 \times1 0^{3} s
$$
C. $$
7. 0 \times1 0^{3} s
$$
D. $$
1. 8 \times1 0^{5} s
$$
E. $$
2. 5 \times1 0^{4} s
$$
F. $$
3. 0 \times1 0^{5} s
$$
G. $$
3. 5 \times1 0^{4} s
$$
H. $$
4. 5 \times1 0^{4} s
$$
I. $$
2. 2 \times1 0^{3} s
$$
J. $$
1. 0 \times1 0^{5} s
$$
Answer: A
If the proton decay occurs through an intermediate boson with a mass of $M_{X}=3 \times 10^{14} \mathrm{~GeV}$, and assuming its coupling constant is the usual weak coupling constant, try to estimate the lifetime of the proton based on the muon's mass of $106 \mathrm{MeV}$ and an average lifetime of $2.2 \mu s$.

Options:
A. $$
6. 7 \times10^{29} \text{ years}
$$
B. $$
2. 1 \times10^{33} \text{ years}
$$
C. $$
3. 5 \times10^{31} \text{ years}
$$
D. $$
4. 8 \times10^{33} \text{ years}
$$
E. $$
2. 4 \times10^{32} \text{ years}
$$
F. $$
1. 0 \times10^{30} \text{ years}
$$
G. $$
7. 1 \times10^{35} \text{ years}
$$
H. $$
9. 2 \times10^{36} \text{ years}
$$
I. $$
8. 9 \times10^{34} \text{ years}
$$
J. $$
5. 3 \times10^{28} \text{ years}
$$
Answer: E
The Jeans mass and Jeans length of a parcel of air at standard temperature and pressure is(). ($T=273 \mathrm{~K}$, $\rho=1.29 \ \mathrm{kg} \ \mathrm{\cdot~m^{-3}}$, Earth's mass = $6\times 10^{24}$kg)

Options:
A. $$
M_J = 2.8 \times 10^{23} \ \mathrm{kg}
$$
$$
\lambda_J = 8.12 \times 10^{7} \mathrm{~ m}
$$
B. $$
M_J = 3.0 \times 10^{23} \ \mathrm{kg}
$$
$$
\lambda_J = 7.00 \times 10^{7} \mathrm{~ m}
$$
C. $$
M_J = 2.2 \times 10^{23} \ \mathrm{kg}
$$
$$
\lambda_J = 6.88 \times 10^{7} \mathrm{~ m}
$$
D. $$
M_J = 3.2 \times 10^{23} \ \mathrm{kg}
$$
$$
\lambda_J = 7.45 \times 10^{7} \mathrm{~ m}
$$
E. $$
M_J = 4.0 \times 10^{23} \ \mathrm{kg}
$$
$$
\lambda_J = 4.77 \times 10^{7} \mathrm{~ m}
$$
F. $$
M_J = 4.5 \times 10^{23} \ \mathrm{kg}
$$
$$
\lambda_J = 5.74 \times 10^{7} \mathrm{~ m}
$$
G. $$
M_J = 2.5 \times 10^{23} \ \mathrm{kg}
$$
$$
\lambda_J = 6.10 \times 10^{7} \mathrm{~ m}
$$
H. $$
M_J = 1.9 \times 10^{23} \ \mathrm{kg}
$$
$$
\lambda_J = 9.01 \times 10^{7} \mathrm{~ m}
$$
I. $$
M_J = 1.5 \times 10^{23} \ \mathrm{kg}
$$
$$
\lambda_J = 5.00 \times 10^{7} \mathrm{~ m}
$$
J. $$
M_J = 1.0 \times 10^{23} \ \mathrm{kg}
$$
$$
\lambda_J = 8.50 \times 10^{7} \mathrm{~ m}
$$
Answer: C
The refractive index $n$ of air at sea level is given by $n-1=2.7 \times 10^{-4}$, and this quantity is proportional to pressure. Calculate the distribution radius at sea level, in meters, of the ring of Cherenkov light produced by an extremely relativistic charged particle traveling vertically downwards through a $100 \; \mathrm{gm \cdot cm^{-2}}$ depth of the atmosphere. (Assume there is an exponential relationship between the density $\rho$ and height $h$ of the atmosphere, given by $\rho=\rho_{0} \exp(-h / H)$, where $H = 6.5 \, \mathrm{km}$. The total depth of the atmosphere is $1030 \; \mathrm{gm \cdot cm^{-2}}$.)

Options:
A. 120m
B. 105m
C. 135m
D. 95m
E. 100m
F. 130m
G. 110m
H. 125m
I. 90m
J. 85m
Answer: G
If the vacuum energy density is quantitatively comparable to today's matter energy density, then when the age of the universe is a fraction $f$ of its current age, the relative contribution of vacuum energy will be ___.

Options:
A. $f^{4}$
B. $f/\ln(f)$
C. $1/f^{2}$
D. $f^{2} - f$
E. $f^{3}$
F. $f^{2}$
G. $f/\sqrt{2}$
H. $f^{2} + 1$
I. $f^{2/3}$
J. $f^{1.5}$
Answer: F
An atomic nucleus with a mass of $M_{R}$ undergoes an elastic collision with a dark matter particle of mass $M_{D}$ and incident kinetic energy $E_{D}$. Derive the expression for the recoil kinetic energy $E_{R}$ of the nucleus, expressed in terms of the exit angle relative to the incident direction.

Options:
A. $$
\frac{2 M_{\mathrm{D}} M_{\mathrm{R}}} {( M_{\mathrm{D}}+M_{\mathrm{R}} )^{2}} E_{\mathrm{D}} \mathrm{c o s}^{2} \, \theta\,.
$$
B. $$
\frac{8 M_{\mathrm{D}} M_{\mathrm{R}}} {( M_{\mathrm{D}}+M_{\mathrm{R}} )^{2}} E_{\mathrm{D}} \mathrm{s i n}^{2} \, \theta\,.
$$
C. $$
\frac{M_{\mathrm{D}} M_{\mathrm{R}}} {( M_{\mathrm{D}}+M_{\mathrm{R}} )^{2}} E_{\mathrm{D}} \mathrm{s i n}^{2} \, \theta\,.
$$
D. $$
\frac{4 M_{\mathrm{D}} M_{\mathrm{R}}} {( M_{\mathrm{D}}+M_{\mathrm{R}} )^{3}} E_{\mathrm{D}} \mathrm{c o s}^{2} \, \theta\,.
$$
E. $$
\frac{4 M_{\mathrm{D}} M_{\mathrm{R}}} {( M_{\mathrm{D}}+M_{\mathrm{R}} )^{2}} E_{\mathrm{D}} \mathrm{c o s}^{2} \, \theta\,.
$$
F. $$
\frac{4 M_{\mathrm{D}}^{2}} {( M_{\mathrm{D}}+M_{\mathrm{R}} )^{2}} E_{\mathrm{D}} \mathrm{c o s}^{2} \, \theta\,.
$$
G. $$
\frac{4 M_{\mathrm{D}} M_{\mathrm{R}}} {( M_{\mathrm{D}}+M_{\mathrm{R}} )^{2}} E_{\mathrm{D}} \mathrm{t a n}^{2} \, \theta\,.
$$
H. $$
\frac{4 M_{\mathrm{R}}^{2}} {( M_{\mathrm{D}}+M_{\mathrm{R}} )^{2}} E_{\mathrm{D}} \mathrm{c o s}^{2} \, \theta\,.
$$
I. $$
\frac{M_{\mathrm{D}} M_{\mathrm{R}}} {( M_{\mathrm{D}}+M_{\mathrm{R}} )^{2}} E_{\mathrm{D}} \mathrm{t a n}^{2} \, \theta\,.
$$
J. $$
\frac{2 M_{\mathrm{D}} M_{\mathrm{R}}} {( M_{\mathrm{D}}+M_{\mathrm{R}} )} E_{\mathrm{D}} \mathrm{s i n}^{2} \, \theta\,.
$$
Answer: E
The shell flies along a flat trajectory (i.e., a trajectory approximated as a straight line) with a speed of $v_{0}=900 \mathrm{~m/s}$, at a shooting latitude of $\varphi=60^{\circ}$, and the target is 18 km away.What is the deviation of the shell caused by the Earth's rotation? Neglecting air resistance.

Options:
A. $\approx11.50\cos\theta$m
B. $\approx12.60\cos\theta$m
C. $\approx14.75\sin\theta$m
D. $\approx16.30\sin\theta$m
E. $\approx15.20\sin\theta$m
F. $\approx14.00\cos\theta$m
G. $\approx12.75\sin\theta$m
H. $\approx10.85\cos\theta$m
I. $\approx13.13\sin\theta$m
J. $\approx13.13\cos\theta$m
Answer: J
To launch a planet from Earth at the third cosmic velocity $v_{3}$ directly towards the Sun ("directly towards the Sun" means relative to Earth).What is the trajectory equation ? (assuming Earth's orbit is approximately circular).

Options:
A. $r=\frac{R_{\mathrm{se}}}{1+v_3^2\sqrt{\frac{R_{\mathrm{se}}}{GM_s}}\cos\left(\theta\right)}.$
B. $r=\frac{2R_{\mathrm{se}}}{1-v_3\sqrt{\frac{R_{\mathrm{se}}}{GM_s}}\sin\left(\theta\right)}.$
C. $r=\frac{R_{\mathrm{se}}}{1+v_3\sqrt{\frac{R_{\mathrm{se}}}{GM_s}}\cos\left(\theta-\frac{\pi}{2}\right)}.$
D. $r=\frac{R_{\mathrm{se}}}{1+\sqrt{\frac{R_{\mathrm{se}}}{GM_s}}\cos\left(v_3\theta\right)}.$
E. $r=\frac{2R_{\mathrm{se}}}{1+v_3\sqrt{\frac{R_{\mathrm{se}}}{GM_s}}\sin\left(\theta+\frac{\pi}{2}\right)}.$
F. $r=\frac{R_{\mathrm{se}}}{v_3\sqrt{\frac{R_{\mathrm{se}}}{GM_s}}-\cos\left(\theta-\frac{\pi}{2}\right)}.$
G. $r=\frac{R_{\mathrm{se}}}{1+v_3\sqrt{\frac{GM_s}{R_{\mathrm{se}}}}\sin\left(\theta-\frac{\pi}{2}\right)}.$
H. $r=\frac{R_{\mathrm{se}}}{2+v_3\sqrt{\frac{R_{\mathrm{se}}}{GM_s}}\sin\left(\theta-\frac{\pi}{2}\right)}.$
I. $r=\frac{R_{\mathrm{se}}}{1+v_3\sqrt{\frac{R_{\mathrm{se}}}{GM_s}}\cos\left(\theta+\frac{\pi}{2}\right)}.$
J. $r=\frac{R_{\mathrm{se}}}{1-v_3\sqrt{\frac{GM_s}{R_{\mathrm{se}}}}\cos\left(\theta\right)}.$
Answer: C
A plane with a mass of $10^{4} \, \mathrm{kg}$ lands on a horizontal surface using skis. Under the pilot's control, the plane lands without vertical velocity or vertical acceleration. The drag force is proportional to the speed, and when the speed is $1 \, \mathrm{m/s}$, the drag force is $10 \, \mathrm{N}$. The lift is proportional to the square of the speed, and when the speed is $1 \, \mathrm{m/s}$, the lift is $30 \, \mathrm{N}$. What is the distance and time of the plane's glide? (Assume the coefficient of friction is $f=0.1$)

Options:
A. $$S=8 6 9. 7 \ \operatorname{m}, T=3 6. 0 \ \operatorname{s.}$$
B. $$S=1 1 0 0. 6 \ \operatorname{m}, T=4 5. 3 \ \operatorname{s.}$$
C. $$S=9 3 5. 8 \ \operatorname{m}, T=4 1. 7 \ \operatorname{s.}$$
D. $$S=9 7 5. 5 \ \operatorname{m}, T=3 9. 8 \ \operatorname{s.}$$
E. $$S=1 0 5 0. 7 \ \operatorname{m}, T=4 2. 3 \ \operatorname{s.}$$
F. $$S=8 0 0. 4 \ \operatorname{m}, T=3 4. 5 \ \operatorname{s.}$$
G. $$S=7 9 9. 9 \ \operatorname{m}, T=3 3. 1 \ \operatorname{s.}$$
H. $$S=9 5 0. 2 \ \operatorname{m}, T=4 0. 9 \ \operatorname{s.}$$
I. $$S=8 5 0. 1 \ \operatorname{m}, T=3 5. 2 \ \operatorname{s.}$$
J. $$
S=9 0 9. 3 \ \operatorname{m}, T=3 8. 7 \ \operatorname{s.}
$$
Answer: J
A body $E$ with mass $m$ is situated on a smooth horizontal surface, with one end of a spring of stiffness $c$ attached to it, and the other end fixed at hinge $O_{1}$. The natural length of the spring is $l_{0}$, and the distance $O O_{1}=l$. Initially, the body $E$ is displaced from the equilibrium position $O$ and is released without initial velocity from the extreme position where $O E=a$.What is the velocity of this body as it passes through the equilibrium position ?

Options:
A. $$
v=\sqrt{\frac{c} {m} \left[ \frac{l_{0}^{2}} {2} + a \cdot ( l-\sqrt{l^{2}+a} ) \right]}.
$$
B. $$
v=\sqrt{\frac{c} {m} \left[ \frac{a^{2}} {3} + l_{0} ( l-\sqrt{l^{2}-a^{2}} ) \right]}.
$$
C. $$
v=\sqrt{\frac{c} {m} \left[ a^{2} + l_{0} \cdot ( l-\sqrt{l^{2}-a} ) \right]}.
$$
D. $$
v=\sqrt{\frac{c} {m} \left[ \frac{a^{2}} {2} + l \cdot l_{0} \right]}.
$$
E. $$
v=\sqrt{\frac{c} {m} \left[ \frac{2a^{2}} {2} + l_{0} ( l-\sqrt{l^{2}+a^{2}} ) \right]}.
$$
F. $$
v=\sqrt{\frac{c} {m} \left[ \frac{a^{2}} {2} + l_{0} \cdot ( l-\sqrt{a^{2}+l^{2}} ) \right]}.
$$
G. $$
v=\sqrt{\frac{2 c} {m} \left[ \frac{a^{2}} {4} + l ( l_{0} - a ) \right]}.
$$
H. $$
v=\sqrt{\frac{2 c} {m} \left[ \frac{a^{2}} {2}+l_{0} ( l-\sqrt{l^{2}+a^{2}} ) \right]}.
$$
I. $$
v=\sqrt{\frac{2 c} {m} \left[ a^{2} + 2l_{0} ( l-\sqrt{l^{2}+a} ) \right]}.
$$
J. $$
v=\sqrt{\frac{2 c} {m} \left[ l_{0} ( l+a^{2} ) \right]}.
$$
Answer: H
Object A is chasing object $B$, with A traveling at three times the speed of $B$. Object $A$ comes to a stop after the collision. What is the ratio of the masses of the two objects ?Assuming a head-on collision with a restitution coefficient of $k=0.8$.

Options:
A. $$
m_{B} / m_{A}=10
$$
B. $$
m_{B} / m_{A}=4
$$
C. $$
m_{B} / m_{A}=5
$$
D. $$
m_{B} / m_{A}=7
$$
E. $$
m_{B} / m_{A}=3
$$
F. $$
m_{B} / m_{A}=2
$$
G. $$
m_{B} / m_{A}=9
$$
H. $$
m_{B} / m_{A}=8
$$
I. $$
m_{B} / m_{A}=6
$$
J. $$
m_{B} / m_{A}=1
$$
Answer: C
When the counting efficiency is 0.3, the counter can accurately record radioactivity that is 30 pulses/min higher than the background. Based on the detectable amount of radioactivity of the isotope $\mathrm{B i^{2 1 2} ( T h C}$), determine the sensitivity of the radiochemical method.

Options:
A. $$
1.93 \times 10^{-15} \text{ grams}
$$
B. $$
5.86 \times 10^{-19} \text{ grams}
$$
C. $$
7.51 \times 10^{-13} \text{ grams}
$$
D. $$
4.17 \times 10^{-15} \text{ grams}
$$
E. $$
2.45 \times 10^{-17} \text{ grams}
$$
F. $$
6.34 \times 10^{-14} \text{ grams}
$$
G. $$
9.47 \times 10^{-18} \text{ grams}
$$
H. $$
3.99 \times 10^{-16} \text{ grams}
$$
I. $$
3.02 \times 10^{-18} \text{ grams}
$$
J. $$
8.26 \times 10^{-20} \text{ grams}
$$
Answer: I
Using chemical methods to analyze uranium-containing ores, it is pointed out: at equilibrium, there is 3.59 × 10^7 grams of radium in 1 U^{238}. Try to find the decay constant $\lambda$ of uranium. The half-life of radium is equal to 1617 years.

Options:
A. $$
\sim7.11 \cdot 10^{-17} \text{ seconds}^{-1}
$$
B. $$
\sim4.88 \cdot 10^{-18} \text{ seconds}^{-1}
$$
C. $$
\sim9.76 \cdot 10^{-19} \text{ seconds}^{-1}
$$
D. $$
\sim1.13 \cdot 10^{-18} \text{ seconds}^{-1}
$$
E. $$
\sim6.22 \cdot 10^{-19} \text{ seconds}^{-1}
$$
F. $$
\sim8.01 \cdot 10^{-19} \text{ seconds}^{-1}
$$
G. $$
\sim5.29 \cdot 10^{-17} \text{ seconds}^{-1}
$$
H. $$
\sim2.54 \cdot 10^{-18} \text{ seconds}^{-1}
$$
I. $$
\sim1.97 \cdot 10^{-17} \text{ seconds}^{-1}
$$
J. $$
\sim3.45 \cdot 10^{-18} \text{ seconds}^{-1}
$$
Answer: B
The flux of neutrons achieving thermal equilibrium through a graphite layer well at room temperature (27°C) strikes a thin boron absorber (for boron, the effective cross-section for thermal neutrons is 703 barns), reducing the intensity of the thermal neutron flux to 90% of its original value after passing through this absorber. If the experiment is conducted at 327°C, by how much will the neutron flux intensity decrease?

Options:
A. Up to 94%
B. Up to 88%
C. Up to 87%
D. Up to 89%
E. Up to 92%
F. Up to 93%
G. Up to 86%
H. Up to 95%
I. Up to 98%
J. Up to 96%
Answer: F
Add 1 milligram (calculated as metal with the isotope carrier) of Pr$^{143}$, which has a specific radioactivity of 1000 counts/min·milligram, to a solution containing nitrogen and praseodymium. After separating using chromatography, 5 milligrams of pure praseodymium are extracted, with a radioactivity of 40 counts/min·milligram. How much praseodymium was in the original solution?

Options:
A. 0 milligrams
B. 10 milligrams
C. 5 milligrams
D. 150 milligrams
E. 80 milligrams
F. 250 milligrams
G. 124 milligrams
H. 200 milligrams
I. 300 milligrams
J. 30 milligrams
Answer: G
The ground state of a real helium atom is, of course, non-degenerate, but let's consider a hypothetical helium atom where the two electrons are replaced by two identical particles with spin 1, each carrying a unit negative charge. Ignoring forces related to spin, what is the degeneracy of the ground state for this hypothetical atom?

Options:
A. $$
12
$$
B. $$
18
$$
C. $$
22
$$
D. $$
20
$$
E. $$
8
$$
F. $$
6
$$
G. $$
16
$$
H. $$
4
$$
I. $$
10
$$
J. $$
14
$$
Answer: F
In zinc $(Z=30)$, the ionization energies of the K and L shells are 9.659 keV and 1.021 keV respectively. Calculate the kinetic energy of the Auger electrons emitted from the L shell caused by KX-ray excitation is____.

Options:
A. $$
9. 1 4 8 ( \mathrm{k e V} )
$$
B. $$
8. 5 3 0 ( \mathrm{k e V} )
$$
C. $$
8. 1 7 5 ( \mathrm{k e V} )
$$
D. $$
7. 2 9 4 ( \mathrm{k e V} )
$$
E. $$
8. 0 9 6 ( \mathrm{k e V} )
$$
F. $$
7. 1 1 2 ( \mathrm{k e V} )
$$
G. $$
6. 8 7 3 ( \mathrm{k e V} )
$$
H. $$
7. 6 1 7 ( \mathrm{k e V} )
$$
I. $$
6. 3 5 9 ( \mathrm{k e V} )
$$
J. $$
5. 9 6 4 ( \mathrm{k e V} )
$$
Answer: H
If a neutron collides with an oxygen molecule and excites its rotational energy levels, calculate the minimum energy the neutron must possess. It is known that the bond length of the oxygen molecule is 0.12 nm is___.

Options:
A. $$
7. 8 \times1 0^{-5} \mathrm{e V}
$$
B. $$
9. 3 \times1 0^{-8} \mathrm{e V}
$$
C. $$
2. 5 \times1 0^{-2} \mathrm{e V}
$$
D. $$
8. 5 \times1 0^{-7} \mathrm{e V}
$$
E. $$
5. 0 \times1 0^{-3} \mathrm{e V}
$$
F. $$
1. 2 \times1 0^{-1} \mathrm{e V}
$$
G. $$
4. 1 \times1 0^{-3} \mathrm{e V}
$$
H. $$
2. 4 \times1 0^{-5} \mathrm{e V}
$$
I. $$
3. 6 \times1 0^{-4} \mathrm{e V}
$$
J. $$
6. 9 \times1 0^{-6} \mathrm{e V}
$$
Answer: I
The magnetic moment of the atomic nucleus HNb measured in the experiment is $\mu\!=\! 6.167 \mu_{\mathrm{N}}$, and it is known that the angular momentum of this nucleus is $I={\frac{9}{2}}$. Then the $g$ factor of this nucleus is____.

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