question stringlengths 152 5.02k | answers listlengths 3 3 |
|---|---|
Topic: Engineering Thermophysics.
Question: Just upstream of a shock wave, the air temperature and pressure are 288 K and 1 atm, respectively; just downstream of the wave, the air temperature and pressure are 690 K and 8.656 atm, respectively. Calculate the changes in enthalpy, internal energy, and entropy across the w... | [
"F",
"$$\n4. 0 3 8 \\times1 0^{5} \\ {\\frac{\\mathrm{j o u l e}} {\\mathrm{k g}}}\n$$\n$$\n2. 8 8 4 \\times1 0^{5} \\ {\\frac{\\mathrm{j o u l e}} {\\mathrm{k g}}}\n$$\n$$\n2 5 8. 2 {\\frac{\\mathrm{j o u l e}} {\\mathrm{k g} \\ \\circ\\mathrm{K}}}\n$$",
"F) $$\n4. 0 3 8 \\times1 0^{5} \\ {\\frac{\\mathrm{j o ... |
Topic: Fundamentals of Dynamics and Control.
Question: In the system shown in figure $m_A=4m,m_B=3m$ and $m_C=8m$. Friction is absent everywhere. String is light and in-extensible. If the system is released from rest find the acceleration of block $B$
A) $\frac{g}{2}$ (left ward)
B) $\frac{g}{8}$ (leftward)
C) $\frac{g... | [
"I",
"$\\frac{g}{4}$ (rightward)",
"I) $\\frac{g}{4}$ (rightward)"
] |
Topic: Electrochemistry.
Question: At 298 K, it is known that $\Lambda_{m}^{\infty} (CH_{3}COOK) = 1.144 \times 10^{-2} \Omega^{-1} \cdot m^2 \cdot mol^{-1}$, $\Lambda_{m}^{\infty} (K_2SO_4) = 3.070 \times 10^{-2} \Omega^{-1} \cdot m^2 \cdot mol^{-1}$, and $\Lambda_{m}^{\infty} (H_2SO_4) = 8.596 \times 10^{-2} \Omega^{... | [
"I",
"$$\n3. 9 0 7 \\times1 0^{-2} \\; \\Omega^{-1} \\cdot{\\mathrm{m}}^{2} \\cdot{\\mathrm{m o l}}^{-1}\n$$",
"I) $$\n3. 9 0 7 \\times1 0^{-2} \\; \\Omega^{-1} \\cdot{\\mathrm{m}}^{2} \\cdot{\\mathrm{m o l}}^{-1}\n$$"
] |
Topic: Analytical Chemistry.
Question: The redox titration method was used for the determination of chromium. The sample is decomposed, Cr(III) is oxidized to Cr(VI), and then titrated with about 0.1 mol/L Fe2+ solution. The sample is known to contain about 10% chromium, and to consume 30 mL of Fe2+ solution, the sampl... | [
"G",
"0.5",
"G) 0.5"
] |
Topic: Probability and Statistics.
Question: A student takes the same course exam twice consecutively. The probability of passing the first time is $p$. If they pass the first time, the probability of passing the second time is also $p$; if they do not pass the first time, the probability of passing the second time is ... | [
"E",
"$$\n\\frac{p^{2}} {p^{2}+\\frac{p} {2} ( 1-p )}-\\frac{2 p} {p+1}.\n$$",
"E) $$\n\\frac{p^{2}} {p^{2}+\\frac{p} {2} ( 1-p )}-\\frac{2 p} {p+1}.\n$$"
] |
Topic: Finance.
Question: Charles will pay Bernice $800 five years from now if she lends him $500 now. What is the rate of return on the $500 loan?
A) 11.86%
B) 14.86%
C) 13.86%
D) 12.86%
E) 6.86%
F) 5.86%
G) 8.86%
H) 10.86%
I) 7.86%
J) 9.86% | [
"J",
"9.86%",
"J) 9.86%"
] |
Topic: Solid State Physics.
Question: The experimental value of molar electron specific heat for metallic potassium at low temperatures is: $c_e=2.08TmJ/mol·K$. Try to calculate its Fermi energy $E_F$=____.
A) $1.999 x 10^-3 eV$
B) $4.165 x 10^-3 eV$
C) $3.125 x 10^-4 eV$
D) $2.235 x 10^-4 eV$
E) $2.235 x 10^-3 eV$
F) ... | [
"E",
"$2.235 x 10^-3 eV$",
"E) $2.235 x 10^-3 eV$"
] |
Topic: Applied Optics.
Question: A spherical glass bulb of diameter d is filled with water $\left[ {\mu = {4 \over 3}} \right]$. The bulb is viewed along its horizontal diameter. What is the apparent diameter? ( Neglect the thickness of glass)
A) $${{7d} \over 5}$$
B) $${{3d} \over 2}$$
C) $${{5d} \over 3}$$
D) $${{3... | [
"E",
"$${d \\over 2}$$",
"E) $${d \\over 2}$$"
] |
Topic: Data Structures.
Question: There is an 8-way merged winner tree with elements 10,9,20,6,8,23,21,17 as leaf nodes. After outputting an element, a new element will be added to the corresponding leaf node. How many elements should be corrected in the reconstructed winning tree?
A) 4
B) 7
C) 1
D) 8
E) 6
F) 10
G) 3
H... | [
"G",
"3",
"G) 3"
] |
Topic: Microelectronics and Solid-State Electronics.
Question: The room-temperature electrical conductivity of silicon that has been doped with $10^{23} \, \text{m}^{-3}$ of arsenic atoms is () .
A) $$
3 2 3 5 \ ( \Omega\mathrm{-m} )^{-1}
$$
B) $$
8 1 7 7 \ ( \Omega\mathrm{-m} )^{-1}
$$
C) $$
7 6 3 8 \ ( \Omega\mathrm{... | [
"F",
"$$\n1 0 4 0 \\ ( \\Omega\\mathrm{-m} )^{-1}\n$$",
"F) $$\n1 0 4 0 \\ ( \\Omega\\mathrm{-m} )^{-1}\n$$"
] |
Topic: Particle and Nuclear Physics.
Question: An incident nucleon collides with another stationary nucleon to produce a $\pi$ meson, with the reaction given by
$$
\mathrm{N+N \to N+N+\pi}
$$
What is the threshold kinetic energy $T_{0}$ for this reaction ?
A) $$
{\frac{1} {2 m_{\mathrm{N}}}} ( 5 m_{\mathrm{N}}+m_{\pi} ... | [
"D",
"$$\n{\\frac{1} {2 m_{\\mathrm{N}}}} ( 4 m_{\\mathrm{N}}+m_{\\pi} ) m_{\\pi} c^{2}\n$$",
"D) $$\n{\\frac{1} {2 m_{\\mathrm{N}}}} ( 4 m_{\\mathrm{N}}+m_{\\pi} ) m_{\\pi} c^{2}\n$$"
] |
Topic: Radiochemistry.
Question: For a strontium salt solution labeled with Sr$^{89}$, the specific radioactivity is 2 mCi/ml. If 0.2 ml of the solution is used to prepare a sample and the counting efficiency is 0.1, how many times must the original solution be diluted to achieve a radioactivity of 1000 counts per minu... | [
"C",
"89 times",
"C) 89 times"
] |
Topic: Ordinary Differential Equations.
Question: The equation of the curve that is orthogonal to the family of integral curves defined by the equation $( x \mathrm{l n} x ) \mathrm{d} x-( y-\mathrm{l n} x ) \mathrm{d} y=0$ and passes through the point $( e, 1 )$ is ( ).
A) $y={\frac{1} {2}} \left( x \ln x+{\frac{x} { ... | [
"D",
"$y={\\frac{1} {2}} \\left( \\ln x+{\\frac{1} {\\ln x}} \\right)$",
"D) $y={\\frac{1} {2}} \\left( \\ln x+{\\frac{1} {\\ln x}} \\right)$"
] |
Topic: Thermodynamics and Statistical Physics.
Question: As shown schematically in the figure, two vessels contain water solutions (at temperature 𝑇) of potassium permanganate $(KMnO_4)$ of different concentrations $𝑛_1$ and $𝑛_2$ ($𝑛_1>𝑛_2$) molecules per unit volume with $\Delta 𝑛=(𝑛_1−𝑛_2)<<𝑛_1$. When they ... | [
"B",
"total number of molecules going across the tube per sec is $\\left(\\dfrac{\\Delta n}{l}\\right)\\left(\\dfrac{k_BT}{\\beta}\\right)S$",
"B) total number of molecules going across the tube per sec is $\\left(\\dfrac{\\Delta n}{l}\\right)\\left(\\dfrac{k_BT}{\\beta}\\right)S$"
] |
Topic: Theoretical Mechanics.
Question: Alpha Centauri is 4.31 light-years away from Earth. One of the twin brothers, $A$, travels to the star in a spaceship moving at 0.8c, and during his journey there and back, he sends a radio signal every 0.01 years (in the spaceship's rest frame). The other brother, $B$, who stays... | [
"A",
"$A$ received 1,075 signals, and $B$ received 645 signals.",
"A) $A$ received 1,075 signals, and $B$ received 645 signals."
] |
Topic: Fundamentals of Dynamics and Control.
Question: A particle performs a horizontal circle of radius r in a funnel type vessel of frictionless surface with a half cone angle $ $. The mass of the particle is m, then the speed of the particle must be
A) $$ v={rgtan \theta } $$
B) $$ v=\sqrt {rg/tan \theta } $$
C) $$... | [
"B",
"$$ v=\\sqrt {rg/tan \\theta } $$",
"B) $$ v=\\sqrt {rg/tan \\theta } $$"
] |
Topic: Water conservancy and Hydropower Engineering.
Question: A sealed vessel contains water upto height h = 3.5 m. The space above the water contains compressed air at pressure 4.2 $P_0 (P_0 = 1 x 10^5 P_a$, atmospheric pressure). The vessel connected to a tube at the bottom as shown in figure. Area of cross-section ... | [
"G",
"Initial speed of the efflux of water is (approximately)",
"G) Initial speed of the efflux of water is (approximately)"
] |
Topic: Subatomic and Atomic Physics.
Question: In a uniform magnetic field of $B$ with the proton and electron flying vertically at the same velocity, the ratio of the proton orbital radius $R_{1}$to the electron orbital radius $R_{2}$ is ____.
A) $$
\frac{m_{\mathrm{e}}} {m_{\mathrm{p}}}
$$
B) $$
\frac{r_{\mathrm{e}}}... | [
"D",
"$$\n\\frac{m_{\\mathrm{p}}} {m_{\\mathrm{c}}}\n$$",
"D) $$\n\\frac{m_{\\mathrm{p}}} {m_{\\mathrm{c}}}\n$$"
] |
Topic: Communication and Information Systems.
Question: Find the radiation resistance of a dipole antenna (1 / 10) wavelengthlong.
A) 10.2 ohms
B) 7.9 ohms
C) 9.8 ohms
D) 2.1 ohms
E) 15.7 ohms
F) 12.5 ohms
G) 5.6 ohms
H) 20.4 ohms
I) 3.9 ohms
J) 6.3 ohms | [
"B",
"7.9 ohms",
"B) 7.9 ohms"
] |
Topic: Thermodynamics.
Question: The surface of a black body is at a temperature $727^{\circ}C$ and its cross section in $1\ m^{2}$. Heat radiated from this surface in one minute in Joules is (Stefan's constant $= 5.7\times 10^{-8}W/m^{2} k^{4})$
A) $$34.2\times 10^{5}$$
B) $$24.2 \times 10^{5}$$
C) $$34.2 \times 10^{4... | [
"A",
"$$34.2\\times 10^{5}$$",
"A) $$34.2\\times 10^{5}$$"
] |
Topic: Relativity.
Question: A particle with a rest mass of $m$ collides with a stationary particle with a rest mass of $m_{1}$, resulting in a reaction that produces many particles with a total rest mass of $M$. If $m+m_{1} < M,$ then the reaction cannot occur when the kinetic energy of the incoming particle is not su... | [
"D",
"$${\\frac{1} {2 m_{1}}} ( M+m_{1}+m ) ( M-m_{1}-m ) c^{2}\n$$",
"D) $${\\frac{1} {2 m_{1}}} ( M+m_{1}+m ) ( M-m_{1}-m ) c^{2}\n$$"
] |
Topic: Thermodynamics.
Question: A $200-cm^3$ glass flask is filled to the brim with mercury at 20°C How much mercury overflows when the temperature of the system is raised to 100°C. The coefficient of linear expansion of the glass is $0.40 \times 10^{-5} K^{-1}. (Unit: cm^3)
A) 2.4
B) 3.6
C) 3.2
D) 4.0
E) 2.1
F) 1.5
G... | [
"G",
"2.7",
"G) 2.7"
] |
Topic: Textile Materials Science.
Question: What are the values for calculating the common moisture regain of 70/30 polyester/cotton blended yarn and the blending percentage at common moisture regain (known as the common moisture regain of 0.4% for polyester and 8.5% for cotton)?
A) $$
2. 8 3 \%,\ 34.63\%
$$
B) $$
3. 2... | [
"E",
"$$\n2. 8 3 \\%,\\ 31.63\\%\n$$",
"E) $$\n2. 8 3 \\%,\\ 31.63\\%\n$$"
] |
Topic: Cryptography.
Question: For $\mathbf{p}=\uparrow\mathbf{1}$ and $\mathbf{q}=1 7$ and choose $\mathrm{e}=7$ . Apply RSA algorithm where PT message=88 and thus what is the CT?
A) 64
B) 45
C) 32
D) 77
E) 28
F) 63
G) 19
H) 52
I) 23
J) 11 | [
"J",
"11",
"J) 11"
] |
Topic: Electrodynamics.
Question: When a charge of amount Q is given to an isolated metal plate X of surface area A, its surface charge density becomes $\sigma _1$. When an isolated identical plate Y is brought close to X, the surface charge density on X becomes $\sigma_2$. When y is earthed, the surface charge densi... | [
"A",
"$$\\sigma_3=\\dfrac{Q}{A}$$",
"A) $$\\sigma_3=\\dfrac{Q}{A}$$"
] |
Topic: Electrodynamics.
Question: An infinite line of charge produces a field of magnitude $4.5 \times$ $10^4 \mathrm{~N} / \mathrm{C}$ at distance $2.0 \mathrm{~m}$. Find the linear charge density.
A) $4.0$$\mu \mathrm{C} / \mathrm{m}$
B) $5.0$$\mu \mathrm{C} / \mathrm{m}$
C) $2.5 \mu \mathrm{C} / \mathrm{m}$
D) $6.5$... | [
"B",
"$5.0$$\\mu \\mathrm{C} / \\mathrm{m}$",
"B) $5.0$$\\mu \\mathrm{C} / \\mathrm{m}$"
] |
Topic: Chemical Transport Engineering.
Question: Air flows between two parallel smooth plates 25 mm apart at a speed of 0.15 m/s at 20°C. Determine how far from the entrance the boundary layers on the two plates merge. The properties of air at 20°C are $\rho = 1.205 \, \mathrm{kg/m}^{3}, \, \mu = 1.81 \times 10^{-5} \,... | [
"H",
"$$\n= 0. 0 6 2 4 \\mathrm{m}\n$$",
"H) $$\n= 0. 0 6 2 4 \\mathrm{m}\n$$"
] |
Topic: Electrical Theory and New Technologies.
Question: A Helmholtz galvanometer has coils of radius $\dfrac {11}{\sqrt {5}}cm$ and the number of turns $70$. Calculate the current through the coil which produces a deflection of $45^{o}$. Given magnetic intensity due to earth along horizontal is $H=\dfrac {80}{\pi}A/m$... | [
"E",
"$$5\\ mA$$",
"E) $$5\\ mA$$"
] |
Topic: Polymer Chemistry and Physics.
Question: How many times is the mean square end-to-end distance of a PE free rotating chain larger than that of a free combined chain?
A) 4
B) 6
C) 1
D) 2
E) 8
F) 3
G) 5
H) 9
I) 7
J) 10 | [
"D",
"2",
"D) 2"
] |
Topic: Probability and Statistics.
Question: Select a point randomly in the interval (0,1) and denote it as X.
$\mathrm{P} \ \ ( \mathrm{X}^{2} \!-\! 3 \mathrm{X} / 4 \!+\! 1 / 8 \! \geq\! 0 )$ is ____.
A) 0.60
B) 0.75
C) 0.50
D) 0.20
E) 0.95
F) 0.40
G) 0.30
H) 0.25
I) 1.00
J) 0.85 | [
"B",
"0.75",
"B) 0.75"
] |
Topic: Quantitative Economics.
Question: A one-sided test of a hypothesis about a population mean, based on a sample of size 14, yields a P-value of 0.075. Which of the following best describes the range of tvalues that would have given this P-value?
A) 1.761 < t< 2.160
B) 1.350 < t< 1.771
C) 1.200 < t< 1.400
D) 1.500 ... | [
"B",
"1.350 < t< 1.771",
"B) 1.350 < t< 1.771"
] |
Topic: Thermodynamics and Statistical Physics.
Question: A mixed gas of $0.1 \, \text{mol}$ helium and $0.2 \, \text{mol}$ nitrogen, with an initial temperature of $T = 300\, \text{K}$ and a volume of $4\, \text{L}$. Prove that when the mixed gas undergoes adiabatic compression, its temperature and pressure changes can... | [
"D",
"$$\n3 0 2 \\ \\mathrm{( K )}\n$$\n$$\n2. 0 \\times1 0^{5} ( \\mathrm{N / m^{2}} )\n$$",
"D) $$\n3 0 2 \\ \\mathrm{( K )}\n$$\n$$\n2. 0 \\times1 0^{5} ( \\mathrm{N / m^{2}} )\n$$"
] |
Topic: Astronomical Observation and Technology.
Question: Radiation from the nearby star Alpha Centauri is observed to be reduced in wavelength (after correction for Earth's orbital motion) by a factor of 0.999933. What is the recession velocity of Alpha Centauri relative to the Sun?
A) $$
- 1 8. 2 ~ \mathrm{k m / s e ... | [
"I",
"$$\n- 2 0. 1 ~ \\mathrm{k m / s e c}\n$$",
"I) $$\n- 2 0. 1 ~ \\mathrm{k m / s e c}\n$$"
] |
Topic: Theoretical Optics.
Question: A beam of partially polarized light consists of linearly polarized light and natural (unpolarized) light with an intensity ratio of 2:8. What is the degree of polarization of this partially polarized light?
A) 0.2
B) 0.4
C) 0.8
D) 0.3
E) 0.5
F) 0.6
G) 0.1
H) 0.7 | [
"A",
"0.2",
"A) 0.2"
] |
Topic: Fundamental Mathematics.
Question: A sequence of positive reals defined by $a_0=x$ , $a_1=y$ , and $a_n\cdot a_{n+2}=a_{n+1}$ for all integers $n\ge 0$ . Given that $a_{2007}+a_{2008}=3$ and $a_{2007}\cdot a_{2008}=\frac 13$ , find $x^3+y^3$ .
A) 652
B) 650
C) 647
D) 645
E) 648
F) 651
G) 649
H) 646
I) 653 | [
"E",
"648",
"E) 648"
] |
Topic: Relativity.
Question: Two particles, each with a rest mass of $m_{0}$, are involved in an interaction. One particle is at rest, while the other has a kinetic energy that is six times its rest energy. The two particles undergo a completely inelastic collision. What are the rest mass and velocity of the composite ... | [
"H",
"$$\n4 m_{0}\n$$\n$$\n{\\frac{\\sqrt{3}} {2}} c\n$$",
"H) $$\n4 m_{0}\n$$\n$$\n{\\frac{\\sqrt{3}} {2}} c\n$$"
] |
Topic: Stellar and Interstellar Evolution.
Question: M87 is a giant elliptical galaxy near the center of the Virgo cluster of galaxies. It is estimated that its mass is approximately $3 \, \times\, 1 0^{1 3} \mathrm{~ M}_{\odot}$ within a radius of 300 kpc. How long would it take for a star near the outer edge of the g... | [
"F",
"$$\n5. 6 \\mathrm{~ G y r}\n$$",
"F) $$\n5. 6 \\mathrm{~ G y r}\n$$"
] |
Topic: Polymer Physics.
Question: Given that the unit cell parameters for polymethyl methacrylate are $a \times b \times c = 2.108 \times 1.217 \times 1.055 \,\, \mathrm{nm}, \, \alpha = \beta = \gamma = 90°$, and the measured density is $\rho = 1.23 \,\, \mathrm{g/cm}^{3}$, with $M_{0} = 100.1$, try to determine the n... | [
"C",
"20",
"C) 20"
] |
Topic: Physical Chemistry.
Question: What percent of the AB particles are dissociated by water if the freezing point of a(.0100 m) AB solution is -0.0193°C? The freezing point lowering constant of water is (-1.86°C / mole).
A) 4%
B) 5%
C) 15%
D) 8%
E) 12%
F) 2%
G) 7%
H) 10%
I) 6%
J) 3% | [
"A",
"4%",
"A) 4%"
] |
Topic: Theoretical Fluid Mechanics.
Question: If a variable ellipsoidal surface
$$
\frac{x^{2}} {a^{2} k^{2} t^{4}}+k t^{2} \biggl( \frac{y^{2}} {b^{2}}+\frac{z^{2}} {c^{2}} \biggr)=1
$$
is the boundary surface of a fluid, where $k, a, b, c$ are constants, and $x, y, z$ are coordinates in the Cartesian coordinate syste... | [
"F",
"$$\\frac{2 x} {t}$$\n$$- \\frac{y} {t}$$\n$$- \\frac{z} {t}$$",
"F) $$\\frac{2 x} {t}$$\n$$- \\frac{y} {t}$$\n$$- \\frac{z} {t}$$"
] |
Topic: Organic Chemistry.
Question: In assessing metabolic processes we are usually more interested in the work that may be performed for the consumption of a given mass of compound than the heat it can produce (which merely keeps the body warm). What is the maximum energy that can be extracted as non-expansion work wh... | [
"G",
"$$\n{3. 1 \\times1 0^{4} \\mathrm{~ k J}}\n$$",
"G) $$\n{3. 1 \\times1 0^{4} \\mathrm{~ k J}}\n$$"
] |
Topic: Particle and Nuclear Physics.
Question: Consider the photoreaction of the $\pi$ meson
$$
\gamma+\mathrm{p} \to \mathrm{p}+\pi^{0}
$$
The rest mass energy of the proton is $938 \mathrm{MeV}$, and the rest mass energy of the $\pi$ meson is $135 \mathrm{MeV}$. If the initial proton is stationary relative to the lab... | [
"A",
"$$\n1 4 4. 7 \\mathrm{M e V}\n$$",
"A) $$\n1 4 4. 7 \\mathrm{M e V}\n$$"
] |
Topic: Principles of Computer Organization.
Question: A certain DRAM chip uses address multiplexing technology, with a capacity of 1024×8 bits. Apart from the power supply and ground pins, the minimum number of pins for this chip is (). (There are two read/write control lines)
A) 21
B) 18
C) 14
D) 16
E) 15
F) 19
G) 20
... | [
"I",
"17",
"I) 17"
] |
Topic: Weapon Systems Science and Engineering.
Question: Two shots are projected from a gun at the top of a hill with the same velocity $u$ at angles of projection $ lpha$ and $ \beta$ respectively. If the shots strike the horizontal ground through the foot of the hill at the same point, find the height h of the hill ... | [
"C",
"$$h=2{ u }^{ 2 }\\left( \\frac { 1-tan\u0007lpha \\ tan \\beta }{ g (tan\u0007lpha + tan\\beta)^2 } \\right) $$",
"C) $$h=2{ u }^{ 2 }\\left( \\frac { 1-tan\u0007lpha \\ tan \\beta }{ g (tan\u0007lpha + tan\\beta)^2 } \\right) $$"
] |
Topic: Thermodynamics.
Question: A glass capillary tube of inner diameter $0.28mm$ is lowered vertically into water in a vessel.The pressure to be applied on the water in the capillary tube so that water level in the tube is same as the vessel in $N /m ^{2}$ is(surface tension of water $= 0.07 N/m$ atmospheric pressure... | [
"A",
"$$10^{3}$$",
"A) $$10^{3}$$"
] |
Topic: Fundamentals of Dynamics and Control.
Question: The trolley travels on a horizontal straight track at a speed of $v=5 \mathrm{~m/s}$, while simultaneously vibrating on a spring with an amplitude of $a=0.008 \mathrm{~m}$ and a period of $T=0.5$ s. It is known that the average distance from the center of mass of t... | [
"J",
"$$1.5+0.0008\\sin0.8\\pi x$$",
"J) $$1.5+0.0008\\sin0.8\\pi x$$"
] |
Topic: Electrodynamics.
Question: A point source of light is placed at a depth $h=0.5 m$ below the surface of a liquid $\left( {\mu = \frac{5}{4}} \right)$. Then, the fraction of light energy that escape directly from the liquid surface is :-
A) 0.25
B) $$0.1$$
C) 0.175
D) 0.225
E) $$0.2$$
F) 0.15
G) $$0.4$$
H) $$0.3$... | [
"E",
"$$0.2$$",
"E) $$0.2$$"
] |
Topic: Genetics.
Question: Kernel color in wheat is determined by the action of two pairs ofpolygenesthat produce colors varying from dark red to white. If AABB (dark red) andaabb(white) are crossed, (a) What fraction of the F_2 generation can be expected to be like either parent? (b) How many F_2 phenotypic classes re... | [
"C",
"(a) 2/16, (b) Five",
"C) (a) 2/16, (b) Five"
] |
Topic: Geometry and Topology.
Question: Length of the latus rectum of the hyperbola $xy-3x-4y+8=0$
A) $$2\sqrt{10}$$
B) $$2\sqrt{2}$$
C) $$8$$
D) $$4$$
E) 4\sqrt{6}
F) 4\sqrt{5}
G) $$4\sqrt{2}$$
H) 4\sqrt{3}
I) none of these
J) 4\sqrt{7} | [
"G",
"$$4\\sqrt{2}$$",
"G) $$4\\sqrt{2}$$"
] |
Topic: Atomic and Molecular Physics.
Question: In an isolated $Li^{2+}$, electron jumps from n $=2$ to n$= 1$. What is the recoil momentum of the ion (in kg- m/s)?
A) 13.6 x 10-27
B) 10.88 x 10-27
C) $$5.44 x 10-27$$
D) 21.76 x 10-27
E) 5.44 x 10-28
F) $$8.16 x 10-27$$
G) 2.72 x 10-27
H) 10.88 x 10-28
I) $$ 16.32 x 10-... | [
"C",
"$$5.44 x 10-27$$",
"C) $$5.44 x 10-27$$"
] |
Topic: Particle and Nuclear Physics.
Question: The half-life of $^{3 2}_{1 5} P$ is 14.3 days. Find the activity of $1.0 \, \mu g_{1 5}^{3 2} P$ in $( \operatorname{Ci} )$.
A) $$
0. 2 0 {\mathrm{C i}}
$$
B) $$
0. 1 5 {\mathrm{C i}}
$$
C) $$
0. 4 1 {\mathrm{C i}}
$$
D) $$
0. 3 5 {\mathrm{C i}}
$$
E) $$
0. 2 9 {\mathrm{C... | [
"E",
"$$\n0. 2 9 {\\mathrm{C i}}\n$$",
"E) $$\n0. 2 9 {\\mathrm{C i}}\n$$"
] |
Topic: Finance.
Question: The net amount of annual credit sales forecasted by a company is 360000 yuan, with an accounts receivable turnover period of 30 days, a variable cost rate of 70%, and a capital cost rate of 7%. Calculate the opportunity cost of accounts receivable ( ) yuan.
A) 1500
B) 1460
C) 1490
D) 1470
E) 1... | [
"D",
"1470",
"D) 1470"
] |
Topic: Particle and Nuclear Physics.
Question: Two particle each of mass $'m'$ are placed at A and C are such $AB=BC=L.$. The gravitational force on the third particle placed at D at a distance Lon the perpendicular bisector of the line AC is
A) $$\cfrac{{G{m^2}}}{{3\sqrt 2 {L^2}}}\,along\,DB$$
B) $$\cfrac{{G{m^2}}}{{\... | [
"F",
"$$\\cfrac{{G{m^2}}}{{\\sqrt 2 {L^2}}}\\,along\\,DB$$",
"F) $$\\cfrac{{G{m^2}}}{{\\sqrt 2 {L^2}}}\\,along\\,DB$$"
] |
Topic: Electrodynamics.
Question: There are two extremely thin concentric metallic spherical shells with radii $a$ and $b$, and the inner shell has a charge of $Q_{1}$. When the electric potential of the shells is zero, what are the potentials at $r \le a$, $a \le r \le b$, and $r \ge b$ respectively?
A) $$
0\ ,\frac{Q... | [
"I",
"$$\n0\\ ,\\frac{Q_{1}} {4 \\pi\\varepsilon_{0}} \\left( \\frac{1} {r}-\\frac{1} {a} \\right),\\ \\frac{Q_{1}} {4 \\pi\\varepsilon_{0} \\, r} \\left( 1-\\frac{b} {a} \\right)\n$$",
"I) $$\n0\\ ,\\frac{Q_{1}} {4 \\pi\\varepsilon_{0}} \\left( \\frac{1} {r}-\\frac{1} {a} \\right),\\ \\frac{Q_{1}} {4 \\pi\\var... |
Topic: Mathematical Analysis.
Question: For a positive integer $n$, let $f_n(x) = \cos(x) \cos(2x) \cos(3x) \cdots \cos(nx)$. Find the smallest $n$ such that $|f_n''(0)| > 2023$.
A) 17
B) 13
C) 20
D) 18
E) 19
F) 21
G) 16
H) 14
I) 15
J) 12 | [
"D",
"18",
"D) 18"
] |
Topic: Pharmaceutics.
Question: The isotonic equivalent of sodium chloride of cephalothiophene sodium is 0.24. How many more grams of sodium chloride is needed to prepare 2% eye drops 100mL?
A) 0.36g
B) 0.58g
C) 0.33g
D) 0.27g
E) 0.61g
F) 0.75g
G) 0.92g
H) 0.53g
I) 0.42g
J) 1.42g | [
"I",
"0.42g",
"I) 0.42g"
] |
Topic: Fundamental Mathematics.
Question: Calculate the double integral:
$$
\int\int_{R}{\left(x \cdot y \cdot \sqrt{x^2+y^2}\right) d A}
$$
where $R=\left\{(x,y)|0 \le x \le 1,0 \le y \le 2\right\}$.
A) frac{25\cdot\sqrt{5}-32}{15}
B) frac{25\cdot\sqrt{5}-38}{15}
C) frac{25\cdot\sqrt{5}-31}{15}
D) frac{25\cdot\sqrt{5}... | [
"D",
"frac{25\\cdot\\sqrt{5}-33}{15}",
"D) frac{25\\cdot\\sqrt{5}-33}{15}"
] |
Topic: Physical Oceanography.
Question: A semi-enclosed tidal bay has a water depth of 10 m, a length of 222 km, and a tidal range of 4 m at the bay's apex. Three bridges are planned at locations A, B, and C along the bay (represented by the diagram below). The distances are as follows: \( DA = AB = 0.5 \times BC \). I... | [
"D",
"A: 11.42 m, B: 10 m, C: 12 m",
"D) A: 11.42 m, B: 10 m, C: 12 m"
] |
Topic: Stellar and Interstellar Evolution.
Question: Evaluate the electron capture rate (18.4.14) numerically for extremely relativistic, degenerate electrons and freely escaping neutrinos is().
$$
\Gamma=\frac{2 \pi} {\hbar} \, \frac{G_{\mathrm{F}}^{2} C_{V}^{2} ( 1 \,+\, 3 a^{2} )} {\left( 2 \pi^{2} \hbar^{3} c^{3} \... | [
"A",
"$$\n6. 2 9 \\times1 0^{-4} \\frac{1} {5} \\left( \\frac{\\mu_{e}} {m_{e} c^{2}} \\right)^{5} \\mathrm{s}^{-1} \\mathrm{p r oton^{-1}}\n$$",
"A) $$\n6. 2 9 \\times1 0^{-4} \\frac{1} {5} \\left( \\frac{\\mu_{e}} {m_{e} c^{2}} \\right)^{5} \\mathrm{s}^{-1} \\mathrm{p r oton^{-1}}\n$$"
] |
Topic: Finance.
Question: Assuming that there are 2 billion yuan in cash in circulation, 10 billion yuan in deposits, 3 billion yuan in reserves in an economy, and the legal deposit reserve ratio is 0.2, then the excess deposit reserves and money multiplier held by commercial banks in the economy are ().
A) 2 billion a... | [
"H",
"1 billion and 2.4",
"H) 1 billion and 2.4"
] |
Topic: Electrodynamics.
Question: An electric field $\overline E = 50\widehat i + 75\widehat jN/C$ exists in a certain region of space. Presuming the potential at the origin to be zero, the potential at point P(1m,2m) will be
A) 50 V
B) -50 V
C) -150 V
D) 100 V
E) 175 V
F) -200 V
G) 150 V
H) -100 V
I) 125 V
J) 200 V | [
"D",
"100 V",
"D) 100 V"
] |
Topic: Relativity.
Question: Evaluate $\rho( r ) / \rho_{\infty}=n ( r ) / n_{\infty}$ at the event horizon is().
A) $$
5. 1 \times1 0^{1 0} \big( T_{\infty} / 1 0^{4} \big)^{-1 / 2}
$$
B) $$
1. 8 \times1 0^{1 1} \big( T_{\infty} / 1 0^{4} \big)^{-3 / 4}
$$
C) $$
4. 3 \times1 0^{1 1} \big( T_{\infty} / 1 0^{4} \big)^{-... | [
"F",
"$$\n3. 7 \\times1 0^{1 1} \\big( T_{\\infty} / 1 0^{4} \\big)^{-3 / 2}\n$$",
"F) $$\n3. 7 \\times1 0^{1 1} \\big( T_{\\infty} / 1 0^{4} \\big)^{-3 / 2}\n$$"
] |
Topic: Fundamentals of Dynamics and Control.
Question: A particle is moving along a circular path of radius $r=5\ m$ with a uniform speed ${5\ ms}^{-1}$. What is the magnitude of average acceleration $( {m/s}^{2})$ during the interval in which the particle complete half revolution?
A) $$\dfrac{12}{\pi}$$
B) \dfrac{15}{... | [
"C",
"$${\\dfrac{10}{\\pi}}$$",
"C) $${\\dfrac{10}{\\pi}}$$"
] |
Topic: Aeronautical and Astronautical Science and Technology.
Question: Transonic airfoil flow is to be initially analyzed using a water tunnel test through air-water analogy. To simulate an airflow with $M_{\infty}$=1.1,a water depth of 50mm is chosen for the water tunnel test. The water depth at the stagnation point ... | [
"B",
"0.0803m",
"B) 0.0803m"
] |
Topic: Atomic and Molecular Physics.
Question: The acceleration of an electron in the first orbit of the hydrogen atom $(n =1)$ is :
A) $$\dfrac{h^2}{\pi^2m^2r^3}$$
B) $$\dfrac {2\pi^2kme^2Z}{\eta h}$$
C) \dfrac{h^2}{6\pi m^2r^3}
D) \dfrac{h^2}{2\pi^2m^2r^3}
E) \dfrac{h^2}{5\pi m^2r^3}
F) \dfrac{h^2}{16\pi m^2r^3}
G) \... | [
"H",
"$$\\dfrac{h^2}{4\\pi m^2r^3}$$",
"H) $$\\dfrac{h^2}{4\\pi m^2r^3}$$"
] |
Topic: Probability and Statistics.
Question: Fold the line segment $[0,a]$ arbitrarily into three folds, so what is the probability that these three folds can form a triangle?
A) $$
{\frac{1} {12}}
$$
B) $$
{\frac{1} {2}}
$$
C) $$
{\frac{1} {4}}
$$
D) $$
{\frac{1} {3}}
$$
E) $$
{\frac{1} {8}}
$$
F) $$
{\frac{1} {9}}
$$... | [
"C",
"$$\n{\\frac{1} {4}}\n$$",
"C) $$\n{\\frac{1} {4}}\n$$"
] |
Topic: Communication Principles.
Question: If six messages having probabilities (1 / 4), (1 / 4), (1 / 8), (1 / 8), (1 / 8) and (1 / 8) can be accommodated in a single communication system, determine the entropy.
A) 2.50 bits/message
B) 3.00 bits/message
C) 1.75 bits/message
D) 4.00 bits/message
E) 1.50 bits/message
F)... | [
"A",
"2.50 bits/message",
"A) 2.50 bits/message"
] |
Topic: Quantitative Economics.
Question: A discount store is offering a special deal on CDs, reducing their price from ₹150 to ₹100. The store manager notes that the quantity demanded rises from 700 CDs to 1,300 CDs. What is the price elasticity of demand for CDs?
A) 0.8
B) 1.5
C) 1.6
D) 1.45
E) None of the other choic... | [
"B",
"1.5",
"B) 1.5"
] |
Topic: Industrial Economics.
Question: Company A has found that if it offers a guarantee on its transistor radios, more will be sold than without the guarantee. In a year, the company expects to sell 100 radios if no guarantee is offered, but if the length of the guarantee is t years then the number sold will be Q = 10... | [
"B",
"4 years",
"B) 4 years"
] |
Topic: Physical Chemistry.
Question: The hydrogen-filled dirigible "Hindenberg" had a gas volume of 1.4 × 10^8 liters. Assuming that it was filled to a pressure of 1 atm at 0°C, how much energy was released when it burned to gaseous products at a reaction temperature of 25°C? The standard heat of formation of water vap... | [
"J",
"360 × 10^6 Kcal",
"J) 360 × 10^6 Kcal"
] |
Topic: Ordinary Differential Equations.
Question: For $\mathbf{a}$ and $\mathbf{b}$, when the condition ( ) is satisfied, the solution $\mathrm{y}(\mathbf{x})$ of the equation $y^{\prime\prime}+ay^{\prime}+by=0$ as $x \to +\infty$ satisfies the relation $y(x)=o(e^{-x})$.
A) $2 < \mathrm{b}+1<\mathrm{a}$
B) $-3 < \mathr... | [
"F",
"$2 < \\mathrm{a} < \\mathrm{b}+1$",
"F) $2 < \\mathrm{a} < \\mathrm{b}+1$"
] |
Topic: Genetics.
Question: Two DNA molecules (① and ②) have the same number of base pairs (1000 bp), but their base compositions are different. ① contains 44% G+C, while ② contains 66% G+C. How many T are there in ① and ②, respectively?
A) 380, 620
B) 600, 320
C) 520, 360
D) 570, 330
E) 480, 240
F) 450, 550
G) 500, 400... | [
"J",
"560, 340",
"J) 560, 340"
] |
Topic: Poromechanics and Reservoir Physics.
Question: For a 1 m long core with a cross-sectional area of 4 cm², permeability of 2.5 × 10-¹² m², viscosity of the fluid passing through it of 1 cp, and a flow rate of 4 cm³/min, what is the pressure difference Δp that needs to be built up at both ends of the model?
A) 0.07... | [
"E",
"0.067 MPa",
"E) 0.067 MPa"
] |
Topic: Thermodynamics.
Question: In a highly rarefied gas with pressure $p$ and temperature $T$, there are two plates A and B moving parallel to each other at velocities $v_{\Lambda}$ and $v_{\mathrm{B}}$, respectively. what is the viscous force per unit area ?
( Assume the molar mass of the gas is $M$. )
A) $$
{\frac{... | [
"G",
"$$\n{\\frac{p} {2}} \\cdot{\\sqrt{\\frac{2 M} {\\pi R T}}} \\cdot( v_{\\mathrm{A}}-v_{\\mathrm{B}} ) \\,\n$$",
"G) $$\n{\\frac{p} {2}} \\cdot{\\sqrt{\\frac{2 M} {\\pi R T}}} \\cdot( v_{\\mathrm{A}}-v_{\\mathrm{B}} ) \\,\n$$"
] |
Topic: Engineering Fluid Mechanics.
Question: In \(2.0\) minutes, a ski lift raises four skiers at constant speed to a height
of \(140 \mathrm{~m}\). The average mass of each skier is \(65 \mathrm{~kg}\).
What is the average power provided by the tension in the cable pulling the
lift?
A) 2973.7 W
B) 2973.8 W
C) 2972.5 ... | [
"F",
"2973 W",
"F) 2973 W"
] |
Topic: Combinatorial Mathematics.
Question: The train has a total of $n$ cars, and $k (k \geq n)$ passengers board the train and choose the car at will. What is the probability that there is at least one passenger in each carriage?
A) $$1-\mathrm{C}_{n}^{1} ( 1-\frac{1} {n} )^{k}$$
B) $$2-\mathrm{C}_{n}^{1} ( 1-\frac{1... | [
"G",
"$$1-\\mathrm{C}_{n}^{1} ( 1-\\frac{1} {n} )^{k}+\\mathrm{C}_{n}^{2} ( 1-\\frac{2} {n} )^{i}-\\cdots+(-1 )^{n+1} \\mathrm{C}_{n}^{n-1} ( 1-\\frac{n-1} {n} )^{k}$$",
"G) $$1-\\mathrm{C}_{n}^{1} ( 1-\\frac{1} {n} )^{k}+\\mathrm{C}_{n}^{2} ( 1-\\frac{2} {n} )^{i}-\\cdots+(-1 )^{n+1} \\mathrm{C}_{n}^{n-1} ( 1-... |
Topic: Electrochemistry.
Question: Find the contributions of the conductivities of individual ions (ionic equivalent conductance \lambda_+ and \lambda_-) when٨(equivalent ٨ conductance of electrolytic solution) = 0.0412 m^2 /(\Omega) (mol) and t_+ = 0.825.
A) \lambda_+ = 0.0411 m^2 / (Ω) (mol), \lambda_- = 0.0001 m^2 /... | [
"I",
"\\lambda_+ = 0.03399 m^2 / (Ω) (mol), \\lambda_- = 0.00721 m^2 / (Ω) (mol)",
"I) \\lambda_+ = 0.03399 m^2 / (Ω) (mol), \\lambda_- = 0.00721 m^2 / (Ω) (mol)"
] |
Topic: Polynomials and Series Expansions.
Question: We now define an algorithm: The definition of a(n) is the number of possible decompositions of the polynomial $n * (x + x^2 + ... + x^q)$, where q > 1, into a sum of k polynomials, not necessarily all different; each of these polynomials is to be of the form $b_1 * x ... | [
"C",
"[1, 13, 5, 3, 5, 7, 1, 15, 5, 5]",
"C) [1, 13, 5, 3, 5, 7, 1, 15, 5, 5]"
] |
Topic: Engineering Fluid Mechanics.
Question: Using a V-notch weir ($q_{\mathrm{V}} = 0.316 \sqrt{2g} H^{2.5}$) to measure a flow rate of $q_{\mathrm{V}} = 0.015 \mathrm{m}^{3} / \mathrm{s}$, if there is a 1 mm error in reading the head over the weir, determine the relative error in the calculated flow rate $\frac{\mat... | [
"G",
"1.5%",
"G) 1.5%"
] |
Topic: Discrete Mathematics.
Question: We now define an algorithm: The definition of a(n) is the number of times one must divide n by 2 to reach 1 in the context of the '3x+1' problem, also known as the Collatz conjecture, or -1 if this never happens. Given the input x_list (a series of values): [67, 68, 69, 70, 71, 72... | [
"C",
"[19, 11, 11, 11, 65, 16, 73, 16, 11, 16]",
"C) [19, 11, 11, 11, 65, 16, 73, 16, 11, 16]"
] |
Topic: Genetics.
Question: The yellow body color of fruit flies is controlled by a sex-linked recessive gene, and the wild-type color is produced by a dominant allele. In a sample from a Hardy-Weinberg population, there are 1,021 wild-type male flies, 997 wild-type female flies, and 3 yellow male flies. What is the est... | [
"A",
"None of the above is correct.",
"A) None of the above is correct."
] |
Topic: Electrochemistry.
Question: A current 2.0 A is passed for 5 hours through a moltal salt deposits 22.2 g of metal(At wt=177).The oxidation state of the metal in the metal salt is:
A) +4
B) +3
C) +7
D) +5
E) +2
F) +9
G) +1
H) +6
I) +10
J) +8 | [
"A",
"+4",
"A) +4"
] |
Topic: Polynomials and Series Expansions.
Question: Let $P_n(x)=1+x+x^2+\cdots+x^n$ and $Q_n(x)=P_1\cdot P_2\cdots P_n$ for all integers $n\ge 1$ . How many more distinct complex roots does $Q_{1004}$ have than $Q_{1003}$ ?
A) 526
B) 530
C) 528
D) 531
E) 524
F) 527
G) 529
H) 522
I) 523
J) 525 | [
"C",
"528",
"C) 528"
] |
Topic: Theoretical Mechanics.
Question: A metal plate of mass 250gm is balanced in air by throwing balls each of mass 25gm vertically up. if the ball rebound at the rate of 20 per second with the same velocity, the velocity with which the balls strike the plate is $ (g = 10ms^-2) $
A) $$ 5 ms^-1 $$
B) $$7.5 ms^-1$$
C) ... | [
"A",
"$$ 5 ms^-1 $$",
"A) $$ 5 ms^-1 $$"
] |
Topic: Electrochemistry.
Question: The measured voltage of the concentration cell Ag\vertAgNO_3 (0.0100m) \vert\vertAgNO_3 (y)\vertAg was 0.0650 V at 25°C. Calculate themolalityy of the right-hand half-cell assuming \gamma_\pm = 1.
A) 0.1205m
B) 0.1005m
C) 0.1755m
D) 0.1505m
E) 0.2005m
F) 0.1405m
G) 0.1105m
H) 0.0805m
... | [
"J",
"0.1255m",
"J) 0.1255m"
] |
Topic: Public Finance.
Question: Norman Stevens lives in a town where 28% of the property tax is passed along to the county government. Mr. Stevens owns a home which was assessed for $17,400. If the town's tax rate is $24.90 per $1,000, how much of his tax was passed along to the county government?
A) $312.26
B) $162.2... | [
"G",
"Both $121.31 and $121.30 + $0.01 are correct",
"G) Both $121.31 and $121.30 + $0.01 are correct"
] |
Topic: Acoustics.
Question: A monochromatic light source S of wavelength $440$ nm is placed slightly above a plane mirror M as shown. Image of S in M can be used as a virtual source to produce interference fringes on the screen. The distance of source S from O is $20.0$cm, and the distance of screen from O is $100.0$ c... | [
"F",
"$2.64$ mm",
"F) $2.64$ mm"
] |
Topic: Thermodynamics.
Question: A spring oscillator performs simple harmonic motion with an amplitude of $12 \text{ cm}$. At a distance of $6 \text{ cm}$ from the equilibrium position, its velocity is $24 \ \text{cm} \cdot \text{s}^{-1}$. Find the displacement when the velocity is $12 \text{ cm} \cdot \text{s}^{-1}$.
... | [
"H",
"$$\n\\approx\\pm1 0. 8 \\, ( \\mathrm{c m} )\n$$",
"H) $$\n\\approx\\pm1 0. 8 \\, ( \\mathrm{c m} )\n$$"
] |
Topic: Hydraulics and Hydrology.
Question: Manning's formula for velocity of flow $V$ in uniform flow in a open channel is written as
$$
V=\frac{1} {n} \; R^{2 / 3} \; S_{0}^{1 / 2}
$$
where $R$ = hydraulic radius, $S_{0}$ = bed slope and
n = Manning's coefficient. Determine the dimen- sions of $n$ .
A) $$
[ \mathrm{L}... | [
"I",
"$$\n[ \\mathrm{L}^{-1 / 3} \\mathrm{T} ]\n$$",
"I) $$\n[ \\mathrm{L}^{-1 / 3} \\mathrm{T} ]\n$$"
] |
Topic: Probability and Statistics.
Question: A person bought a total of 11 fruits, of which 3 are second-grade and 8 are first-grade. The fruits are randomly distributed among $A$, $B$, and $C$, with each person receiving 4, 6, and 1 fruit, respectively. What is the probability that both $A$ and $B$ receive second-grad... | [
"G",
"$$\n{\\frac{3 2} {5 5}}\n$$",
"G) $$\n{\\frac{3 2} {5 5}}\n$$"
] |
Topic: Acoustics.
Question: For a piston sound source with a radius of 0.12 m mounted on an infinitely large rigid baffle, emitting sound waves at a frequency of 2000 Hz, find the beamwidth where the sound pressure level decreases by 6 dB. (Operating in air)
A) $$
2 5^{\circ} \times2=5 0^{\circ}
$$
B) $$
2 8^{\circ} \t... | [
"H",
"$$\n3 0^{\\circ} \\times2=6 0^{\\circ}\n$$",
"H) $$\n3 0^{\\circ} \\times2=6 0^{\\circ}\n$$"
] |
Topic: Thermal Energy Engineering.
Question: For a thermodynamic system undergoing a state change, the relationship between pressure and volume is given by \( p V^{1.3} = \text{constant} \). If the initial state of the thermodynamic system is \( p_{1} = 600 \ \mathrm{kPa}, \ V_{1} = 0.3 \ \mathrm{m}^{3} \), what is the... | [
"H",
"$$\n3 4. 3 6 k J\n$$",
"H) $$\n3 4. 3 6 k J\n$$"
] |
Topic: Applied Optics.
Question: The principal axis of an optical device is along $y=-1$, image of a small body placed at ($-30, 3$) is formed at a point ($60, -3$). Then the optical device is:-
A) A concave lens of focal length $20\ cm$
B) A convex mirror of focal length $60\ cm$
C) A concave lens of focal length $30\... | [
"D",
"A convex lens of focal length $20\\ cm$",
"D) A convex lens of focal length $20\\ cm$"
] |
Topic: Number Theory.
Question: Find all natural numbers that satisfy $3^{m}-1$ being divisible by $2^{m}$.
A) 3,5,7
B) 1,4,5
C) 2,5,6
D) 1,3,5
E) 2,4,6
F) 1,2,4
G) 1,3,4
H) 2,3,5
I) 2,3,4
J) 1,2,3 | [
"F",
"1,2,4",
"F) 1,2,4"
] |
Topic: Thermodynamics and Statistical Physics.
Question: If the vapor pressure of ethyl alcohol, C_2H_5OH, is 0.132 atm at 34.9°C, and 0.526 atm at 63.5°C what do you predict it will be at 19.0°C?
A) 0.132 atm
B) 0.3 atm
C) 0.4 atm
D) 0.65 atm
E) 0.2 atm
F) 0.7 atm
G) 0.526 atm
H) 0.025 atm
I) 0.0545 atm
J) 0.08 atm | [
"I",
"0.0545 atm",
"I) 0.0545 atm"
] |
Topic: Geometry and Topology.
Question: The option that represents the area of the plane figure enclosed by ( x = 1 - {y^2},;x = 0 ) is
A) ( int_0^1 {left[ {sqrt {1 - x} + sqrt {1 - x} } right]dx} )
B) ( int_0^1 {left[ {sqrt {1 - x} - sqrt {1 - x} } right]dx} )
C) ( int_0^1 {left[ {sqrt {1 - x} - ( - sqrt {1 - x} )} ri... | [
"C",
"( int_0^1 {left[ {sqrt {1 - x} - ( - sqrt {1 - x} )} right]dx} )",
"C) ( int_0^1 {left[ {sqrt {1 - x} - ( - sqrt {1 - x} )} right]dx} )"
] |
Topic: Mechatronic Engineering.
Question: Suppose a nickel element is used (calculate the temperature coefficient of resistance at least with 4-digit precision). If the resistance element is taken as being 100 Ω at 0°C what are its resistance at 30°C and 50°C?
A) 121.1 Ω and 133.6 Ω
B) 121.1 Ω and 134.5 Ω
C) 121.1 Ω and... | [
"D",
"121.1 Ω and 133.5 Ω",
"D) 121.1 Ω and 133.5 Ω"
] |
Topic: Elements of Chemical Reaction Engineering.
Question: Using series-connected continuously stirred tank reactors (CSTRs) for a first-order irreversible reaction, assuming that the volume and operating temperature of each reactor are identical, the rate constant at this temperature is known to be $k \!=\! 0.92 \, \... | [
"I",
"$$\n25.3m^{3}\n$$",
"I) $$\n25.3m^{3}\n$$"
] |
Topic: Discrete Mathematics.
Question: We now define an algorithm: The definition of a(n) is the exponent of the highest power of 2 dividing n, also known as the binary carry sequence, the ruler sequence, or the 2-adic valuation of n. Given the input x_list (a series of values): [102, 103, 104, 105, 106, 107, 108, 109,... | [
"E",
"[1, 0, 3, 0, 1, 0, 2, 0, 1, 0]",
"E) [1, 0, 3, 0, 1, 0, 2, 0, 1, 0]"
] |
Topic: Physical Chemistry.
Question: If for $2A_2B(g) \rightleftharpoons 2A_2(g) + B_2(g)$, $K_p$ = total pressure (at equilibrium ) and starting the dissociation from 4 mol of $A_2B$ then :
A) degree of dissociation of $A_2B$ will be (2/3).
B) at equilibrium the no. of moles of $A_2B$ are equal to the no. of moles of ... | [
"G",
"at equilibrium the no. of moles of $A_2B$ are not equal to the no. of moles of $B_2$.",
"G) at equilibrium the no. of moles of $A_2B$ are not equal to the no. of moles of $B_2$."
] |
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