question stringlengths 152 5.02k | answers listlengths 3 3 |
|---|---|
Topic: Textile Chemistry and Dyeing Engineering.
Question: Assume that the cotton yarn count is represented by 𝑁_𝑡, the cotton yarn English count is represented by 𝑁_𝑒, the standard moisture regain for cotton yarn in tex is 𝑊_𝑘e=8.5%, and the standard moisture regain for cotton yarn in English count is 𝑊_𝑘t=9.8... | [
"G",
"583",
"G) 583"
] |
Topic: Fluid Machinery and Engineering.
Question: A uniform flow with a depth of 1mm passes over the glass roof. If the temperature is 15°, and the roof slope is 0.08, what is the flow rate per meter of the roof?
A) $$
q \,=\, 0. 0 0 0 1 2 0 {\mathrm{m}}^{3} / ( {\mathrm{s}} \cdot{\mathrm{m}} )
$$
B) $$
q \,=\, 0. 0 0 ... | [
"B",
"$$\nq \\,=\\, 0. 0 0 0 2 3 0 {\\mathrm{m}}^{3} / ( {\\mathrm{s}} \\cdot{\\mathrm{m}} )\n$$",
"B) $$\nq \\,=\\, 0. 0 0 0 2 3 0 {\\mathrm{m}}^{3} / ( {\\mathrm{s}} \\cdot{\\mathrm{m}} )\n$$"
] |
Topic: Physical Chemistry.
Question: The partial molar volumes of propanone and trichloromethane in a mixture in which the mole fraction of CHClg is 0.4693 are 74.166 cm3 moll and 80.235 cm3 moll,respectively. What is the volume of a solution of total mass 1.000 kq?
A) $$
{7 8 2. 2 \, \mathrm{c m}^{3}}
$$
B) $$
{8 5 7.... | [
"H",
"$$\n{8 8 6. 8 \\, \\mathrm{c m}^{3}}\n$$",
"H) $$\n{8 8 6. 8 \\, \\mathrm{c m}^{3}}\n$$"
] |
Topic: Physical Chemistry.
Question: The equilibrium constant for the following equilibrium is given at $0^\circ C$.
$N{a_2}HP{O_4}.12{H_2}O \rightleftharpoons N{a_2}HP{O_4}.7{H_2}O(s) + 5{H_2}O(g),$ ${K_p} = 31.25 \times {10^{ - 23}}$
At equilibrium what will be partial pressure of water vapour:
A) $2 \times 10^{-3}$... | [
"B",
"$\\frac {1}{5} \\times 10^{-3}$ atm",
"B) $\\frac {1}{5} \\times 10^{-3}$ atm"
] |
Topic: Physical Chemistry.
Question: Enthalpy change for the following reaction has been given as follows:
$$\mathrm { M } _ { ( \mathrm { g } ) } \longrightarrow \mathrm { M } _ { ( \mathrm { g } ) } ^ { 2 + } + 2 \mathrm { e } ^ { - } \quad \Delta \mathrm { H } = 280 \mathrm { KJ } / \mathrm { mole }$$
$\mathrm { M }... | [
"F",
"$\\mathrm { IP } _ { 2 }$ of $\\mathrm { M } _ { ( \\mathrm { g } ) }$ is 280$\\mathrm { KJ } / \\mathrm { mole }$",
"F) $\\mathrm { IP } _ { 2 }$ of $\\mathrm { M } _ { ( \\mathrm { g } ) }$ is 280$\\mathrm { KJ } / \\mathrm { mole }$"
] |
Topic: Fundamentals of Dynamics and Control.
Question: A bob of mass $2m$ hangs by a string attached to the block of mass $m$ of a spring block system. The whole arrangement is in a state of equilibrium. The bob of mass $2m$ is pulled down slowly by a distance $ x_0 $ and released.Then:
A) the motion will remain simple... | [
"D",
"the motion will remain simple harmonic for $\\displaystyle x_0 \\le \\frac {3mg} {k} $",
"D) the motion will remain simple harmonic for $\\displaystyle x_0 \\le \\frac {3mg} {k} $"
] |
Topic: Polymer Physics.
Question: Assuming a polymer sample contains three components with relative molecular masses of 10,000, 20,000, and 30,000, the number-average relative molecular mass $M_{\mathrm{n}}$ of the sample is measured to be 20,000, and the weight-average relative molecular mass $M_{\mathrm{w}}$ is 23,00... | [
"H",
"$W_1=0.15,W_2=0.4,W_3=0.45$",
"H) $W_1=0.15,W_2=0.4,W_3=0.45$"
] |
Topic: Power Electronics and Electrical Drives.
Question: If an alternating current $i=i_{m} \sin \omega t$ is flowing through a capacitor then voltage drop $\Delta V_{C}$ across capacitor $C$ will be?
A) -\dfrac{i_{m}}{\omega C} \cos \left(\omega t - \dfrac{\pi}{2}\right)
B) -\dfrac{i_{m}}{\omega C} \sin \left(\omega ... | [
"J",
"$$-\\dfrac{i_{m}}{\\omega C} \\sin \\omega t$$",
"J) $$-\\dfrac{i_{m}}{\\omega C} \\sin \\omega t$$"
] |
Topic: Atomic and Molecular Physics.
Question: The mass of $_{ 17 }{ { CI }^{ 35 } }$ is $34.9800$ amu. Calculate its binding energy (mass of $_{ 0 }{ { n }^{ 1 } }=1.008665$ amu $_{ 1 }{ { H }^{ 1 } }=1.007825$ amu):
A) 28.88 MeV
B) 28.0 MeV
C) 288 MeV
D) $$28.8 MeV$$
E) 2800 MeV
F) $$2.88 MeV$$
G) $$2880 MeV$$
H) 28.... | [
"I",
"$$280 MeV$$",
"I) $$280 MeV$$"
] |
Topic: Analytical Chemistry.
Question: The equivalent weight of $Cr_2(SO_4)_3 \,\, [mot wt. = M]$ in the following reaction is
$$Cr_2(SO_4)_3 + H_2O_2 + NaOH \rightarrow Na_2CrO_4 + Na_2SO_4 + H_2O$$
A) $$\displaystyle \frac{M}{4}$$
B) $$\displaystyle \frac{M}{3}$$
C) $$\displaystyle \frac{M}{2}$$
D) $$\frac{M}{5}$$
E)... | [
"B",
"$$\\displaystyle \\frac{M}{3}$$",
"B) $$\\displaystyle \\frac{M}{3}$$"
] |
Topic: Thermodynamics.
Question: At a temperature of °C, the equilibrium vapor pressure of mercury $p=1.85 \times 10^{-4} \mathrm{mm Hg}$. If the vapor of mercury is quickly removed:
What is the numerical value of $r$ ?
A) $$
0. \, 6 5 \mathbf{k} \mathbf{g} \cdot\mathbf{s}^{-1} \cdot\mathbf{m}^{-2}
$$
B) $$
0. \, 8 5 \... | [
"J",
"$$\n0. \\, 7 2 \\mathbf{k} \\mathbf{g} \\cdot\\mathbf{s}^{-1} \\cdot\\mathbf{m}^{-2}\n$$",
"J) $$\n0. \\, 7 2 \\mathbf{k} \\mathbf{g} \\cdot\\mathbf{s}^{-1} \\cdot\\mathbf{m}^{-2}\n$$"
] |
Topic: Electrodynamics.
Question: The potential energy $U$ for a force field $\overrightarrow { F } $ is such that $U=-kxy$ where $K$ is a constant. Then
A) the force $\overrightarrow { F } = -kx\hat { i } + ky\hat { j }$ is a non-conservative force
B) the force $\overrightarrow { F } $ is a non-conservative force
C) t... | [
"J",
"the force $\\overrightarrow { F } $ is a conservative force",
"J) the force $\\overrightarrow { F } $ is a conservative force"
] |
Topic: Hydraulics and Hydrology.
Question: In a known closed basin, the multi-year average runoff depth is 500mm, and the multi-year average rainfall depth is 1000mm. What is the multi-year average value of AS ?
A) 1500mm
B) 500mm
C) 750mm
D) 1000mm
E) 0mm
F) -500mm
G) 250mm
H) -1000mm | [
"E",
"0mm",
"E) 0mm"
] |
Topic: Physical Chemistry.
Question: For the reaction, $A(g)\rightarrow B(g)+C(g)$ rate law is $- \cfrac{d[A]}{dt}=K[A]$
At the start pressure is 100 mm and after 10 min, pressure is 120 mm, hence, rate constant (min)
A) $$\cfrac {2.303}{10}log \cfrac 5 3$$
B) $$\cfrac {2.303}{10}log \cfrac 6 5$$
C) $$\cfrac {2.303}{10... | [
"G",
"$$\\cfrac {2.303}{10}log \\cfrac 5 6$$",
"G) $$\\cfrac {2.303}{10}log \\cfrac 5 6$$"
] |
Topic: Discrete Mathematics.
Question: We now define an algorithm: The definition of a(n) is the number of digits required to write the prime factors of n, including their multiplicities. For example, for n = 30, the prime factors are 2, 3, and 5, which require a total of 3 digits. Given the input x_list (a series of v... | [
"H",
"[2, 3, 4, 4, 3, 4, 3, 5, 3, 3]",
"H) [2, 3, 4, 4, 3, 4, 3, 5, 3, 3]"
] |
Topic: Fluid Physics.
Question: A cylindrical container with an open top has a height of 0.6m and a diameter of 0.45m. Initially filled with water before rotating, it is now spinning about its vertical central axis at a constant angular velocity $\omega$. The angular velocity when the center of the water surface just t... | [
"D",
"$$\n1 5. 2 4 \\mathrm{r a d / s ;}\n$$",
"D) $$\n1 5. 2 4 \\mathrm{r a d / s ;}\n$$"
] |
Topic: Inorganic Chemistry.
Question: A chemist finds that 30.82 $\mathrm{g}$ of nitrogen will react with 17.60 $g,$ 35.20 $g,$ 70.40 $g,$ or 88.00 $g$ of oxygen to form four different compounds.
A) 1.0, 2.0, 4.0, 5.0
B) 1.1, 2.2, 4.4, 5.5
C) 1.0, 2.5, 4.0, 6.0
D) 0.8, 2.5, 4.2, 5.2
E) 0.5, 1.5, 3.0, 4.5
F) 1.0, 3.0, 6... | [
"A",
"1.0, 2.0, 4.0, 5.0",
"A) 1.0, 2.0, 4.0, 5.0"
] |
Topic: Acoustics.
Question: In an air medium, the resonance frequency of a Helmholtz resonator with an inlet tube radius of 0.01m, an inlet tube length of 0.1m, a container radius of 0.1m, and a container height of 0.2m is ( ).
A) 52Hz
B) 55Hz
C) 60Hz
D) 47Hz
E) 40Hz
F) 45Hz
G) 30Hz
H) 50Hz
I) 32Hz
J) 38Hz | [
"D",
"47Hz",
"D) 47Hz"
] |
Topic: Military Chemistry and Pyrotechnics.
Question: A mixture of \(20 \, \text{mL}\) of \(0.10 \, \text{mol} \, \text{L}^{-1} \, \text{HCl}\) and \(20 \, \text{mL}\) of \(0.20 \, \text{mol} \, \text{L}^{-1} \, \text{NH}_3 \cdot \text{H}_2\text{O}\). What is the \(pH\) of the solution \[K_b(\text{NH}_3 \cdot \text{H}_... | [
"H",
"9.25",
"H) 9.25"
] |
Topic: Discrete Mathematics.
Question: Division of (131B6C3) base 16 by (A2F) base 16 yeilds ____.
A) 3AC
B) 8AE
C) 6AE
D) 4AF
E) 7AD
F) 5AB
G) DAD
H) BAD
I) 9AD
J) 1AD | [
"I",
"9AD",
"I) 9AD"
] |
Topic: Thermodynamics and Statistical Physics.
Question: A cylindrical piston of mass $M$ slides smoothly inside a long metallic cylinder closed at one end, enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harm... | [
"E",
"$$T=2\\pi \\sqrt { (\\frac { Mh }{P_0A } ) } $$",
"E) $$T=2\\pi \\sqrt { (\\frac { Mh }{P_0A } ) } $$"
] |
Topic: Traffic Information Engineering and Control.
Question: How many basic variables are there in the transportation problem where sales exceed production across 5 production locations and 6 sales locations?
A) 9
B) 8
C) 13
D) 10
E) 11
F) 14
G) 7
H) 16
I) 12
J) 15 | [
"E",
"11",
"E) 11"
] |
Topic: Communication Principles.
Question: Given that $n(t)$ is the output of a narrowband filter with a center frequency of $f_{\mathrm{c}}$, applied to white noise $n_{\mathrm{w}}(t)$, and the power of $n(t)$ is $P_{1 \circ}$, if $n(t)$ is coherently demodulated with the carrier $2 \cos 2 \pi f_{\mathrm{e}} t$, what ... | [
"C",
"$$\nP_{1}\n$$",
"C) $$\nP_{1}\n$$"
] |
Topic: Semiconductor Physics.
Question: A $\mathbf{p}$-type semiconductor sample measuring 30 mm in length, 6 mm in width, and 1 mm in thickness, has a resistance of $500\Omega$. When placed in a 0.5 T magnetic field perpendicular to the sample plane and a current of 10 mA passes through the sample, a Hall voltage of $... | [
"D",
"$$\n1 0^{2} [ \\mathrm{\\ c m^{2} ( \\ V \\cdot\\ s )} ]\n$$",
"D) $$\n1 0^{2} [ \\mathrm{\\ c m^{2} ( \\ V \\cdot\\ s )} ]\n$$"
] |
Topic: Iron and Steel Metallurgy.
Question: Conduct a kinetics experiment of desulfurization of molten steel in a crucible. The initial sulfur concentrations in the molten steel and slag are $w[\mathrm{S}] = 0.8\%$ and $w(\mathrm{S}) = 0.01\%$, respectively. The crucible diameter is $d = 0.04\ \mathrm{m}$. Determine th... | [
"B",
"$$\n1. \\, 3 7 \\times1 0^{-4} \\mathrm{~ m o l / s},176s\n$$",
"B) $$\n1. \\, 3 7 \\times1 0^{-4} \\mathrm{~ m o l / s},176s\n$$"
] |
Topic: Hydraulics and Hydrology.
Question: A closed container filled with water has its bottom circular hole sealed by a metal sphere. The sphere weighs 19.6 N and has a diameter $D = 0.1 \text{ m}$, while the diameter of the circular hole is $d = 0.08 \text{ m}$. The water depth is $h_{1} = 0.5 \text{ m}$, and the ext... | [
"C",
"$$\n0. 2 0 5 \\ \\mathrm{( N )}\n$$",
"C) $$\n0. 2 0 5 \\ \\mathrm{( N )}\n$$"
] |
Topic: Materials Physics and Chemistry.
Question: What is the diffusion coefficient for coper in aluminum at 600°C?Preexponential and activation energy values for this system are $6. 5 \times1 0^{-5} m^2 / s$ and 136,000 J/mol, respectively.
A) $$
6. 8 \times1 0^{-1 4} \mathrm{~ m^{2} / s}
$$
B) $$
5. 4 \times1 0^{-1 6... | [
"J",
"$$\n4. 7 \\times1 0^{-1 3} \\mathrm{~ m^{2} / s}\n$$",
"J) $$\n4. 7 \\times1 0^{-1 3} \\mathrm{~ m^{2} / s}\n$$"
] |
Topic: Public Finance.
Question: A certain enterprise located in the county town sold a certain product in June and obtained sales revenue (including tax) of 650000 yuan. The input tax for that month was 8600 yuan. Given that the consumption tax rate is 3% and the value-added tax rate is 17%, what is the amount of urba... | [
"G",
"5482.46",
"G) 5482.46"
] |
Topic: Fluid Flow and Heat Transfer in Chemical Engineering.
Question: The boiling point of a NaCl aqueous solution with a known concentration of 0.25 at an absolute pressure of 19.6 kPa is 65.8°C. Use Duhring's rule to determine the boiling point of this solution at an absolute pressure of 50 kPa is ().
A) 86.78°C
B) ... | [
"F",
"87.91°C",
"F) 87.91°C"
] |
Topic: Thermodynamics and Statistical Physics.
Question: Following data is given for the reaction
$CaCO_{3}(s)$$\rightarrow$$CaO(s)+CO_{2}(g)$
$$\triangle_{f}H^{0}[CaO(s)]=-635.1 kJ mol^{-1}$$
$$\triangle_{f}H^{0}[CO_{2}(g)]=-393.5.1 kJ mol^{-1}$$
$$\triangle_{f}H^{0}[CaCO_{3}(s)]=-1206.9 kJ mol^{-1}$$
Predicate the ef... | [
"D",
"both a & b",
"D) both a & b"
] |
Topic: Economic Statistics.
Question: Find the degree ofskewnessof the distribution representing thesedata. Class Limit Frequency Class Midpoint 49 - 54 6 51.5 55 - 60 15 57.5 61 - 66 24 63.5 67 - 72 33 69.5 73 - 78 22 75.5
A) -1.05
B) - .44
C) 1.2
D) -0.75
E) - .89
F) 0.33
G) 2.1
H) 0.58
I) 0.99
J) 1.67 | [
"B",
"- .44",
"B) - .44"
] |
Topic: Geotechnical Engineering.
Question: The structure uses an independent square footing under the column, with the foundation's base dimensions being $2.4 \mathrm{m} \times 2.4 \mathrm{m}$, and the column's cross-sectional dimensions being $0.4 \mathrm{m} \times 0.4 \mathrm{m}$. The axial force acting at the center... | [
"I",
"105.73kN·m",
"I) 105.73kN·m"
] |
Topic: Water conservancy and Hydropower Engineering.
Question: A thrift lock has four basins of the same length (225m) as the lock, and each of width 20m. If the width of the lock chamber is 12m, its total lift is 24m, and the residual head on each thrift basin is 0.20m, what is the daily saving in water consumption if... | [
"G",
"$$\n8 1 9 2 5 0 \\, \\mathrm{m}^{3}\n$$",
"G) $$\n8 1 9 2 5 0 \\, \\mathrm{m}^{3}\n$$"
] |
Topic: Inorganic Chemistry.
Question: The composition of nickel oxide is $Ni_{0.98}O$. What fraction of Ni exists as $Ni^{+2}$ and $Ni^{+3}$ ions?
A) $Ni^{2+}=0.84, Ni^{+3}=0.16$
B) $Ni^{2+}=0.16$, $Ni^{+3}=0.84$
C) $Ni^{2+}=0.12$, $Ni^{+3}=0.88$
D) $Ni^{2+}=0.08$, $Ni^{+3}=0.92$
E) $Ni^{2+}=0.86$, $Ni^{+3}=0.12$
F) $N... | [
"H",
"$Ni^{2+}=0.06$, $Ni^{+3}=0.94$",
"H) $Ni^{2+}=0.06$, $Ni^{+3}=0.94$"
] |
Topic: Theoretical Optics.
Question: A thin prism of glass is placed in air and water respectively. If $n_g=\cfrac 3 2 \quad and \quad n_w=\cfrac 4 3 $, then the ratio of deviation produced by the prism for a small angle of incidence when placed in air and water seperately is:
A) \cfrac 3 4
B) $$ 4$$
C) \cfrac 3 8
D) \... | [
"J",
"$$\\cfrac 1 2$$",
"J) $$\\cfrac 1 2$$"
] |
Topic: Acoustics.
Question: In the above question, the intensity of the waves reaching a point P far away on the x-axis from each of the four sources is almost the same and equal to $I_0.$ Then,
A) If $d=\lambda /6,$ the intensity at P is $3I_0.$
B) If $d=\lambda /6,$ the intensity at P is $5I_0.$
C) If $d=\lambda /4,$... | [
"A",
"If $d=\\lambda /6,$ the intensity at P is $3I_0.$",
"A) If $d=\\lambda /6,$ the intensity at P is $3I_0.$"
] |
Topic: Electrodynamics.
Question: A particle is projected at an angle $\theta$ from ground with speed $u(g=10m/s^2)$, then which of the following is true?
A) If $u=10m/s$ and $\theta=30^o$, then after 1 sec velocity becomes perpendicular to initial velocity
B) If $u=10m/s$ and $\theta=30^o$, then after 0.75 sec veloci... | [
"D",
"If $u=10m/s$ and $\\theta=30^o$, then velocity never becomes perpendicular to intial velocity during its flight",
"D) If $u=10m/s$ and $\\theta=30^o$, then velocity never becomes perpendicular to intial velocity during its flight"
] |
Topic: Communication Principles.
Question: In mobile communications, the transmitter's carrier frequency is $900 \mathrm{~MHz}$. A car is moving at a speed of 80 km/h. Try calculating the car's onboard receiver carrier frequency when the car is moving in a straight line towards the transmitter.
A) $$
f_{1}=f-\Delta f=(... | [
"H",
"$$\nf_{1}=f-\\Delta f=( \\, 9 0 0-0. \\, 2 4 \\, ) \\, \\mathrm{M H z}=8 9 9. \\, 7 6 \\, \\mathrm{M H z}\n$$",
"H) $$\nf_{1}=f-\\Delta f=( \\, 9 0 0-0. \\, 2 4 \\, ) \\, \\mathrm{M H z}=8 9 9. \\, 7 6 \\, \\mathrm{M H z}\n$$"
] |
Topic: Signal and Information Processing.
Question: Directly compute the convolution sum of the following two sequences $y(n) = x(n) * h(n)$.
$$
h(n) = \left\{\begin{aligned}
& a^n, & 0 \leqslant n \leqslant N-1 \\
& 0, & \text{others} \\
\end{aligned} \right.
$$
$$
x(n) = \left\{\begin{cases}
\beta^{n-n_0}, & n_0 \leq... | [
"H",
"(1) When $n < n_{0}$, $y(n) = 0.$\n(2) When $n_{0} \\leq n \\leq n_{0} + N - 1$,\n$$\ny(n) = \\alpha^{n-n_{0}}(n+1-n_{0}), \\quad \\alpha=\\beta\n$$\n$$\ny(n) = \\frac{\\alpha^{n+1-n_{0}}-\\beta^{n+1-n_{0}}}{\\alpha-\\beta}, \\quad \\alpha \\neq \\beta\n$$\n(3) When $n > n_{0} + N - 1$,\n$$\ny(n) = N \\alph... |
Topic: Combinatorial Mathematics.
Question: In Zuminglish, all words consist only of the letters $M$ , $O$ , and $P$ . As in English, $O$ is said to be a vowel and $M$ and $P$ are consonants. A string of $M$ 's, $O$ 's, and $P$ 's is a word in Zuminglish if and only if between any two $O$ 's there appear at least two c... | [
"D",
"936",
"D) 936"
] |
Topic: Geometry and Topology.
Question: What is the largest possible radius of a circle contained in a 4-dimensional hypercube of side length 1?
A) \frac{\sqrt{3}}{2}
B) \frac{\sqrt{2}}{3}
C) \frac{\sqrt{2}}{4}
D) \frac{\sqrt{2}}{2}
E) \frac{\sqrt{5}}{2}
F) \frac{\sqrt{1}}{2}
G) \frac{\sqrt{4}}{2} | [
"D",
"\\frac{\\sqrt{2}}{2}",
"D) \\frac{\\sqrt{2}}{2}"
] |
Topic: Fluid Flow and Heat Transfer in Chemical Engineering.
Question: For constant pressure filtration of the suspension, the filtration constant $K$ is measured to be $4 \times 10^{-5} \mathrm{m^{2} / s}$ at an operating pressure differential of $46 \, \mathrm{kPa}$. What is the filtration constant $K$ in $\mathrm{m^... | [
"D",
"$$\n8. 7 \\times1 0^{-5}\n$$",
"D) $$\n8. 7 \\times1 0^{-5}\n$$"
] |
Topic: Numerical Analysis.
Question: Using the bisection method, what is the smallest positive root of the equation $f(x) = x^{3} - 2x - 5 = 0$? Accurate to $10^{-3}$.
A) $$
x^{*}=2. 0 9 5
$$
B) $$
x^{*}=2. 0 8 5
$$
C) $$
x^{*}=1. 9 9 5
$$
D) $$
x^{*}=2. 1 5 5
$$
E) $$
x^{*}=2. 2 0 5
$$
F) $$
x^{*}=1. 9 8 5
$$
G) $$
x^... | [
"A",
"$$\nx^{*}=2. 0 9 5\n$$",
"A) $$\nx^{*}=2. 0 9 5\n$$"
] |
Topic: Rigid Body Mechanics.
Question: Two balls A and B moving in the same direction collide. The mass of B is p times that of
A) $$p>= \dfrac{q}{q+1}$$
B) $$p>-1$$
C) $$\dfrac{p+q}{pq+q}$$
D) $$p>= \dfrac{q}{q+2}$$
E) $$e=\dfrac{p+q}{pq-p}$$
F) $$p>= \dfrac{q}{q-4}$$
G) $$p>= \dfrac{q}{q-1}$$
H) $$p>= \dfrac{q}{q-2}$... | [
"H",
"$$p>= \\dfrac{q}{q-2}$$",
"H) $$p>= \\dfrac{q}{q-2}$$"
] |
Topic: Elements of Chemical Reaction Engineering.
Question: A certain liquid-phase reaction takes place in a stirred tank with a volume of $V_{\mathrm{R}}$. The reaction is a first-order irreversible reaction with a rate constant of $k$ and a feed flow rate of $v$. The conversion rate of the reactant is calculated as $... | [
"A",
"$$\nc_{A0}x_{A\\mathrm{f}}\\frac v2=\\frac{kc_{A0}V_{\\mathrm{R}}}{1+2k\\frac{V_{\\mathrm{R}}}v}\n$$",
"A) $$\nc_{A0}x_{A\\mathrm{f}}\\frac v2=\\frac{kc_{A0}V_{\\mathrm{R}}}{1+2k\\frac{V_{\\mathrm{R}}}v}\n$$"
] |
Topic: Finance.
Question: The covariance between Stock A and the market index is 88, while their standard deviations are respectively 19% and 14%. What is the beta of Stock A?
A) 0.85
B) 0.24
C) 0.75
D) 0.65
E) 0.45
F) 0.35
G) 0.55
H) 0.245
I) 0.95
J) 1.05 | [
"E",
"0.45",
"E) 0.45"
] |
Topic: Theoretical Mechanics.
Question: A ball rolls off the top of a stairway with horizontal velocity ${v}_{0}m{S}^{-1}$. If the steps are $h$ metre high and $w$ metre wide, the ball will hit the edge of $n$th step if
A) $$n=\cfrac{2h{v}_{0}^{2}}{g{w}^{2}}$$
B) $$n=\cfrac{2h{v}_{0}^{2}}{5g{w}^{2}}$$
C) n=\cfrac{2h{v}... | [
"F",
"$$n=\\cfrac{2h{v}_{0}^{}}{g{w}^{2}}$$",
"F) $$n=\\cfrac{2h{v}_{0}^{}}{g{w}^{2}}$$"
] |
Topic: Special Number Theory.
Question: We now define an algorithm: The definition of a(n) is the nth entry in the sequence representing triangle T(n, k) of rencontres numbers, which count the number of permutations of n elements with exactly k fixed points. Given the input x_list (a series of values): [56, 57, 58, 59,... | [
"C",
"[1334960, 667485, 222480, 55650, 11088, 1890, 240, 45, 0, 1]",
"C) [1334960, 667485, 222480, 55650, 11088, 1890, 240, 45, 0, 1]"
] |
Topic: Semiconductor Physics.
Question: In the experiment to determine the Hall coefficient of a semiconductor, the current induced by the external electric field $\mathscr{E}_x$ is called the primary current. Under the influence of the Lorentz force and the Hall electric field, a transverse electron current $J_{\mathr... | [
"D",
"$$\nB ( \\mu_{\\mathrm{h}}+\\mu_{\\mathrm{e}} ) \\; \\frac{\\sigma_{\\mathrm{h}} \\sigma_{\\mathrm{e}}} {( \\sigma_{\\mathrm{h}}+\\sigma_{\\mathrm{e}} )^{2}}\n$$",
"D) $$\nB ( \\mu_{\\mathrm{h}}+\\mu_{\\mathrm{e}} ) \\; \\frac{\\sigma_{\\mathrm{h}} \\sigma_{\\mathrm{e}}} {( \\sigma_{\\mathrm{h}}+\\sigma_{... |
Topic: Heat Transfer.
Question: A tube heat exchanger, tube specifications for φ38x3mm, tube length 3m, the number of tubes 127, the outer surface area Az = () m ², and the inner surface area of the heat transfer area A1 = () m ².
A) 45.3, 38.5
B) 45.5, 38.3
C) 43.5, 36.8
D) 42.8, 36.3
E) 38.3, 45.5
F) 46.5, 37.3
G) 43... | [
"B",
"45.5, 38.3",
"B) 45.5, 38.3"
] |
Topic: Applied Optics.
Question: Camera lenses usually contain an aperture of variable diameter to control exposure. Consider a lens of focal length 50 mm and diameter 25 mm, with a resolution of 200 [(lines) / mm]. How far can this lens be stopped down before diffraction effects begin to limit the image quality?
A) 4 ... | [
"C",
"6 mm",
"C) 6 mm"
] |
Topic: Engineering Fluid Mechanics.
Question: A fluid flows steadily through a horizontal, constant-diameter circular pipe of length $\ell$. Given that the friction factor along the path is $f$, the wall shear stress is $\tau$, the cross-sectional average velocity is $\nu$, and the fluid density is $\rho$, find the val... | [
"F",
"$\\tau={\\frac{\\lambda} {8}} \\rho v^{2}$",
"F) $\\tau={\\frac{\\lambda} {8}} \\rho v^{2}$"
] |
Topic: Signal and Information Processing.
Question: Given $f(t)Longleftrightarrow F(jomega)$, then the Fourier transform of $f(4-3t)$ is
A) $3F(j3omega)e^{-jfrac{3}{4}omega} $
B) $3F(-jfrac{omega}{3})e^{-jfrac{4}{3}omega} $
C) $frac{1}{3}F(-jfrac{omega}{3})e^{-jfrac{3}{4}omega} $
D) $3F(-j3omega)e^{-jfrac{3}{4}omega} $... | [
"I",
"$frac{1}{3}F(-jfrac{omega}{3})e^{-jfrac{4}{3}omega} $",
"I) $frac{1}{3}F(-jfrac{omega}{3})e^{-jfrac{4}{3}omega} $"
] |
Topic: Inorganic Chemistry.
Question: When kaolinate clay Al2(Si2O5)(OH)4 is heated to a sufficient high temperature, chemical water is driven off.
Under these circumstances, what is the composition of the remaining product (in weight percent A12O3)?
A) $$
5 0. 1 {\mathrm{~ w t}} \%
$$
B) $$
4 6. 8 {\mathrm{~ w t}} \%
... | [
"J",
"$$\n4 5. 9 {\\mathrm{~ w t}} \\%\n$$",
"J) $$\n4 5. 9 {\\mathrm{~ w t}} \\%\n$$"
] |
Topic: Communication Principles.
Question: In the OFDM signal with a data rate of 64Mb/s, the number of carriers is 16, and each carrier uses 16-QAM transmission. The frequency spacing between adjacent sub-carriers is ____, and the spectral efficiency is ____.
A) 24MHz; 3b/(s·Hz)
B) 8MHz; 6b/(s·Hz)
C) 4MHz; 8b/(s·Hz)
D... | [
"E",
"16MHz; 4b/(s·Hz)",
"E) 16MHz; 4b/(s·Hz)"
] |
Topic: Fundamentals of Dynamics and Control.
Question: A particle with mass $m$ moves along the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$. The particle's acceleration is parallel to the $y$-axis when $t=0$. At this time, the particle's coordinates are: $x=0, y=b$, and the initial velocity is $v_{0}$.What is t... | [
"A",
"$$\nF_{y}=-m \\frac{v_{0}^{2} b^{4}} {a^{2} y^{3}}.\n$$",
"A) $$\nF_{y}=-m \\frac{v_{0}^{2} b^{4}} {a^{2} y^{3}}.\n$$"
] |
Topic: Subatomic and Atomic Physics.
Question: An electron accelerator is to be designed to study properties of linear dimensions of 1 fm. What kinetic energy is required?
A) $240 \text{ MeV}$
B) $220 \text{ MeV}$
C) 205 \text{ MeV}
D) $210 \text{ MeV}$
E) $230 \text{ MeV}$
F) $190 \text{ MeV}$
G) $200 \text{ MeV}$
H) ... | [
"G",
"$200 \\text{ MeV}$",
"G) $200 \\text{ MeV}$"
] |
Topic: Mineral Processing Engineering.
Question: A merchant sells 100 accessories at a unit price of 80 CNY (excluding VAT). When purchasing these accessories, the merchant pays 60 CNY per unit (including VAT). The VAT rate is 17%. What is the VAT payable by the merchant?
A) 500.00 CNY
B) 477.34 CNY
C) 488.21 CNY
D) 52... | [
"C",
"488.21 CNY",
"C) 488.21 CNY"
] |
Topic: Communication Principles.
Question: An open pipe is in resonance in 2nd harmonic with frequency ${ f }_{ 1 }$ Now one end of the tube is closed and frequency is increased to ${ f }_{ 2 }$ such that the resonance again occurs in nth harmonic, Choose the correct option
A) n=3,{ f }_{ 2 }=\dfrac { 2 }{ 4 } { f }_{ ... | [
"D",
"$$n=3,{ f }_{ 2 }=\\dfrac { 3 }{ 4 } { f }_{ 1 }$$",
"D) $$n=3,{ f }_{ 2 }=\\dfrac { 3 }{ 4 } { f }_{ 1 }$$"
] |
Topic: Polynomials and Series Expansions.
Question: Consider the equation 4x^3 - 6x^2 + 3x - 2 = 0. Which one of the following statements is TRUE?
A) There is a root between -5 and -20
B) There is a root between 1.5 and 2.5
C) There is no root in R
D) There is a root between 0.5 and 1.5
E) There is a root between 1 and... | [
"H",
"There is a root between 1 and 2",
"H) There is a root between 1 and 2"
] |
Topic: Fluid Physics.
Question: The resistance on a spherical bubble with radius $a$ moving slowly in a straight line at constant velocity in a homogeneous, incompressible fluid is ( ) .
( Assume body forces are negligible and the viscosity coefficient $\mu$ is constant. )
A) $$
5 \pi\mu a^2
$$
B) $$
\pi\mu a^3 U
$$
C)... | [
"G",
"$$\n4 \\pi\\mu a U\n$$",
"G) $$\n4 \\pi\\mu a U\n$$"
] |
Topic: Electromagnetic Field and Microwave Technology.
Question: 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?
A) $$
= 2. 0 5 \times1 0^{-4} \mathrm{~ m}
$$
B) $$
= 1. 7 0 \times1 0... | [
"C",
"$$\n= 1. 7 5 \\times1 0^{-4} \\mathrm{~ m}\n$$",
"C) $$\n= 1. 7 5 \\times1 0^{-4} \\mathrm{~ m}\n$$"
] |
Topic: Fluid Flow and Heat Transfer in Chemical Engineering.
Question: In a single-effect evaporator, a certain aqueous solution is concentrated from a concentration of 0.10 to 0.35 (both mass fractions, the same applies hereafter), with a throughput of 3000 kg of raw material per hour. If the actual amount of water ev... | [
"I",
"0.2",
"I) 0.2"
] |
Topic: Industrial Economics.
Question: Suppose an economy possesses presently 60 million automo-biles; and that each automobile must be replaced every 5 years. Suppose also that the present population of 240 million people grows 2% per year. Calculate on the basis of these data, all other things remaining equal, the ex... | [
"H",
"13.2 million automobiles",
"H) 13.2 million automobiles"
] |
Topic: Human Anatomy and Histology-Embryology.
Question: The resting potential of nerve cells is -70mV, the Na+equilibrium potential is+60mV, and the electrochemical driving force of Na+is ( ).
A) +130mV
B) -100mV
C) +10mV
D) -60mV
E) +30mV
F) -80mV
G) +50mV
H) -130mV
I) +70mV
J) - 10mV | [
"H",
"-130mV",
"H) -130mV"
] |
Topic: Ordinary Differential Equations.
Question: Find the minimum positive real value $s$ for which there exist two differentiable functions $y, d: \mathbb{R} \to \mathbb{R}$ that satisfy all of the following conditions:
\begin{enumerate}
\item[(a)] The value of $y$ at zero is positive: $y(0) > 0$
\item[(b)] The value... | [
"H",
"\\frac{\\pi}{2}",
"H) \\frac{\\pi}{2}"
] |
Topic: Tourism Management and Technological Economics Management.
Question: A company plans to build a new factory to expand the production of a certain product. According to market forecasts, the probability of good product sales is 0.7, and the probability of poor sales is 0.3. There are three options to choose from:... | [
"D",
"Plan 1 is 3400000,Plan 2 is 2300000, Plan 3 is 3595000",
"D) Plan 1 is 3400000,Plan 2 is 2300000, Plan 3 is 3595000"
] |
Topic: Mass Transport and Separation Process in Chemical Engineering.
Question: How many times does the total mass transfer coefficient increase when the gas flow rate doubles while absorbing ammonia from the mixed gas with water and keeping other conditions constant?
A) 1.2 times
B) 2 times
C) Uncertain
D) 3 times
E) ... | [
"C",
"Uncertain",
"C) Uncertain"
] |
Topic: Solid State Physics.
Question: A 0.1 kg Ge single crystal, doped with $3.2 \times 10^{-9} \text{ kg}$ of Sb. Assuming all impurities are ionized, calculate the resistivity of this material as (). (given $\mu_{\mathrm{n}} = 0.39 \, \mathrm{m}^2/\mathrm{V} \cdot \mathrm{s}$, the density of Ge single crystal is 5.3... | [
"G",
"$$\n1. 9 ( \\Omega\\mathrm{c m} )\n$$",
"G) $$\n1. 9 ( \\Omega\\mathrm{c m} )\n$$"
] |
Topic: Thermodynamics.
Question: A flask with a stopper, with a volume of $2.0 \times 10^{-3} \mathrm{~m}^{3}$, contains oxygen at 0.1 MPa and 300 K. When the system is heated to 400 K, the stopper pops open, and it is immediately closed again and heating is stopped. The flask gradually cools back down to 300 $\mathbf{... | [
"C",
"0.0019kg",
"C) 0.0019kg"
] |
Topic: Rigid Body Mechanics.
Question: A rope of length L and mass M is being pulled on a rough horizontal floor by a constant horizontal force $F=Mg$. The force is acting at one end of the rope in the same direction as the length of the rope. The coefficient of kinetic friction between rope and floor is $1/2$. Then, t... | [
"E",
"$$\\dfrac{Mg}{2}$$",
"E) $$\\dfrac{Mg}{2}$$"
] |
Topic: Thermodynamics and Statistical Physics.
Question: Find the amount of work done to increase the temperature of one mole of ideal gas by $30^0C$ it is expanding under the condition $V\propto T^{1/3}(R=8.31J/mol-k)$
A) $$16.62J$$
B) $$16.620J$$
C) $$1662J$$
D) $$166.20J$$
E) $$16620J$$
F) $$1.662J$$
G) $$166.2J$$ | [
"G",
"$$166.2J$$",
"G) $$166.2J$$"
] |
Topic: Heat Transfer.
Question: A double-layer flat wall furnace composed of a 100mm thick layer of firebrick and a 100mm thick layer of regular brick has thermal conductivities of 0.9 W·m⁻¹·K⁻¹ and 0.7 W·m⁻¹·K⁻¹ for each layer, respectively. When in steady operation, the measured temperature of the inner surface of th... | [
"C",
"68.5%",
"C) 68.5%"
] |
Topic: Power Electronics and Electrical Drives.
Question: The switch shown in the figure is closed at $t=0$. The charge on the capacitor as a function of time is given by
A) $$CV(1-e^{-3t/RC})$$
B) CV(1-e^{-2t/RC})
C) CV(1-e^{-t/6RC})
D) CV(1-e^{-t/4RC})
E) $$3CV(1-e^{-t/RC})$$
F) $$CV(1-e^{-t/3RC})$$
G) CV(1-e^{-t/2RC... | [
"A",
"$$CV(1-e^{-3t/RC})$$",
"A) $$CV(1-e^{-3t/RC})$$"
] |
Topic: Finance.
Question: On October 25 RalphMuffetaccepted a draft for $620 that was dated October 10 and due 3 months after sight. It was discounted on November 16 at 4 (1/2)%. The bank charges (1/8)% collection fee. Find the proceeds of the draft.
A) $610.33
B) $613.79
C) $620.00
D) $0.78
E) $615.50
F) $600.25
G) $6... | [
"B",
"$613.79",
"B) $613.79"
] |
Topic: Fundamentals of Dynamics and Control.
Question: In the given system all the strings & pulleys are mass less and there is no friction between surfaces.If ${ m }_{ 1 }=10kg$, ${ m }_{ 2 }=4kg$ and ${ m }_{ 3 }=2kg$, then the acceleration of the system is
A) $$\dfrac { 5g }{ 3 } $$
B) $$\dfrac { 5g }{ 9 }$$
C) $$\d... | [
"J",
"$$\\dfrac { 5g }{ 8 } $$",
"J) $$\\dfrac { 5g }{ 8 } $$"
] |
Topic: Advanced Algebra.
Question: Find vector $\vec{c} \times \left(\vec{a}+3 \cdot \vec{b}\right)$ where
$$
\vec{a}=\begin{vmatrix} \vec{i} & \vec{j} & \vec{k} \\ 5 & 0 & 9 \\ 0 & 1 & 0 \end{vmatrix}, \quad
\vec{b}=\begin{vmatrix} \vec{i} & \vec{j} & \vec{k} \\ 0 & -1 & 1 \\ 7 & 1 & -1 \end{vmatrix}, \quad \text{and}... | [
"F",
"21\\cdot\\vec{i}-17\\cdot\\vec{j}+21\\cdot\\vec{k}",
"F) 21\\cdot\\vec{i}-17\\cdot\\vec{j}+21\\cdot\\vec{k}"
] |
Topic: Thermodynamics and Statistical Physics.
Question: Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The mass of gas $A$ is $m_{A}$ and that in $B$ is $m_{B}$. The change in the pressure in $A$ and $B$ are found to be $\trian... | [
"B",
"$$3m_{A} = 2m_{B}$$",
"B) $$3m_{A} = 2m_{B}$$"
] |
Topic: Mathematical Analysis.
Question: Compute the limit:
$$
\lim_{x \to 0}\left(\frac{ -\sin(x) }{ x }\right)^{\frac{ 1 }{ 4 \cdot x^2 }}
$$
A) e^{-\frac{1}{20}}
B) e^{-\frac{1}{32}}
C) e^{-\frac{1}{30}}
D) e^{-\frac{1}{26}}
E) e^{-\frac{1}{16}}
F) e^{-\frac{1}{24}}
G) e^{-\frac{1}{12}}
H) e^{-\frac{1}{48}}
I) e^{-\f... | [
"F",
"e^{-\\frac{1}{24}}",
"F) e^{-\\frac{1}{24}}"
] |
Topic: Electrochemistry.
Question: The standard reduction potential at $25^{\circ} C$ of the reaction $2H_2O + 2e^{-} \rightleftharpoons H_2 + 2\overset{\ominus}{O}H$ is -0.8277 V. The equilibrium constant for the reaction $2H_2O \rightleftharpoons H_3O^{\oplus} +\, \overset{\ominus}{O}$ at $25^{\circ}C$ is:
A) $$K_w =... | [
"A",
"$$K_w = 9.35\\, \\times\\, 10^{-15}$$",
"A) $$K_w = 9.35\\, \\times\\, 10^{-15}$$"
] |
Topic: Number Theory.
Question: Let $P$ be the positive integer consisting of 1998 decimal digits, all of which are 1; that is, \[P=1111\cdots 11.\] Determine the $303$th digit after the decimal point in the decimal expansion of $\sqrt{P}$.
A) 9
B) 3
C) 5
D) 7
E) 2
F) 1
G) 6
H) 4
I) 8 | [
"B",
"3",
"B) 3"
] |
Topic: Physical Chemistry.
Question: For gaseous decomposition of ${PCI}_{5}$ in a closed vessel the degree of dissociation '$\alpha $', equilibrium pressure 'P' & ${'K}_{p}'$ are related as
A) $$\alpha =\sqrt { { K }_{ p }+P } $$
B) $$\alpha =\frac { 1 }{ \sqrt { { K }_{ p }+P } } $$
C) \(\alpha =\sqrt { \frac { P }{ ... | [
"F",
"$$\\alpha =\\sqrt { \\frac { { K }_{ p } }{ P } } $$",
"F) $$\\alpha =\\sqrt { \\frac { { K }_{ p } }{ P } } $$"
] |
Topic: Data Structures.
Question: Given the main string T="abaabaabcabaabe", and the pattern string S="abaabc", using the KMP algorithm for pattern matching, the number of individual character comparisons made until a successful match is achieved is ( ).
A) 16
B) 15
C) 12
D) 10
E) 11
F) 14
G) 9
H) 13
I) 8
J) 17 | [
"D",
"10",
"D) 10"
] |
Topic: Quantum Mechanics.
Question: The equilibrium populations of the 1H energy levels of a molecule are nα = nαeq and nβ = nβeq. What are the populations after a 5.0 μs pulse when B1 = 4.697 mT?
A) nα = nβeq/2 and nβ = 2nαeq
B) nα = nαeq + nβeq and nβ = nαeq + nβeq
C) nα = nαeq - nβeq and nβ = nβeq - nαeq
D) nα = nβe... | [
"D",
"nα = nβeq and nβ = nαeq",
"D) nα = nβeq and nβ = nαeq"
] |
Topic: Solid Earth Geophysics.
Question: The moment of inertia of a planet is used to evaluate its interior structure. In this problem you will construct asimple two-zone modelof the interior of Earth, assuming spherical symmetry Take the average densities of the core and mantle to be 10,900 kg m $- 3$ and 4500 kg m" r... | [
"E",
"0.54",
"E) 0.54"
] |
Topic: Solid Mechanics.
Question: A steel rod of cross-sectional area $16 cm^2$ and two brass rods of cross section area $10 cm^2$ together support a load of 5000 kg. The stress in steel rod will be : (Take Y for steel $= 2.0 \times 10^6 N/cm^2$ and for brass $= 1.0 \times 10^6 N/cm^2$)
A) $$151.2 N/cm^2$$
B) $$161.2 N... | [
"B",
"$$161.2 N/cm^2$$",
"B) $$161.2 N/cm^2$$"
] |
Topic: Subatomic and Atomic Physics.
Question: According to the Bohr model of the hydrogen atom, the radius of an excited state with $n=100$ is approximately().
A) $$
\mathrm{20 nm}
$$
B) $$
\mathrm{25 nm}
$$
C) $$
\mathrm{5 n m}
$$
D) $$
\mathrm{3 mm}
$$
E) $$
\mathrm{10 \mu m}
$$
F) $$
\mathrm{1 mm}
$$
G) $$
\mathrm{... | [
"C",
"$$\n\\mathrm{5 n m}\n$$",
"C) $$\n\\mathrm{5 n m}\n$$"
] |
Topic: Quantum Mechanics.
Question: In a double slit experiment, the separation between the slits is d = 0.25 cm and the distance of the screen D = 100 cm from the slits, If the wavelength of light used is $\lambda = 6000\mathop {\text{A}}\limits^{\text{o}} \,{\text{and}}\,{{\text{I}}_{\text{0}}}$ is the intensity of ... | [
"A",
"$${I_0}$$",
"A) $${I_0}$$"
] |
Topic: Applied Optics.
Question: From a point (- 2, 3) a ray of light is sent at an angle $\alpha$ (tan $\alpha$ = 3) to the axis of x. Upon reaching the x-axis the ray is reflected from it. Find the equation of the straight line which contains the reflected ray.
A) $$ y + 3x + 6 = 0$$
B) $$y + 3x + 7 = 0$$
C) $$y + 3x... | [
"A",
"$$ y + 3x + 6 = 0$$",
"A) $$ y + 3x + 6 = 0$$"
] |
Topic: Power Electronics and Electrical Drives.
Question: Two coils have a mutual inductance of $5mH.$ Current changes in the first coil according to the equation $I = {I_o}\cos \omega t$ where ${I_4} = 10A\,\,and\,\,\omega = 100\pi \,rad/s.$ maximum value of $e.m.f$ induced in the second coil is
A) 8\pi \,\,volt
B) 6... | [
"I",
"$$2\\pi \\,\\,volt$$",
"I) $$2\\pi \\,\\,volt$$"
] |
Topic: Atomic and Molecular Physics.
Question: If $'\lambda_1'$ and $'\lambda_2'$ are wavelengths of first lines is Lymas and Balnar series of H-atom respectively then wavelength of radiation needed to excite the electron from $n=1$ and $n=3$ is?
A) \frac{\lambda_1 - \lambda_2}{\lambda_1 + \lambda_2}
B) \frac{1}{\lambd... | [
"F",
"$$\\displaystyle\\frac{1}{\\lambda_1 +\\lambda_2}$$",
"F) $$\\displaystyle\\frac{1}{\\lambda_1 +\\lambda_2}$$"
] |
Topic: Ordinary Differential Equations.
Question: If the function y=y(x) is continuous and satisfies $y=e^{x}+\int_{0}^{x}y\left(t\right)\mathrm{d}t$, what is the expression for the function y=y(x)?
A) $\mathrm{y=2e^{x}~(x+1)}$
B) $\mathrm{y=e^{x}~(x+1)}$
C) $\mathrm{y=e^{x}-(x+1)}$
D) $\mathrm{y=e^{x}}~(x-1)$
E) $\mat... | [
"B",
"$\\mathrm{y=e^{x}~(x+1)}$",
"B) $\\mathrm{y=e^{x}~(x+1)}$"
] |
Topic: Physical Chemistry.
Question: 0.001 mol ofNaOHis added to 100 ml. of a solution that is 0.5 M HC_2H_3O_2 and 0.5 M NaC_2H_3O_2. Determine the pH of this Solution; theK_dissof acetic acid is 1.8 × 10^-5.
A) 4.90
B) 4.80
C) 4.68
D) 4.76
E) 5.20
F) 4.82
G) 4.70
H) 5.00
I) 5.10
J) 4.74 | [
"D",
"4.76",
"D) 4.76"
] |
Topic: Electrochemistry.
Question: A current of 2.68 A is passed for one hour through an aqueous solution of $CuSO_4$ using copper electrodes. Calculate the change in mass of cathode and that of the anode. (At. mass of copper = 63.5).
A) Increase in the mass of cathode = 6.348g
B) Decrease in the mass of anode = 3.176g... | [
"I",
"Decrease in the mass of anode = 3.174g",
"I) Decrease in the mass of anode = 3.174g"
] |
Topic: Engineering Fluid Mechanics.
Question: A new water pipeline, pipe diameter $d=0 . 4m$,tube length $l=1 0 0 \mathrm{m}$ , roughness factor $n=0 . 011$,linear loss $h_{f}=0 . 4m$,water flow is turbulent rough region. How much is the flow?
A) $0.150m^{3}/s$
B) $0.140m^{3}/s$
C) $0.180m^{3}/s$
D) $0.165m^{3}/s$
E) $... | [
"J",
"$0.156m^{3}/s$",
"J) $0.156m^{3}/s$"
] |
Topic: Particle and Nuclear Physics.
Question: A radioactive sample has an initial activity of $28\ dpm$, half hour later the activity is $14\ dpm$. How many atoms of the radioactive nuclide were there originally?
$$(\ln\ 2=0.7)$$
A) $$200$$
B) 480
C) $$300$$
D) $$12$$
E) $$600$$
F) 150
G) 24
H) 18
I) 240 | [
"D",
"$$12$$",
"D) $$12$$"
] |
Topic: Geotechnical Engineering.
Question: The width of the strip foundation is $3.6 \mathrm{m}$, with the self-weight of the foundation and the weight of the soil on the foundation being $G_{\mathrm{k}}=100 \mathrm{kN/m}$. The vertical force transmitted from the superstructure to the top surface of the foundation is $... | [
"B",
"116kPa",
"B) 116kPa"
] |
Topic: Stochastic Processes.
Question: If customers arrive according to a Poisson process at an average rate of 2 per minute, find the probability that a total of 3 customers arrive in the time intervals $[1, 3)$ and $[3, 5)$ is ().
A) $$
\frac{2 5 6} {3} \mathrm{e}^{-8}
$$
B) $$
\frac{2 5 7} {3} \mathrm{e}^{-8}
$$
C) ... | [
"A",
"$$\n\\frac{2 5 6} {3} \\mathrm{e}^{-8}\n$$",
"A) $$\n\\frac{2 5 6} {3} \\mathrm{e}^{-8}\n$$"
] |
Topic: Principles of Computer Organization.
Question: There is a (7, 4) code with the polynomial G(x) = $x^{3}$ + x + 1. Write out the cyclic redundancy check code for the codeword 1001 is ().
A) $$
\mathsf{M} \left( \mathbf{x} \right) \cdot\mathbf{x}^{3}+\mathsf{R} \left( \mathbf{x} \right)=1 1 0 1 0 1 0
$$
B) $$
\mat... | [
"C",
"$$\n\\mathsf{M} \\left( \\mathbf{x} \\right) \\cdot\\mathbf{x}^{3}+\\mathsf{R} \\left( \\mathbf{x} \\right)=1 0 0 1 1 1 0\n$$",
"C) $$\n\\mathsf{M} \\left( \\mathbf{x} \\right) \\cdot\\mathbf{x}^{3}+\\mathsf{R} \\left( \\mathbf{x} \\right)=1 0 0 1 1 1 0\n$$"
] |
Topic: Fluid Physics.
Question: An open capillary tube is lowered in a vessel with mercury. The difference between the levels of the mercury in the vessel and in the
capillary tube $\triangle h=4.6\ mm$. What is the radius of curvature of the mercury meniscus in the capillary tube? Surface tension
of mercury is $0.46... | [
"I",
"$$\\dfrac { 1 }{ 680 }\\ m$$",
"I) $$\\dfrac { 1 }{ 680 }\\ m$$"
] |
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