MikaStars39/nano-eval huggingface dataset:
The spectral line of yttrium atom (Y) with a wavelength of 407.7359 nm is emitted during the $\mathrm{^2 F}_{5 / 2} \rightarrow \mathrm{^2 D}_{3 / 2}$ transition. In a weak external magnetic field of 1T, this spectral line will undergo Zeeman splitting. How many spectral lines can be observed perpendicular to the direction of the magnetic field? How many spectral lines can be observed parallel to the direction of the magnetic field?

Options:
A. 14 lines are observed perpendicular to the direction of the magnetic field, and 6 lines are observed parallel to the direction of the magnetic field.
B. 12 lines are observed perpendicular to the direction of the magnetic field, and 10 lines are observed parallel to the direction of the magnetic field.
C. 16 lines are observed perpendicular to the direction of the magnetic field, and 12 lines are observed parallel to the direction of the magnetic field.
D. 10 lines are observed perpendicular to the direction of the magnetic field, and 12 lines are observed parallel to the direction of the magnetic field.
E. 12 lines are observed perpendicular to the direction of the magnetic field, and 8 lines are observed parallel to the direction of the magnetic field.
F. 10 lines are observed perpendicular to the direction of the magnetic field, and 8 lines are observed parallel to the direction of the magnetic field.
G. 14 lines are observed perpendicular to the direction of the magnetic field, and 10 lines are observed parallel to the direction of the magnetic field.
H. 8 lines are observed perpendicular to the direction of the magnetic field, and 6 lines are observed parallel to the direction of the magnetic field.
I. 18 lines are observed perpendicular to the direction of the magnetic field, and 8 lines are observed parallel to the direction of the magnetic field.
J. 10 lines are observed perpendicular to the direction of the magnetic field, and 6 lines are observed parallel to the direction of the magnetic field.
Answer: E
The center frequency of the $^{1}H ^{35}Cl$ absorption band is $f_{0}=8.66 \times 10^{13} \mathrm{Hz}$, with an interval of approximately $\Delta f \approx 6 \times 10^{11} \mathrm{Hz}$ between each absorption peak on either side of the center. What is the zero-point vibrational energy of the HCl molecule?

Options:
A. $$
0.150eV
$$
B. $$
0.125eV
$$
C. $$
0.179eV
$$
D. $$
0.185eV
$$
E. $$
0.195eV
$$
F. $$
0.165eV
$$
G. $$
0.220eV
$$
H. $$
0.140eV
$$
I. $$
0.210eV
$$
J. $$
0.200eV
$$
Answer: C
What is the number of spectral lines with different wavelengths emitted when electrons in zinc (Zn) atoms transition from 4s4d to 4s4p?

Options:
A. 12
B. 8
C. 3
D. 4
E. 9
F. 7
G. 6
H. 11
I. 5
J. 10
Answer: F
What is the atomic number of the anode target material of the X-ray tube if the wavelength of the emitted Kα line is 0.071 nm?

Options:
A. 43
B. 48
C. 44
D. 39
E. 46
F. 38
G. 47
H. 40
I. 42
J. 45
Answer: I
The radiative transitions from state $2 \mathsf{p 3 d}^{3} \mathsf{D}_{3, 2, 1}$ to $2 \mathrm{s 2 p}^{3} \mathrm{P_{2, 1, 0}}$ can produce how many spectral lines?

Options:
A. 3
B. 12
C. Cannot happen
D. 9
E. 6
F. 10
G. 4
H. 8
I. 5
J. 11
Answer: C
What is the kinetic energy operator of a one-dimensional free particle?

Options:
A. $$
\frac{\hbar^{2}} {2 m^{2}} \frac{d^{2}} {d x}
$$
B. $$
- \frac{\hbar^{2}} {2 m} \frac{d} {d x}
$$
C. $$
\frac{\hbar^{2}} {2} \frac{d^{2}} {d x^{2}}
$$
D. $$
- \frac{\hbar} {2 m} \frac{d^{2}} {d x^{2}}
$$
E. $$
\frac{\hbar^{2}} {2 m} \frac{d^{2}} {d x^{2}}
$$
F. $$
- \frac{\hbar^{2}} {2 m} \frac{d^{2}} {d x^{2}}
$$
G. $$
- \frac{\hbar^{2}} {2 m^{2}} \frac{d^{2}} {d x^{2}}
$$
H. $$
- \frac{\hbar^{2}} {m} \frac{d^{2}} {d x}
$$
I. $$
- \frac{\hbar^{2}} {2 m} \frac{d^{3}} {d x^{2}}
$$
J. $$
- \frac{\hbar^{2}} {4 m} \frac{d^{2}} {d x^{2}}
$$
Answer: F
If the $\mathbf{B}^{+}$ ion of boron (Z=5) is in the first excited state, what is the electron configuration?

Options:
A. $$
2p^2
$$
B. $$
2s^1
$$
C. $$
2s2p
$$
D. $$
1s^22s
$$
E. $$
1s2p
$$
F. $$
2s^2
$$
G. $$
1s^2
$$
H. $$
2p^1
$$
I. $$
2s^22p
$$
J. $$
1s^12p
$$
Answer: C
In the non-stoichiometric compound $Fe_xO$, where $\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+} = 0.1$, calculate the value of $\mathbf{x}$ in $Fe_xO$ and the concentration of vacancy defects is ().

Options:
A. 0.948,2.1%
B. 0.952,2.3%
C. 0.940,2.0%
D. 0.960,2.5%
E. 0.957,2.2%
F. 0.945,1.8%
G. 0.962,2.7%
H. 0.963,2.6%
I. 0.950,1.9%
J. 0.955,2.4%
Answer: E
FeO has an NaCl-type structure. Assuming the number of iron ions and oxygen ions is the same, and given that the radius of the iron ion is 0.074 nm and the radius of the oxygen ion is 0.140 nm (the relative atomic masses of Fe and O are known to be 55.8 and 16.0, respectively), calculate the lattice constant of FeO, the density of FeO, and the space-filling factor it occupies is ().

Options:
A. 0.452nm,6.250g/cm³,65.1%
B. 0.420nm,6.050g/cm³,64.5%
C. 0.435nm,5.900g/cm³,70.2%
D. 0.440nm,6.100g/cm³,66.0%
E. 0.425nm,6.080g/cm³,65.6%
F. 0.450nm,6.150g/cm³,66.8%
G. 0.410nm,6.300g/cm³,68.5%
H. 0.430nm,6.120g/cm³,68.0%
I. 0.415nm,6.200g/cm³,67.0%
J. 0.428nm,6.085g/cm³,67.3%
Answer: J
A powder compact (green body) with an average particle size of 5μm is provided. After 1 hour of sintering, the shrinkage rate of the green body is △L/L=0.1. Without considering grain growth, when the green body is sintered until △L/L=0.2, compare the time required for sintering via diffusion mass transfer and dissolution-precipitation mass transfer methods is ().

Options:
A. 6.2h,8.4h
B. 5.8h,7.8h
C. 5.65h,8h
D. 5.6h,8.7h
E. 6.3h,8.1h
F. 6.1h,8.3h
G. 5.7h,8.5h
H. 6h,7.5h
I. 5.9h,8.2h
J. 5.5h,7.9h
Answer: C
In cyclonic circulation, the geostrophic wind is () than the gradient wind, while in anticyclonic circulation, the geostrophic wind is () than the gradient wind. In anticyclonic circulation, the maximum gradient wind is () times the geostrophic wind.

Options:
A. Equal, equal, half of it
B. Small, equal, three times as much
C. Equal, smaller, one and a half times
D. Small, large, half as much
E. Large, small, twice as much
F. Smaller, larger, twice as much
G. Larger, smaller, three times as much
H. Large, equal, similar to
I. Equal, small, double the value
J. Larger, equal, twice as much
Answer: E
The magnetic pressure in the center of the umbra of a large sunspot. Assume that the magnetic field strength is 0.2 T. Compare your answer with a typical value of $2 \times1 0^{4} \; \mathrm{N} \; /\mathrm{m}^{-2}$ for the gas pressure at the base of the photosphere is().

Options:
A. $P_{m}=B^{2} / 2 \mu_{0}$ . Using $B=0. 2 \mathrm{~ T}$ gives $P_{m}=1. 4 5 \times1 0^{4} \; \mathrm{N} \; \mathrm{m}^{-2}$ . Thus, $P_{m} / P_{g} \sim0. 7$
B. $P_{m}=B^{2} / 2 \mu_{0}$ . Using $B=0. 2 \mathrm{~ T}$ gives $P_{m}=1. 5 5 \times1 0^{4} \; \mathrm{N} \; \mathrm{m}^{-2}$ . Thus, $P_{m} / P_{g} \sim0. 8$
C. $P_{m}=B^{2} / 2 \mu_{0}$ . Using $B=0. 2 \mathrm{~ T}$ gives $P_{m}=1. 3 9 \times1 0^{4} \; \mathrm{N} \; \mathrm{m}^{-2}$ . Thus, $P_{m} / P_{g} \sim0. 7$
D. $P_{m}=B^{2} / 2 \mu_{0}$ . Using $B=0. 2 \mathrm{~ T}$ gives $P_{m}=1. 0 9 \times1 0^{4} \; \mathrm{N} \; \mathrm{m}^{-2}$ . Thus, $P_{m} / P_{g} \sim0. 5$
E. $P_{m}=B^{2} / 2 \mu_{0}$ . Using $B=0. 2 \mathrm{~ T}$ gives $P_{m}=1. 5 9 \times1 0^{4} \; \mathrm{N} \; \mathrm{m}^{-2}$ . Thus, $P_{m} / P_{g} \sim0. 8$
F. $P_{m}=B^{2} / 2 \mu_{0}$ . Using $B=0. 2 \mathrm{~ T}$ gives $P_{m}=2. 3 9 \times1 0^{4} \; \mathrm{N} \; \mathrm{m}^{-2}$ . Thus, $P_{m} / P_{g} \sim1. 2$
G. $P_{m}=B^{2} / 2 \mu_{0}$ . Using $B=0. 2 \mathrm{~ T}$ gives $P_{m}=1. 2 0 \times1 0^{4} \; \mathrm{N} \; \mathrm{m}^{-2}$ . Thus, $P_{m} / P_{g} \sim0. 6$
H. $P_{m}=B^{2} / 2 \mu_{0}$ . Using $B=0. 2 \mathrm{~ T}$ gives $P_{m}=1. 7 0 \times1 0^{4} \; \mathrm{N} \; \mathrm{m}^{-2}$ . Thus, $P_{m} / P_{g} \sim0. 9$
I. $P_{m}=B^{2} / 2 \mu_{0}$ . Using $B=0. 2 \mathrm{~ T}$ gives $P_{m}=1. 8 9 \times1 0^{4} \; \mathrm{N} \; \mathrm{m}^{-2}$ . Thus, $P_{m} / P_{g} \sim0. 9$
J. $P_{m}=B^{2} / 2 \mu_{0}$ . Using $B=0. 2 \mathrm{~ T}$ gives $P_{m}=2. 0 0 \times1 0^{4} \; \mathrm{N} \; \mathrm{m}^{-2}$ . Thus, $P_{m} / P_{g} \sim1. 0$
Answer: E
Assuming for simplicity that Earth is a sphere of constant density, compute the rate of change in rotational angular momentum of Earth due to the tidal influence of the Moon. Is the change positive or negative?

Options:
A. $$
-2. 4 3 \times1 0^{1 6} \; \mathrm{k g \; m^{2} \; s^{-2} < 0.}
$$
B. $$
8. 1 0 \times1 0^{1 6} \; \mathrm{k g \; m^{2} \; s^{-2} < 0.}
$$
C. $$
6. 7 9 \times1 0^{1 5} \; \mathrm{k g \; m^{2} \; s^{-2} < 0.}
$$
D. $$
-7. 1 6 \times1 0^{1 7} \; \mathrm{k g \; m^{2} \; s^{-2} < 0.}
$$
E. $$
-4. 1 6 \times1 0^{1 6} \; \mathrm{k g \; m^{2} \; s^{-2} < 0.}
$$
F. $$
3. 4 8 \times1 0^{1 6} \; \mathrm{k g \; m^{2} \; s^{-2} < 0.}
$$
G. $$
5. 2 3 \times1 0^{1 5} \; \mathrm{k g \; m^{2} \; s^{-2} < 0.}
$$
H. $$
1. 5 7 \times1 0^{1 5} \; \mathrm{k g \; m^{2} \; s^{-2} < 0.}
$$
I. $$
2. 9 5 \times1 0^{1 6} \; \mathrm{k g \; m^{2} \; s^{-2} < 0.}
$$
J. $$
-5. 8 6 \times1 0^{1 6} \; \mathrm{k g \; m^{2} \; s^{-2} < 0.}
$$
Answer: E
What is the ratio of the Sun's tidal force per unit mass on Mercury at perihelion to the Sun's tidal force per unit mass on Earth? How has this difference in tidal effects contributed to differences in the orbital and/or rotational characteristics of the two planets?

Options:
A. $$
\frac{6 G M_{\odot} R} {r^{5}}
$$
10.1
B. $$
\frac{3 G M_{\odot} R} {r^{2}}
$$
8.7
C. $$
\frac{5 G M_{\odot} R} {r^{4}}
$$
15.3
D. $$
\frac{2 G M_{\odot} R} {r^{4}}
$$
13.7
E. $$
\frac{4 G M_{\odot} R} {r^{3}}
$$
9.2
F. $$
\frac{6 G M_{\odot} R} {r^{3}}
$$
9.8
G. $$
\frac{5 G M_{\odot} R} {r^{2}}
$$
16.0
H. $$
\frac{2 G M_{\odot} R} {r^{3}}
$$
12.5
I. $$
\frac{3 G M_{\odot} R} {r^{6}}
$$
11.4
J. $$
\frac{4 G M_{\odot} R} {r^{6}}
$$
14.2
Answer: H
Estimate the Roche limit for the Earth-Moon system. Express your answer in units of the radius of Earth.

Options:
A. $$
0. 0 4 8 a_{\mathrm{M o o n}}
$$
B. $$
0. 1 0 4 a_{\mathrm{M e r c u r y}}
$$
C. $$
0. 0 7 9 a_{\mathrm{M a r s}}
$$
D. $$
0. 3 2 8 a_{\mathrm{N e p t u n e}}
$$
E. $$
0. 2 1 6 a_{\mathrm{J u p i t e r}}
$$
F. $$
0. 0 9 1 a_{\mathrm{V e n u s}}
$$
G. $$
0. 1 5 3 a_{\mathrm{E a r t h}}
$$
H. $$
0. 0 5 2 a_{\mathrm{S a t u r n}}
$$
I. $$
0. 2 5 0 a_{\mathrm{U r a n u s}}
$$
J. $$
0. 0 2 3 a_{\mathrm{P l u t o}}
$$
Answer: A
The E ring is known to contain dust particles having average radii of 1 um. If the density of the particles is 3000 kg m $- 3$ , how long would it take for a typical particle to spiral into the planet from an initial distance of 5 Rs?

Options:
A. $$
1.2 \times1 0^{6} \mathrm{~ y r}.
$$
B. $$
6.8 \times1 0^{5} \mathrm{~ y r}.
$$
C. $$
9 \times1 0^{4} \mathrm{~ y r}.
$$
D. $$
8.5 \times1 0^{4} \mathrm{~ y r}.
$$
E. $$
2 \times1 0^{5} \mathrm{~ y r}.
$$
F. $$
6 \times1 0^{5} \mathrm{~ y r}.
$$
G. $$
3 \times1 0^{6} \mathrm{~ y r}.
$$
H. $$
5 \times1 0^{4} \mathrm{~ y r}.
$$
I. $$
7 \times1 0^{5} \mathrm{~ y r}.
$$
J. $$
4.5 \times1 0^{5} \mathrm{~ y r}.
$$
Answer: F
Vesta orbits the Sun at a distance 2.362 AU and has an albedo of 0.38 (unusually reflective for an asteroid).
Estimate Vesta's blackbody temperature, assuming that the temperature is uniform across the asteroid's surface.

Options:
A. $$
1 4 5 \mathrm{~ K}.
$$
B. $$
2 3 0 \mathrm{~ K}.
$$
C. $$
1 8 9 \mathrm{~ K}.
$$
D. $$
2 0 7 \mathrm{~ K}.
$$
E. $$
1 7 2 \mathrm{~ K}.
$$
F. $$
2 4 5 \mathrm{~ K}.
$$
G. $$
1 6 1 \mathrm{~ K}.
$$
H. $$
3 2 0 \mathrm{~ K}.
$$
I. $$
1 5 0 \mathrm{~ K}.
$$
J. $$
1 9 5 \mathrm{~ K}.
$$
Answer: G
The Minimum Mass Solar Nebula is the smallest nebula that could be formed and still have sufficient mass to create all of the objects in the Solar System. Make a rough estimate of the mass of the Minimum Mass Solar Nebula.

Options:
A. $$
3 \times1 0^{2 8} \mathrm{~ k g.}
$$
B. $$
5 \times1 0^{2 6} \mathrm{~ k g.}
$$
C. $$
1 \times1 0^{2 9} \mathrm{~ k g.}
$$
D. $$
6 \times1 0^{2 7} \mathrm{~ k g.}
$$
E. $$
4 \times1 0^{2 7} \mathrm{~ k g.}
$$
F. $$
9 \times1 0^{2 6} \mathrm{~ k g.}
$$
G. $$
2 \times1 0^{2 7} \mathrm{~ k g.}
$$
H. $$
7 \times1 0^{2 7} \mathrm{~ k g.}
$$
I. $$
8 \times1 0^{2 5} \mathrm{~ k g.}
$$
J. $$
3 \times1 0^{2 6} \mathrm{~ k g.}
$$
Answer: E
A 30 km long optical fiber line has a loss of 0.5 dB/km. If the loss of the optical fiber becomes 0.25 dB/km, what will the required input optical power be?

Options:
A. $$
1. 7 0 \mu\mathbf{W}
$$
B. $$
1. 7 5 \mu\mathbf{W}
$$
C. $$
1. 6 0 \mu\mathbf{W}
$$
D. $$
1. 6 5 \mu\mathbf{W}
$$
E. $$
1. 6 9 \mu\mathbf{W}
$$
F. $$
1. 8 5 \mu\mathbf{W}
$$
G. $$
1. 5 8 \mu\mathbf{W}
$$
H. $$
1. 5 5 \mu\mathbf{W}
$$
I. $$
1. 8 0 \mu\mathbf{W}
$$
J. $$
1. 7 2 \mu\mathbf{W}
$$
Answer: E
In a step-index optical fiber, $n_{1}=1.52$, $n_{2}=1.49$. The optical fiber is immersed in water $(n_{0}=1.33)$. Find the maximum acceptance angle for light entering the fiber end face from water as().

Options:
A. $$
1 0^{\circ}
$$
B. $$
1 1^{\circ}
$$
C. $$
1 8^{\circ}
$$
D. $$
1 5^{\circ}
$$
E. $$
1 2^{\circ}
$$
F. $$
1 4^{\circ}
$$
G. $$
2 5^{\circ}
$$
H. $$
1 7^{\circ}
$$
I. $$
2 0^{\circ}
$$
J. $$
1 3^{\circ}
$$
Answer: J
Let the energy of the high energy level and low energy level of the laser be $E_{1}$ and $E_{2}$, the frequency be $f$, and the particle densities at the corresponding energy levels be $N_{1}$ and $N_{2}$. If $N_{2} / N_{1}=0.1$ when 1 um is entered, what is the ambient temperature $T$? (Calculated according to Boltzmann distribution law)

Options:
A. $$6253K$$
B. $$5820K$$
C. $$6005K$$
D. $$6100K$$
E. $$7230K$$
F. $$5900K$$
G. $$7000K$$
H. $$6450K$$
I. $$6490K$$
J. $$6785K$$
Answer: A
The sensitivity of a certain digital optical receiver has been measured as $\overline{{{{P}}}}_{\mathrm{r}}=10 ~ \mu{\bf W}$. Calculate its value in dBm as _____.

Options:
A. $- 1 6$ dBm
B. $- 1 0$ dBm
C. $- 1 2$ dBm
D. $- 2 1$ dBm
E. $- 2 0$ dBm
F. $- 2 2$ dBm
G. $- 2 5$ dBm
H. $- 1 5$ dBm
I. $- 3 0$ dBm
J. $- 1 8$ dBm
Answer: E
A certain 1.3 $\mu$m optical wavelength system operates at a rate of 100 Mb/s, using an InGaAsP LED light source. The average power coupled into the single-mode optical fiber is 0.1 $\mathrm{mW}$. The fiber loss is 1 dB/km, with a connection loss of 0.2 dB every 2 km. At both ends of the fiber link, there is an active connector with an insertion loss of 1 dB each. A PIN receiver is employed with a sensitivity of 100 nW. A system margin of 6 dB is required. Perform a power budget analysis to determine the maximum transmission distance as _____.

Options:
A. 20km
B. 19km
C. 17km
D. 22km
E. 24km
F. 21km
G. 15km
H. 23km
I. 18km
J. 25km
Answer: A
The band gap of the active layer of the two semiconductor light sources is 1.43 eV and 0.8 eV respectively. What is the wavelength of the central radiation?

Options:
A. $$
0. 9 5 \ \mu\mathrm{m}
$$
$$
1.45 \ \mu\mathrm{m}
$$
B. $$
0. 8 4 \ \mu\mathrm{m}
$$
$$
1.49 \ \mu\mathrm{m}
$$
C. $$
0. 9 0 \ \mu\mathrm{m}
$$
$$
1.50 \ \mu\mathrm{m}
$$
D. $$
0. 8 7 \ \mu\mathrm{m}
$$
$$
1.55 \ \mu\mathrm{m}
$$
E. $$
0. 8 9 \ \mu\mathrm{m}
$$
$$
1.59 \ \mu\mathrm{m}
$$
F. $$
0. 8 2 \ \mu\mathrm{m}
$$
$$
1.51 \ \mu\mathrm{m}
$$
G. $$
0. 8 8 \ \mu\mathrm{m}
$$
$$
1.52 \ \mu\mathrm{m}
$$
H. $$
0. 7 8 \ \mu\mathrm{m}
$$
$$
1.60 \ \mu\mathrm{m}
$$
I. $$
0. 9 2 \ \mu\mathrm{m}
$$
$$
1.48 \ \mu\mathrm{m}
$$
J. $$
0. 7 5 \ \mu\mathrm{m}
$$
$$
1.54 \ \mu\mathrm{m}
$$
Answer: D
The quantum efficiency of the PIN photodiode is $0.9$, $\lambda = 1.3 \; \mu\mathrm{m}$. Calculate: the photocurrent when the incident optical power is $-30$ dBm is ____.

Options:
A. $$
1. 1 5 \times1 0^{-6} \mathrm{~ A}
$$
B. $$
1. 2 3 \times1 0^{-6} \mathrm{~ A}
$$
C. $$
1. 0 0 \times1 0^{-6} \mathrm{~ A}
$$
D. $$
7. 9 0 \times1 0^{-7} \mathrm{~ A}
$$
E. $$
8. 3 2 \times1 0^{-7} \mathrm{~ A}
$$
F. $$
8. 7 6 \times1 0^{-7} \mathrm{~ A}
$$
G. $$
1. 3 0 \times1 0^{-6} \mathrm{~ A}
$$
H. $$
9. 1 8 \times1 0^{-7} \mathrm{~ A}
$$
I. $$
7. 5 4 \times1 0^{-7} \mathrm{~ A}
$$
J. $$
9. 4 4 \times1 0^{-7} \mathrm{~ A}
$$
Answer: J
The theory states that the longitudinal mode frequency spacing of the LD (Laser Diode) is $\Delta f={\frac{c}{2 n L}}$, where $n$ is the refractive index of the semiconductor material in the resonant cavity, and $L$ is the length of the resonant cavity. If a certain GaAs laser diode has $\lambda=850 \, \mathrm{nm}$, $L=0.5 \, \mathrm{mm}$, and $n=3.7$, what is the longitudinal mode wavelength spacing of this laser?

Options:
A. 0.320nm
B. 0.180nm
C. 0.195nm
D. 0.300nm
E. 0.250nm
F. 0.150nm
G. 0.210nm
H. 0.275nm
I. 0.225nm
J. 0.240nm
Answer: C
The precise value of the relative refractive index difference of the optical fiber is $\Delta = {\frac{n_{1}^{2} - n_{2}^{2}} {2n_{1}^{2}}}$, and its approximate value is $\Delta' = {\frac{n_{1} - n_{2}} {n_{1}}}$. If the refractive indices of the optical fiber are $n_{1} = 1.49$ and $n_{2} = 1.48$, calculate: the precise value $\Delta$, the approximate value $\Delta'$, as well as the absolute error and relative error between $\Delta$ and $\Delta'$. Fill in the blanks_____.

Options:
A. $$
\Delta\approx0. 0 0 6 6 7 8 5
$$
$$
\Delta^\prime\approx0. 0067133
$$
$$
e\approx2. 6 1 \times1 0^{-5}
$$
$$
e/\Delta\approx3.28 \times1 0^{-3}
$$
B. $$
\Delta\approx0. 0 0 6 6 7 7 6
$$
$$
\Delta^\prime\approx0. 0067124
$$
$$
e\approx2. 4 0 \times1 0^{-5}
$$
$$
e/\Delta\approx3.32 \times1 0^{-3}
$$
C. $$
\Delta\approx0. 0 0 6 6 8 8 9
$$
$$
\Delta^\prime\approx0. 0067114
$$
$$
e\approx2. 2 5 \times1 0^{-5}
$$
$$
e/\Delta\approx3.37 \times1 0^{-3}
$$
D. $$
\Delta\approx0. 0066688
$$
$$
\Delta^\prime\approx0. 0071010
$$
$$
e\approx2. 3 5 \times1 0^{-5}
$$
$$
e/\Delta\approx3.30 \times1 0^{-3}
$$
E. $$
\Delta\approx0. 0 0 6 6 7 7 9
$$
$$
\Delta^\prime\approx0. 0071214
$$
$$
e\approx3. 2 5 \times1 0^{-5}
$$
$$
e/\Delta\approx3.27 \times1 0^{-3}
$$
F. $$
\Delta\approx0. 0 0 6 6 9 9 2
$$
$$
\Delta^\prime\approx0. 0067214
$$
$$
e\approx2. 1 5 \times1 0^{-5}
$$
$$
e/\Delta\approx3.39 \times1 0^{-3}
$$
G. $$
\Delta\approx0. 0066691
$$
$$
\Delta^\prime\approx0. 0071130
$$
$$
e\approx2. 4 1 \times1 0^{-5}
$$
$$
e/\Delta\approx3.33 \times1 0^{-3}
$$
H. $$
\Delta\approx0. 0 0 6 6 8 8 1
$$
$$
\Delta^\prime\approx0. 0067110
$$
$$
e\approx2. 3 5 \times1 0^{-5}
$$
$$
e/\Delta\approx3.31 \times1 0^{-3}
$$
I. $$
\Delta\approx0. 0066690
$$
$$
\Delta^\prime\approx0. 0071114
$$
$$
e\approx3. 0 1 \times1 0^{-5}
$$
$$
e/\Delta\approx3.35 \times1 0^{-3}
$$
J. $$
\Delta\approx0. 0 0 6 6 8 9 2
$$
$$
\Delta^\prime\approx0. 0067109
$$
$$
e\approx2. 5 5 \times1 0^{-5}
$$
$$
e/\Delta\approx3.29 \times1 0^{-3}
$$
Answer: C
The material dispersion coefficient of a certain optical fiber at $1.55\mu m$ is $8 \, \mathrm{ps} / (\mathrm{nm} \cdot \mathrm{km})$. If a light source with a spectral width of $\Delta\lambda = 2 \mathrm{nm}$ is used, what is the material dispersion time delay difference for this optical fiber over a length of 10 km? What is the material dispersion bandwidth?

Options:
A. $$0.13ns$$
$$
\approx3 1 0 0 \mathrm{M H z}
$$
B. $$0.20ns$$
$$
\approx2 4 0 0 \mathrm{M H z}
$$
C. $$0.15ns$$
$$
\approx3 0 0 0 \mathrm{M H z}
$$
D. $$0.16ns$$
$$
\approx2 7 5 6 \mathrm{M H z}
$$
E. $$0.14ns$$
$$
\approx2 5 0 0 \mathrm{M H z}
$$
F. $$0.17ns$$
$$
\approx2 8 0 0 \mathrm{M H z}
$$
G. $$0.12ns$$
$$
\approx3 5 0 0 \mathrm{M H z}
$$
H. $$0.19ns$$
$$
\approx2 6 0 0 \mathrm{M H z}
$$
I. $$0.11ns$$
$$
\approx3 6 0 0 \mathrm{M H z}
$$
J. $$0.18ns$$
$$
\approx2 7 0 0 \mathrm{M H z}
$$
Answer: D
Performing PCM time-division multiplexing transmission for 10-channel voice signals, with a known sampling rate of $8 kHz$, the sampled signal is quantized with an $\mathbf{M}$-level quantization and encoded in binary. The transmitted signal waveform is a half-duty-cycle return-to-zero rectangular pulse. Find: When $M = 8$ and 128, what is the required bandwidth for transmitting the 10-channel PCM time-division multiplexed signal in each case?

Options:
A. $$
\approx2 4 0 k \mathrm{H z}
$$
$$
\approx6 4 0 k \mathrm{H z}
$$
B. $$
\approx2 3 0 k \mathrm{H z}
$$
$$
\approx6 3 0 k \mathrm{H z}
$$
C. $$
\approx3 0 0 k \mathrm{H z}
$$
$$
\approx7 0 0 k \mathrm{H z}
$$
D. $$
\approx3 5 0 k \mathrm{H z}
$$
$$
\approx7 5 0 k \mathrm{H z}
$$
E. $$
\approx2 5 0 k \mathrm{H z}
$$
$$
\approx6 5 0 k \mathrm{H z}
$$
F. $$
\approx2 8 0 k \mathrm{H z}
$$
$$
\approx7 2 0 k \mathrm{H z}
$$
G. $$
\approx2 1 0 k \mathrm{H z}
$$
$$
\approx6 1 0 k \mathrm{H z}
$$
H. $$
\approx2 6 0 k \mathrm{H z}
$$
$$
\approx6 4 0 k \mathrm{H z}
$$
I. $$
\approx2 2 0 k \mathrm{H z}
$$
$$
\approx6 6 0 k \mathrm{H z}
$$
J. $$
\approx2 4 0 k \mathrm{H z}
$$
$$
\approx5 5 0 k \mathrm{H z}
$$
Answer: A
On the $xy$ plane, there is a regular $n$-sided polygonal wire loop. The center of the loop is at the origin, and the distance from the vertices of the $n$-sided polygon to the origin is $R$. The current in the wire is $I$. The magnetic induction at the origin when $n$ equals $3$ is ().

Options:
A. $$\frac{3\mu_0I}{2\pi R^2}e_α$$
B. $$\frac{2\sqrt{3}\mu_0I}{\pi R}e_α$$
C. $$\frac{\sqrt{3}\mu_0I}{\pi R^2}e_α$$
D. $$\frac{\mu_0I}{\pi R}e_α$$
E. $$\frac{3\sqrt{3}\mu_0I}{2\pi R}e_α$$
F. $$\frac{n\mu_0I}{\pi R^2}e_α$$
G. $$\frac{\mu_0I}{n\pi R}e_α$$
H. $$\frac{3\mu_0I}{\pi R}e_α$$
I. $$\frac{\mu_0I}{2\pi R}e_α$$
J. $$\frac{\sqrt{3}\mu_0I}{4\pi R}e_α$$
Answer: E
A coaxial cylindrical capacitor has an inner radius of $r_{1}=1 \, \mathrm{cm}$ and an outer radius of $r_{2}=4 \, \mathrm{cm}$, with a length of $l=0.5 \, \mathrm{m}$. The dielectric constant of the material between the plates is $4 \varepsilon_{0}$. An alternating current (AC) voltage is applied between the plates, given by $u=6000\sqrt{2} \sin(100\pi t) \, \mathrm{V}$. At $t=1.0 \, \mathrm{s}$, what is the displacement current density at any point between the plates?

Options:
A. $$
{\frac{8. 5 0 \times1 0^{-6}} {r^3}} e_{r} \mathrm{~ A / m}^{2}
$$
B. $$
{\frac{2. 6 7 \times1 0^{-5}} {r^3}} e_{r} \mathrm{~ A / m}^{2}
$$
C. $$
{\frac{6. 8 1 \times1 0^{-5}} {r}} e_{r} \mathrm{~ A / m}^{2}
$$
D. $$
{\frac{5. 7 2 \times1 0^{-5}} {r}} e_{\theta} \mathrm{~ A / m}^{2}
$$
E. $$
{\frac{6. 8 1 \times1 0^{-5}} {r^2}} e_{\theta} \mathrm{~ A / m}^{2}
$$
F. $$
{\frac{7. 2 3 \times1 0^{-5}} {r^2}} e_{r} \mathrm{~ A / m}^{2}
$$
G. $$
{\frac{3. 4 8 \times1 0^{-5}} {r}} e_{r} \mathrm{~ A / m}^{2}
$$
H. $$
{\frac{9. 0 4 \times1 0^{-6}} {r}} e_{r} \mathrm{~ A / m}^{2}
$$
I. $$
{\frac{4. 5 9 \times1 0^{-4}} {r}} e_{r} \mathrm{~ A / m}^{2}
$$
J. $$
{\frac{1. 2 9 \times1 0^{-4}} {r}} e_{r} \mathrm{~ A / m}^{2}
$$
Answer: C
In the air, there is an equilateral triangular loop with a side length of $b$ and a long straight wire. One side of the triangular loop is parallel to the straight wire at a distance of $a$, while the other vertex of the triangular loop is farther away from the straight wire. When the straight wire and the triangular loop carry currents $I_{1}$ and $I_{2}$ respectively, what is the mutual magnetic field energy between the triangular loop and the straight wire?

Options:
A. $$
\frac{\mu_{0} I_{1} I_{2}} {\pi} \left[ \left( \frac{2a} {\sqrt{3}}+\frac{b} {4} \right) \operatorname{l n} \frac{a+\frac{b} {3}} {a}-\frac{1} {2a} \times b \right]
$$
B. $$
\frac{\mu_{0} I_{1} I_{2}} {\pi} \left[ \left( \frac{2a} {\sqrt{3}}-\frac{b} {2} \right) \operatorname{l n} \frac{a+2b} {a}-\frac{1} {\sqrt{3} a} \times b \right]
$$
C. $$
\frac{\mu_{0} I_{1} I_{2}} {\pi} \left[ \left( \frac{b} {\sqrt{3}}+\frac{a} {2} \right) \operatorname{l n} \frac{a+b/2} {a}-\frac{\sqrt{3}} {2a} \times b \right]
$$
D. $$
\frac{\mu_{0} I_{1} I_{2}} {\pi} \left[ \left( \frac{a} {\sqrt{2}}+\frac{b} {3} \right) \operatorname{l n} \frac{a+\frac{1} {\sqrt{2}} b} {a}-\frac{2} {a} \times\frac{b} {3} \right]
$$
E. $$
\frac{\mu_{0} I_{1} I_{2}} {\pi} \left[ \left( \frac{a} {\sqrt{3}}+\sqrt{2}b \right) \operatorname{l n} \frac{a+\frac{\sqrt{2}} {\sqrt{3}} b} {a}-\frac{2} {a} \times b \right]
$$
F. $$
\frac{\mu_{0} I_{1} I_{2}} {\pi} \left[ \left( \frac{a} {2}+\frac{b\sqrt{3}} {2} \right) \operatorname{l n} \frac{a+\sqrt{3} b} {a}-\frac{2} {a} \times\frac{b} {3} \right]
$$
G. $$
\frac{\mu_{0} I_{1} I_{2}} {\pi} \left[ \left( \frac{a} {\sqrt{3}}+\frac{b} {2} \right) \operatorname{l n} \frac{a+\frac{\sqrt{3}} {2} b} {a}-\frac{1} {a} \times\frac{\sqrt{3}} {2} b \right]
$$
H. $$
\frac{\mu_{0} I_{1} I_{2}} {\pi} \left[ \left( \frac{a} {4}+\frac{\sqrt{3} b} {3} \right) \operatorname{l n} \frac{a+b} {a}-\frac{1} {\sqrt{3} a} \times b \right]
$$
I. $$
\frac{\mu_{0} I_{1} I_{2}} {\pi} \left[ \left( b+\frac{a} {\sqrt{3}} \right) \operatorname{l n} \frac{a+b} {a}-\frac{1} {\sqrt{3} a} \times b \right]
$$
J. $$
\frac{\mu_{0} I_{1} I_{2}} {\pi} \left[ \left( \sqrt{3}a+\frac{b} {2} \right) \operatorname{l n} \frac{a+b/2} {a}-\frac{2} {\sqrt{3} a} \times b \right]
$$
Answer: G
The wavelength of a uniform plane wave in free space is 12 cm. When it propagates in a lossless medium, its wavelength is $8 \, \mathrm{cm}$, and it is known that the amplitudes of $E$ and $H$ in this medium are 50 V/m and 0.1 A/m, respectively. What are the frequency of this plane wave and the values of $\mu_{\tau}$ and $\varepsilon_{\tau}$ for this lossless medium?

Options:
A. $$
\mu_{r}=2. 1 0 0 \,, \ \ \varepsilon_{r}=1. 2 5
$$
B. $$
\mu_{r}=1. 8 9 5 \,, \ \ \varepsilon_{r}=1. 1 2
$$
C. $$
\mu_{r}=1. 9 8 9 \,, \ \ \varepsilon_{r}=1. 1 3
$$
D. $$
\mu_{r}=1. 9 8 0 \,, \ \ \varepsilon_{r}=1. 1 0
$$
E. $$
\mu_{r}=2. 0 1 0 \,, \ \ \varepsilon_{r}=1. 2 0
$$
F. $$
\mu_{r}=1. 8 5 0 \,, \ \ \varepsilon_{r}=1. 0 9
$$
G. $$
\mu_{r}=1. 7 9 9 \,, \ \ \varepsilon_{r}=1. 0 8
$$
H. $$
\mu_{r}=2. 0 0 2 \,, \ \ \varepsilon_{r}=1. 1 5
$$
I. $$
\mu_{r}=2. 2 0 0 \,, \ \ \varepsilon_{r}=1. 3 0
$$
J. $$
\mu_{r}=1. 9 9 0 \,, \ \ \varepsilon_{r}=1. 1 6
$$
Answer: C
Given two vectors $A = e_{x} 2 + e_{y} 3 - e_{z} 4$ and $B = e_{x} 4 - e_{y} 5 + e_{z} 6$, find the angle between them and the component of $A$ on $B$ is ().

Options:
A. $$
=-2. 8 -1 7
$$
B. $$
=0. 5 5 3
$$
C. $$
=-4. 3 3 5
$$
D. $$
=1. 4 -3 2
$$
E. $$
=2. 5 -4 1
$$
F. $$
=1. 6 -2 4
$$
G. $$
=3. 7 1 -3
$$
H. $$
=-1. 5 4 -4
$$
I. $$
=-3. 5 3 2
$$
J. $$
=2. 6 4 -1
$$
Answer: I
The electric field and magnetic field of a uniform plane wave in an ideal medium are given as follows:
$$
E \,=\, e_{x} \, 10 \, \cos \left( \, 6 \, \pi \times 10^{7} t \,-\, 0. 8 \, \pi z \, \right) \, \mathrm{V / m},
$$
$$
H \,=\, e_y \, \frac{1} {6 \, \pi} \cos \left( \, 6 \, \pi \times 10^{7} t \,-\, 0.8 \, \pi z \, \right) \, \mathrm{A / m}.
$$
Find the relative permeability $\mu_{r}$ and the relative permittivity $\varepsilon_{r}$ of the medium.

Options:
A. $$
\mu_{\mathrm{r}} \,=\, 3 \,, \varepsilon_{\mathrm{r}} \,=\, 8
$$
B. $$
\mu_{\mathrm{r}} \,=\, 4 \,, \varepsilon_{\mathrm{r}} \,=\, 2
$$
C. $$
\mu_{\mathrm{r}} \,=\, 4 \,, \varepsilon_{\mathrm{r}} \,=\, 8
$$
D. $$
\mu_{\mathrm{r}} \,=\, 1 \,, \varepsilon_{\mathrm{r}} \,=\, 6
$$
E. $$
\mu_{\mathrm{r}} \,=\, 3 \,, \varepsilon_{\mathrm{r}} \,=\, 4
$$
F. $$
\mu_{\mathrm{r}} \,=\, 2 \,, \varepsilon_{\mathrm{r}} \,=\, 6
$$
G. $$
\mu_{\mathrm{r}} \,=\, 3 \,, \varepsilon_{\mathrm{r}} \,=\, 6
$$
H. $$
\mu_{\mathrm{r}} \,=\, 2 \,, \varepsilon_{\mathrm{r}} \,=\, 8
$$
I. $$
\mu_{\mathrm{r}} \,=\, 1 \,, \varepsilon_{\mathrm{r}} \,=\, 8
$$
J. $$
\mu_{\mathrm{r}} \,=\, 1 \,, \varepsilon_{\mathrm{r}} \,=\, 4
$$
Answer: H
It is known that at 100 MHz, the skin depth of graphite is 0.16 mm. Find: At 1 GHz, how far does an electromagnetic wave propagate in graphite before its amplitude attenuates by 30 dB?

Options:
A. $$
= 2. 0 5 \times1 0^{-4} \mathrm{~ m}
$$
B. $$
= 1. 7 0 \times1 0^{-4} \mathrm{~ m}
$$
C. $$
= 1. 7 5 \times1 0^{-4} \mathrm{~ m}
$$
D. $$
= 1. 5 5 \times1 0^{-4} \mathrm{~ m}
$$
E. $$
= 1. 8 0 \times1 0^{-4} \mathrm{~ m}
$$
F. $$
= 2. 1 0 \times1 0^{-4} \mathrm{~ m}
$$
G. $$
= 1. 8 5 \times1 0^{-4} \mathrm{~ m}
$$
H. $$
= 2. 0 0 \times1 0^{-4} \mathrm{~ m}
$$
I. $$
= 1. 9 0 \times1 0^{-4} \mathrm{~ m}
$$
J. $$
= 1. 6 5 \times1 0^{-4} \mathrm{~ m}
$$
Answer: C
A uniform plane wave is normally incident on the interface between two lossless dielectrics. When the magnitudes of the reflection coefficient and the transmission coefficient are equal, what is the standing wave ratio?

Options:
A. $$
\varepsilon_{r2}=9 \varepsilon_{r 1}
$$
B. $$
\varepsilon_{r2}=4 \varepsilon_{r 1}
$$
C. $$
\varepsilon_{r2}=49 \varepsilon_{r 1}
$$
D. $$
\varepsilon_{r2}=12.25 \varepsilon_{r 1}
$$
E. $$
\varepsilon_{r2}=36 \varepsilon_{r 1}
$$
F. $$
\varepsilon_{r2}=64 \varepsilon_{r 1}
$$
G. $$
\varepsilon_{r2}=2.25 \varepsilon_{r 1}
$$
H. $$
\varepsilon_{r2}=6 \varepsilon_{r 1}
$$
I. $$
\varepsilon_{r2}=16 \varepsilon_{r 1}
$$
J. $$
\varepsilon_{r2}=25 \varepsilon_{r 1}
$$
Answer: A
The simplest radome is a single-layer dielectric plate. Given that the dielectric constant of the plate is $\varepsilon = 2.8_{\varepsilon_{0}}$, what should the thickness of the dielectric plate be to ensure that an electromagnetic wave with a frequency of 3 GHz, incident perpendicularly on the surface of the plate, has no reflection? How much does the reflection increase when the frequencies are 3.1 GHz and 2.9 GHz, respectively?

Options:
A. $$
= 0. 4 8 \%
$$
B. $$
= 0. 2 1 \%
$$
C. $$
= 0. 3 0 \%
$$
D. $$
= 0. 3 8 \%
$$
E. $$
= 0. 4 2 \%
$$
F. $$
= 0. 2 5 \%
$$
G. $$
= 0. 1 8 \%
$$
H. $$
= 0. 1 5 \%
$$
I. $$
= 0. 6 2 \%
$$
J. $$
= 0. 5 0 \%
$$
Answer: F
The spacing between the wires of a parallel twin-wire transmission line is $D = 8 \ \mathrm{cm}$, the diameter of the wires is $d = 1 \ \mathrm{cm}$, and the surrounding medium is air. Calculate the following: The phase coefficient and characteristic impedance when $f = 600 \ \mathrm{MHz}$ $(R_{1} = 0, G_{1} = 0)$ is ()

Options:
A. $$
= 2 5 8 \ \Omega
$$
B. $$
= 3 3 3 \ \Omega
$$
C. $$
= 3 7 7 \ \Omega
$$
D. $$
= 3 9 0 \ \Omega
$$
E. $$
= 3 8 2 \ \Omega
$$
F. $$
= 2 6 0 \ \Omega
$$
G. $$
= 1 2 5 \ \Omega
$$
H. $$
= 4 5 6 \ \Omega
$$
I. $$
= 4 1 1 \ \Omega
$$
J. $$
= 2 7 9 \ \Omega
$$
Answer: B
The element spacing of a uniform linear antenna array is $d={\frac{\lambda} {2}}$. If the maximum radiation direction is required to deviate from the antenna array axis by ±60°, what should be the phase difference between the elements?

Options:
A. $$
=-\, {\frac{\pi} {4}}
$$
B. $$
=-\, {\frac{\pi} {2}}
$$
C. $$
=-\, {\frac{2\pi} {3}}
$$
D. $$
=-\, {\frac{\pi} {3}}
$$
E. $$
=-\, {\frac{3\pi} {4}}
$$
F. $$
=+\, {\frac{\pi} {4}}
$$
G. $$
=+\, {\frac{\pi} {3}}
$$
H. $$
=+\, {\frac{3\pi} {8}}
$$
I. $$
=\, 0
$$
J. $$
=+\, {\frac{\pi} {2}}
$$
Answer: B
The complex vector of the electric field intensity for a uniform plane wave propagating in free space is given by $E \!=\! e_{x} 10^{-4} \, \mathrm{e}^{\mathrm{j 20} \pi z}+\! e_{y} 10^{-4} \, \mathrm{e}^{-\mathrm{j ( 20 \pi z-\frac{\pi} {2} )}} \quad( \mathrm{V / m} )$, and the magnetic field intensity is denoted as $H$ is ().

Options:
A. $$
=-e_{x} 2. 6 5 \times 10^{-7} \mathrm{e}^{-\mathrm{j} ( 10 \pi z-{\frac{\pi } {2}} )}-e_{y} 3. 6 5 \times10^{-7} \mathrm{e}^{-\mathrm{i} 2 2 \pi z} ( \mathrm{A} / \mathrm{m} )
$$
B. $$
=-e_{y} 2. 6 0 \times 10^{-5} \mathrm{e}^{-\mathrm{j} ( 10 \pi z-{\frac{3 } {2}} )}+e_{x} 2. 6 0 \times10^{-7} \mathrm{e}^{-\mathrm{i} 2 0 \pi z} ( \mathrm{A} / \mathrm{m} )
$$
C. $$
=-e_{x} 2. 6 5 \times 10^{-7} \mathrm{e}^{\mathrm{j} ( 1 2 \pi z-{\frac{\pi } {4}} )}+e_{y} 2. 6 5 \times10^{-6} \mathrm{e}^{-\mathrm{i} 25 \pi z} ( \mathrm{A} / \mathrm{m} )
$$
D. $$
=-e_{x} 2. 6 0 \times 10^{-6} \mathrm{e}^{\mathrm{j} ( 20 \pi z-{\frac{5 } {2}} )}+e_{y} 2. 6 0 \times10^{-7} \mathrm{e}^{-\mathrm{i} 20 \pi z} ( \mathrm{A} / \mathrm{m} )
$$
E. $$
=-e_{x} 2. 6 5 \times 10^{-7} \mathrm{e}^{-\mathrm{j} ( 15 \pi z-{\frac{5} {4}} )}+e_{y} 2. 6 5 \times10^{-7} \mathrm{e}^{\mathrm{i} 15 \pi z} ( \mathrm{A} / \mathrm{m} )
$$
F. $$
=-e_{y} 2. 2 5 \times10^{-8} \mathrm{e}^{-\mathrm{j} ( 20 \pi z-{\frac{5} {4}} )}+e_{x} 3. 1 5 \times 10^{-7} \mathrm{e}^{-\mathrm{i} 15 \pi z} ( \mathrm{A} / \mathrm{m} )
$$
G. $$
=-e_{x} 2. 6 5 \times1 0^{-7} \mathrm{e}^{-\mathrm{j} ( 1 0 \pi z-{\frac{5} {2}} )}+e_{y} 2. 6 5 \times1 0^{-7} \mathrm{e}^{-\mathrm{i} 2 0 \pi z} ( \mathrm{A} / \mathrm{m} )
$$
H. $$
=-e_{x} 3. 0 0 \times10^{-7} \mathrm{e}^{-\mathrm{j} ( 1 0 \pi z-{\frac{3} {2}} )}+e_{y} 3. 0 \times 10^{-7} \mathrm{e}^{-\mathrm{i} 2 5 \pi z} ( \mathrm{A} / \mathrm{m} )
$$
I. $$
=-e_{y} 2. 7 5 \times10^{-6} \mathrm{e}^{-\mathrm{j} ( 20 \pi z-{\frac{\pi } {2}} )}-e_{x} 2. 7 5 \times10^{-7} \mathrm{e}^{-\mathrm{i} 12 \pi z} ( \mathrm{A} / \mathrm{m} )
$$
J. $$
=-e_{y} 3. 6 5 \times10^{-7} \mathrm{e}^{\mathrm{j} ( 20 \pi z-{\frac{5 } {2}} )}+e_{x} 2. 6 5 \times10^{-6} \mathrm{e}^{-\mathrm{i} 10 \pi z} ( \mathrm{A} / \mathrm{m} )
$$
Answer: G
At a temperature of 25°C, if the reaction rate doubles for every 10°C increase in temperature, what should the activation energy of the reaction be?

Options:
A. $$
4 3 9 8 6 \ \mathrm{J} / \mathrm{m o l}
$$
B. $$
5 4 8 9 1 \ \mathrm{J} / \mathrm{m o l}
$$
C. $$
5 2 9 2 8 \ \mathrm{J} / \mathrm{m o l}
$$
D. $$
6 2 7 4 0 \ \mathrm{J} / \mathrm{m o l}
$$
E. $$
6 5 8 3 1 \ \mathrm{J} / \mathrm{m o l}
$$
F. $$
4 8 5 7 3 \ \mathrm{J} / \mathrm{m o l}
$$
G. $$
7 0 1 2 9 \ \mathrm{J} / \mathrm{m o l}
$$
H. $$
5 8 3 7 2 \ \mathrm{J} / \mathrm{m o l}
$$
I. $$
4 9 7 2 4 \ \mathrm{J} / \mathrm{m o l}
$$
J. $$
6 1 2 3 5 \ \mathrm{J} / \mathrm{m o l}
$$
Answer: C
In an ideal batch reactor with a volume of 2.5 m³, a liquid-phase reaction
$$
\mathrm{A+B} \longrightarrow \mathrm{P}
$$
is carried out under isothermal conditions at 75°C. The experimentally determined rate equation is:
$$
(-r_A) = k c_A c_B \quad \text{kmol/(L} \cdot \text{s)}
$$
where $k = 2.78 \times 10^{-3} \, \text{kmol/(L} \cdot \text{s)}$. When the initial concentrations of reactants $\mathrm{A}$ and $\mathrm{B}$ are $c_{\mathrm{A0}} = c_{\mathrm{B0}} = 4 \, \text{mol/L}$, and the conversion of $\mathrm{A}$ reaches $x_{\mathrm{A}} = 0.8$, this batch reactor is capable of processing 0.684 kmol of reactant $\mathrm{A}$ per minute on average.
Now, if the reaction is transferred to an ideal plug flow reactor (PFR) with a diameter of 125 mm, maintaining isothermal operation at 75°C, while keeping the same throughput and required conversion rate, what length of reactor is needed?

Options:
A. $$
72.4m
$$
B. $$
88.3m
$$
C. $$
78.9m
$$
D. $$
95.1m
$$
E. $$
91.2m
$$
F. $$
86.7m
$$
G. $$
74.5m
$$
H. $$
83.6m
$$
I. $$
80.1m
$$
J. $$
69.8m
$$
Answer: H
Ammonia and formaldehyde react to produce hexamethylenetetramine:
$$
(A) 4 \mathrm{NH}_{3} + (B) 6 \mathrm{HCHO} \to (P) (\mathrm{CH}_{2})_{6}\mathrm{N}_{4} + (S) 6 \mathrm{H}_{2}\mathrm{O}
$$
The reaction is carried out in a continuous stirred tank reactor (CSTR) with baffles. The reactor volume is $490 \ \mathrm{cm}^{3}$, and the stirring speed is 1,800 r/min to ensure complete mixing. The studied rate equation is:
$$
(-r_{\mathrm{A}}) = k c_{\mathrm{A}} c_{\mathrm{B}}^{2} \ \mathrm{mol/(L \cdot s)}
$$
$$
k = 1.42 \times 10^{3} \, \mathrm{e}^{-3090 / T}
$$
The concentration of ammonia is $4.06 \ \mathrm{mol/L}$, the concentration of formaldehyde is $6.32 \ \mathrm{mol/L}$, and the flow rates for both are $1.50 \ \mathrm{cm}^{3}/\mathrm{s}$. The reaction temperature is $36^\circ \mathrm{C}$.
Find the outlet concentrations $c_{\mathrm{Af}}$ and $c_{\mathrm{Bf}}$ for the reactor is ().

Options:
A. $$
c_{\mathrm{Af}}=0.475\mathrm{mol/L}\\c_{\mathrm{Bf}}=0.710\mathrm{mol/L}
$$
B. $$
c_{\mathrm{Af}}=0.300\mathrm{mol/L}\\c_{\mathrm{Bf}}=0.620\mathrm{mol/L}
$$
C. $$
c_{\mathrm{Af}}=0.340\mathrm{mol/L}\\c_{\mathrm{Bf}}=0.690\mathrm{mol/L}
$$
D. $$
c_{\mathrm{Af}}=0.360\mathrm{mol/L}\\c_{\mathrm{Bf}}=0.680\mathrm{mol/L}
$$
E. $$
c_{\mathrm{Af}}=0.410\mathrm{mol/L}\\c_{\mathrm{Bf}}=0.673\mathrm{mol/L}
$$
F. $$
c_{\mathrm{Af}}=0.450\mathrm{mol/L}\\c_{\mathrm{Bf}}=0.750\mathrm{mol/L}
$$
G. $$
c_{\mathrm{Af}}=0.512\mathrm{mol/L}\\c_{\mathrm{Bf}}=0.680\mathrm{mol/L}
$$
H. $$
c_{\mathrm{Af}}=0.365\mathrm{mol/L}\\c_{\mathrm{Bf}}=0.663\mathrm{mol/L}
$$
I. $$
c_{\mathrm{Af}}=0.500\mathrm{mol/L}\\c_{\mathrm{Bf}}=0.640\mathrm{mol/L}
$$
J. $$
c_{\mathrm{Af}}=0.390\mathrm{mol/L}\\c_{\mathrm{Bf}}=0.700\mathrm{mol/L}
$$
Answer: H
First-order series reaction $\mathrm{A} \stackrel{k_{1}}{\longrightarrow} \mathrm{P} \stackrel{k_{2}}{\longrightarrow} \mathrm{S}$
$$
(-r_{\mathrm{A}}) \!=\! k_{1} c_{\mathrm{A}}, \qquad r_{\mathrm{P}} \!=\! k_{1} c_{\mathrm{A}} \!-\! k_{2} c_{\mathrm{P}}
$$
where $\mathrm{A}$ represents $\mathrm{C_{6}H_{6}}$ (benzene), $\mathrm{P}$ represents $\mathrm{C_{5}H_{5}Cl}$ (chlorobenzene), and $\mathrm{S}$ represents $\mathrm{C_{6}H_{4}Cl_{2}}$ (dichlorobenzene).
Given:
$k_{1} = 1$, $k_{2} = 0.5$, $c_{\mathrm{A 0}} = 1 \, \mathrm{mol/L}$, $c_{\mathrm{P 0}} = c_{\mathrm{B 0}} = 0$
Find the ratio of $c_\mathrm{P}$ to $c_\mathrm{S}$ in a plug flow reactor is (). $\tau = 1$.

Options:
A. 2.30
B. 1.92
C. 3.50
D. 4.12
E. 3.08
F. 3.75
G. 3.00
H. 2.50
I. 2.85
J. 2.10
Answer: E
The monomer for producing chloroprene rubber, 2-chlorobutadiene-1,3, is obtained through the dehydrochlorination of 3,4-dichlorobutene in ethanol using a base. The reaction equation is as follows:
$$
\text{CH}_2 = \text{CH}-\text{CHCl}-\text{CH}_2\text{Cl} \xrightarrow{\text{NaOH} / \text{C}_2\text{H}_5\text{OH}} \text{CH}_2 = \text{CCl}-\text{CH} = \text{CH}_2 + \text{HCl}
$$
Simplified as $\mathrm{A} \stackrel{\mathrm{B}} {\longrightarrow} \mathrm{P+R}$ (where B is NaOH).
When ${\frac{c_{\mathrm{B o}}-c_{\mathrm{A 0}}} {c_{\mathrm{A o}}}}=M$, the conversion rate in a batch reactor is calculated using the following equation:
$$
\operatorname{l n} {\frac{1+M-x_{\mathrm{A}}} {( 1+M ) ( 1-x_{\mathrm{A}} )}}=c_{\mathrm{A 0}} M k t
$$
It is known that at 40°C, $k = 0.07 \, \text{(mol/L)}^{-1} \, \text{min}^{-1}$. The batch reactor's operating conditions are $c_{A0} = 2.2 \, \text{mol/L}$, $M = 0.25$, $T=40°C$, and $t=50 \, \text{min}$. What is the conversion rate?

Options:
A. 0.854
B. 0.839
C. 0.967
D. 0.785
E. 0.590
F. 0.908
G. 0.679
H. 0.512
I. 0.643
J. 0.721
Answer: C
Within the range $8 \leq x \leq 10$ and $2 \leqslant y \leqslant 4$, what is the linearized expression of the nonlinear equation?
$$
z = x^{2} + 4xy + 6y^{2}
$$

Options:
A. $$
z \,-\, 2 7 x \,-\, 6 9 y \,+\, 2 3 9 \,=\, 0
$$
B. $$
z \,-\, 2 5 x \,-\, 6 5 y \,+\, 2 3 7 \,=\, 0
$$
C. $$
z \,-\, 2 6 x \,-\, 6 7 y \,+\, 2 3 8 \,=\, 0
$$
D. $$
z \,-\, 3 3 x \,-\, 7 4 y \,+\, 2 4 6 \,=\, 0
$$
E. $$
z \,-\, 3 2 x \,-\, 7 5 y \,+\, 2 4 5 \,=\, 0
$$
F. $$
z \,-\, 3 0 x \,-\, 7 2 y \,+\, 2 4 3 \,=\, 0
$$
G. $$
z \,-\, 2 9 x \,-\, 7 1 y \,+\, 2 4 4 \,=\, 0
$$
H. $$
z \,-\, 3 1 x \,-\, 7 0 y \,+\, 2 4 0 \,=\, 0
$$
I. $$
z \,-\, 2 8 x \,-\, 6 8 y \,+\, 2 4 1 \,=\, 0
$$
J. $$
z \,-\, 3 0 x \,-\, 7 3 y \,+\, 2 4 2 \,=\, 0
$$
Answer: F
There is currently a conical water tank system. It is known that the fluid flow through the valve is turbulent and its relationship with the water head $H$ is given by
$$
Q = 0.005 \sqrt{H}
$$
where $Q$ is the flow rate, measured in $\mathbf{m}^3 / \mathbf{s}$, and $H$ is measured in meters (m).
Assume the water head is 2 m at $t=0$. What will the water head be at $t=60$ seconds?

Options:
A. $$
x=1. 4 7 6 8 m
$$
B. $$
x=1. 5 8 9 2 m
$$
C. $$
x=1. 4 8 2 3 m
$$
D. $$
x=1. 8 2 5 9 m
$$
E. $$
x=1. 6 3 0 7 m
$$
F. $$
x=1. 5 3 4 7 m
$$
G. $$
x=1. 6 9 4 5 m
$$
H. $$
x=1. 7 2 0 1 m
$$
I. $$
x=1. 7 1 8 9 m
$$
J. $$
x=1. 6 5 2 1 m
$$
Answer: J
Consider the following characteristic equation:
$$
s^{4} + 2s^{3} + (4 + K)s^{2} + 9s + 25 = 0
$$
Try to apply the Hurwitz stability criterion. What is the stability range for $K$?

Options:
A. $$
K > \frac{1 0 9} {1 8}
$$
B. $$
K > \frac{2 2 2} {5 3}
$$
C. $$
K < \frac{8 1} {4 2}
$$
D. $$
K = \frac{5 4} {3 6}
$$
E. $$
K \leq \frac{2 0} {1 0}
$$
F. $$
K = \frac{9 0} {2 7}
$$
G. $$
K \geq \frac{5 8} {3 3}
$$
H. $$
K < \frac{1 0 9} {9}
$$
I. $$
K > \frac{7 2} {5 0}
$$
J. $$
K < \frac{1 9 5} {3 8}
$$
Answer: A
Consider a unity feedback control system, with its closed-loop transfer function given as
$$
\frac{C(s)}{R(s)} = \frac{K s + b}{s^2 + a s + b}
$$
What is its open-loop transfer function $G(s)$?
In the unit ramp response, what is the system's steady-state error?

Options:
A. $$
G_(s)=\frac{{Ks}+6}{s(s+a+b)} ,
\\\frac{K-a}{b}
$$
B. $$
G_(s)=\frac{{Ks}+6}{s(s+a-K)} ,
\\\frac{b-K}{a}
$$
C. $$
G_(s)=\frac{{K}+b}{s(s+a-6)} ,
\\\frac{a-K}{6}
$$
D. $$
G_(s)=\frac{{K}+b}{s(s+a-b)} ,
\\\frac{a-b}{K}
$$
E. $$
G_(s)=\frac{{Ks}+b}{s(s+a-K)} ,
\\\frac{a+K}{6}
$$
F. $$
G_(s)=\frac{{K}+b}{s(s+a-b)} ,
\\\frac{6-a}{K}
$$
G. $$
G_(s)=\frac{{K+b}}{s(s+a-K)} ,
\\\frac{K-a}{6}
$$
H. $$
G_(s)=\frac{{Ks}+6}{s(s+a+b)} ,
\\\frac{a+b}{K}
$$
I. $$
G_(s)=\frac{{K}+6}{s(s+a)} ,
\\\frac{a+K}{b}
$$
J. $$
G_(s)=\frac{{Ks}+6}{s(s+a-K)} ,
\\\frac{a-K}{b}
$$
Answer: J
Given a system with its open-loop transfer function defined as
$$
G(s)H(s) = \frac{K(s - 0.6667)}{s^4 + 3.3401s^3 + 7.0325s^2}
$$
what is the equation of the asymptotes of the root locus for this system?

Options:
A. $$
G_{j} ( s ) H_{j} ( s ) \,=\, \frac{K} {s^{3} \,+\, 3. 6 9 7 4 s^{2} \,+\, 5. 9 8 3 4 s \,+\, 1. 9 7 4 2}
$$
B. $$
G_{b} ( s ) H_{b} ( s ) \,=\, \frac{K} {s^{3} \,+\, 5. 1 0 2 3 s^{2} \,+\, 3. 8 9 2 9 s \,+\, 1. 9 8 3 4}
$$
C. $$
G_{e} ( s ) H_{e} ( s ) \,=\, \frac{K} {s^{3} \,+\, 4. 3 2 4 5 s^{2} \,+\, 5. 4 9 1 2 s \,+\, 2. 0 8 7 6}
$$
D. $$
G_{h} ( s ) H_{h} ( s ) \,=\, \frac{K} {s^{3} \,+\, 3. 9 8 0 7 s^{2} \,+\, 7. 2 4 8 5 s \,+\, 2. 2 3 7 5}
$$
E. $$
G_{d} ( s ) H_{d} ( s ) \,=\, \frac{K} {s^{3} \,+\, 4. 9 9 7 2 s^{2} \,+\, 7. 0 1 2 3 s \,+\, 2. 1 2 5 7}
$$
F. $$
G_{a} ( s ) H_{a} ( s ) \,=\, \frac{K} {s^{3} \,+\, 4. 0 0 6 8 s^{2} \,+\, 5. 3 5 1 5 s \,+\, 2. 3 8 2 5}
$$
G. $$
G_{c} ( s ) H_{c} ( s ) \,=\, \frac{K} {s^{3} \,+\, 3. 8 0 1 5 s^{2} \,+\, 6. 7 4 2 1 s \,+\, 2. 4 7 1 2}
$$
H. $$
G_{g} ( s ) H_{g} ( s ) \,=\, \frac{K} {s^{3} \,+\, 5. 2 3 1 3 s^{2} \,+\, 6. 0 5 9 8 s \,+\, 1. 7 4 6 2}
$$
I. $$
G_{i} ( s ) H_{i} ( s ) \,=\, \frac{K} {s^{3} \,+\, 4. 2 4 6 2 s^{2} \,+\, 6. 2 1 7 1 s \,+\, 2. 5 3 9 8}
$$
J. $$
G_{f} ( s ) H_{f} ( s ) \,=\, \frac{K} {s^{3} \,+\, 3. 7 5 8 4 s^{2} \,+\, 5. 8 2 3 5 s \,+\, 2. 2 1 3 8}
$$
Answer: F
Given
$$
G(s) = \frac{\omega_{n}^{2}}{s^{2} + 2\zeta\omega_{n}s + \omega_{n}^{2}}
$$
find $$|G(j\omega_{n})|$$What is it?

Options:
A. $\frac{\zeta + \omega_n} {2 \zeta}$
B. $\frac{1} {\zeta + 1}$
C. $\frac{\omega_n} {\zeta}$
D. $\frac{\zeta} {1 + \zeta^2}$
E. $\frac{\zeta} {\omega_n}$
F. $\frac{\zeta} {2}$
G. $\frac{1} {2 \zeta}$
H. $\frac{\omega_n^2} {2 \zeta \omega_n}$
I. $\frac{1} {\zeta^2}$
J. $\frac{1 + \zeta^2} {2 \zeta}$
Answer: G
Consider a unit feedback control system with an open-loop transfer function given by
$$
G(s) = \frac{K}{s(s^2 + s + 0.5)}
$$
In order for the resonant peak in the frequency response to be 2 decibels, i.e., $M_r = 2 \mathrm{~dB}$, what is the value of the gain $K$?

Options:
A. 0.1394
B. 0.1765
C. 0.1542
D. 0.1853
E. 0.1326
F. 0.1237
G. 0.1489
H. 0.1978
I. 0.1621
J. 0.1714
Answer: J
System
$$
\left[ \begin{matrix} {{{\dot{x}_{1}}}} \\ {{{\dot{x}_{2}}}} \\ \end{matrix} \right]=\left[ \begin{matrix} {{{-1}}} & {{{-0.5}}} \\ {{{1}}} & {{{0}}} \\ \end{matrix} \right] \left[ \begin{matrix} {{{x_{1}}}} \\ {{{x_{2}}}} \\ \end{matrix} \right]+\left[ \begin{matrix} {{{0.5}}} \\ {{{0}}} \\ \end{matrix} \right] u, \ \ \ \ \ \left[ \begin{matrix} {{{x_{1} ( 0 )}}} \\ {{{x_{2} ( 0 )}}} \\ \end{matrix} \right]=\left[ \begin{matrix} {{{0}}} \\ {{{0}}} \\ \end{matrix} \right]
$$
$$
y=[ 1 \ -0 ] {\left[ \begin{matrix} {{x_{1}}} \\ {{x_{2}}} \\ \end{matrix} \right]}
$$
What is the response $y(t)$? In the equation, $u(t)$ is a unit step input at $t=0$, i.e., $u(t) = 1(t)$.

Options:
A. $$
e^{-t} \operatorname{cos} 0.5 t
$$
B. $$
e^{-0. 5 t} \operatorname{s i n} 0. 5 t
$$
C. $$
e^{-0.5 t} + t
$$
D. $$
e^{-t} \operatorname{sin} 0.5 t
$$
E. $$
e^{-0.5 t} \operatorname{cos} 0.5 t
$$
F. $$
e^{-0.5 t} \operatorname{sin} t
$$
G. $$
t \cdot e^{-0.5 t}
$$
H. $$
e^{-t} \operatorname{cos} t
$$
I. $$
t \cdot e^{-t}
$$
J. $$
1 - e^{-t}
$$
Answer: B
Consider the following matrix:
$$
\mathbf{A}=\left[ \begin{matrix} {{0}} & {{1}} \\ {{-2}} & {{-3}} \\ \end{matrix} \right]
$$
What is $e^{A t}$?

Options:
A. $$
\left[ \begin{matrix} {{{2 \, e^{-t}-e^{-2 t}}}} & {{{e^{-t}-e^{-2 t}}}} \\ {{{-2 \, e^{-t}+2 \, e^{-2 t}}}} & {{{-e^{-t}+2 \, e^{-2 t}}}} \\ \end{matrix} \right]
$$
B. $$
\left[ \begin{matrix} {{{e^{-3 t}+2 \, e^{-2 t}}}} & {{{e^{-t}-e^{-2 t}}}} \\ {{{-e^{-t}+e^{-3 t}}}} & {{{2 \, e^{-t}-e^{-3 t}}}} \\ \end{matrix} \right]
$$
C. $$
\left[ \begin{matrix} {{{e^{-t}-2 \, e^{-3 t}}}} & {{{2 \, e^{-t}-e^{-2 t}}}} \\ {{{e^{-2 t}-e^{-t}}}} & {{{e^{-3 t}+e^{-t}}}} \\ \end{matrix} \right]
$$
D. $$
\left[ \begin{matrix} {{{2 \, e^{-2 t}-e^{-t}}}} & {{{-e^{-t}+e^{-3 t}}}} \\ {{{e^{-3 t}-2 \, e^{-t}}}} & {{{e^{-t}+e^{-2 t}}}} \\ \end{matrix} \right]
$$
E. $$
\left[ \begin{matrix} {{{2 \, e^{-2 t}-e^{-t}}}} & {{{e^{-3 t}+e^{-t}}}} \\ {{{-e^{-t}+e^{-2 t}}}} & {{{e^{-t}-2 \, e^{-3 t}}}} \\ \end{matrix} \right]
$$
F. $$
\left[ \begin{matrix} {{{e^{-t}+e^{-3 t}}}} & {{{2 \, e^{-2 t}-e^{-t}}}} \\ {{{-e^{-t}+e^{-3 t}}}} & {{{e^{-2 t}-2 \, e^{-t}}}} \\ \end{matrix} \right]
$$
G. $$
\left[ \begin{matrix} {{{e^{-t}+e^{-2 t}}}} & {{{e^{-t}-2 \, e^{-3 t}}}} \\ {{{-e^{-t}+e^{-3 t}}}} & {{{2 \, e^{-2 t}-e^{-t}}}} \\ \end{matrix} \right]
$$
H. $$
\left[ \begin{matrix} {{{e^{-2 t}-2 \, e^{-t}}}} & {{{e^{-t}+2 \, e^{-3 t}}}} \\ {{{-2 \, e^{-t}-e^{-t}}}} & {{{e^{-3 t}+e^{-2 t}}}} \\ \end{matrix} \right]
$$
I. $$
\left[ \begin{matrix} {{{e^{-2 t}-e^{-t}}}} & {{{e^{-t}+e^{-3 t}}}} \\ {{{e^{-3 t}-2 \, e^{-t}}}} & {{{e^{-t}+e^{-2 t}}}} \\ \end{matrix} \right]
$$
J. $$
\left[ \begin{matrix} {{{e^{-3 t}-e^{-t}}}} & {{{2 \, e^{-2 t}-e^{-t}}}} \\ {{{-e^{-3 t}+e^{-t}}}} & {{{e^{-t}+e^{-2 t}}}} \\ \end{matrix} \right]
$$
Answer: A
The transfer function of the controlled plant in the regulator system is
$$
\frac{Y(s)}{U(s)} = \frac{10}{(s+1)(s+2)(s+3)}
$$
Define the state variables as:
$$
\begin{array}{l}
x_{1}=y \\
x_{2}=\dot{x}_{1} \\
x_{3}=\dot{x}_{2} \\
\end{array}
$$
Using state feedback control $u = -\mathbf{K}\mathbf{x}$, configure the closed-loop poles to
$$
s = -2 + j 2\sqrt{3}, \qquad s = -2 - j 2\sqrt{3}, \qquad s = -10
$$
What is the required state feedback gain matrix $\mathbf{K}$?

Options:
A. $\begin{bmatrix}{17.1} & {3.2} & {0.7}\end{bmatrix}$
B. $\begin{bmatrix}{14.8} & {4.6} & {1.0}\end{bmatrix}$
C. $\begin{bmatrix}{13.9} & {5.3} & {1.1}\end{bmatrix}$
D. $\begin{bmatrix}{15.0} & {4.0} & {0.6}\end{bmatrix}$
E. $\begin{bmatrix}{16.0} & {4.1} & {0.5}\end{bmatrix}$
F. $\begin{bmatrix}{14.3} & {5.6} & {1.2}\end{bmatrix}$
G. $\begin{bmatrix}{16.7} & {3.8} & {0.9}\end{bmatrix}$
H. $\begin{bmatrix}{18.2} & {2.8} & {1.3}\end{bmatrix}$
I. $\begin{bmatrix}{12.5} & {6.2} & {1.5}\end{bmatrix}$
J. $\begin{bmatrix}{15.4} & {4.5} & {0.8}\end{bmatrix}$
Answer: J
If four processes share the same program segment and up to three processes are allowed to enter the program segment at the same time, using P and V operations as the synchronization mechanism, the range of values for the semaphore is ().

Options:
A. $$
4, 3, 2, 1, 0
$$
B. $$
4, 3, 1, 0, -1
$$
C. $$
3, 2, 0, -1, -2
$$
D. $$
3, 1, 0, -1, -2
$$
E. $$
4, 2, 1, 0, -1
$$
F. $$
5, 4, 3, 2, 1
$$
G. $$
3, 2, 1, -1, -2
$$
H. $$
2, 1, 0, -1, -2
$$
I. $$
2, 0, -1, -2, -3
$$
J. $$
3, 2, 1, 0,-1
$$
Answer: J
In page-based, segment-based, and segment-page-based storage management, suppose a page-based storage system is equipped with a TLB (Translation Lookaside Buffer), and most active page table entries can be stored in it. If the page table is stored in memory, the memory access time is 1 µs, and the TLB lookup time is 0.2 µs. If the TLB hit rate is 85%, what is the effective access time? If the TLB hit rate is 50%, what is the effective access time?

Options:
A. $$
1. 4 0 \mu s
$$
$$
1. 8 \mu s
$$
B. $$
1. 3 4 \mu s
$$
$$
1. 6 \mu s
$$
C. $$
1. 4 5 \mu s
$$
$$
1. 9 \mu s
$$
D. $$
1. 2 9 \mu s
$$
$$
1. 6 \mu s
$$
E. $$
1. 2 7 \mu s
$$
$$
1. 0 \mu s
$$
F. $$
1. 3 5 \mu s
$$
$$
1. 7 \mu s
$$
G. $$
1. 3 8 \mu s
$$
$$
1. 2 \mu s
$$
H. $$
1. 3 1 \mu s
$$
$$
1. 5 \mu s
$$
I. $$
1. 3 7 \mu s
$$
$$
1. 9 \mu s
$$
J. $$
1. 3 6 \mu s
$$
$$
1. 8 \mu s
$$
Answer: F
In an existing demand-paged system, the page table is stored in registers. If there is an available empty page or the replaced page has not been modified, it takes $8\mu s$ to handle a page fault interrupt; if the replaced page has been modified, then handling a page fault interrupt requires $20\mu s$ due to the additional time required to write back to external storage. The memory access time is $1\mu s$. Assuming that 70% of the replaced pages have been modified, what is the maximum acceptable page fault rate to ensure the effective access time does not exceed $2\mu s$?

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