question stringlengths 152 5.02k | answers listlengths 3 3 |
|---|---|
Topic: Power Electronics and Electrical Drives.
Question: A DC motor system powered by a single-phase fully controlled bridge rectifier circuit requires continuous armature current, with its average value adjustable within the range of 10 to 100 A, $U_{2}=220 \text{V}$. What is the inductance value of the smoothing rea... | [
"B",
"$$\n94.71 \\mathrm{m H}\n$$",
"B) $$\n94.71 \\mathrm{m H}\n$$"
] |
Topic: Physical Chemistry.
Question: For a weak acid $HA$ of concentration $C(mol \ I^{-}$ and degree of dissociation $(\alpha)$ Ostwald's ilution law is represented by the equation
A) $$K_{a}=\dfrac {C^{2}\alpha}{(1-\alpha)}$$
B) $$K_{a}=\dfrac {C^{2}\alpha}{(1+\alpha)}$$
C) $$K_{a}=\dfrac {C^{2} \alpha}{(1 - 2\alpha)... | [
"G",
"$$K_{a}=\\dfrac {C\\alpha^{2}}{(1-\\alpha)}$$",
"G) $$K_{a}=\\dfrac {C\\alpha^{2}}{(1-\\alpha)}$$"
] |
Topic: Theoretical Optics.
Question: One end of a cylindrical glass rod $ (\mu =1.5 ) $ in given in the shape of a concave refracting surface of radius 10 cm. an air bubble is situated in the glass rod at a point on its axis such that it appears to be at a distance 10 cm from the surface inside the glass when seen from... | [
"J",
"30 cm inside the glass",
"J) 30 cm inside the glass"
] |
Topic: Particle and Nuclear Physics.
Question: An atom that does not have a permanent magnetic moment is called a diamagnetic atom. If we ignore the spin of the electron, find the induced magnetic moment produced by a weak magnetic field $B$ acting on a ground state hydrogen atom is___.
A) $$
\mu\equiv-\frac{\partial( ... | [
"H",
"$$\n\\mu\\equiv-\\frac{\\partial( \\Delta E )} {\\partial B}=-\\frac{e^{2} a^{2}} {4 8 m c^{2}} B\n$$",
"H) $$\n\\mu\\equiv-\\frac{\\partial( \\Delta E )} {\\partial B}=-\\frac{e^{2} a^{2}} {4 8 m c^{2}} B\n$$"
] |
Topic: Discrete Mathematics.
Question: We now define an algorithm: The definition of a(n) is k appears 2k-1 times in the sequence and each number is the square root of its position in the sequence, rounded up. Given the input x_list (a series of values): [87, 88, 89, 90, 91, 92, 93, 94, 95, 96], determine the correspon... | [
"F",
"[10, 10, 10, 10, 10, 10, 10, 10, 10, 10]",
"F) [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]"
] |
Topic: Fundamental Mathematics.
Question: Regarding the monotonicity of the function \( y = \frac{x^2}{1 + x} \), which of the following statements is correct?
A) It is monotonically increasing on \( (-\infty, -2) \)
B) It is monotonically increasing on \( (-1, 0) \)
C) It is monotonically decreasing on \( (-1, 0) \)
D... | [
"A",
"It is monotonically increasing on \\( (-\\infty, -2) \\)",
"A) It is monotonically increasing on \\( (-\\infty, -2) \\)"
] |
Topic: Stochastic Processes.
Question: Let $N_1(t)$ and $N_2(t)$ be two independent Posson processes with rate $\lambda_1 = 1$ and $\lambda_2 = 2$, respectively. Let N(t) be the merged process N(t) = N_1(t) + N_2(t). Given that N(1) = 2, Find the probability that N_1(1) = 1.
A) 0.1839
B) 0.2635
C) 0.4444
D) 0.3333
E) 0... | [
"C",
"0.4444",
"C) 0.4444"
] |
Topic: Manufacturing Automation.
Question: For a pair of cylindrical gear transmissions, when other conditions remain unchanged, if the load on the gear transmission is increased to 4 times the original load, what will happen to the contact stress on the tooth surface?
A) Increase to 5 times the original stress
B) Incr... | [
"B",
"Increase to 2 times the original stress",
"B) Increase to 2 times the original stress"
] |
Topic: Physical Chemistry.
Question: The initial concentration of a reactant in a second-order reaction is $0.4 \times 10^{3} \mathrm{mol/m}^{3}$. Within 80 minutes, 30% of this reaction is completed. Determine the time required for the reaction to reach 80% completion.
A) $659min$
B) $0.321min$
C) $513min$
D) $746min$... | [
"D",
"$746min$",
"D) $746min$"
] |
Topic: Operations Research and Cybernetics.
Question: A factory plans to produce two kinds of products, A and B, and the equipment time, raw materials A and B, the profits that can be obtained, and the amount of resources available for each set of products are shown in the following table. The plan should be arranged a... | [
"F",
"Production of 1 set of A and 4 sets of B",
"F) Production of 1 set of A and 4 sets of B"
] |
Topic: Astrophysics.
Question: The known surface temperature of the Sun is $5,780 \ \mathrm{K}$, with a radius of $7 \times 10^{8} \ \mathrm{m}$. The Sun's energy is provided by the fusion of hydrogen into helium. If 5% of the Sun's hydrogen has currently fused into helium, and the Sun's luminosity remains constant, th... | [
"H",
"5 billion years",
"H) 5 billion years"
] |
Topic: Economic Statistics.
Question: In May, the sales revenue of goods was 600,000 yuan. The seasonal index for that month was 120%. After eliminating the impact of seasonal factors, the sales revenue of goods for that month was () yuan.
A) 47
B) 52
C) 60
D) 48
E) 55
F) 58
G) 51.2
H) 45
I) 50
J) 72 | [
"I",
"50",
"I) 50"
] |
Topic: Number Theory.
Question: Find the remainder when $11^{2005}$ is divided by $1000$ .
A) 151
B) 111
C) 351
D) 251
E) 451
F) 211
G) 51
H) 101
I) 161 | [
"G",
"51",
"G) 51"
] |
Topic: Signal and Information Processing.
Question: For $$
\mathrm{~ x ~} ( \mathrm{~ n ~} ) \mathrm{~=~} a^{| \mathrm{~ n ~} |}
$$
,a is a real number, what is the convergence domain of X(z)?
A) $$| \mathrm{a} | > 1 \,, \ | \mathrm{a} | < | \mathrm{z} | > 1 / | \mathrm{a} |$$
B) $$| \mathrm{a} | > 1, | \mathrm{z} | > ... | [
"H",
"$$| \\mathrm{a} | < 1 \\,, \\ | \\mathrm{a} | < | \\mathrm{z} | < 1 / | \\mathrm{a} |$$",
"H) $$| \\mathrm{a} | < 1 \\,, \\ | \\mathrm{a} | < | \\mathrm{z} | < 1 / | \\mathrm{a} |$$"
] |
Topic: Water conservancy and Hydropower Engineering.
Question: A wall that is 6 meters high is subjected to water pressure over its entire vertical surface. Where is the center of water pressure on the wall ?
A) It lies $0.5 \ \mathrm{m}$ underwater
B) It lies $6 \ \mathrm{m}$ above base
C) It is $4 \ \mathrm{m}$ under... | [
"C",
"It is $4 \\ \\mathrm{m}$ underwater",
"C) It is $4 \\ \\mathrm{m}$ underwater"
] |
Topic: Acoustics.
Question: An open organ pipe resonated with frequency ` $\mathrm{f}_{1}$' and $2^{\mathrm{n}\mathrm{d}}$ harmonic. Now one end is closed and the frequency is slowly increased then it resonates with frequency $\mathrm{f}_{2}$ and nth harmonic then
A) $$\mathrm{n}=5,\ \displaystyle \mathrm{f}_{2}=\frac{... | [
"G",
"$$\\mathrm{n}=5,\\ \\displaystyle \\mathrm{f}_{2}=\\frac{5}{4}\\mathrm{f}_{1}$$",
"G) $$\\mathrm{n}=5,\\ \\displaystyle \\mathrm{f}_{2}=\\frac{5}{4}\\mathrm{f}_{1}$$"
] |
Topic: Military Chemistry and Pyrotechnics.
Question: What is the reliability of an ignition sequence composed of two primary ignition components and three continuous ignition components, if the design reliability of each ignition component (\(R_i\)) is 0.99?
A) 0.951
B) 0.953
C) 0.960
D) 0.945
E) 0.952
F) 0.930
G) 0.9... | [
"A",
"0.951",
"A) 0.951"
] |
Topic: Geometry and Topology.
Question: Find the area of the region bounded by the parametric curves and the indicated values of the parameter:
$$
x = a \cdot \sin(2 \cdot t), \quad y = b \cdot \sin(t), \quad 0 \le t < 2 \cdot \pi
$$
(the "hourglass").
A) 8/3 * a * b
B) 18/3 * a * b
C) 16/3 * a * b
D) 6/3 * a * b
E) 4/... | [
"A",
"8/3 * a * b",
"A) 8/3 * a * b"
] |
Topic: Optoelectronic Technology.
Question: It was noted that the intensity of light absorbed while passing through a 16-km length of optical fiber glass is equivalent to the light intensity absorbed through a 25-mm thickness of ordinary window glass. Calculate the absorption coefficient $\beta$ of the optical fiber gl... | [
"H",
"$$\n1. 5 6 \\times1 0^{-1 0} \\, {\\mathrm{m m}}^{-1}\n$$",
"H) $$\n1. 5 6 \\times1 0^{-1 0} \\, {\\mathrm{m m}}^{-1}\n$$"
] |
Topic: Antenna and Radio Communication.
Question: What is the radiation resistance of an electric fundamental oscillator of length $\frac{\lambda_{0}} {10}$ ($\lambda_{0}$ is the free space wavelength)?
A) $$
8. 3 \Omega
$$
B) $$
2. 9 \Omega
$$
C) $$
0. 7 \Omega
$$
D) $$
3. 4 \Omega
$$
E) $$
9. 1 \Omega
$$
F) $$
6. 5 \... | [
"H",
"$$\n7. 9 \\Omega\n$$",
"H) $$\n7. 9 \\Omega\n$$"
] |
Topic: Heat Transfer.
Question: Try to compare the thermal resistance of the cylinder wall with that of a flat wall of the same material and thickness. If the temperature conditions are the same and the area of the plane is equal to the inner surface of the cylinder wall, the thermal resistance of the flat wall is comp... | [
"J",
"greater",
"J) greater"
] |
Topic: Solid State Physics.
Question: For a one-dimensional monoatomic lattice, under the simple harmonic approximation, consider that each atom interacts with all other atoms. Calculate the dispersion relation of the lattice wave______.
A) $$ M \omega^{2}=\sum_{m=1}^{\infty} \beta_{m} \left( e^{i q m a}+e^{-i q m a}-1... | [
"B",
"$$ - M \\omega^{2}=\\sum_{m=1}^{\\infty} \\beta_{m} \\left( e^{i q m a}+e^{-i q m a}-2 \\right) $$",
"B) $$ - M \\omega^{2}=\\sum_{m=1}^{\\infty} \\beta_{m} \\left( e^{i q m a}+e^{-i q m a}-2 \\right) $$"
] |
Topic: Physical Chemistry.
Question: The vapor pressure of a volatile liquid can be determined by slowly bubbling a known volume of gas through it at a known temperature and pressure. In an experiment, 5.00 L of $\mathrm{N_{2}}$ gas is passed through 7.2146 g of liquid benzene, $\mathrm{C}_{6} \mathrm{H}_{6},$ at 26.0 ... | [
"D",
"$$\n9 8. 7 \\mathrm{~ t o r r}\n$$",
"D) $$\n9 8. 7 \\mathrm{~ t o r r}\n$$"
] |
Topic: Communication Principles.
Question: The frequency range of a commercially broadcast FM signal is 88 to 108 MHz, with carrier swing of 125 kHz. Find the percentage modulation of the signal.
A) 125%
B) 50%
C) 110%
D) 57.1%
E) 93.8%
F) 90%
G) 75%
H) 100%
I) 83.3%
J) 62.5% | [
"I",
"83.3%",
"I) 83.3%"
] |
Topic: Electrodynamics.
Question: If radius vector of a point varies with time $t$ as $\vec { r } =\vec { b } t\left( 1-\alpha t \right) $ where $\vec { b } $ is a constant vector and a is a positive constant, then its
A) Magnitude of acceleration is changing but direction of acceleration is constant
B) Magnitude of ve... | [
"F",
"Magnitude of acceleration is constant but direction of acceleration is changing",
"F) Magnitude of acceleration is constant but direction of acceleration is changing"
] |
Topic: Quantum Mechanics.
Question: If you were to perform an equivalent of the basic NMR experiment on a free electron (a.k.a. an ESR or electron spin resonance experiment), what field strength would you need to produce the same electron resonance frequency as you get from a proton NMR experiment?
A) 10.1 mT field
B) ... | [
"B",
"2.3 mT field",
"B) 2.3 mT field"
] |
Topic: Electrochemistry.
Question: Consider a hydrogen electrode in HBr(aq) at 25°C operating at 1.45 bar. Estimate the change in the electrode potential when the solution is changed from 5.0 mmol dm$^{-3}$ to 15.0 mmol dm$^{-3}$ .
A) $$
7 2 \ \mathrm{m V}
$$
B) $$
4 1 \ \mathrm{m V}
$$
C) $$
9 0 \ \mathrm{m V}
$$
D) $... | [
"E",
"$$\n2 8 \\ \\mathrm{m V}\n$$",
"E) $$\n2 8 \\ \\mathrm{m V}\n$$"
] |
Topic: Thermodynamics.
Question: Protons of mass 1.67 × 10^-27 kg and moving with a velocity of 2 × 10^7 m \textbullet s^-1 strike a target of mass1 g and specific heat capacity 0.334 cal \textbullet g^-1 \textbullet C deg^-1. The proton stream corresponds to a current of 4.8\muA. At what rate does the temperatureof th... | [
"H",
"2.39°C",
"H) 2.39°C"
] |
Topic: Oil and Gas Field Development and Storage & Transportation Engineering.
Question: The total weight of the oil barrel is 300 kg, with a barrel diameter of 0.6 m and a height of 1.2 m. What is the density of the machine oil ?
A) $$
\rho=8 4 4 \mathrm{k g} / \mathrm{m}^{3}
$$
B) $$
\rho=8 5 0 \mathrm{k g} / \mathrm... | [
"A",
"$$\n\\rho=8 4 4 \\mathrm{k g} / \\mathrm{m}^{3}\n$$",
"A) $$\n\\rho=8 4 4 \\mathrm{k g} / \\mathrm{m}^{3}\n$$"
] |
Topic: Biophysics.
Question: In a FRET experiment designed to monitor conformational changes in T4 lysozyme, the fluorescence intensity fluctuates between 5000 and 10,000 counts per second.
Assuming that 7500 counts represents a FRET efficiency of 0.5 , what is the change in FRET pair separation distance during the rea... | [
"E",
"12 $Å$",
"E) 12 $Å$"
] |
Topic: Numerical Analysis.
Question: Compute $\sqrt[5]{1000}$ with accuracy $10^{-5}$.
A) 3.981072
B) 3.981076
C) 3.981070
D) 3.981075
E) 3.981073
F) 3.981074
G) 3.981079
H) 3.981077
I) 3.981078
J) 3.981071 | [
"A",
"3.981072",
"A) 3.981072"
] |
Topic: Mathematical Analysis.
Question: Evaluate $\lim_{x \to 0}\left(\left(\frac{ \sin(4 \cdot x) }{ 4 \cdot x }\right)^{\frac{ 1 }{ 3 \cdot x^2 }}\right)$.
A) e^{-\frac{14}{9}}
B) e^{-\frac{7}{9}}
C) e^{-\frac{8}{9}}
D) e^{-\frac{4}{9}}
E) e^{-\frac{2}{9}}
F) e^{-\frac{12}{9}}
G) e^{-\frac{10}{9}}
H) e^{-\frac{18}{9}... | [
"C",
"e^{-\\frac{8}{9}}",
"C) e^{-\\frac{8}{9}}"
] |
Topic: Analytical Chemistry.
Question: When $0.575 \times 10^{-2} kg$ of Glauber's salt ($Na_2SO_4\cdot 10 H_2O$) is dissolved in $3$ g water, we get $1$ $dm^3$ of a solution of density $1077.2 \:kg\: m^{-3}$. Calculate the molarity, molality and mole fraction of $Na_2SO_4$ in the solution:
A) $$Molarity (M) = 0.2502, ... | [
"C",
"$Molarity (M) = 0.2502$, $Molality (m) = 0.2402$, $Mole\\ fraction=4.304\\times 10^{-3}$",
"C) $Molarity (M) = 0.2502$, $Molality (m) = 0.2402$, $Mole\\ fraction=4.304\\times 10^{-3}$"
] |
Topic: Thermodynamics and Statistical Physics.
Question: $0.5$ mole each of two ideal gas $A \left( C _ { v , m } = \dfrac { 5 } { 2 } R \right)$ and $B \left( C _ { v , m } = 3 R \right)$ are taken in a container and expanded reversibly and adiabatically, during this process temperature of gaseous mixture decreas... | [
"G",
"$$-375R$$",
"G) $$-375R$$"
] |
Topic: Mass Transport and Separation Process in Chemical Engineering.
Question: Chloride samples are prepared for analysis by using $NaCl, KCl$ and $ NH_{4}Cl $ separately or as mixture. What minimum volume of $5$% by weight $AgNO_{3}$ solution (specific gravity $= 1.02\:g\:mL^{-1})$ must be added to a sample of $0.321... | [
"C",
"$20$ mL",
"C) $20$ mL"
] |
Topic: Antenna and Radio Communication.
Question: 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 ().
A) 5.140GHz
B) 2.983GHz
C) 4.872GHz
D) 1.875GHz
E) 3.529GHz
F) 4.125GHz
G) 3.659GHz
H... | [
"G",
"3.659GHz",
"G) 3.659GHz"
] |
Topic: Rigid Body Mechanics.
Question: Two point masses \( m \) and \( 2m \), moving in the same horizontal plane with speeds \( 2v \) and \( v \), respectively, strike a uniform bar of length \( 8m \) and mass \( M \), initially at rest; the mass \( m \) strikes at a point \( 2a \) to the left of the bar's center \( C... | [
"A",
"$$E=\\dfrac{3}{5}mv^{2}$$ and $$v_{c}=0$$ and $$\\omega =\\dfrac{v}{5a}$$",
"A) $$E=\\dfrac{3}{5}mv^{2}$$ and $$v_{c}=0$$ and $$\\omega =\\dfrac{v}{5a}$$"
] |
Topic: Communication Principles.
Question: If an audio baseband signal has a maximum frequency of 4.8 kHz and an information rate of 2.4 kb/s, what is the bandwidths for a 2ASK signal?
A) 9.6kHz
B) 2.4kHz
C) 8.0kHz
D) 1.2kHz
E) 3.2kHz
F) 4.8kHz
G) 5.6kHz
H) 6.4kHz
I) 4.0kHz
J) 7.2kHz | [
"F",
"4.8kHz",
"F) 4.8kHz"
] |
Topic: Computer Networks.
Question: For a 100Mb/s Ethernet switch, when the output port is not queued and an Ethernet frame (excluding the preamble) is forwarded using cut-through switching, the introduced forwarding delay is at least ( ).
A) $$
1. 8 3 \mu s
$$
B) $$
0. 6 9 \mu s
$$
C) $$
0. 5 5 \mu s
$$
D) $$
0. 0 7 \... | [
"E",
"$$\n0. 4 8 \\mu s\n$$",
"E) $$\n0. 4 8 \\mu s\n$$"
] |
Topic: Physical Chemistry.
Question: CuSO$_4.$5$H_2O$(s) $\rightleftharpoons$ CuSO$_4$.3H$_2O$(s) + 2H$_2O$(g); $k_p$ = 4 $10^{4}$ atm$^2.$ If the vapour pressure of water is 38 torr then percentage of relative humidity is : (Assume all data at constant temperature)
A) 20
B) 40
C) 50
D) 30
E) 25
F) 10
G) 4
H) 35
I) Non... | [
"B",
"40",
"B) 40"
] |
Topic: Physical Oceanography.
Question: If a tsunami forms in Hawaii, how long will it take to reach the west coast of the United States? Assume an average water depth of 4000 meters and a distance of approximately 3800 km between the two locations.
A) 5.7 hours
B) 5.2 hours
C) 2.8 hours
D) 7 hours
E) 4.8 hours
F) 4.2 ... | [
"H",
"5 hours",
"H) 5 hours"
] |
Topic: Atomic and Molecular Physics.
Question: Electron transition in ${ He }^{ + }$ ion takes from ${ n }_{ 2 }$ to ${ n }_{ 1 }$ shell such that:$2{ n }_{ 2 }+3{ n }_{ 1 }=18$ ....(i)$2{ n }_{ 2 }-3{ n }_{ 1 }=6$ ....(ii)What will be the total number of photons emitted when electrons ... | [
"I",
"$$10$$",
"I) $$10$$"
] |
Topic: Fuzzy Mathematics.
Question: Let $U=\{u_{1}, u_{2}, u_{3}\}$ and $V=\{v_{1}, v_{2}, v_{3}, v_{4}\}$, and let
$$
R=\left\{ \begin{matrix} {{{0.2}}} & {{{0.7}}} & {{{0}}} & {{{0.1}}} \\ {{{0}}} & {{{1}}} & {{{0.3}}} & {{{0.2}}} \\ {{{0.4}}} & {{{0.5}}} & {{{0}}} & {{{0.6}}} \\ \end{matrix} \right\}, \quad R \in \m... | [
"G",
"$T_{R}(A)=(0.2,1,0.3,0.2),T_{R}(B)=(0.4,0.5,0.3,0.6)$",
"G) $T_{R}(A)=(0.2,1,0.3,0.2),T_{R}(B)=(0.4,0.5,0.3,0.6)$"
] |
Topic: Fluid Machinery and Engineering.
Question: In a small hydroelectric power station, water flows into the turbine at a speed of 3 m/s and exits at a speed of 1 m/s. The outflow water level is 1.6 m lower than the inflow water level, and the water flow rate is 1 m³/s. If 75% of the water's energy is provided to the... | [
"F",
"$\\frac{3}{25},\\ \\frac{95}{11}$",
"F) $\\frac{3}{25},\\ \\frac{95}{11}$"
] |
Topic: Ordinary Differential Equations.
Question: The general solution of the equation $y''+y= sin 2 x$ is
A) $y= C_1 sin x + C_2 cos x - \frac{cos 2x}{4}$
B) $y= C_1 x sin x + C_2 cos x - frac{x cos 2x}{2}$
C) $y= C_1 sin x + C_2 cos x + frac{x cos 2x}{2}$
D) $y= C_1 sin x + C_2 cos x - \frac{sin 2x}{6}$
E) $y= C_1 si... | [
"J",
"$y= C_1 sin x + C_2 cos x - frac{sin 2x}{3}$",
"J) $y= C_1 sin x + C_2 cos x - frac{sin 2x}{3}$"
] |
Topic: Engineering Fluid Mechanics.
Question: To measure the flow rate $q_{\mathrm{V}}=0.30 \mathrm{m}^{3} / \mathrm{s}$, given that the weir height $h_{\mathrm{p}}=0.5 \mathrm{m}$ limits the head $H$ to be below 0.2m, try designing the weir width $b$ for a rectangular thin-plate weir is ().
A) 2.10m
B) 1.50m
C) 2.05m
... | [
"E",
"1.73m",
"E) 1.73m"
] |
Topic: Electromagnetic Field and Microwave Technology.
Question: It is known that in a vacuum, there is a uniform plane wave with an electric field strength $\boldsymbol{E}=E_{x} \boldsymbol{e}_{x}+E_{y} \boldsymbol{e}_{y}$. Here, $E_{x}=100 \cos (2 \pi \times 10^{8} t - 0.21 z) \; \mathrm{V/m}$, and $E_{y}=100 \cos (2... | [
"D",
"$$\n\\dot{H}=0. 1 8 7 e^{-0. 2 1 z} \\big( \\boldsymbol{e}_{y}-\\mathrm{j} e_{x} \\big) \\, \\mathrm{A / m}\n$$",
"D) $$\n\\dot{H}=0. 1 8 7 e^{-0. 2 1 z} \\big( \\boldsymbol{e}_{y}-\\mathrm{j} e_{x} \\big) \\, \\mathrm{A / m}\n$$"
] |
Topic: Functions of Complex Variables.
Question: Determine the order of the following functions at the zero point $z=0$. (1) $z^{2} ( e^{z^{2}}-1 )$; (2) 6sin $z^{3} + z^{3} ( z^{6}-6 )$.
A) $$5$$
$$10$$
B) $$2$$
$$15$$
C) $$3$$
$$12$$
D) $$4$$
$$10$$
E) $$4$$
$$15$$
F) $$4$$
$$13$$
G) $$6$$
$$15$$
H) $$3$$
$$15$$
I) $... | [
"E",
"$$4$$\n$$15$$",
"E) $$4$$\n$$15$$"
] |
Topic: Finance.
Question: Mr. Green, who is 35 years old, has just purchased a new car. The car is classified as symbol 5, and is kept in 06 territory. He has had one accident in the last three years. If he uses the new car for business, what is the difference in cost between $50-deductible and $100-deductible collisio... | [
"E",
"$45",
"E) $45"
] |
Topic: Signal and Information Processing.
Question: The differential equation for a linear causal continuous system is:
$$
y''(t) + 2y'(t) + y(t) = f'(t) + f(t),
$$
with initial conditions $y(0-) = 1$ and $y'(0-) = 2$, and the excitation is $f(t) = e^{-t}u(t)$.
Then the complete response $y(t)$ is ( ).
A) $y(t)=(4t+1)e... | [
"H",
"$y(t)=(4t+1)e^{-t}u(t)$",
"H) $y(t)=(4t+1)e^{-t}u(t)$"
] |
Topic: Acoustics.
Question: The sound from a very high burst of fireworks takes $ 5\,s $ to arrive at the observer. The burst occurs $ 1662\,m $ above the observer and travels vertically through two stratifier layers of air, the top one of thickness $ d_1 $ at $ 0^{\circ}\,C $ and the bottom one of thickness $ d_2 $ a... | [
"H",
"$$ d_2 = 342\\,m $$",
"H) $$ d_2 = 342\\,m $$"
] |
Topic: Traffic Information Engineering and Control.
Question: The maximum speed with which a car can be driven safely along a curved road of radius 17.32 m and banked at $30^{\circ}$ with the horizontal is $ [ g = 10 m /s ^{2} ] $
A) 6 m /s
B) 20 m /s
C) 7.5 m /s
D) 12.5 m /s
E) 8.5 m /s
F) 4.5 m /s
G) 10 m /s
H) 5 m ... | [
"H",
"5 m /s",
"H) 5 m /s"
] |
Topic: Electrodynamics.
Question: Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: [position] = $[position]=[X^{\alpha}];[speed]=... | [
"B",
"$p+q-r=\\beta$ and $\\alpha+p=2\\beta$",
"B) $p+q-r=\\beta$ and $\\alpha+p=2\\beta$"
] |
Topic: Engineering Fluid Mechanics.
Question: Two wheels of radii $R$ and 3$R$ are coupled by using a conveyor belt. At $t = 0$ small wheel starts which angular acceleration $\pi \mathrm { rad } / \mathrm { s } ^ { 2 } .$ The time after which bigger wheel has angular speed of 100$\mathrm { rpm }$ is
A) 25$\mathrm { s }... | [
"B",
"5$\\mathrm { s }$",
"B) 5$\\mathrm { s }$"
] |
Topic: Discrete Mathematics.
Question: We now define an algorithm: The definition of a(n) is the "amusical permutation" of the nonnegative numbers: a(2n)=3n, a(4n+1)=3n+1, a(4n-1)=3n-1. Given the input x_list (a series of values): [62, 63, 64, 65, 66, 67, 68, 69, 70, 71], determine the corresponding output sequence y_l... | [
"A",
"[93, 47, 96, 49, 99, 50, 102, 52, 105, 53]",
"A) [93, 47, 96, 49, 99, 50, 102, 52, 105, 53]"
] |
Topic: Materials Processing Engineering.
Question: At approximately what temperature would a specimen of y-iron have to be carburized for 4 h to produce the same diffusion result as carburization at 1000°C for 12 h?
A) $$
1 0 0 0^{\circ} \mathrm{C}
$$
B) $$
1 0 5 0^{\circ} \mathrm{C}
$$
C) $$
9 5 0^{\circ} \mathrm{C}
$... | [
"J",
"$$\n1 1 0 8^{\\circ} \\mathrm{C}\n$$",
"J) $$\n1 1 0 8^{\\circ} \\mathrm{C}\n$$"
] |
Topic: Geotechnical Engineering.
Question: A gravity retaining wall is 6.1 meters high, with a vertical, smooth back, and a level backfill surface. The backfill consists of medium sand, with an internal friction angle of 30° and a unit weight of $17.3\mathrm{kN/m^{3}}$. Try using the wedge method to calculate the magni... | [
"F",
"$$\n1 0 7. 2 \\mathbf{k N} / \\mathbf{m}\n$$",
"F) $$\n1 0 7. 2 \\mathbf{k N} / \\mathbf{m}\n$$"
] |
Topic: Manufacturing Automation.
Question: There is a deep groove ball bearing with a basic rated life of 8000h, when its load is increased by 1 times, and the speed is 12 of the original speed, other conditions remain the same, then how long is the basic rated life of the bearing?
A) 16000h
B) 12000h
C) 6000h
D) 3200h... | [
"J",
"2000h",
"J) 2000h"
] |
Topic: Group Theory.
Question: We now define an algorithm: The definition of a(n) is: Follow n+1 by n. Also, this sequence is (essentially) the Molien series of the 2-dimensional quaternion group Q_8. Given the input x_list (a series of values): [65, 66, 67, 68, 69, 70, 71, 72, 73, 74], determine the corresponding outp... | [
"C",
"[32, 34, 33, 35, 34, 36, 35, 37, 36, 38]",
"C) [32, 34, 33, 35, 34, 36, 35, 37, 36, 38]"
] |
Topic: Fluid Flow and Heat Transfer in Chemical Engineering.
Question: A plate-and-frame filter press operates under constant pressure to filter a water suspension with a solid content of 0.1 kg solid per kg of suspension. The porosity of the filter cake is $\varepsilon = 0.4$; the density of the particles is $\rho_{\m... | [
"I",
"$0.11m^3$",
"I) $0.11m^3$"
] |
Topic: Communication Principles.
Question: In a certain PAM baseband transmission system, disregarding noise, the output signal of the receiving filter is
$y ( t )=\\sum_{n=0}^{\\infty} b_{n} h ( t-n T_{\\mathrm{s}} )$
where $\\{b_{0}, b_{1}, b_{2}, \\cdots\\}$ is the amplitude sequence transmitted by the PAM system. G... | [
"E",
"$$\n\\begin{array} {l} {{h_{0}=1, ~ h_{\\pm1}=\\frac{1} {2}, ~ h_{\\pm2}=0}} \\\\ {{y_{0}=b_{0}+\\frac{1} {2} b_{1}, ~ ~ y_{1}=b_{1}+\\frac{b_{0}+b_{2}} {2}, ~ ~ y_{2}=b_{2}+\\frac{b_{1}+b_{3}} {2}}} \\\\ \\end{array}\n$$",
"E) $$\n\\begin{array} {l} {{h_{0}=1, ~ h_{\\pm1}=\\frac{1} {2}, ~ h_{\\pm2}=0}} \... |
Topic: Oil and Gas Field Development and Storage & Transportation Engineering.
Question: The stratum's shear modulus is 6 GPa, with a difference of 12 MPa between the horizontal stress and the bottom hole pressure. How much does this cause the wellbore diameter of 10 cm to contract?
A) 0.2mm
B) 0.1m
C) 0.5mm
D) 10mm
E)... | [
"G",
"0.1mm",
"G) 0.1mm"
] |
Topic: Power Systems and Automation.
Question: A three-phase transformer, $\mathrm{S_{N}=750 \, kV \cdot A \, , \, \ U_{N1} / U_{N2}=10000 \, V / 400 \, V \, , \, \ Y, \, \ yn0 \,}$ connection, yielded $\mathrm{I}_{0}=60 \, \mathrm{A} \; , \; \; \mathrm{p}_{0}=3800 \, \mathrm{w}$ during a no-load test on the low-voltag... | [
"E",
"2394Ω,5.85Ω",
"E) 2394Ω,5.85Ω"
] |
Topic: Number Theory.
Question: An integer $n$ is fixed with respect to $m$ if $n$ and $n^2$ leave the same remainder when divided by $m.$ Let $M$ be the largest integer such that $1000$ is fixed with respect to $M.$ Find the number of positive integer divisors of $M.$
A) 129
B) 130
C) 122
D) 119
E) 112
F) 121
G) 120
H... | [
"H",
"128",
"H) 128"
] |
Topic: Fluid Physics.
Question: Outside a stationary cylinder with a radius of $a$, there is a stationary point vortex with strength $\varGamma$. Let the distance from the point vortex to the center of the cylinder be $b$. Give the resultant force exerted by the fluid on the unit length of the cylinder.
( Assume the fl... | [
"I",
"$$\n\\frac{\\rho\\Gamma^{2} a^{2}} {2 \\pi b \\left( b^{2}-a^{2} \\right)}\n$$",
"I) $$\n\\frac{\\rho\\Gamma^{2} a^{2}} {2 \\pi b \\left( b^{2}-a^{2} \\right)}\n$$"
] |
Topic: Atomic and Molecular Physics.
Question: The dissociation energy of a hydrogen molecule is 4.478 eV, and the dissociation energy of a hydrogen molecular ion is 2.651 eV. Based on this information, calculate the first ionization energy of the hydrogen molecule ().
A) 13.894
B) 12.129
C) 6.827
D) 15.425
E) 18.355
F... | [
"D",
"15.425",
"D) 15.425"
] |
Topic: Electrical Theory and New Technologies.
Question: A copper sphere of $10cm$ diameter is lowered into a water filled hemispherical copper vessel of $20cm$ diameter so that the sphere and the vessel becomes concentric. Electrical conductivity of water is $\sigma={10}^{-3}S/m$. The electrical resistance between the... | [
"F",
"$$1591.6\\Omega$$",
"F) $$1591.6\\Omega$$"
] |
Topic: Stochastic Processes.
Question: Calls arriving at the exchange (with infinitely many channels) follow a Poisson process with an arrival rate of $\lambda$, and each call duration follows an exponential distribution with a mean of $1 / \mu$. Let $X(t)$ be the number of calls in progress at time $t$. What is the pr... | [
"C",
"$$\n\\begin{array} {c} {{{P \\{X ( t )=0 \\}=\\operatorname{e x p} \\Bigl[-\\frac{\\lambda} {\\mu} ( 1-\\mathrm{e}^{-\\mu t} ) \\Bigr]}}} \\\\ \\end{array}\n$$",
"C) $$\n\\begin{array} {c} {{{P \\{X ( t )=0 \\}=\\operatorname{e x p} \\Bigl[-\\frac{\\lambda} {\\mu} ( 1-\\mathrm{e}^{-\\mu t} ) \\Bigr]}}} \\... |
Topic: Nuclear Energy and Reactor Technology.
Question: Given a heavy water-uranium reactor core with a $k_{\infty} = 1.28$, $L^{2} = 1.8 \times 10^{-2} \mathrm{~ m^{2}}$, and $\tau = 1.20 \times 10^{-2} \mathrm{~ m^{2}}$. According to the single-group theory, correct the critical equation for the single-group theory. ... | [
"E",
"$$0.7813,~0.68$$",
"E) $$0.7813,~0.68$$"
] |
Topic: Radiochemistry.
Question: To prepare 10 mL of $Na_3$P $^{32}$ $O_{4}$ aqueous solution with a specific radioactivity of $3 \times 10^{4}$ pulses/min·mL, how much $Na_3$P $^{32}$ $O_{4}$ solution with a specific radioactivity of 2.7 millicurie/mL is needed? The counting efficiency is 0.005.
A) $2.5 \times 10^{-3}... | [
"C",
"$10^{-3}$ milliliters",
"C) $10^{-3}$ milliliters"
] |
Topic: Operating Systems.
Question: Assuming the size of a disk block is 1KB, for a 540MB hard disk, how much storage space is the minimum required for its File Allocation Table (FAT)?
A) $$
1 4 0 0 \mathrm{K B}
$$
B) $$
1 3 5 0 \mathrm{K B}
$$
C) $$
1 4 7 5 \mathrm{K B}
$$
D) $$
1 8 0 0 \mathrm{K B}
$$
E) $$
1 2 0 0 \... | [
"B",
"$$\n1 3 5 0 \\mathrm{K B}\n$$",
"B) $$\n1 3 5 0 \\mathrm{K B}\n$$"
] |
Topic: Physical Chemistry.
Question: Which of the following aqueous solutions produce the same osmotic pressure
A) 1.0 \,g \,of \,a \,non - electrolyte \,solute \,(X) \,in \,200 \,ml \,solution \,(Molar \,mass \,of \,X = 200)
B) $1.0 \,g$ of a non - electrolyte solute (X) in $150 \,ml$ solution (Molar mass of $X = 200$... | [
"D",
"$1.0 \\,g$ of a non - electrolyte solute (X) in $50 \\,ml$ solution (Molar mass of $X = 200$)",
"D) $1.0 \\,g$ of a non - electrolyte solute (X) in $50 \\,ml$ solution (Molar mass of $X = 200$)"
] |
Topic: Ecology.
Question: Orcas consume sea lions which consume mackerel (fish) which consume capelin (fish) which comsume phytoplankton. How many pounds of phytoplankton would be needed to support one orca (extimated 4000 lbs.)?
A) 400,000 lbs
B) 400 lbs
C) 100,000 lbs.
D) 600,000 lbs.
E) 4000 lbs
F) 300,000 lbs.
G) 8... | [
"A",
"400,000 lbs",
"A) 400,000 lbs"
] |
Topic: Rigid Body Mechanics.
Question: A solid sphere of radius $R$ is placed on smooth horizontal surface. A horizontal force $'F'$ is applied at height $'h'$ from the lowest point. For the maximum acceleration of centre of mass, which is correct ?
A) $$h = \frac{3R}{2}$$
B) $$h = R$$
C) $$h = \frac{R}{2}$$
D) $$h = \... | [
"G",
"No relation between $h$ and $R$.",
"G) No relation between $h$ and $R$."
] |
Topic: Solid State Physics.
Question: Titanium (Ti) has an HCP crystal structure and a density of $4.51 g/cm^{3}$. What is the volume of its unit cell in cubic meters?
A) $$
1. 0 5 8 \times1 0^{-2 8} \, \mathrm{m}^{3} / \mathrm{u n i t \, c e l l}
$$
B) $$
1 . 9 7 \times 1 0^{-2 9} \, \mathrm{m}^{3} / \mathrm{u n i t \... | [
"A",
"$$\n1. 0 5 8 \\times1 0^{-2 8} \\, \\mathrm{m}^{3} / \\mathrm{u n i t \\, c e l l}\n$$",
"A) $$\n1. 0 5 8 \\times1 0^{-2 8} \\, \\mathrm{m}^{3} / \\mathrm{u n i t \\, c e l l}\n$$"
] |
Topic: Circuits and Systems.
Question: In the laboratory, you test the frequency characteristics of a single transistor amplifier circuit. When $f=5$ kHz, $10$ kHz, $20$ kHz, $30$ kHz, $40$ kHz, the voltage gain is 100. When $f=500$ kHz, the voltage gain drops to 10. What is the upper cutoff frequency $f_{\mathrm{H}}$?... | [
"J",
"50 kHz",
"J) 50 kHz"
] |
Topic: Signal and Information Processing.
Question: The frequency response of the continuous-time causal LTI system is $\mathbf{H} ( \omega)=\omega^{2} / ( 5-\omega^{2}+2 \mathbf{j} \omega)$,then the unit step response of the system $s(t)$ is ( ).
A) $= \mathrm{e}^{-4t} ( \frac{1} {3} \operatorname{s i n} 4 t - \operat... | [
"H",
"$= \\mathrm{e}^{-t} ( \\frac{1} {2} \\operatorname{s i n} 2 t-\\operatorname{c o s} 2 t ) u ( t )$",
"H) $= \\mathrm{e}^{-t} ( \\frac{1} {2} \\operatorname{s i n} 2 t-\\operatorname{c o s} 2 t ) u ( t )$"
] |
Topic: Physical Chemistry.
Question: The following reaction has $\Delta_{\mathrm{r}} G_{\mathrm{m}}^{\Theta}( 630 \, \mathrm{K} )=44.3 \, \mathrm{kJ} \cdot \mathrm{mol}^{-1}$.
$2 \mathrm{HgO} (s)= 2 \mathrm{Hg} (g) + \mathrm{O}_{2} (g)$.
If the container contains $\mathrm{O_{2} (g)}$ at standard pressure $p^{\Theta}$ b... | [
"G",
"$$\n1 4 5 2 \\, \\mathrm{P a}\n$$",
"G) $$\n1 4 5 2 \\, \\mathrm{P a}\n$$"
] |
Topic: Water conservancy and Hydropower Engineering.
Question: A dam foundation is to be built upon a strong limestone with the following characteristics: Uniaxial compressive strength of 80 MPa. A RQD of 80%.Spacing between joints is 80 mm.The joint set has been described as follows:Average discontinuity length is 4 m... | [
"G",
"$RMR=53$",
"G) $RMR=53$"
] |
Topic: Circuits and Systems.
Question: The electric field is perpendicular to the length of the length-extending chip made of PZT-4, with a density and compliance constants of $p=7.5×10^{3}$ kg/m$^{3}$, $s^E_{11}=12.3×10^{-12}$ m$^{2}$/N, $s^D_{33}=7.9×10^{-12}$ m$^{2}$/N. If the fundamental resonant frequency is 30 kH... | [
"D",
"l=5.48cm",
"D) l=5.48cm"
] |
Topic: Probability and Statistics.
Question: Your statistical mechanics class has twenty-five students. What is the probability that at least two classmates have the same birthday?
A) 0.5837
B) 0.7214
C) 0.4587
D) 0.4712
E) 0.6894
F) 0.5128
G) 0.6105
H) 0.4925
I) 0.5343
J) 0.6421 | [
"A",
"0.5837",
"A) 0.5837"
] |
Topic: Mechatronic Engineering.
Question: The force that can be applied by the actuator will depend on its stroke. Under what condition of a magnetic force (N), a pull-type linear solenoid actuator from Magnet Schultz (R16xR16, 24V10%) is specified when the duty cycle is 10% and the maximum time of 60 s with a stroke of... | [
"D",
"2.6",
"D) 2.6"
] |
Topic: Thermodynamics.
Question: A Pendulum on Mars. A certain simple pendulum has a period on the earth of
1.60 s. What is its period on the surface of Mars, where \(g=3.71 \mathrm{~m} /
\mathrm{s}^{2} ?\)
A) 2.57
B) 2.04
C) 2.45
D) 2.72
E) 2.68
F) 2.34
G) 2.41
H) 2.13
I) 2.29
J) 2.61 | [
"A",
"2.57",
"A) 2.57"
] |
Topic: Theoretical Fluid Mechanics.
Question: Obtain a relevant stream function to each of the following sets of velocity components of steady, incompressible flow:
$$
\begin{array} {c} {{{\mathrm{( i )} \ \ u=-\ c x / y}}} \\ {{{\mathrm{~ v=c ~ l n ~ x y}}}} \\ \end{array}
$$
$$
\begin{array} {r l} {{{\mathrm{( i i )}... | [
"C",
"$$\n\\psi=-\\ \\mathbf{c} x \\ \\mathbf{l n} \\ x y+\\mathbf{c} x+\\mathbf{c}_{2}\n$$\n$$\n\\psi={\\frac{1} {2}} \\ ( y^{2}-x^{2} )+x y+c\n$$\n$$\n\\psi=2 \\mathbf{c} x y+\\mathbf{c}_{1}\n$$",
"C) $$\n\\psi=-\\ \\mathbf{c} x \\ \\mathbf{l n} \\ x y+\\mathbf{c} x+\\mathbf{c}_{2}\n$$\n$$\n\\psi={\\frac{1} {... |
Topic: Electrodynamics.
Question: A plane light wave of intensity $I = 0.20 \,W \,cm^{-2}$ falls on a plane mirror surface with reflection coefficient $\rho = 0.8$. The angle of incidence is $45^o$. In terms of corpuscular theory, find the magnitude of the normal pressure exerted on that surface.
A) $$0.5 \,N \,cm^{-2}... | [
"F",
"$$1.2 \\,N \\,cm^{-2}$$",
"F) $$1.2 \\,N \\,cm^{-2}$$"
] |
Topic: Computer Networks.
Question: On a certain satellite channel, the sender transmits frames with a length of 512B from one direction, and the data transmission rate of the sender is 64kb/s. The receiver at the other end returns a very short acknowledgment frame. Given that the one-way propagation delay of the satel... | [
"C",
"$$\n6. 8 \\mathrm{k b / s}\n$$\n$$\n47.5 \\mathrm{k b / s}\n$$\n$$\n64\\mathrm{k b / s}\n$$\n$$\n64\\mathrm{k b / s}\n$$",
"C) $$\n6. 8 \\mathrm{k b / s}\n$$\n$$\n47.5 \\mathrm{k b / s}\n$$\n$$\n64\\mathrm{k b / s}\n$$\n$$\n64\\mathrm{k b / s}\n$$"
] |
Topic: Relativity.
Question: A stationary observer at the Schwarzschild radius $r_{1}$ releases free-falling hail inward with an initial velocity $V$. What is the expression for the velocity measured by a local stationary observer when the hail reaches the Schwarzschild radius $r_{2}$ ?
A) $$
\sqrt{1+\frac{1-2 M / r_{2... | [
"C",
"$$\nV_2 = \\sqrt{1-\\frac{1-2 M / r_{2}} {1-2 M / r_{1}} \\left( 1-V^{2} \\right)}\n$$",
"C) $$\nV_2 = \\sqrt{1-\\frac{1-2 M / r_{2}} {1-2 M / r_{1}} \\left( 1-V^{2} \\right)}\n$$"
] |
Topic: Theoretical Mechanics.
Question: To vertically project an object upwards from the ground to a height equal to the Earth's radius while only considering Earth's gravity, which is inversely proportional to the square of the distance from the object's center to the Earth's center, what initial velocity should be gi... | [
"H",
"$$\n7. 9 \\mathrm{~ k m / s}\n$$",
"H) $$\n7. 9 \\mathrm{~ k m / s}\n$$"
] |
Topic: Geometry and Topology.
Question: Forestria is a world made when two regular tetrahedrons of side length 100 km are combined among a common face. Fox lives on the center of one face, and Squirrel lives on the center of another face that does not share an edge with Fox's face. Fox wishes to ambush Squirrel, and ca... | [
"B",
"100",
"B) 100"
] |
Topic: Electrodynamics.
Question: A metal rod $AB$ of length $l$ is rotated with a constant angular velocity $\omega$ about an axis passing through $O$ and normal to its length. Potential difference between ends of rod in absence of external magnetic field is: (where $e=$ electric charge)
A) $$\dfrac{m\omega^{2}l^{2}}{... | [
"D",
"$$\\dfrac{m\\omega^{2}l^{2}}{4e}$$",
"D) $$\\dfrac{m\\omega^{2}l^{2}}{4e}$$"
] |
Topic: Geotechnical Engineering.
Question: In a seismic zone with an intensity of $8$, sand needs to be compacted to a relative density $D_{r}=0.7$ or higher. Tests show that the maximum dry density of sand from a certain site is $\rho_{\mathrm{dmax}}=1.96 \mathrm{g/cm}^{3}$ and the minimum dry density is $\rho_{\mathr... | [
"F",
"$$\n1. 7 8 \\mathrm{g / c m}^{3}\n$$",
"F) $$\n1. 7 8 \\mathrm{g / c m}^{3}\n$$"
] |
Topic: Rigid Body Mechanics.
Question: A block of mass 10 kg is released on a fixed wedge inside a cart which is moving with constant velocity 10 $\displaystyle ms^{-1}$ towards right. There is no relative motion between block and cart. Then work done by normal reaction on block in two seconds from ground frame will be... | [
"D",
"$$960 J$$",
"D) $$960 J$$"
] |
Topic: Power Electronics and Electrical Drives.
Question: A solenoid of inductance $L$ and resistance $r$ is connected in parallel to a resistance $R$ and a battery of emf $E$. Initially if the switch is closed for a long time and at $t=0$, then the :
A) current through solenoid at any time $t$, after opening the switc... | [
"D",
"current through solenoid at any time $t$, after opening the switch is $\\dfrac{E}{r}e^{-(R+r)t/L}$",
"D) current through solenoid at any time $t$, after opening the switch is $\\dfrac{E}{r}e^{-(R+r)t/L}$"
] |
Topic: Communication Principles.
Question: A bipolar rectangular non-return-to-zero 2PAM signal is subject to interference from power spectral density of $n_{0}/2$ additive white Gaussian noise $n_{w}(t)$. Given that the probabilities of transmitting a positive polarity pulse $S_{1} (t)$ and a negative polarity pulse $... | [
"G",
"$n_{0}ln2/4$",
"G) $n_{0}ln2/4$"
] |
Topic: Electromagnetic Field and Microwave Technology.
Question: When a uniform plane wave is perpendicularly incident from free space onto a certain medium plane at $( z=0 )$, a standing wave is formed in the free space. It is known that the standing wave ratio is 2.7 and a node appears on the medium plane. Find the d... | [
"G",
"$\\varepsilon_{2}=2. 7^{2} \\varepsilon_{0} \\approx7. 3 \\varepsilon_{0} ($ or $\\approx6. 4 7 \\times1 0^{-1 1} ) \\quad\\mathrm{F / m}$",
"G) $\\varepsilon_{2}=2. 7^{2} \\varepsilon_{0} \\approx7. 3 \\varepsilon_{0} ($ or $\\approx6. 4 7 \\times1 0^{-1 1} ) \\quad\\mathrm{F / m}$"
] |
Topic: Management Science and Engineering.
Question: The daily water pump delivery required by the dishwasher is 8 units, with a standard deviation in demand of 3 units, a lead time of 4 days, and a service level of 95%. The reorder point is ( ).
A) around 46 units
B) approximately 32 units
C) around 25 units
D) approx... | [
"F",
"More than 40 units",
"F) More than 40 units"
] |
Topic: Theoretical Optics.
Question: A point object is situated at a distance of 36 cm from the centre of the sphere of radius 12 cm and refractive index 1.5. Locate the position of the image due to refraction through sphere.
A) 18 cm from the surface
B) 20 cm from the centre
C) 12 cm from the centre
D) 36 cm from the ... | [
"J",
"18 cm from the centre.",
"J) 18 cm from the centre."
] |
Topic: Probability and Statistics.
Question: Each box contains 20 glass cups, with probabilities of having 0, 1, and 2 defective cups being 0.8, 0.1, and 0.1, respectively. A customer randomly selects a box and then randomly takes 4 glass cups from the box. If there are no defective cups, the customer buys the box; oth... | [
"I",
"0.943",
"I) 0.943"
] |
Topic: Electromagnetic Field and Microwave Technology.
Question: 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?
A) $$
\varepsilon_{r2}=9 \varepsilo... | [
"A",
"$$\n\\varepsilon_{r2}=9 \\varepsilon_{r 1}\n$$",
"A) $$\n\\varepsilon_{r2}=9 \\varepsilon_{r 1}\n$$"
] |
Topic: Fluid Machinery and Engineering.
Question: Given that the diameter $d$ at the inlet cross-section of a certain power plant's spiral casing is 6200mm, the static pressure head at the center of this cross-section is measured to be $60 \mathrm{m}$, the flow rate $Q$ through the turbine is 123m$^3/\mathrm{s}$, and t... | [
"F",
"62.36m",
"F) 62.36m"
] |
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