MikaStars39/nano-eval huggingface dataset:
Let $X(t)$ be a one-dimensional nanoprocess, and it is known that $E[X^{t}(t)] = \sigma_{x}^{t} t$. Define another stochastic process $Y(t) = \frac{1}{t} \int_{0}^{t} X(u) \mathrm{d} u$, find ${{p}}_{Y}(y)$ is ().

Options:
A. $$
p_{\mathrm{Y}} ( y )=\frac{1} {\sqrt{2 \pi\sigma_{x}^{2} t}} \mathrm{e x p} \Bigl(-\frac{y^{2}} {4 \sigma_{x}^{2} t} \Bigr)
$$
B. $$
p_{\mathrm{Y}} ( y )=\frac{1} {\sqrt{2 \pi\sigma_{x}^{2} t / 5}} \mathrm{e x p} \Bigl(-\frac{5 y^{2}} {2 \sigma_{x}^{2} t} \Bigr)
$$
C. $$
p_{\mathrm{Y}} ( y )=\frac{1} {\sqrt{2 \pi\sigma_{x} t}} \mathrm{e x p} \Bigl(-\frac{4 y^{2}} {2 \sigma_{x}^{2} t} \Bigr)
$$
D. $$
p_{\mathrm{Y}} ( y )=\frac{1} {\sqrt{2 \pi\sigma_{y}^{2} t}} \mathrm{e x p} \Bigl(-\frac{y^{2}} {2 \sigma_{y} t} \Bigr)
$$
E. $$
p_{\mathrm{Y}} ( y )=\frac{1} {\sqrt{4 \pi\sigma_{x}^{2} t}} \mathrm{e x p} \Bigl(-\frac{y} {2 \sigma_{x}^{2} t} \Bigr)
$$
F. $$
p_{\mathrm{Y}} ( y )=\frac{1} {\sqrt{2 \pi\sigma_{x}^{2} t / 2}} \mathrm{e x p} \Bigl(-\frac{2 y^{2}} {\sigma_{x}^{2} t} \Bigr)
$$
G. $$
p_{\mathrm{Y}} ( y )=\frac{1} {\sqrt{\pi\sigma_{x}^{2} t}} \mathrm{e x p} \Bigl(-\frac{y^{2}} {2 \sigma_{x} t} \Bigr)
$$
H. $$
p_{\mathrm{Y}} ( y )=\frac{1} {\sqrt{2 \pi\sigma_{x}^{2} / t}} \mathrm{e x p} \Bigl(-\frac{y^{2}} {\sigma_{x}^{2} t} \Bigr)
$$
I. $$
p_{\mathrm{Y}} ( y )=\frac{1} {\sqrt{2 \pi\sigma_{x}^{2} t / 3}} \mathrm{e x p} \Bigl(-\frac{3 y^{2}} {2 \sigma_{x}^{2} t} \Bigr)
$$
J. $$
p_{\mathrm{Y}} ( y )=\frac{1} {\sqrt{3 \pi\sigma_{x}^{2} t}} \mathrm{e x p} \Bigl(-\frac{y^{3}} {2 \sigma_{x}^{2} t} \Bigr)
$$
Answer: I
Let $X(t)$ be a Poisson process, and a new stochastic process $Y(t)$ is constructed as follows:
$$
Y(0)=0, \quad Y(t)=\sum_{n=1}^{X(t)} Z_{n}
$$
where $Z_n$ is a set of independent and identically distributed random variables, which are independent of $X(t)$. It is known that the characteristic function of $Z_n$ is $\phi_Z(v)$. Find the first-order characteristic function $\phi_{Y}(v)$ of $Y(t)$.

Options:
A. $$\phi_{Y}(v)=\mathrm{e}^{-\lambda t\phi_{Z}(v)^2}$$
B. $$\phi_{Y}(v)=\mathrm{e}^{\lambda t(\phi_{Z}(v)-2)}$$
C. $$\phi_{Y}(v)=\mathrm{e}^{\lambda t(1+\phi_{Z}(v))}$$
D. $$\phi_{Y}(v)=\mathrm{e}^{-\lambda t\left[\phi_{2}(n)-1\right]}
$$
E. $$\phi_{Y}(v)=\mathrm{e}^{\phi_{Z}(v)-\lambda t}$$
F. $$\phi_{Y}(v)=\mathrm{e}^{-\lambda t\phi_{Z}(v-1)}$$
G. $$\phi_{Y}(v)=\mathrm{e}^{-\lambda t(1-\phi_{Z}(v)^2)}$$
H. $$\phi_{Y}(v)=\mathrm{e}^{\phi_{Z}(v)\left[\lambda t-1\right]}$$
I. $$\phi_{Y}(v)=\mathrm{e}^{\lambda t[\phi_{Z}(v)+1]}$$
J. $$\phi_{Y}(v)=\mathrm{e}^{\lambda t(1-\phi_{Z}(v))}$$
Answer: D
Let $\{X_{n}, n \in N^{+} \}$ be a Markov chain with state space $I=\{a, b, c \}$, and transition matrix
$$P=\left[ \begin{matrix} {{{\frac{1} {2}}}} & {{{\frac{1} {4}}}} & {{{\frac{1} {4}}}} \\ {{{\frac{2} {3}}}} & {{{0}}} & {{{\frac{1} {3}}}} \\ {{{\frac{3} {5}}}} & {{{\frac{2} {5}}}} & {{{0}}} \\ \end{matrix} \right]
$$
Find $P \{X_{n+2}=c \, | \, X_{n}=b \}$ is ().

Options:
A. $$
\frac{2} {9}
$$
B. $$
\frac{1} {8}
$$
C. $$
\frac{5} {12}
$$
D. $$
\frac{2} {11}
$$
E. $$
\frac{1} {6}
$$
F. $$
\frac{1} {9}
$$
G. $$
\frac{4} {15}
$$
H. $$
\frac{1} {4}
$$
I. $$
\frac{3} {10}
$$
J. $$
\frac{7} {18}
$$
Answer: E
The mechanized supporting scheme applicable for the construction of a shaft with a diameter of $5 \mathrm{m}$ and a depth of $600 \mathrm{m}$ is ____.

Options:
A. Type X $\mathrm{X_{O}}$ system, 4JK3/20 jack, FWD-5 umbrella drill, YGM strategic model
B. Type IV $\mathrm{I V_{G}}$ derrick, 2JK3/15.5 hoist, FJD-4 umbrella drill, YJM series template
C. Type VIII $\mathrm{V I I I_{P}}$ brace, 2JK1/19 pulley, FJD-2 canopy drill, YTM draft design
D. Type I $\mathrm{I_{J}}$ scaffold, 2JK2/14.5 hoist, FJD-6 umbrella drill, YJM variant outline
E. Type IX $\mathrm{I X_{N}}$ lattice, 1JK6/18.5 winch, FJD-4 parasol drill, YKN series prototype
F. Type VI $\mathrm{V_{F}}$ rig, 2JK4/16 jack, FJD-5 umbrella drill, YHM structural plan
G. Type VII $\mathrm{V I I_{D}}$ mast, 3JK5/17 hoist, FHD-4 canopy drill, YSM conceptual template
H. Type V $\mathrm{I V_{H}}$ tower, JK4/12 pulley, FJD-3 canopy drill, YJM model framework
I. Type III $\mathrm{I I I_{M}}$ framework, 3JK2/13.5 lift, GFD-5 canopy drill, YRM design template
J. Type II $\mathrm{I I_{L}}$ gantry, JK5/14 winch, FJD-3 umbrella drill, YLM series template
Answer: B
After blasting during shaft and tunnel excavation, relevant regulations stipulate that workers are only allowed to enter the blasting site after ventilation for ____ min.

Options:
A. 20
B. 35
C. 30
D. 12
E. 5
F. 18
G. 15
H. 10
I. 25
J. 22
Answer: G
Calculate the radii of the octahedral and tetrahedral interstices in a face-centered cubic structure, and express the size of the interstices using the ratio of the interstice radius to the atomic radius $r_{\mathrm{B}} / r_{\mathrm{A}}$.

Options:
A. $$
r_B = \frac{\sqrt{2} - 1}{3} a
$$
$$
r_{B} / r_{A}=0.577
$$
B. $$
r_B = \frac{3 - \sqrt{3}}{4} a
$$
$$
r_{B} / r_{A}=0.333
$$
C. $$
r_B = \frac{\sqrt{3} - 1}{4} a
$$
$$
r_{B} / r_{A}=0.291
$$
D. $$
r_B = \frac{\sqrt{5} - 2}{4} a
$$
$$
r_{B} / r_{A}=0.225
$$
E. $$
r_B = \frac{4 - \sqrt{6}}{4} a
$$
$$
r_{B} / r_{A}=0.250
$$
F. $$
r_B = \frac{2 - \sqrt{2}}{4} a
$$
$$
r_{B} / r_{A}=0.414
$$
G. $$
r_B = \frac{1 - \sqrt{2}}{3} a
$$
$$
r_{B} / r_{A}=0.648
$$
H. $$
r_B = \frac{\sqrt{6} - 4}{4} a
$$
$$
r_{B} / r_{A}=0.707
$$
I. $$
r_B = \frac{5 - \sqrt{5}}{4} a
$$
$$
r_{B} / r_{A}=0.447
$$
J. $$
r_B = \frac{\sqrt{8} - 1}{5} a
$$
$$
r_{B} / r_{A}=0.816
$$
Answer: F
A 20-meter-long aluminum rod with a diameter of $14.0 \mathrm{~mm}$ is drawn through a die with an aperture of $12.7 \mathrm{~mm}$. What is the engineering line strain and true strain on this aluminum rod?

Options:
A. ${16.7} \%,$ ${15.5} \%$
B. ${18.5} \%,$ ${17.3} \%$
C. ${15.0} \%,$ ${14.0} \%$
D. ${22.0} \%,$ ${20.0} \%$
E. ${22.2} \%,$ ${20.4} \%$
F. ${20.8} \%,$ ${19.1} \%$
G. ${17.9} \%,$ ${16.8} \%$
H. ${19.5} \%,$ ${18.0} \%$
I. ${23.0} \%,$ ${21.3} \%$
J. ${21.5} \%,$
${19.47} \%$
Answer: J
After the high temperature recovery, several dislocations form a sub-grain boundary with an orientation difference of $0.057^{\circ}$. Assuming there is no interaction between these dislocations, how many times the original distortion energy is the energy after forming the sub-grain? (Assume the core radius of the dislocation $r_{0}\approx b\approx 10^{-8} \ \text{cm}$, and that the range of the dislocation stress field before the formation of the sub-grain is $R=10^{-4} \ \text{cm}$.)

Options:
A. $$
\frac{9} {10}
$$
B. $$
\frac{5} {9}
$$
C. $$
\frac{2} {5}
$$
D. $$
\frac{3} {5}
$$
E. $$
\frac{1} {3}
$$
F. $$
\frac{1} {2}
$$
G. $$
\frac{5} {6}
$$
H. $$
\frac{7} {8}
$$
I. $$
\frac{3} {4}
$$
J. $$
\frac{4} {7}
$$
Answer: I
Carburize industrial pure iron at 920°C. If the carbon concentration on the surface of the workpiece remains constant, i.e., $w_{\mathrm{C}}=1.2$%, with a diffusion coefficient of $D=1.5 \times 10^{-11} \mathrm{m}^{2}/s$, and for a duration of 10 hours, determine the depth of the carburized layer, specified as the depth from the surface to where the mass fraction of carbon is 0.2% is ().

Options:
A. 1.55 mm
B. 3.56 mm
C. 0.98 mm
D. 5.27 mm
E. 4.11 mm
F. 1.44 mm
G. 1.76 mm
H. 3.14 mm
I. 6.03 mm
J. 2.33 mm
Answer: F
Adding CaO with a mass fraction of 10% to $\mathrm{ZrO_{2}}$ can form a $\mathrm{CaF_{2}}$-type structure. Given that the radius of the cation $\mathrm{Zr}^{4+}$ is 0.079 nm, and the radius of the anion $O^{2-}$ is $0.140 \mathrm{~nm}$, determine how many anion vacancies are in $1 \mathrm{m}^{3}$ of this substance?

Options:
A. $9.721 \times 10^{27}$ (pieces)
B. $7.110 \times 10^{27}$ (pieces)
C. $3.547 \times 10^{27}$ (pieces)
D. $7.633 \times 10^{27}$ (pieces)
E. $6.739 \times 10^{27}$ (pieces)
F. $2.668 \times 10^{27}$ (pieces)
G. $8.312 \times 10^{27}$ (pieces)
H. $5.845 \times 10^{27}$ (pieces)
I. $4.950 \times 10^{27}$ (pieces)
J. $1.785 \times 10^{27}$ (pieces)
Answer: E
Given that the pure aluminum has $\tau_{c}=0.79\, \mathrm{MPa}$, causing slip in the [101] direction on the $(\overline111)$ plane, what magnitude of force should be applied in the [001] direction?

Options:
A. $$
\approx1. 0 5 \mathrm{~ M P a}
$$
B. $$
\approx0. 6 3 \mathrm{~ M P a}
$$
C. $$
\approx1. 7 8 \mathrm{~ M P a}
$$
D. $$
\approx2. 1 2 \mathrm{~ M P a}
$$
E. $$
\approx3. 0 1 \mathrm{~ M P a}
$$
F. $$
\approx1. 9 4 \mathrm{~ M P a}
$$
G. $$
\approx0. 8 4 \mathrm{~ M P a}
$$
H. $$
\approx1. 5 6 \mathrm{~ M P a}
$$
I. $$
\approx2. 8 9 \mathrm{~ M P a}
$$
J. $$
\approx2. 5 0 \mathrm{~ M P a}
$$
Answer: F
There is a silicon $PN$ junction, with the doping concentrations of the $P$ region and the $N$ region being $N_{A} = 9 \times 10^{16} \text{ cm}^{-3}$ and $N_{D} = 2 \times 10^{16} \text{ cm}^{-3}$, respectively. In the $P$ region, the mobilities of holes and electrons are $350 \text{ cm}^2/\text{V}\cdot\text{s}$ and $500 \text{ cm}^2/\text{V}\cdot\text{s}$, respectively. In the $N$ region, the mobilities of holes and electrons are $300 \text{ cm}^2/\text{V}\cdot\text{s}$ and $900 \text{ cm}^2/\text{V}\cdot\text{s}$, respectively. Assume the lifetime of non-equilibrium carriers in both regions is $1 \text{ µs}$, and the cross-sectional area of the $PN$ junction is $10 \text{ cm}^2$. The value of ${\frac{q}{kT}}$ is $38.7 \text{ V}^{-1}$. When an external forward voltage $\boldsymbol{u}=0.65 \text{ V}$ is applied, determine the expressions for the total electron current as it varies with $x$ in the $N$ region

Options:
A. $$= 8.20 + 7.11 \exp(-350x) \ \text{m} \ \boldsymbol{A}$$
B. $$= 5.27 - 4.09 \exp(-357x) \ \text{m} \ \boldsymbol{A}$$
C. $$= 5.60 - 4.33 \exp(-310x) \ \text{m} \ \boldsymbol{A}$$
D. $$= 3.15 + 2.58 \exp(-200x) \ \text{m} \ \boldsymbol{A}$$
E. $$= 9.10 + 8.24 \exp(-280x) \ \text{m} \ \boldsymbol{A}$$
F. $$= 4.87 - 3.21 \exp(-400x) \ \text{m} \ \boldsymbol{A}$$
G. $$= 7.42 + 6.55 \exp(-300x) \ \text{m} \ \boldsymbol{A}$$
H. $$= 2.75 - 1.89 \exp(-150x) \ \text{m} \ \boldsymbol{A}$$
I. $$= 1.95 - 1.45 \exp(-170x) \ \text{m} \ \boldsymbol{A}$$
J. $$= 6.30 + 5.12 \exp(-250x) \ \text{m} \ \boldsymbol{A}$$
Answer: B
The center frequency $f_{0} = 10.7$ MHz of the staggered-tuned amplifier is composed of two pairs of critically detuned single-loop resonant amplifiers. It is known that each single-loop resonant amplifier has $K_{u0} = 20$ and $\Delta f_{0.7} = 400 \mathrm{kHz}$. Determine the total gain, the passband, and the resonant frequency of each stage of the amplifier.

Options:
A. $$
= 4 2 5 0 0
$$
$$
= 4 6 2 \mathrm{k} \mathrm{H} \mathrm{z}
$$
$$
= 9 . 8 \mathrm{M H z}
$$
B. $$
= 4 3 5 0 0
$$
$$
= 4 5 1 \mathrm{k} \mathrm{H} \mathrm{z}
$$
$$
= 1 0 . 8 \mathrm{M H z}
$$
C. $$
= 4 1 5 0 0
$$
$$
= 4 6 7 \mathrm{k} \mathrm{H} \mathrm{z}
$$
$$
= 1 1 . 5 \mathrm{M H z}
$$
D. $$
= 3 9 5 0 0
$$
$$
= 4 5 9 \mathrm{k} \mathrm{H} \mathrm{z}
$$
$$
= 1 0 . 7 \mathrm{M H z}
$$
E. $$
= 4 3 0 0 0
$$
$$
= 4 4 8 \mathrm{k} \mathrm{H} \mathrm{z}
$$
$$
= 1 1 . 2 \mathrm{M H z}
$$
F. $$
= 4 0 0 0 0
$$
$$
= 4 5 3 \mathbf{k} \mathbf{H} \mathbf{z}
$$
$$
= 1 0. 5 \mathrm{M H z}
$$
G. $$
= 3 9 0 0 0
$$
$$
= 4 5 5 \mathrm{k} \mathrm{H} \mathrm{z}
$$
$$
= 1 1 . 0 \mathrm{M H z}
$$
H. $$
= 4 2 0 0 0
$$
$$
= 4 6 0 \mathrm{k} \mathrm{H} \mathrm{z}
$$
$$
= 9 . 5 \mathrm{M H z}
$$
I. $$
= 4 0 5 0 0
$$
$$
= 4 6 5 \mathrm{k} \mathrm{H} \mathrm{z}
$$
$$
= 1 0 . 3 \mathrm{M H z}
$$
J. $$
= 4 1 0 0 0
$$
$$
= 4 5 7 \mathrm{k} \mathrm{H} \mathrm{z}
$$
$$
= 1 0 . 4 \mathrm{M H z}
$$
Answer: F
In the parallel resonant power amplifier operating at critical condition, a 3DG12B transistor is used. It is known that the utilization factor of the collector voltage at critical condition §cr is $0.94$, $E_{c} = 18 \, \mathbf{V}$, and $\theta = 90^\circ$. It is required that the output power $P_{o}$ is $2 \, \mathbf{W}$. Try to find the resonant impedance $R_{e}$, the power supplied by the power source $P_{dc}$, the collector efficiency $\eta$, and the amplitude of the AC voltage $U_{cm}$.

Options:
A. $$
R_e=68 \Omega
$$
$$
P_{dc}=3.48 \mathbf{W}
$$
$$
\eta=65.12 \%
$$
$$
U_{cm}=17.5 \mathbf{V}
$$
B. $$
R_e=75.0 \Omega
$$
$$
P_{dc}=2.85 \mathbf{W}
$$
$$
\eta=74.02 \%
$$
$$
U_{cm}=18.3 \mathbf{V}
$$
C. $$
R_e=69.8 \Omega
$$
$$
P_{dc}=3.10 \mathbf{W}
$$
$$
\eta=71.43 \%
$$
$$
U_{cm}=16.1 \mathbf{V}
$$
D. $$
R_e=74.5 \Omega
$$
$$
P_{dc}=2.50 \mathbf{W}
$$
$$
\eta=76.00 \%
$$
$$
U_{cm}=18.0 \mathbf{V}
$$
E. $$
R_e=73.6 \Omega
$$
$$
P_{dc}=2.60 \mathbf{W}
$$
$$
\eta=75.05 \%
$$
$$
U_{cm}=15.9 \mathbf{V}
$$
F. $$
R_e=67.9 \Omega
$$
$$
P_{dc}=3.20 \mathbf{W}
$$
$$
\eta=68.75 \%
$$
$$
U_{cm}=16.5 \mathbf{V}
$$
G. $$
R_e=71.5 \Omega
$$
$$
P_{dc}=2.72 \mathbf{W}
$$
$$
\eta=73.53 \%
$$
$$
U_{cm}=16.9 \mathbf{V}
$$
H. $$
R_e=72.2 \Omega
$$
$$
P_{dc}=3.00 \mathbf{W}
$$
$$
\eta=70.00 \%
$$
$$
U_{cm}=15.7 \mathbf{V}
$$
I. $$
R_e=76.1 \Omega
$$
$$
P_{dc}=2.35 \mathbf{W}
$$
$$
\eta=77.02 \%
$$
$$
U_{cm}=17.3 \mathbf{V}
$$
J. $$
R_e=70.4 \Omega
$$
$$
P_{dc}=2.95 \mathbf{W}
$$
$$
\eta=72.30 \%
$$
$$
U_{cm}=17.0 \mathbf{V}
$$
Answer: G
Suppose a certain BJT is in an active state. If $i_{\mathrm{B}} = 50 \, \mathrm{\mu A}$ and $i_{\mathrm{C}} = 2.65 \, \mathrm{mA}$, find $\beta, \alpha$, and $i_{\mathrm{E}}$.

Options:
A. $$
= 5 5
$$
$$
\approx0. 9 3 2
$$
$$
= 2. 9 \; \; \mathrm{m A}
$$
B. $$
= 5 8
$$
$$
\approx0. 9 5 6
$$
$$
= 3. 1 \; \; \mathrm{m A}
$$
C. $$
= 5 2
$$
$$
\approx0. 9 8 3
$$
$$
= 2. 6 \; \; \mathrm{m A}
$$
D. $$
= 5 6
$$
$$
\approx0. 9 7 1
$$
$$
= 3. 0 \; \; \mathrm{m A}
$$
E. $$
= 4 9
$$
$$
\approx0. 9 7 9
$$
$$
= 2. 4 \; \; \mathrm{m A}
$$
F. $$
= 5 4
$$
$$
\approx0. 9 5 2
$$
$$
= 2. 8 \; \; \mathrm{m A}
$$
G. $$
= 5 3
$$
$$
\approx0. 9 8 1
$$
$$
= 2. 7 \; \; \mathrm{m A}
$$
H. $$
= 5 0
$$
$$
\approx0. 9 6 9
$$
$$
= 2. 5 \; \; \mathrm{m A}
$$
I. $$
= 6 0
$$
$$
\approx0. 9 2 5
$$
$$
= 3. 2 \; \; \mathrm{m A}
$$
J. $$
= 5 1
$$
$$
\approx0. 9 4 3
$$
$$
= 2. 6 \; \; \mathrm{m A}
$$
Answer: G
The open-loop voltage gain of an amplifier circuit is $A_{\mathrm{v o}}=10^{4}$. When configured as a negative feedback amplifier circuit, its closed-loop voltage gain is $A_{v f}=50$. If $A_{v o}$ changes by 10%, how much does $A_{\mathrm{v f}}$ change?

Options:
A. $$
3. 0 0 \%
$$
B. $$
2. 0 0 \%
$$
C. $$
4. 0 0 \%
$$
D. $$
1. 1 0 \%
$$
E. $$
0. 1 0 \%
$$
F. $$
0. 0 5 \%
$$
G. $$
5. 0 0 \%
$$
H. $$
0. 5 0 \%
$$
I. $$
0. 2 5 \%
$$
J. $$
0. 8 0 \%
$$
Answer: F
A coil with a resistance of $R_{L}$ and an air-variable capacitor are connected in series with a thermoelectric milliammeter having an internal resistance of 20Ω, connected to an external 400kHz constant amplitude sinusoidal voltage source. When the capacitor is adjusted to 376pF and 558pF, the current amplitude drops to $1/\sqrt{2}$ of its maximum value. The inductance of the coil at 400kHz and the quality factor at this frequency are ().

Options:
A. $$
0. 3 2 0 \mathrm{m} \mathrm{H}, ~ ~ Q=6. 2 0
$$
B. $$
0. 3 4 0 \mathrm{m} \mathrm{H}, ~ ~ Q=6. 0 0
$$
C. $$
0. 3 5 2 \mathrm{m} \mathrm{H}, ~ ~ Q=4. 0 0
$$
D. $$
0. 3 6 0 \mathrm{m} \mathrm{H}, ~ ~ Q=5. 9 0
$$
E. $$
0. 3 7 5 \mathrm{m} \mathrm{H}, ~ ~ Q=5. 0 0
$$
F. $$
0. 4 0 0 \mathrm{m} \mathrm{H}, ~ ~ Q=6. 0 0
$$
G. $$
0. 3 3 0 \mathrm{m} \mathrm{H}, ~ ~ Q=5. 7 0
$$
H. $$
0. 3 5 0 \mathrm{m} \mathrm{H}, ~ ~ Q=5. 5 0
$$
I. $$
0. 3 5 2 \mathrm{m} \mathrm{H}, ~ ~ Q=5. 8 0
$$
J. $$
0. 2 5 0 \mathrm{m} \mathrm{H}, ~ ~ Q=4. 5 0
$$
Answer: I
What is the autocorrelation function $R(\tau)$ of the sine wave? $u = A \cos(\omega_c t + \phi)$.

Options:
A. $R \left( \tau\right)=A^{2} \operatorname{sin} \omega_{c}\tau$
B. $R \left( \tau\right)=0.5 A^{2} \operatorname{tan} \omega_{c}t$
C. $R \left( \tau\right)=2 A^{2} \operatorname{sin} \omega_{c}t$
D. $R \left( \tau\right)=A A^{2} \operatorname{cos} \omega_{c}t$
E. $R \left( \tau\right)=A^{2} \operatorname{cos} \omega_{c}\tau$
F. $R \left( \tau\right)=A^{2} \operatorname{tan} \omega_{c}\tau$
G. $R \left( \tau\right)=\frac{1}{2} A^{2} \operatorname{sin} \omega_{c}t$
H. $R \left( \tau\right)=\frac{1}{3} A^{2} \operatorname{cos} \omega_{c}t$
I. $R \left( \tau\right)=\frac{1}{2} A \operatorname{cos} \omega_{c}t$
J. $R \left( \tau\right)=\frac{1} {2} A^{2} \operatorname{cos} \omega_{c}t$
Answer: J
A double sideband amplitude modulated signal $u=A ( 1+m \cos \omega_{M} t ) \cos \omega_{\epsilon}$ passes through a filter that removes the lower sideband. Assuming the resulting signal is fed into an envelope detector, the ratio of the fundamental frequency to the second harmonic present in the detector's output voltage is ().

Options:
A. 1/m
B. 2/m
C. 5/m
D. 9/m
E. 6/m
F. 3/m
G. 10/m
H. 7/m
I. 8/m
J. 4/m
Answer: I
A sequence of equal-amplitude DC pulses has a pulse duration of 5μs and a repetition frequency of 20kHz. What is the bandwidth required for the transmission of the signal?

Options:
A. 190kHz
B. 180kHz
C. 240kHz
D. 200kHz
E. 220kHz
F. 170kHz
G. 230kHz
H. 150kHz
I. 260kHz
J. 250kHz
Answer: D
Transmit three 5MHz limited bandwidth signals using PCM. Assume that the system is designed to have at least a 50dB signal-to-quantization noise power ratio, and assume that each sample also transmits one bit for marking and synchronization. What is the total bit rate of the entire system?

Options:
A. 280bit/s
B. 330bit/s
C. 340bit/s
D. 310bit/s
E. 300bit/s
F. 360bit/s
G. 290bit/s
H. 270bit/s
I. 350bit/s
J. 320bit/s
Answer: E
Ten signals with a bandwidth of 0 to 100 Hz are sampled at the lowest rate, then transmitted as PPM signals over a TDM system. Each pulse width is 0.2 ms, and the time delay without modulation signal is 0.25 ms.What is the maximum allowable pulse position variation?

Options:
A. ±0.05ms
B. ±0.45ms
C. ±0.25ms
D. ±0.20ms
E. ±0.30ms
F. ±0.35ms
G. ±0.10ms
H. ±0.40ms
I. ±0.15ms
J. ±0.50ms
Answer: I
A circular air dielectric waveguide with a radius of 50 mm operates in the ${H}_{01}$ mode, which is a circular electromagnetic wave. The cutoff frequency of the ${H}_{01}$ wave is ().

Options:
A. 5.140GHz
B. 2.983GHz
C. 4.872GHz
D. 1.875GHz
E. 3.529GHz
F. 4.125GHz
G. 3.659GHz
H. 3.210GHz
I. 3.820GHz
J. 4.532GHz
Answer: G
A square loop antenna has each side measuring 0.3m, with a number of turns $= 10$, and the total inductance of the antenna is 100μH. This antenna is connected to a receiver with an input impedance of 100Ω. The voltage amplification factor from the input to the DC output of the detector is $10^{5}$. The quality factor (Q value) of the loop antenna at 1.2MHz is 120. When the loop antenna is adjusted for maximum output, the field strength of a 1.2MHz signal that produces an output power of 300mV at the detector is ().

Options:
A. 1.0088mV/m
B. 1.1098mV/m
C. 1.0097mV/m
D. 1.0198mV/m
E. 1.0008mV/m
F. 1.0998mV/m
G. 1.0090mV/m
H. 1.2098mV/m
I. 1.0098mV/m
J. 1.1998mV/m
Answer: I
A three-phase asynchronous motor, rated frequency $f_{\mathrm{N}}=50 \ \ \mathrm{Hz}$, rated speed $n_{N}=960 \; \; \mathrm{r/min}$, calculate the rated slip $S_{\mathrm{N}}$.

Options:
A. $$0.11$$
B. $$0.12$$
C. $$0.02$$
D. $$0.08$$
E. $$0.10$$
F. $$0.03$$
G. $$0.04$$
H. $$0.06$$
I. $$0.14$$
J. $$0.09$$
Answer: G
A hollow shaft with an outer diameter $D=100 \, \mathrm{mm}$, an inner diameter $d=50 \, \mathrm{mm}$, $G=80 \, \mathrm{GPa}$, and $[\theta]=0.75^{\circ} / \mathrm{m}$ is given. Determine the maximum torque $T_{\mathrm{max}}$ that the shaft can withstand.

Options:
A. $$11.25kN·m$$
B. $$9.90kN·m$$
C. $$10.50kN·m$$
D. $$8.89kN·m$$
E. $$7.77kN·m$$
F. $$9.00kN·m$$
G. $$10.98kN·m$$
H. $$8.02kN·m$$
I. $$12.14kN·m$$
J. $$9.63kN·m$$
Answer: J
Given a four-lane highway with a design speed of $100 \mathrm{km/h}$, a one-way peak hour traffic volume $V_{\mathrm{p}}=1800$ vehicles/hour, with large vehicles accounting for $40\%$, a lane width of 3.50m, lateral clearance of $1.70 \mathrm{m}$, and obstacles closely flanking both sides of the driving lanes, located in a rolling terrain. Determine how much more traffic volume can be added before reaching its actual capacity is ().

Options:
A. 900 vehicles/hour
B. 720 vehicles/hour
C. 625 vehicles/hour
D. 810 vehicles/hour
E. 790 vehicles/hour
F. 940 vehicles/hour
G. 655 vehicles/hour
H. 850 vehicles/hour
I. 746 vehicles/hour
J. 700 vehicles/hour
Answer: I
At a T-shaped intersection, a left-turning car collided with an oncoming vehicle, which left a braking skid mark of 32.5 meters long. The car was equipped with a hydraulic braking system, and the road was a straight, dry asphalt surface. Calculate the speed of the car at the time of collision using the braking skid mark is ().

Options:
A. 55.6km/h
B. 68.3km/h
C. 50.5km/h
D. 92.0km/h
E. 80.7km/h
F. 85.4km/h
G. 73.1km/h
H. 60.2km/h
I. 66.8km/h
J. 77.9km/h
Answer: G
At an unsignalized intersection, the bidirectional traffic flow on the main road is 1200 vehicles per hour, and vehicle arrivals follow a Poisson distribution. The critical headway required for vehicles on the minor road to cross is $t_{0}=6 \, s$. The headway for vehicles in a platoon is $t=3 \, s$. Determine the number of vehicles on the minor road that can cross the main road traffic flow is ().

Options:
A. 235pcu/h
B. 174pcu/h
C. 248pcu/h
D. 189pcu/h
E. 213pcu/h
F. 262pcu/h
G. 271pcu/h
H. 304pcu/h
I. 257pcu/h
J. 281pcu/h
Answer: I
Assume the relationship between the speed and density of traffic flow is $V = 88 - 1.6K$. If the actual traffic flow needs to be restricted to no more than 0.8 times the maximum flow, try to find the maximum values of speed and density under this condition is ().(assuming the optimal density of traffic flow is $K_m$).

Options:
A. 68.4km/h,13.9veh/km
B. 63.7km/h,15.2veh/km
C. 60.5km/h,16.4veh/km
D. 56.1km/h,18.3veh/km
E. 59.2km/h,17.8veh/km
F. 65.9km/h,14.6veh/km
G. 47.5km/h,21.3veh/km
H. 53.8km/h,19.1veh/km
I. 75.2km/h,11.7veh/km
J. 71.0km/h,12.4veh/km
Answer: B
Planning a highway, the projected traffic volume for its long-term design is 45,000 vehicles per day, with large vehicles making up 30% of the total traffic. The direction factor is $K_{D}=0.6$, and the terrain is flat. The design hourly traffic volume coefficient is $K=0.12$. Design the number of lanes for the highway and determine its level of service under this traffic condition is ().(Assume a design speed of 100 km/h; $f_{w}=0.9$; $E_{HV}=2$; $f_{P}=1$)

Options:
A. 1.02
B. 0.65
C. 0.95
D. 0.88
E. 0.78
F. 1.25
G. 0.83
H. 1.36
I. 1.10
J. 1.14
Answer: E
Place a small object into a high-pressure container. Under a hydrostatic pressure of $p=0.45 \mathrm{N} / \mathrm{mm}^{2}$, the volumetric strain is measured at $e=-3.6 \times 10^{-5}$. Given that the Poisson's ratio $\nu=0.3$, find the elastic modulus $E$ of the object.

Options:
A. $$
E=1. 3 \times1 0^{4} \mathrm{N / m m}^{2}
$$
B. $$
E=2. 5 \times1 0^{4} \mathrm{N / m m}^{2}
$$
C. $$
E=1. 6 \times1 0^{4} \mathrm{N / m m}^{2}
$$
D. $$
E=1. 7 \times1 0^{4} \mathrm{N / m m}^{2}
$$
E. $$
E=1. 5 \times1 0^{4} \mathrm{N / m m}^{2}
$$
F. $$
E=2. 1 \times1 0^{4} \mathrm{N / m m}^{2}
$$
G. $$
E=1. 2 \times1 0^{4} \mathrm{N / m m}^{2}
$$
H. $$
E=2. 0 \times1 0^{4} \mathrm{N / m m}^{2}
$$
I. $$
E=1. 8 \times1 0^{4} \mathrm{N / m m}^{2}
$$
J. $$
E=2. 2 \times1 0^{4} \mathrm{N / m m}^{2}
$$
Answer: E
Given a brick masonry compression member with $e / h=0.18$; height-to-thickness ratio $\beta=17$, seismic fortification intensity of 7 degrees, and Class $\mathbf{II}$ site soil, please select a masonry structural component plan that is safe and reliable, economically reasonable, and convenient for construction is().

Options:
A. Rammed earth wall with a smooth finish and vibration resistance core
B. Fired-clay bricks laid with vertical hollow cores and cement grout
C. Double-wythe brickwork with no additional structural reinforcement
D. Interlocked clay tiles with hydraulic cement overlay layer
E. Plain brickwork with an external stucco finish for added resistance
F. Solid concrete blocks with a thin layer of non-structural mortar
G. Lightweight aerated concrete blocks with surface bonding agent
H. Masonry wall with external veneer and minimal reinforcement component
I. Hollow-core brick masonry with unbonded reinforcing bars
J. Composite masonry of brickwork and reinforced concrete surface layer or reinforced mortar layer
Answer: J
In a certain single-story industrial building, there are two cranes with a capacity of $Q=32/5 \mathrm{t}$, equipped with soft-hooks and of the bridge type. Each crane has two wheels on each side, with a wheelbase of $4.7 \mathrm{m}$. The standard value of the maximum wheel load is $P_{\operatorname* {max}}=275 \mathrm{kN}$. The standard weight of the crane's transverse trolley is $g=108.8 \mathrm{kN}$, and the height of the crane rail is $h_{\mathrm{R}}=130 \mathrm{mm}$. Assuming the crane is operating under heavy-duty conditions, which of the following values is the closest to the standard value of the lateral horizontal load acting on each wheel (in kN)?

Options:
A. 13.5
B. 35.5
C. 18.5
D. 29.5
E. 36.5
F. 27.5
G. 22.5
H. 24.5
I. 16.5
J. 11.5
Answer: F
A significant large bridge features a constant-height prestressed concrete box-section beam structure, with a design safety level of Grade 1. The standard value of the structural gravity moment for a certain section of this beam is $M_{\mathrm{g}}$, and the standard value of the bending moment due to vehicle load is $M_{\mathrm{k}}$. In the limit state of load-bearing capacity, which of the following represents the basic combination formula for its effect?

Options:
A. $1. 1 \times( 1. 4 M_{g}+1. 1 M_{k} )$
B. $1. 1 \times( 1. 5 M_{g}+1. 3 M_{k} )$
C. $1. 1 \times( 1. 0 M_{g}+1. 2 M_{k} )$
D. $1. 1 \times( 1. 3 M_{g}+1. 2 M_{k} )$
E. $1. 1 \times( 1. 1 M_{g}+1. 3 M_{k} )$
F. $1. 1 \times( 1. 4 M_{g}+1. 5 M_{k} )$
G. $1. 1 \times( 1. 0 M_{g}+1. 5 M_{k} )$
H. $1. 1 \times( 1. 2 M_{g}+1. 4 M_{k} )$
I. $1. 1 \times( 1. 3 M_{g}+1. 4 M_{k} )$
J. $1. 1 \times( 1. 2 M_{g}+1. 1 M_{k} )$
Answer: H
The existing solution is composed of 10 kg of solute A and 120 kg of original solvent B. It is extracted and separated using 150 kg of pure solvent S. Components B and S can be considered completely immiscible. Under the operating conditions, the distribution coefficient, expressed as a mass ratio, can be taken as a constant, $K=2.6$. Try to compare the final raffinate phase composition $X$ of the three extraction operations.

Options:
A. During a three-stage counter-current extraction, the raffinate composition peaks, revealing minimal efficiency. The single-stage method follows, while cross-current has greatest efficiency.
B. In a single-stage extraction, the final composition decreases significantly, showing highest efficiency. The three-stage cross-current method is less effective, while counter-current is minimal.
C. The final composition in a three-stage cross-current extraction is lowest, highlighting the best efficiency. Counter-current method follows, with single-stage as least effective.
D. A single-stage extraction yields a medium raffinate composition, suggesting average extraction efficiency. Cross-current extraction is superior, while counter-current is not effective.
E. The final raffinate composition is highest in a single-stage extraction, indicating poor extraction efficiency. The three-stage counter-current method is next, with cross-current most effective.
F. In a three-stage counter-current extraction, the final raffinate composition is the lowest, indicating the best extraction efficiency. The three-stage cross-current extraction is next, while single-stage extraction is the least effective.
G. In a three-stage cross-current extraction, the final raffinate composition is highest, proving reduced extraction efficiency. Single-stage extraction follows, with counter-current as least effective.
H. In a single-stage extraction, the final composition is lowest, denoting exceptional efficiency. The three-stage counter-current process follows, with cross-current being least effective.
I. In a three-stage counter-current extraction, raffinate composition maximizes, showing reduced efficiency. Single-stage extraction comes next, while cross-current is most effective.
J. In a three-stage cross-current extraction, the raffinate composition is moderate, reflecting average efficiency. Counter-current follows, with the single-stage as least effective.
Answer: F
In the absorption tower, water is used to absorb ammonia mixed in the air. It is known that the ammonia content in the mixed gas entering the tower is 5% (mass fraction, the same below), and after absorption, the ammonia content in the gas exiting the tower is 0.1%. Try to calculate the molar ratio of ammonia in the gas entering and exiting the tower $Y_{1}, Y_{2}$.

Options:
A. $$
Y_{1}{=0. 0 6 7 4}
$$
$$
Y_{2} =\! 0. 0 0 2 3
$$
B. $$
Y_{1}{=0. 0 5 6 3}
$$
$$
Y_{2} =\! 0. 0 0 4 4
$$
C. $$
Y_{1}{=0. 0 8 4 5}
$$
$$
Y_{2} =\! 0. 0 0 3 1
$$
D. $$
Y_{1}{=0. 0 7 9 2}
$$
$$
Y_{2} =\! 0. 0 0 1 9
$$
E. $$
Y_{1}{=0. 0 8 8 4}
$$
$$
Y_{2} =\! 0. 0 0 4 1
$$
F. $$
Y_{1}{=0. 0 9 5 1}
$$
$$
Y_{2} =\! 0. 0 0 1 8
$$
G. $$
Y_{1}{=0. 0 9 1 0}
$$
$$
Y_{2} =\! 0. 0 0 2 0
$$
H. $$
Y_{1}{=0. 0 7 6 5}
$$
$$
Y_{2} =\! 0. 0 0 3 3
$$
I. $$
Y_{1}{=0. 0 8 2 7}
$$
$$
Y_{2} =\! 0. 0 0 2 2
$$
J. $$
Y_{1}{=0. 0 8 9 8}
$$
$$
Y_{2} =\! 0. 0 0 1 7
$$
Answer: J
Gas mixtures A and B undergo steady-state diffusion between two planes 0.15 m apart. It is known that the total pressure is 101.3 kPa and the temperature is 273 K. The partial pressures on the two planes are $p_{\mathrm{A1}}=20 \mathrm{kPa}$ and $p_{\mathrm{A2}}=6.7 \mathrm{kPa}$, respectively. The diffusion coefficient of the mixture is 1.85 $\times 10^{-5}$ m²/s. If B cannot pass through plane 1, and both A and B can pass through two planes, component A diffuses to plane z and undergoes a chemical reaction with solid C: $\frac{1} {2} \mathrm{A}+\mathrm{C}_{( s )} \longrightarrow\mathrm{B}$.Calculate the molar fluxes of A and B, $N_{\mathrm{A}}$ and $N_{\mathrm{B}}$.

Options:
A. $$
N_{\mathrm{A}} \!=\! 7. 4 1 \! \times\! 1 0^{-7} \mathrm{~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \,, \mathrm{~ N_{\mathrm{B}} \!=\!-\! 9. 7 6 \! \times\! 1 0^{-7} ~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
B. $$
N_{\mathrm{A}} \!=\! 6. 4 9 \! \times\! 1 0^{-7} \mathrm{~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \,, \mathrm{~ N_{\mathrm{B}} \!=\!-\! 1. 2 4 \! \times\! 1 0^{-6} ~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
C. $$
N_{\mathrm{A}} \!=\! 7. 0 5 \! \times\! 1 0^{-7} \mathrm{~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \,, \mathrm{~ N_{\mathrm{B}} \!=\!-\! 1. 1 8 \! \times\! 1 0^{-6} ~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
D. $$
N_{\mathrm{A}} \!=\! 6. 3 9 \! \times\! 1 0^{-7} \mathrm{~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \,, \mathrm{~ N_{\mathrm{B}} \!=\!-\! 1. 2 8 \! \times\! 1 0^{-6} ~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
E. $$
N_{\mathrm{A}} \!=\! 5. 9 2 \! \times\! 1 0^{-7} \mathrm{~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \,, \mathrm{~ N_{\mathrm{B}} \!=\!-\! 1. 4 8 \! \times\! 1 0^{-6} ~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
F. $$
N_{\mathrm{A}} \!=\! 6. 8 3 \! \times\! 1 0^{-7} \mathrm{~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \,, \mathrm{~ N_{\mathrm{B}} \!=\!-\! 1. 0 5 \! \times\! 1 0^{-6} ~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
G. $$
N_{\mathrm{A}} \!=\! 6. 1 7 \! \times\! 1 0^{-7} \mathrm{~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \,, \mathrm{~ N_{\mathrm{B}} \!=\!-\! 1. 3 6 \! \times\! 1 0^{-6} ~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
H. $$
N_{\mathrm{A}} \!=\! 5. 2 4 \! \times\! 1 0^{-7} \mathrm{~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \,, \mathrm{~ N_{\mathrm{B}} \!=\!-\! 1. 4 3 \! \times\! 1 0^{-6} ~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
I. $$
N_{\mathrm{A}} \!=\! 6. 0 1 \! \times\! 1 0^{-7} \mathrm{~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \,, \mathrm{~ N_{\mathrm{B}} \!=\!-\! 1. 3 9 \! \times\! 1 0^{-6} ~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
J. $$
N_{\mathrm{A}} \!=\! 5. 7 9 \! \times\! 1 0^{-7} \mathrm{~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} ) \,, \mathrm{~ N_{\mathrm{B}} \!=\!-\! 1. 5 9 \! \times\! 1 0^{-6} ~ k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
Answer: D
Under a total pressure of 110 kPa, ammonia gas mixed in air is absorbed using clean water in a packed column. At a certain cross-section of the column, the gas and liquid phase compositions of ammonia are $\mathbf{y=0.03}$ and $c_{L}=1 \mathbf{kmol/m}^{3}$, respectively. If the gas film absorption coefficient $k_{G}=5 \times 10^{-6} \mathrm{kmol/(m^{2} \cdot s \cdot kPa)}$, and the liquid film absorption coefficient $k_{L}=1.5 \times 10^{-4} \mathrm{m/s}$. Assuming that under operational conditions, the equilibrium relationship follows Henry's Law, with a solubility coefficient $H = 0.73 \mathrm{kmol/(m^{3} \cdot kPa)}$. Try to determine the overall driving force for absorption expressed in terms of $\Delta p_{G}$ and $\Delta c_{L}$, as well as the corresponding overall absorption coefficient.

Options:
A. $$
5. 4 3 \times1 0^{-5} \, {\mathrm{m / s}}
$$
B. $$
7. 9 0 \times1 0^{-3} \, {\mathrm{m / s}}
$$
C. $$
3. 9 1 \times1 0^{-8} \, {\mathrm{m / s}}
$$
D. $$
9. 5 6 \times1 0^{-4} \, {\mathrm{m / s}}
$$
E. $$
2. 0 4 \times1 0^{-7} \, {\mathrm{m / s}}
$$
F. $$
2. 6 7 \times1 0^{-4} \, {\mathrm{m / s}}
$$
G. $$
8. 2 1 \times1 0^{-7} \, {\mathrm{m / s}}
$$
H. $$
4. 8 3 \times1 0^{-9} \, {\mathrm{m / s}}
$$
I. $$
6. 5 5 \times1 0^{-6} \, {\mathrm{m / s}}
$$
J. $$
1. 1 2 \times1 0^{-8} \, {\mathrm{m / s}}
$$
Answer: I
Using a packed tower, absorb methanol vapor mixed in air with clean water at 101.3 kPa and 20°C. If under operating conditions the equilibrium relationship conforms to Henry's law, the solubility coefficient of methanol in water is $H = 1.995 \text{ kmol/(m}^3 \cdot \text{kPa)}$. At a certain section in the tower, the partial pressure of methanol in the gas phase is $5 \text{ kPa}$, the composition of the liquid phase is $2.11 \text{ kmol/m}^3$, the liquid film absorption coefficient is $k_{\mathrm{L}} = 2.08 \times 10^{-5} \, \text{m/s}$, and the overall gas phase absorption coefficient is $K_{\mathrm{G}} = 1.122 \times 10^{-5} \text{ kmol/(m}^2 \cdot \text{s} \cdot \text{kPa)}$. Determine the absorption rate at that section.

Options:
A. $$
0. 2 0 1 4 \mathrm{k m o l / ( m^{2} \cdot h )}
$$
B. $$
0. 2 0 9 3 \mathrm{k m o l / ( m^{2} \cdot h )}
$$
C. $$
0. 1 5 7 8 \mathrm{k m o l / ( m^{2} \cdot h )}
$$
D. $$
0. 1 5 0 6 \mathrm{k m o l / ( m^{2} \cdot h )}
$$
E. $$
0. 1 3 6 9 \mathrm{k m o l / ( m^{2} \cdot h )}
$$
F. $$
0. 1 5 9 2 \mathrm{k m o l / ( m^{2} \cdot h )}
$$
G. $$
0. 1 8 4 5 \mathrm{k m o l / ( m^{2} \cdot h )}
$$
H. $$
0. 1 6 4 2 \mathrm{k m o l / ( m^{2} \cdot h )}
$$
I. $$
0. 1 4 5 1 \mathrm{k m o l / ( m^{2} \cdot h )}
$$
J. $$
0. 1 7 8 3 \mathrm{k m o l / ( m^{2} \cdot h )}
$$
Answer: F
During foundation construction at a certain site, water needs to be added to the soil to compact it. A soil sample of 3 kg is taken, and its moisture content is measured at $\omega=16$\%. How much water needs to be added to prepare a soil sample with $\omega=20$\%?

Options:
A. 0.11kg
B. 0.15kg
C. 0.22kg
D. 0.08kg
E. 0.20kg
F. 0.17kg
G. 0.16kg
H. 0.24kg
I. 0.29kg
J. 0.23kg
Answer: A
Given that the maximum principal stress at a certain point in the foundation is $\sigma_{1}=600 \, \text{kPa}$, and the minimum principal stress is $\sigma_{3}=100 \, \text{kPa}$. Calculate the normal stress and shear stress acting on the plane inclined at 30° to the plane of the minimum principal stress.

Options:
A. $$
2 8 0. 0 \mathbf{k P a}
$$
B. $$
3 0 0. 0 \mathbf{k P a}
$$
C. $$
3 5 0. 0 \mathbf{k P a}
$$
D. $$
2 1 6. 5 \mathbf{k P a}
$$
E. $$
2 3 4. 4 \mathbf{k P a}
$$
F. $$
1 5 0. 0 \mathbf{k P a}
$$
G. $$
2 5 0. 0 \mathbf{k P a}
$$
H. $$
1 8 0. 2 \mathbf{k P a}
$$
I. $$
2 7 5. 5 \mathbf{k P a}
$$
J. $$
1 9 0. 0 \mathbf{k P a}
$$
Answer: D
A strip foundation has a base width $b=1.8 \mathrm{m}$ and a burial depth $d=1.2 \mathrm{m}$. The foundation soil is clay with a standard internal friction angle $\varphi_{k}=20^{\circ}$ and a standard cohesion value $c_{k}=12 \mathrm{kPa}$. The groundwater level is at the same level as the base of the foundation. The effective unit weight of the soil is $\gamma^{\prime}=10 \mathrm{kN/m}^{3}$, and the unit weight of the soil above the base is $\gamma_{m}=18.3 \mathrm{kN/m}^{3}$. Determine the characteristic value of the foundation bearing capacity $f_{a}$ is__.

Options:
A. $$
1 4 4. 3 \mathrm{k P a}
$$
B. $$
1 2 0. 9 \mathrm{k P a}
$$
C. $$
1 3 2. 4 \mathrm{k P a}
$$
D. $$
1 8 9. 2 \mathrm{k P a}
$$
E. $$
2 0 5. 7 \mathrm{k P a}
$$
F. $$
1 5 8. 3 \mathrm{k P a}
$$
G. $$
1 9 5. 1 \mathrm{k P a}
$$
H. $$
1 4 0. 7 \mathrm{k P a}
$$
I. $$
1 7 3. 5 \mathrm{k P a}
$$
J. $$
1 1 6. 6 \mathrm{k P a}
$$
Answer: A
From top to bottom, the structure consists of a permeable sand layer, a saturated cohesive soil layer, and an impermeable bedrock. A large area load $P$ is applied to the ground (considered as an infinitely distributed load). It is known that $P = 200 \mathrm{kPa} (2.0 \mathrm{kg/cm}^{2})$. The cohesive soil layer is 6.0 meters thick, with a compression modulus $E_{s} = 6.0 \mathrm{MPa}$, and a consolidation coefficient $C_{v} = 5.0 \times 10^{-3} \, \mathrm{cm}^{2}/\mathrm{s}$. When the degree of consolidation reaches 50%, the time factor $T_{v} = 0.197$. Try to estimate the time needed to reach a 50% degree of consolidation is__.

Options:
A. $$
4 0 9\ \mathrm{days}
$$
B. $$
2 8 5\ \mathrm{days}
$$
C. $$
2 2 0\ \mathrm{days}
$$
D. $$
2 4 1\ \mathrm{days}
$$
E. $$
2 7 3\ \mathrm{days}
$$
F. $$
3 3 7\ \mathrm{days}
$$
G. $$
1 9 6\ \mathrm{days}
$$
H. $$
1 6 4\ \mathrm{days}
$$
I. $$
1 8 3\ \mathrm{days}
$$
J. $$
3 0 2\ \mathrm{days}
$$
Answer: H
In a certain irrigation district, wheat is planted, with an irrigation quota of $\mathrm{m=50 m^{3}/}$ mu, and the infiltration rate is moderate. From soil infiltration test data, it is known that the average infiltration rate within the first hour is $\mathrm{i_{0}=150 \, mm/h,} \quad\mathrm{a=0.5e.}$ The surface slope (in the direction of the furrow slope) is 0.002. Calculate the inflow per unit width of furrow $[\mathrm{L}/(\mathrm{s} \cdot \mathrm{m})]$.

Options:
A. $$
8. 2 9 \ \mathrm{L} / ( \mathrm{s} \cdot\mathrm{m} )
$$
B. $$
4. 9 5 \ \mathrm{L} / ( \mathrm{s} \cdot\mathrm{m} )
$$
C. $$
5. 8 3 \ \mathrm{L} / ( \mathrm{s} \cdot\mathrm{m} )
$$
D. $$
5. 5 0 \ \mathrm{L} / ( \mathrm{s} \cdot\mathrm{m} )
$$
E. $$
7. 5 8 \ \mathrm{L} / ( \mathrm{s} \cdot\mathrm{m} )
$$
F. $$
6. 1 1 \ \mathrm{L} / ( \mathrm{s} \cdot\mathrm{m} )
$$
G. $$
7. 0 4 \ \mathrm{L} / ( \mathrm{s} \cdot\mathrm{m} )
$$
H. $$
4. 2 6 \ \mathrm{L} / ( \mathrm{s} \cdot\mathrm{m} )
$$
I. $$
5. 3 9 \ \mathrm{L} / ( \mathrm{s} \cdot\mathrm{m} )
$$
J. $$
6. 8 7 \ \mathrm{L} / ( \mathrm{s} \cdot\mathrm{m} )
$$
Answer: C
The radius of Mars is half of Earth's radius, and its mass is $1/9$ of Earth's mass. An astronaut has a mass of $72 \mathbf{kg}$. What is the gravitational force acting on him on Mars? The astronaut can lift a maximum weight of $100 \mathbf{kg}$ on Earth. How much mass can he lift at most on Mars?

Options:
A. 335N, 232kg
B. 340N, 235kg
C. 310N, 220kg
D. 320N, 225kg
E. 300N, 210kg
F. 330N, 230kg
G. 315N, 218kg
H. 305N, 215kg
I. 345N, 240kg
J. 325N, 228kg
Answer: D
The Sun is approximately $2.5 \times 10^{4}$ light-years away from the center of the Milky Way galaxy. The orbit of the Sun around the center of the Milky Way can be considered circular, with a period of about $1.7 \times 10^{2}$ years. It takes approximately 500 seconds for sunlight to reach the Earth. Based on this, how many times the mass of the Sun is the mass of the Milky Way? (Use two significant figures)

Options:
A. $$\mathrm{7.} \, 1 \times 10^{12}$$
B. $$\mathrm{5.} \, 7 \times 10^{11}$$
C. $$\mathrm{1.} \, 9 \times 10^{13}$$
D. $$\mathrm{8.} \, 4 \times 10^{15}$$
E. $$\mathrm{2.} \, 3 \times 10^{12}$$
F. $$\mathrm{9.} \, 8 \times 10^{10}$$
G. $$\mathrm{6.} \, 3 \times 10^{11}$$
H. $$\mathrm{3.} \, 2 \times 10^{10}$$
I. $$\mathrm{4.} \, 5 \times 10^{14}$$
J. $$\mathrm{1.} \, 4 \times1 0^{1 1}
$$
Answer: J
Calculate the energy carried away by the neutrino in the decay process $\pi^{+} \to \mu^{+} + \nu_{\mu}$ within the rest frame of the $\pi$. The relevant masses are $m_{\pi} c^{2} = 139 \, \mathrm{MeV}$, $m_{\mu} c^{2} = 106 \, \mathrm{MeV}$, and $m_{\nu} \sim 0$. Also consider the case when the $\pi$ is flying with an energy of 10 GeV. What are the maximum and minimum energy values of the muon in these decays?

Options:
A. $$
2 8. 0 \mathrm{~ M e V} : 9. 5 \mathrm{~ G e V} : 5. 6 \mathrm{~ G e V}.
$$
B. $$
3 9. 7 \mathrm{~ M e V} : 1 3 \mathrm{~ G e V} : 8. 3 \mathrm{~ G e V}.
$$
C. $$
3 7. 2 \mathrm{~ M e V} : 1 2 \mathrm{~ G e V} : 7. 5 \mathrm{~ G e V}.
$$
D. $$
5 1. 3 \mathrm{~ M e V} : 1 1 \mathrm{~ G e V} : 7. 9 \mathrm{~ G e V}.
$$
E. $$
3 3. 6 \mathrm{~ M e V} : 9. 2 \mathrm{~ G e V} : 6. 0 \mathrm{~ G e V}.
$$
F. $$
2 9. 8 \mathrm{~ M e V} : 1 0 \mathrm{~ G e V} : 5. 7 \mathrm{~ G e V}.
$$
G. $$
4 2. 4 \mathrm{~ M e V} : 9. 8 \mathrm{~ G e V} : 6. 1 \mathrm{~ G e V}.
$$
H. $$
4 6. 2 \mathrm{~ M e V} : 1 2 \mathrm{~ G e V} : 7. 0 \mathrm{~ G e V}.
$$
I. $$
4 4. 8 \mathrm{~ M e V} : 1 0 \mathrm{~ G e V} : 7. 2 \mathrm{~ G e V}.
$$
J. $$
2 5. 1 \mathrm{~ M e V} : 8. 7 \mathrm{~ G e V} : 5. 4 \mathrm{~ G e V}.
$$
Answer: F
The power of gravitational radiation emitted by the Moon in its orbit around the Earth is (). (Earth's mass = $6 \times 10^{24} \ \mathrm{kg}$, Moon's mass = $7.4 \times 10^{22} \ \mathrm{kg}$, average Earth-Moon distance = $3.8 \times 10^{5}$ km, orbital period of the Moon = $27.3$ days.)

Options:
A. 7mW
B. 1mW
C. 5mW
D. 10mW
E. 9mW
F. 2mW
G. 3mW
H. 4mW
I. 8mW
J. 6mW
Answer: C
If an object is composed of normal atomic matter (without requiring electron degeneracy pressure to resist gravitational collapse), and its density is $10^{4} \ \mathrm{kg} / \mathrm{m}^{3}$, what is its maximum possible mass?

Options:
A. $$5 \times 10^{27} \mathrm{kg}$$
B. $$ 3 \times 10^{26} \mathrm{kg} $$
C. $$ 6 \times 10^{29} \mathrm{kg} $$
D. $$ 4 \times 10^{30} \mathrm{kg} $$
E. $$ 8 \times 10^{25} \mathrm{kg} $$
F. $$ 2 \times 10^{23} \mathrm{kg} $$
G. $$ 2 \times 10^{25} \mathrm{kg} $$
H. $$ 1 \times 10^{24} \mathrm{kg} $$
I. $$ 7 \times 10^{28} \mathrm{kg} $$
J. $$ 9 \times 10^{31} \mathrm{kg} $$
Answer: A
Given the average Earth density of $3.5 \ \mathrm{gm \cdot cm}^{-3}$ and the Earth radius of 6400 km, estimate the fraction of neutrinos interacting when a $1 \mathrm{GeV}$
$μ$ neutrino passes through the diameter of the Earth.

Options:
A. $$
8 \times1 0^{-4}
$$
B. $$
6 \times1 0^{-5}
$$
C. $$
9 \times1 0^{-5}
$$
D. $$
3 \times1 0^{-4}
$$
E. $$
7 \times1 0^{-4}
$$
F. $$
4 \times1 0^{-6}
$$
G. $$
2 \times1 0^{-6}
$$
H. $$
2 \times1 0^{-3}
$$
I. $$
5 \times1 0^{-5}
$$
J. $$
1 \times1 0^{-6}
$$
Answer: D
Estimate the value of a certain $k T$, below which deuterium in the expanding universe will "freeze out" from the reaction $\mathrm{n+p} \leftrightarrow\mathrm{d}+\gamma+Q$, where $Q=2.22 \, \mathrm{MeV}$ is the binding energy of deuterium.

Options:
A. $$
0. 1 4 \mathrm{~ M e V}
$$
B. $$
0. 0 2 \mathrm{~ M e V}
$$
C. $$
0. 1 5 \mathrm{~ M e V}
$$
D. $$
0. 8 4 \mathrm{~ M e V}
$$
E. $$
0. 9 1 \mathrm{~ M e V}
$$
F. $$
3. 5 1 \mathrm{~ M e V}
$$
G. $$
0. 3 0 \mathrm{~ M e V}
$$
H. $$
1. 2 0 \mathrm{~ M e V}
$$
I. $$
0. 1 9 \mathrm{~ M e V}
$$
J. $$
0. 0 6 \mathrm{~ M e V}
$$
Answer: J
The pillar crane consists of the arm $AB$ and the chain $CB$. The arm $AB$ is hinged at point $A$ on the pillar, and a weight $P = 2 \, \text{kN}$ is hanging at end $B$. Given that $\angle BAC = 15^\circ$ and $\angle ACB = 135^\circ$.What is the tension $T$ in $CB$ and the internal force $Q$ in $AB$ ?

Options:
A. $$
T=0. 9 5 \mathrm{~ k N, ~} Q=3. 2 0 \mathrm{~ k N.}
$$
B. $$
T=1. 1 0 \mathrm{~ k N, ~} Q=2. 9 0 \mathrm{~ k N.}
$$
C. $$
T=1. 1 5 \mathrm{~ k N, ~} Q=2. 7 0 \mathrm{~ k N.}
$$
D. $$
T=1. 3 2 \mathrm{~ k N, ~} Q=2. 6 8 \mathrm{~ k N.}
$$
E. $$
T=1. 2 4 \mathrm{~ k N, ~} Q=2. 4 8 \mathrm{~ k N.}
$$
F. $$
T=0. 8 9 \mathrm{~ k N, ~} Q=3. 1 0 \mathrm{~ k N.}
$$
G. $$
T=1. 2 0 \mathrm{~ k N, ~} Q=2. 5 7 \mathrm{~ k N.}
$$
H. $$
T=0. 9 8 \mathrm{~ k N, ~} Q=3. 0 4 \mathrm{~ k N.}
$$
I. $$
T=1. 0 1 \mathrm{~ k N, ~} Q=2. 9 2 \mathrm{~ k N.}
$$
J. $$
T=1. 0 4 \mathrm{~ k N, ~} Q=2. 8 3 \mathrm{~ k N.}
$$
Answer: J
In an electromagnetic field, the motion of a charged particle with charge $q$ can be described by the Lagrangian function $L = {\frac{1}{2}} m v^{2} - ( q \varphi - q A \cdot \boldsymbol{v} )$, where $\varphi$ is the scalar potential and $A$ is the vector potential.What is the corresponding Lagrange equation ?

Options:
A. $$m\dot{\boldsymbol{v}}=q\boldsymbol{E}+v\times B$$
B. $$q\dot{\boldsymbol{v}}=m\boldsymbol{E}+q\boldsymbol{v}\times B$$
C. $$m\dot{\boldsymbol{v}}=q\boldsymbol{E}-q\boldsymbol{v}\times B$$
D. $$m\dot{\boldsymbol{v}}=q\boldsymbol{E}+q\boldsymbol{B}\times v$$
E. $$m\dot{v}=q\boldsymbol{E}+q\boldsymbol{v}\times B$$
F. $$m\dot{\boldsymbol{v}}=q\boldsymbol{E}+q\boldsymbol{v}\times B$$
G. $$m\dot{\boldsymbol{v}}=q\boldsymbol{E}+q\boldsymbol{v}+B$$
H. $$m\boldsymbol{v}=q\boldsymbol{E}+q\boldsymbol{v}\times B$$
I. $$m\dot{\boldsymbol{v}}=q\boldsymbol{E}+q\boldsymbol{v}\cdot B$$
J. $$m\dot{\boldsymbol{v}}=q\boldsymbol{B}-q\boldsymbol{v}\cdot E$$
Answer: F
The meshing device that makes the grinding wheel rotate at high speed is as follows: Rod $IV$ rotates about axis $O_{1}$ with an angular velocity of $\omega_{4}$ using a special handle. At the end of the rod, $O_{2}$ is equipped with a pin, which loosely fits a wheel $II$ with a radius of $r_{2}$. When the handle turns, the pin forces wheel $II$ to roll purely on the inside surface of a fixed gear $III$ with an outer radius of $r_{3}$. At this moment, due to friction, wheel $II$ drives wheel $I$ with a radius of $r_{1}$ to roll purely. Wheel $I$ is loosely fitted onto axis $O_{1}$ and is firmly connected to the grinding wheel shaft. The $r_{1}$ based on the radius $r_{3}$ of the fixed outer gear $III$ such that $\omega_{1} / \omega_{4} = 12$. What is the grinding wheel rotates 12 times faster than the handle ?

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