source stringclasses 1
value | id stringclasses 173
values | question stringlengths 10 4.67k | options listlengths 4 4 | answer stringclasses 4
values | reasoning null |
|---|---|---|---|---|---|
MMLU | MMLU-57 | Let V be the vector space, under the usual operations, of real polynomials that are of degree at most 3. Let W be the subspace of all polynomials p (x) in V such that p (0) = p(1) = p(-1) = 0. Then dim V + dim W is | [
"4",
"5",
"6",
"7"
] | B | null |
MMLU | MMLU-58 | If V and W are 2-dimensional subspaces of R^4 ,what are the possible dimensions of the subspace V intersect W? | [
"1 only",
"2 only",
"0 and 1 only",
"0, 1, and 2 only"
] | D | null |
MMLU | MMLU-59 | The curves y = (sin x + cos x)^4 and y = (sin x - cos x)^4 intersect at x = 0. If a is the smallest positive value of x at which these curves next intersect, determine the area between these curves from x = 0 to x = a. | [
"2",
"π",
"4",
"3π/2"
] | C | null |
MMLU | MMLU-60 | If f is a linear transformation from the plane to the real numbers and if f(1, 1) = 1 and f(-1, 0) = 2, then f(3, 5) = | [
"9",
"8",
"0",
"-5"
] | A | null |
MMLU | MMLU-61 | How many real roots does the polynomial 2x^5 + 8x - 7 have? | [
"None",
"One",
"Two",
"Three"
] | B | null |
MMLU | MMLU-62 | A university’s mathematics department has 10 professors and will offer 20 different courses next semester. Each professor will be assigned to teach exactly 2 of the courses, and each course will have exactly one professor assigned to teach it. If any professor can be assigned to teach any course, how many different com... | [
"20!/2^(10)",
"10!/2^9",
"10^(20) - 2^(10)",
"10^(20) - 100"
] | A | null |
MMLU | MMLU-63 | Which of the following are true: | [
"It is possible to place an linear order relation ≤ on the complex numbers C such that (C, +, ×, ≤) is not an ordered field.",
"It is possible to place a linear order relation on the complex numbers C which make (C, +, ×, ≤) an ordered field.",
"Neither (a) nor (b)",
"Both (a) and (b)."
] | A | null |
MMLU | MMLU-64 | In a game two players take turns tossing a fair coin; the winner is the first one to toss a head. The probability that the player who makes the first toss wins the game is | [
"1/4",
"1/3",
"1/2",
"2/3"
] | D | null |
MMLU | MMLU-65 | Which of the following is NOT a group? | [
"The integers under addition",
"The nonzero integers under multiplication",
"The nonzero real numbers under multiplication",
"The complex numbers under addition"
] | B | null |
MMLU | MMLU-66 | Let x and y be positive integers such that 3x + 7y is divisible by 11. Which of the following must also be divisible by 11? | [
"4x + 6y",
"x + y + 5",
"9x + 4y",
"4x - 9y"
] | D | null |
MMLU | MMLU-67 | What is the minimum value of the expression x + 4z as a function defined on R^3, subject to the constraint x^2 + y^2 + z^2 <= 2? | [
"0",
"-2",
"-sqrt(34)",
"-sqrt(35)"
] | C | null |
MMLU | MMLU-68 | Let R be a ring and let U and V be (two-sided) ideals of R. Which of the following must also be ideals of R ?
I. {u + v : u \in and v \in V}
II. {uv : u \in U and v \in V}
III. {x : x \in U and x \in V} | [
"II only",
"III only",
"I and II only",
"I and III only"
] | D | null |
MMLU | MMLU-69 | The region bounded by the x-axis and the function f(x) = x/(1 + x^3) is rotated about the x-axis. What is the volume of the solid generated? | [
"π/3",
"π/4",
"π",
"2π"
] | A | null |
MMLU | MMLU-70 | Suppose today is Wednesday. What day of the week will it be 10^(10^(10)) days from now? | [
"Sunday",
"Monday",
"Tuesday",
"Wednesday"
] | A | null |
MMLU | MMLU-71 | Water drips out of a hole at the vertex of an upside down cone at a rate of 3 cm^3 per minute. The
cone’s height and radius are 2 cm and 1 cm, respectively. At what rate does the height of the water change
when the water level is half a centimeter below the top of the cone? The volume of a cone is V = (π/3)*r^2*h,
wher... | [
"−48/π cm/min",
"−4/(3π) cm/min",
"−8/(3π) cm/min",
"−16/(3π) cm/min"
] | D | null |
MMLU | MMLU-72 | Consider the system of linear equations
w + 3x + 2y + 2z = 0
w + 4x + y = 0
3w + 5x + 10 y + 14z = 0
2w + 5x + 5y + 6z = 0
with solutions of the form (w, x, y, z), where w x, y, and z are real. Which of the following statements is FALSE? | [
"The system is consistent.",
"The system has infinitely many solutions.",
"The sum of any two solutions is a solution.",
"Every solution is a scalar multiple of (-5, 1, 1, 0)."
] | D | null |
MMLU | MMLU-73 | If c > 0 and f(x) = e^x - cx for all real numbers x, then the minimum value of f is | [
"f(c)",
"f(e^c)",
"f(1/c)",
"f(log c)"
] | D | null |
MMLU | MMLU-74 | Suppose A is a 3 × 3 matrix such that det(A − λI) = −λ^3 + 3λ^2 + λ − 3, where I is the 3 × 3 identity matrix. Which of the following are TRUE of A?
I. The trace of A is 3.
II. The determinate of A is −3.
III. The matrix A has eigenvalues −3 and 1. | [
"I only",
"II only",
"III only",
"I and II only"
] | D | null |
MMLU | MMLU-75 | Let y = f(x) be a solution of the differential equation x dy + (y - xe^x) dx = 0 such that y = 0 when x = 1. What is the value of f(2)? | [
"1/(2e)",
"1/e",
"e^2/2",
"2e"
] | C | null |
MMLU | MMLU-76 | A fair coin is to be tossed 100 times, with each toss resulting in a head or a tail. If H is the total number of heads and T is the total number of tails, which of the following events has the greatest probability? | [
"H = 50",
"T >= 60",
"51 <= H <= 55",
"H >= 48 and T >= 48"
] | D | null |
MMLU | MMLU-77 | Statement 1 | Suppose f : [a, b] is a function and suppose f has a local maximum. f'(x) must exist and equal 0? Statement 2 | There exist non-constant continuous maps from R to Q. | [
"True, True",
"True, False",
"False, True",
"False, False"
] | D | null |
MMLU | MMLU-78 | Let I != A != -I, where I is the identity matrix and A is a real 2 x 2 matrix. If A = A^(-1), then the trace of A is | [
"2",
"1",
"0",
"-1"
] | C | null |
MMLU | MMLU-79 | A total of x feet of fencing is to form three sides of a level rectangular yard. What is the maximum possible area of the yard, in terms of x ? | [
"x^2/9",
"x^2/8",
"x^2/4",
"x^2"
] | B | null |
MMLU | MMLU-80 | Statement 1 | If A is connected, the closure of A must be connected. Statement 2 | Every continuous function f : (0, 1) → (0, 1) has a fixed point. | [
"True, True",
"True, False",
"False, True",
"False, False"
] | B | null |
MMLU | MMLU-81 | Which of the following sets has the greatest cardinality? | [
"R",
"The set of all functions from Z to Z",
"The set of all functions from R to {0, 1}",
"The set of all finite subsets of R"
] | C | null |
MMLU | MMLU-82 | Let f(x) be a function whose graph passes through the origin. If f(2n) = n^2 + f[2(n - 1)] for every integer n, what is the value of f(8)? | [
"24",
"30",
"32",
"36"
] | B | null |
MMLU | MMLU-83 | How many structurally distinct Abelian groups have order 72? | [
"4",
"6",
"8",
"9"
] | B | null |
MMLU | MMLU-84 | If the finite group G contains a subgroup of order seven but no element (other than the identity) is its own inverse, then the order of G could be | [
"27",
"28",
"35",
"37"
] | C | null |
MMLU | MMLU-85 | Let f(x, y) = x^3 + y^3 + 3xy for all real x and y. Then there exist distinct points P and Q such that f has a | [
"local maximum at P and at Q",
"saddle point at P and at Q",
"local maximum at P and a saddle point at Q",
"local minimum at P and a saddle point at Q"
] | C | null |
MMLU | MMLU-86 | If A is a subset of the real line R and A contains each rational number, which of the following must be true? | [
"If A is open, then A = R.",
"If A is closed, then A = R.",
"If A is uncountable, then A = R.",
"If A is uncountable, then A is open."
] | B | null |
MMLU | MMLU-87 | Let M be a 5 x 5 real matrix. Exactly four of the following five conditions on M are equivalent to each other. Which of the five conditions is equivalent to NONE of the other four? | [
"For any two distinct column vectors u and v of M, the set {u, v} is linearly independent.",
"The homogeneous system Mx = 0 has only the trivial solution.",
"The system of equations Mx = b has a unique solution for each real 5 x 1 column vector b.",
"The determinant of M is nonzero."
] | A | null |
MMLU | MMLU-88 | How many positive numbers x satisfy the equation cos(97x) = x? | [
"1",
"15",
"31",
"49"
] | C | null |
MMLU | MMLU-89 | For which of the following rings is it possible for the product of two nonzero elements to be zero? | [
"The ring of complex numbers",
"The ring of integers modulo 11",
"The ring of continuous real-valued functions on [0, 1]",
"The ring {a + b * sqrt(2) : a and b are rational numbers}"
] | C | null |
MMLU | MMLU-90 | The map x -> axa^2 of a group G into itself is a homomorphism if and only if | [
"G is abelian",
"G = {e}",
"a^3 = e",
"a^2 = a"
] | C | null |
MMLU | MMLU-91 | If A is the 2 by 2 matrix whose (i, j) entry is equal to i + j, and B is the 3 by 3 matrix whose (i, j) entry is equal to i + j, find the value of the sum detA + detB. | [
"-2",
"-1",
"0",
"2"
] | B | null |
MMLU | MMLU-92 | If f : (0, 1) → (0, 1], then which of the following could be TRUE?
I. f is one-to-one and onto.
II. The image of f is compact.
III. f is continuous, one-to-one, and onto. | [
"I only",
"II only",
"I and II only",
"I and III only"
] | C | null |
MMLU | MMLU-93 | If a real number x is chosen at random in the interval [0, 3] and a real number y is chosen at random in the interval [0, 4], what is the probability that x < y? | [
"1/2",
"7/12",
"5/8",
"2/3"
] | C | null |
MMLU | MMLU-94 | The probability that a point (x, y) in R^2 is chosen follows a uniform random distribution within the region described by the inequality 0 < |x| + |y| < 1 . What is the probability that 2(x + y) > 1? | [
"0",
"1/4",
"sqrt(2)/4",
"1/sqrt(2)"
] | B | null |
MMLU | MMLU-95 | (1+i)^10 = | [
"1",
"i",
"32",
"32i"
] | D | null |
MMLU | MMLU-96 | If U and V are 3-dimensional subspaces of R^5, what are the possible dimensions of U ∩ V? | [
"0",
"1",
"0 or 1",
"1, 2, or 3"
] | D | null |
MMLU | MMLU-97 | Let S be the subset of R^2 consisting of all points (x, y) in the unit square [0, 1] × [0, 1] for which x or y, or both, are irrational. With respect to the standard topology on R^2, S is | [
"closed",
"open",
"connected",
"totally disconnected"
] | C | null |
MMLU | MMLU-98 | Which of the following circles has the greatest number of points of intersection with the parabola x^2 = y + 4 ? | [
"x^2 + y^2 = 1",
"x^2 + y^2 = 2",
"x^2 + y^2 = 9",
"x^2 + y^2 = 16"
] | C | null |
MMLU | MMLU-99 | X is a finite set with the following property: The number of subsets of X that contain exactly 3 elements is 14 more than the number of subsets of X that contain exactly 2 elements. How many subsets of X contain exactly 4 elements? | [
"24",
"25",
"28",
"35"
] | D | null |
MMLU | MMLU-100 | Let T: R^2 -> R^2 be the linear transformation that maps the point (1, 2) to (2, 3) and the point (-1, 2) to (2, -3). Then T maps the point (2, 1) to | [
"(1, 6)",
"(-1, 4)",
"(3, 2)",
"(-4, 3)"
] | A | null |
MMLU | MMLU-1 | The quantum efficiency of a photon detector is 0.1. If 100 photons are sent into the detector, one after the other, the detector will detect photons | [
"an average of 10 times, with an rms deviation of about 4",
"an average of 10 times, with an rms deviation of about 3",
"an average of 10 times, with an rms deviation of about 1",
"an average of 10 times, with an rms deviation of about 0.1"
] | B | null |
MMLU | MMLU-2 | White light is normally incident on a puddle of water (index of refraction 1.33). A thin (500 nm) layer of oil (index of refraction 1.5) floats on the surface of the puddle. Of the following, the most strongly reflected wavelength is | [
"500 nm",
"550 nm",
"600 nm",
"650 nm"
] | C | null |
MMLU | MMLU-3 | Which of the following is true about any system that undergoes a reversible thermodynamic process? | [
"There are no changes in the internal energy of the system.",
"The temperature of the system remains constant during the process.",
"The entropy of the system and its environment remains unchanged.",
"The entropy of the system and its environment must increase."
] | C | null |
MMLU | MMLU-4 | The best type of laser with which to do spectroscopy over a range of visible wavelengths is | [
"a dye laser",
"a helium-neon laser",
"an excimer laser",
"a ruby laser"
] | A | null |
MMLU | MMLU-5 | Excited states of the helium atom can be characterized as para- (antiparallel electron spins) and ortho- (parallel electron spins). The observation that an ortho- state has lower energy than the corresponding para- state can be understood in terms of which of the following? | [
"The Heisenberg uncertainty principle",
"The Pauli exclusion principle",
"The Bohr model of the atom",
"Nuclear hyperfine coupling"
] | B | null |
MMLU | MMLU-6 | Which of the following gives the total spin quantum number of the electrons in the ground state of neutral nitrogen (Z = 7)? | [
"1/2",
"1",
"3/2",
"5/2"
] | C | null |
MMLU | MMLU-7 | Consider three identical, ideal capacitors. The first capacitor is charged to a voltage and then disconnected from the battery. The other two capacitors, initially uncharged and connected in series, are then connected across the first capacitor. What is the final voltage on the first capacitor? | [
"V_0/5",
"V_0/3",
"V_0/2",
"2V_0/3"
] | D | null |
MMLU | MMLU-8 | Protons used in cancer therapy are typically accelerated to about 0.6c. How much work must be done on a particle of mass m in order for it to reach this speed, assuming it starts at rest? | [
"0.25mc^2",
"0.60mc^2",
"0.67mc^2",
"1.25mc^2"
] | A | null |
MMLU | MMLU-9 | De Broglie hypothesized that the linear momentum and wavelength of a free massive particle are related by which of the following constants? | [
"Planck’s constant",
"Boltzmann’s constant",
"The Rydberg constant",
"The speed of light"
] | A | null |
MMLU | MMLU-10 | If the total energy of a particle of mass m is equal to twice its rest energy, then the magnitude of the particle’s relativistic momentum is | [
"mc/2",
"mc/(2^(1/2))",
"mc",
"(3^(1/2))mc"
] | D | null |
MMLU | MMLU-11 | In the diamond structure of elemental carbon, the nearest neighbors of each C atom lie at the corners of a | [
"square",
"hexagon",
"cube",
"tetrahedron"
] | D | null |
MMLU | MMLU-12 | The coefficient of static friction between a small coin and the surface of a turntable is 0.30. The turntable rotates at 33.3 revolutions per minute. What is the maximum distance from the center of the turntable at which the coin will not slide? | [
"0.024 m",
"0.048 m",
"0.121 m",
"0.242 m"
] | D | null |
MMLU | MMLU-13 | The sign of the charge carriers in a doped semiconductor can be deduced by measuring which of the following properties? | [
"Specific heat",
"Thermal conductivity",
"Electrical resistivity",
"Hall coefficient"
] | D | null |
MMLU | MMLU-14 | The primary source of the Sun’s energy is a series of thermonuclear reactions in which the energy produced is c^2 times the mass difference between | [
"two hydrogen atoms and one helium atom",
"four hydrogen atoms and one helium atom",
"six hydrogen atoms and two helium atoms",
"three helium atoms and one carbon atom"
] | B | null |
MMLU | MMLU-15 | Electromagnetic radiation provides a means to probe aspects of the physical universe. Which of the following statements regarding radiation spectra is NOT correct? | [
"Lines in the infrared, visible, and ultraviolet regions of the spectrum reveal primarily the nuclear structure of the sample.",
"The wavelengths identified in an absorption spectrum of an element are among those in its emission spectrum.",
"Absorption spectra can be used to determine which elements are present... | A | null |
MMLU | MMLU-16 | Which of the following statements about bosons and/or fermions is true? | [
"Bosons have symmetric wave functions and obey the Pauli exclusion principle.",
"Bosons have antisymmetric wave functions and do not obey the Pauli exclusion principle.",
"Fermions have symmetric wave functions and obey the Pauli exclusion principle.",
"Fermions have antisymmetric wave functions and obey the ... | D | null |
MMLU | MMLU-17 | Excited states of the helium atom can be characterized as para- (antiparallel electron spins) and ortho- (parallel electron spins). The observation that an ortho- state has lower energy than the corresponding para- state can be understood in terms of which of the following? | [
"The Heisenberg uncertainty principle",
"The Pauli exclusion principle",
"The Bohr model of the atom",
"Nuclear hyperfine coupling"
] | B | null |
MMLU | MMLU-18 | One end of a horizontal, massless spring is attached to a wall. A mass of 0.30 kg is attached to the other end of the spring and rests on a table. The mass is displaced 0.030 m from its equilibrium position and released. It has a speed of 0.040 m/s as it passes through its equilibrium position. In the absence of fricti... | [
"0.24 mJ",
"0.38 mJ",
"0.48 mJ",
"0.75 mJ"
] | A | null |
MMLU | MMLU-19 | A meter stick with a speed of 0.8c moves past an observer. In the observer’s reference frame, how long does it take the stick to pass the observer ? | [
"1.6 ns",
"2.5 ns",
"4.2 ns",
"6.9 ns"
] | B | null |
MMLU | MMLU-20 | Protons used in cancer therapy are typically accelerated to about 0.6c . How much work must be done on a particle of mass m in order for it to reach this speed, assuming it starts at rest? | [
"0.25mc^2",
"0.60mc^2",
"0.67mc^2",
"1.25mc^2"
] | A | null |
MMLU | MMLU-21 | Characteristic X rays, appearing as sharp lines on a continuous background, are produced when high-energy electrons bombard a metal target. Which of the following processes results in the characteristic X rays? | [
"Electrons producing Čerenkov radiation",
"Electrons colliding with phonons in the metal",
"Electrons filling inner shell vacancies that are created in the metal atoms",
"Electrons combining with protons to form neutrons"
] | C | null |
MMLU | MMLU-22 | An atom has filled n = 1 and n = 2 levels. How many electrons does the atom have? | [
"2",
"4",
"6",
"10"
] | D | null |
MMLU | MMLU-23 | Light from a laser falls on a pair of very narrow slits separated by 0.5 micrometer, and bright fringes separated by 1.0 millimeter are observed on a distant screen. If the frequency of the laser light is doubled, what will be the separation of the bright fringes? | [
"0.25 mm",
"0.5 mm",
"1.0 mm",
"2.0 mm"
] | B | null |
MMLU | MMLU-24 | Assume that the solar flux at Earth’s surface is 1,000 W/m^2 and that the sunlight is normal to a completely reflecting surface with an area of 3 m^2. What is the total radiation force exerted on the surface? | [
"2 x 10^-6 N",
"1 x 10^-5 N",
"2 x 10^-5 N",
"3 N"
] | C | null |
MMLU | MMLU-25 | The sign of the charge carriers in a doped semiconductor can be deduced by measuring which of the following properties? | [
"Magnetic susceptibility",
"Hall coefficient",
"Electrical resistivity",
"Thermal conductivity"
] | B | null |
MMLU | MMLU-26 | Which of the following ions CANNOT be used as a dopant in germanium to make an n-type semiconductor? | [
"As",
"P",
"Sb",
"B"
] | D | null |
MMLU | MMLU-27 | An astronomer observes a very small moon orbiting a planet and measures the moon’s minimum and maximum distances from the planet’s center and the moon’s maximum orbital speed. Which of the following CANNOT be calculated from these measurements? | [
"Mass of the moon",
"Mass of the planet",
"Minimum speed of the moon",
"Period of the orbit"
] | A | null |
MMLU | MMLU-28 | A rod measures 1.00 m in its rest system. How fast must an observer move parallel to the rod to measure its length to be 0.80 m? | [
"0.50c",
"0.60c",
"0.70c",
"0.80c"
] | B | null |
MMLU | MMLU-29 | A proton moves in the +z-direction after being accelerated from rest through a potential difference V. The proton then passes through a region with a uniform electric field E in the +x-direction and a uniform magnetic field B in the +y-direction, but the proton’s trajectory is not affected. If the experiment were repea... | [
"deflected in the +x-direction",
"deflected in the -x-direction",
"deflected in the +y-direction",
"deflected in the -y-direction"
] | B | null |
MMLU | MMLU-30 | A magnetic field is directed perpendicular to the plane of a circular coil of area 0.2 m^2 and 250 turns. If the magnetic field is increased from 0.01 T to 0.06 T during a time interval of 0.25 s, the average induced EMF in the coil is | [
"0.04 V",
"0.1 V",
"2.5 V",
"10 V"
] | D | null |
MMLU | MMLU-31 | Light of variable frequency shines on the metal surface of a photoelectric tube. Einstein’s theory of the photoelectric effect predicts that the | [
"work function of the metal is proportional to the frequency",
"work function of the metal is proportional to the wavelength",
"current in the tube is a linear function of the wavelength",
"potential difference necessary to stop the emitted electrons is a linear function of the frequency above the threshold f... | D | null |
MMLU | MMLU-32 | If the Sun were suddenly replaced by a black hole of the same mass, it would have a Schwarzschild radius of 3,000 m. What effect, if any, would this change have on the orbits of the planets? | [
"The planets would move directly toward the Sun.",
"The planets would move in spiral orbits.",
"The planets would oscillate about their former elliptical orbits.",
"The orbits would remain unchanged."
] | D | null |
MMLU | MMLU-33 | At 20°C, a pipe open at both ends resonates at a frequency of 440 hertz. At what frequency does the same pipe resonate on a particularly cold day when the speed of sound is 3 percent lower than it would be at 20°C ? | [
"414 Hz",
"427 Hz",
"433 Hz",
"440 Hz"
] | B | null |
MMLU | MMLU-34 | The quantum efficiency of a photon detector is 0.1. If 100 photons are sent into the detector, one after the other, the detector will detect photons | [
"exactly 10 times",
"an average of 10 times, with an rms deviation of about 0.1",
"an average of 10 times, with an rms deviation of about 1",
"an average of 10 times, with an rms deviation of about 3"
] | D | null |
MMLU | MMLU-35 | A three-dimensional harmonic oscillator is in thermal equilibrium with a temperature reservoir at temperature T. The average total energy of the oscillator is | [
"(1/2) k T",
"kT",
"(3/2) k T",
"3kT"
] | D | null |
MMLU | MMLU-36 | A student makes 10 one-second measurements of the disintegration of a sample of a long-lived radioactive isotope and obtains the following values: 3, 0, 2, 1, 2, 4, 0, 1, 2, 5. How long should the student count to establish the rate to an uncertainty of 1 percent? | [
"80 s",
"160 s",
"2,000 s",
"5,000 s"
] | D | null |
MMLU | MMLU-37 | By definition, the electric displacement current through a surface S is proportional to the | [
"magnetic flux through S",
"rate of change of the magnetic flux through S",
"time integral of the magnetic flux through S",
"rate of change of the electric flux through S"
] | D | null |
MMLU | MMLU-38 | The negative muon, mu^-, has properties most similar to which of the following? | [
"Electron",
"Meson",
"Photon",
"Boson"
] | A | null |
MMLU | MMLU-39 | The speed of light inside of a nonmagnetic dielectric material with a dielectric constant of 4.0 is | [
"1.2 x 10^9 m/s",
"3.0 x 10^8 m/s",
"1.5 x 10^8 m/s",
"1.0 x 10^8 m/s"
] | C | null |
MMLU | MMLU-40 | The energy from electromagnetic waves in equilibrium in a cavity is used to melt ice. If the Kelvin temperature of the cavity is increased by a factor of two, the mass of ice that can be melted in a fixed amount of time is increased by a factor of | [
"2",
"4",
"8",
"16"
] | D | null |
MMLU | MMLU-41 | A resistor in a circuit dissipates energy at a rate of 1 W. If the voltage across the resistor is doubled, what will be the new rate of energy dissipation? | [
"0.25 W",
"0.5 W",
"1 W",
"4 W"
] | D | null |
MMLU | MMLU-42 | A gas cell with an optical path length of 10 cm is placed in one arm of a Michelson interferometer. If the light source for the interferometer is a laser with wavelength 632.2 nm, then 100 fringes are counted as the gas cell is evacuated. What is the index of refraction of the original gas? | [
"1.00063",
"1.00032",
"1.00016",
"0.99968"
] | B | null |
MMLU | MMLU-43 | Under certain conditions, a beam of electrons impinging on a crystal surface will diffract and a scattering pattern of the beam can be obtained. What is the approximate kinetic energy of the electrons needed in order to see the pattern? (Assume the lattice spacing of the crystal to be 0.4 nm.) | [
"0.1 eV",
"1 eV",
"10 eV",
"100 eV"
] | C | null |
MMLU | MMLU-44 | A uniform solid disk starts from rest and rolls down an inclined plane without slipping. After some time, what fraction of the disk’s total kinetic energy is rotational kinetic energy? | [
"1/4",
"1/3",
"1/2",
"2/3"
] | B | null |
MMLU | MMLU-45 | Blue light of wavelength 480 nanometers is most strongly reflected off a thin film of oil on a glass slide when viewed near normal incidence. Assuming that the index of refraction of the oil is 1.2 and that of the glass is 1.6, what is the minimum thickness of the oil film (other than zero) ? | [
"150 nm",
"200 nm",
"300 nm",
"400 nm"
] | B | null |
MMLU | MMLU-46 | A heat pump is to extract heat from an outdoor environment at 7°C and heat the environment indoors to 27°C. For each 15,000 J of heat delivered indoors, the smallest amount of work that must be supplied to the heat pump is approximately | [
"500 J",
"1,000 J",
"1,100 J",
"2,000 J"
] | B | null |
MMLU | MMLU-47 | The driver of a police car hears an echo of the car’s siren from a wall toward which the car is moving with a speed of 3.5 m/s. If the speed of sound is 350 m/s and the frequency of the siren is 600 Hz, the driver hears the echo at a frequency nearest to which of the following? | [
"600 Hz",
"606 Hz",
"612 Hz",
"618 Hz"
] | C | null |
MMLU | MMLU-48 | A particle decays in 2.0 ms in its rest frame. If the same particle moves at v=0.60c in the lab frame, how far will it travel in the lab before decaying? | [
"150 m",
"288 m",
"360 m",
"450 m"
] | D | null |
MMLU | MMLU-49 | A tube of water is traveling at 1/2 c relative to the lab frame when a beam of light traveling in the same direction as the tube enters it. What is the speed of light in the water relative to the lab frame? (The index of refraction of water is 4/3.) | [
"1/2 c",
"2/3 c",
"5/6 c",
"10/11 c"
] | D | null |
MMLU | MMLU-50 | The rest mass of a particle with total energy 5.0 GeV and momentum 4.9 GeV/c is approximately | [
"0.1 GeV/c^2",
"0.2 GeV/c^2",
"0.5 GeV/c^2",
"1.0 GeV/c^2"
] | D | null |
MMLU | MMLU-51 | A grating spectrometer can just barely resolve two wavelengths of 500 nm and 502 nm, respectively. Which of the following gives the resolving power of the spectrometer? | [
"2",
"250",
"5,000",
"10,000"
] | B | null |
MMLU | MMLU-52 | The best type of laser with which to do spectroscopy over a range of visible wavelengths is | [
"a dye laser",
"a helium-neon laser",
"an excimer laser",
"a ruby laser"
] | A | null |
MMLU | MMLU-53 | The eigenvalues of a Hermitian operator are always | [
"real",
"imaginary",
"degenerate",
"linear"
] | A | null |
MMLU | MMLU-54 | A net force F_A acts on object A, and a net force F_B acts on object B. The mass of object B is twice the mass of object A, and the acceleration of object B is twice that of object A. Which of the following is true of forces F_A and F_B? | [
"F_B = 1/4 F_A",
"F_B = 1/2 F_A",
"F_B = 2F_A",
"F_B = 4F_A"
] | D | null |
MMLU | MMLU-55 | Under ideal conditions, the electric and magnetic fields inside a superconductor are zero. Maxwell’s equations imply that which of the following must be true just outside the surface of the superconductor? | [
"B = 0",
"B is perpendicular to the surface.",
"B is tangential to the surface.",
"B is time independent."
] | C | null |
MMLU | MMLU-56 | Two students perform an experiment in which they drop a ball from rest from a known height above the ground and measure the speed of the ball just before it strikes the ground. From repeated measurement, the students estimate the uncertainty in the measured speed of the ball to be 10 percent. Which of the following giv... | [
"5%",
"10%",
"15%",
"20%"
] | D | null |
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