MikaStars39/nano-eval huggingface dataset:
What type of slide should be used for microscopic examination of the starch granules?

Options:
A. Chloroform liquid holding slide
B. Xylene on microscopic slide
C. Sudan II Liquid Solution
D. Water setup piece
E. Ethanol under glass slide
F. Chloral Hydrate Liquid Preparations
G. Glycerin as a wet mount
H. Slide with Dilute Iodine Solution
I. Formalin keeping the sample
J. Carbolic Acid sample mount
Answer: D
There are two identical containers with fixed volumes. One contains ammonia gas and the other contains hydrogen gas (both considered as ideal gases with rigid molecules). Their pressures and temperatures are equal. When 5J of heat is transferred to the hydrogen gas, causing its temperature to rise. To raise the ammonia gas to the same temperature, the amount of heat that needs to be transferred to ammonia is: ( )

Options:
A. 4 J
B. 7 J
C. 6 J
D. 2 J
E. 5 J
F. 1 J
G. 10 J
H. 8 J
I. 9 J
J. 3 J
Answer: C
The artificial crystal diamond ring is made of glass (with a refractive index of $n_1$) and is coated with a layer of silica film (with a refractive index of $n_2$, where $n_2 < n_1$) to enhance reflection. To achieve enhanced reflection when light of wavelength $\lambda$ is incident perpendicularly, what should be the minimum thickness of the coating?

Options:
A. $e = \frac{2\lambda}{3n_{2}}$
B. $e = \frac{\lambda}{4n_{2}}$
C. $e = \frac{\lambda}{2n_{1}}$
D. $e = \frac{\lambda}{2n_{2}}$
E. $e = \frac{\lambda}{3n_{2}}$
F. $e = \frac{3\lambda}{4n_{2}}$
G. $e = \frac{\lambda}{4n_{1}}$
H. $e = \frac{\lambda}{n_{1}}$
I. $e = \frac{3\lambda}{2n_{2}}$
J. $e = \frac{2\lambda}{n_{2}}$
Answer: B
What are the criteria for distinguishing between ion pairs and complexes?

Options:
A. Condition status of hydration shell layer
B. Frequency of electrical conductivity
C. Connection state of hydration shell layer
D. Intensity of ionic bond radiation
E. Integration state of hydration shell layer
F. Configuration state of hydration shell layer
G. Distance of electron transfer events
H. Direction of molecular orbital overlap
Answer: C
"Banded Iron Formations" (BIFs) are most commonly associated with which geological period?

Options:
A. Cenozoic
B. Triassic
C. Precambrian
D. Proterozoic
E. Mesozoic
F. Cambrian
G. Archean
H. Paleozoic
I. Jurassic
J. Hadean
Answer: C
For a retaining wall with clay as the backfill, if the active earth pressure intensity within a certain depth range from the backfill surface is zero, then this depth is called ____.

Options:
A. Static depth
B. Passive pressure depth
C. Equilibrium depth
D. Critical depth
E. Compression depth
F. Inactive depth
G. Transition depth
H. Release depth
I. Neutral depth
J. Stable depth
Answer: D
Additional stress in the foundation $\mathrm{p_o}$ as it acts, the additional stress in the foundation decreases with increasing depth $Z$. The starting point for $Z$ is ( ).

Options:
A. Exterior design ground
B. Interior design ground
C. Natural ground
D. Habitat surface
E. Engineered fill
F. Base surface
G. Horizon level
H. Groundwater level
I. Height datum
J. Excavation layer
Answer: F
The vertical additional stress coefficient at the corner of a uniformly distributed rectangular load is $\mathrm{K_{c}=0.1752}$ when $l / \mathrm{b} = 1$ and $\mathrm{Z} / \mathrm{b} = 1$; and $\mathrm{K_{e}=0.084}$ when $l / \mathrm{b}=1$ and $\mathrm{Z / b} = 2$. If the additional stress on the foundation $\mathrm{p_{0}=100 kPa}$ and the side length of the foundation $l = \mathrm{b} = 2 \mathrm{m}$, the vertical additional stress at the center point under the foundation at $Z = 2 \mathrm{m}$ is ( ).

Options:
A. 17.52kPa
B. 8.4kPa
C. 42.4kPa
D. 48.0kPa
E. 25.2kPa
F. 70.08kPa
G. 29.8kPa
H. 10.5kPa
I. 33.6kPa
J. 61.2kPa
Answer: I
What is indicated by the level of dielectric loss factor in an insulating material?

Options:
A. Chemical durability stance
B. Electrical conductivity levels
C. Radiative emission specifics
D. Thermal properties of materials
E. Physical hardness scores
F. Biological degradation rates
G. Acoustic absorption ratio
H. Electrical resistance measures
I. Magnetic resistance capacity
J. Optical reflectivity properties
Answer: D
In which form is the energy produced by a partial discharge primarily?

Options:
A. luminous and heat energy
B. kinetic and potential energy
C. heat and light energy
D. pressure and chemical energy
E. radiant and gravitational energy
F. thermal and optical energy
G. sound and kinetic energy
H. motion and sound energy
I. thermal and nuclear energy
Answer: C
What is most significant to the identification of fossil mammals?

Options:
A. A single vertebra.
B. A patch of skin.
C. A piece of tail.
D. A single tooth.
E. A strand of hair.
F. A complete fossilized leaf.
G. An isolated claw.
H. A fragment of bone.
I. A single feather.
J. A complete skeleton.
Answer: J
What does the internal force diagram look like at the section where the beam is under concentrated load?

Options:
A. M diagram has a sudden change, Q diagram has a turn
B. M diagram has no change, Q diagram is smooth and continuous
C. Q diagram has no change, M diagram has no turn
D. Q diagram is smooth and continuous, M diagram is smooth and continuous
E. M diagram has a sudden change, Q diagram is smooth and continuous
F. Q diagram has a sudden change, M diagram has a turn
G. M diagram is smooth and continuous, Q diagram has no turn
H. Q diagram has a sudden change, M diagram is smooth and continuous
I. M diagram has no turn, Q diagram is smooth and continuous
Answer: F
The cross-section of ( ) is the critical section of an axially loaded member.

Options:
A. greatest normal stress
B. greatest elastic strain
C. greatest displacement
D. largest bending moment
E. least torsional rigidity
F. smallest area
G. greatest axial force
H. highest flexural stress
I. lowest shear strength
J. maximum internal force
Answer: A
What is the most efficient method for desiliconization in sodium aluminate solution?

Options:
A. Two-stage process involving heat treatment and mechanical filtration
B. Increase the alkalinity of the solution and use a silica precipitant
C. Accelerate silicon precipitation by increasing the sodium carbonate concentration
D. Enhanced method with pH adjustment and high-pressure distillation
E. Desiliconization using chemicals at high temperatures
F. Introducing complexing agents for intermediate silica bonding
G. Regular low-pressure desiliconization with continuous lime exposure
H. Using high sodium hydroxide concentration for single-stage removal
I. Modified desiliconization method involving pressure adjustments and lime integration
J. Conventional high-pressure one-stage desiliconization and deep two-stage desiliconization with lime
Answer: J
DDZ-II type transmitters ( )

Options:
A. Adopt a four-wire system on site
B. Connect with a seven-wire arrangement on site
C. Are intrinsically safe explosion-proof instruments
D. Each unit has 24V power supply
E. Use a single-wire system on site
F. Feature a five-wire setup on site
G. Operate with 12V power supply
H. Employ a three-wire system on site
I. Adopt a two-wire system on site
J. Include a six-wire framework on site
Answer: A
Which of the following ore body morphologies is most suitable for underground mining using the room-and-pillar method?

Options:
A. horizontal ore body
B. inclined ore body
C. spherical ore body
D. fragmented ore body
E. pocketed ore body
F. folded ore body
G. thick ore body
H. thin ore body
I. vertical ore body
J. irregular ore body
Answer: G
Using a pure solvent to absorb solutes from a mixed gas through countercurrent operation, the equilibrium relationship satisfies Henry's law. When the inlet gas concentration $y_{1}$ increases, while other inlet conditions remain unchanged, the changes in outlet gas concentration $y_{2}$ and absorption rate are ( ).

Options:
A. $y_{2}$ stays constant, absorption rate decreases
B. $y_{2}$ stays constant, absorption rate remains unchanged
C. $y_{2}$ increases, undefined absorption rate is uncertain
D. $y_{2}$ decreases, absorption rate changes consistently
E. $y_{2}$ decreases, absorption rate increases
F. $y_{2}$ increases, absorption rate remains unchanged
G. $y_{2}$ increases, absorption rate decreases
H. $y_{2}$ increases, absorption rate drop is consistent
I. $y_{2}$ decreases, absorption rate remains unchanged
Answer: F
In a semiconductor laser, assuming the carrier density in the active region is $N = 1 \times 10^{18} \text{ cm}^{-3}$, and the gain coefficient is $g = 5000 \text{ cm}^{-1}$, calculate the threshold current density $J_{th}$.

Options:
A. 400 kA/cm\(^2\)
B. 1000 kA/cm\(^2\)
C. 250 kA/cm\(^2\)
D. 100 kA/cm\(^2\)
E. 10 kA/cm\(^2\)
F. 300 kA/cm\(^2\)
G. 50 kA/cm\(^2\)
H. 200 kA/cm\(^2\)
I. 500 kA/cm\(^2\)
J. 1 kA/cm\(^2\)
Answer: D
A fiber optic communication system operates at a wavelength of 1310 nm with a dispersion parameter of 17ps/(nm·km). If the signal's spectral width is 10 nm and the transmission distance is 50 km, calculate the total dispersion (ps).

Options:
A. 2550
B. 85
C. 8500
D. 7650
E. 850000
F. 425
G. 1720
H. 170
I. 340
J. 850
Answer: J
In a fiber optic communication system, the signal passes through a nonlinear medium with a third-order dispersion parameter of $-3 \ \text{ps}^3/\text{km}$. If the central wavelength of the signal is 1550 nm and the transmission distance is 100 km, calculate the accumulated third-order dispersion of the signal (in fs³).

Options:
A. -300
B. -120000
C. -3000
D. -75000
E. -60000
F. -30000
G. -15000
H. -90000
I. -300000
J. -45000
Answer: F
In a fiber optic communication system, the signal passes through a dispersion compensator with a dispersion of +200 ps/nm. If the signal's spectral width is 30 nm, calculate the total dispersion compensation provided by the compensator (in ps).

Options:
A. 4800
B. 2000
C. 4000
D. 5600
E. 6000
F. 3400
G. 600
H. 200
I. 1200
J. 3000
Answer: I
In photonics, for an ideal Fiber Bragg Grating (FBG) reflector, how does the Free Spectral Range (FSR) of its reflection spectrum relate to the refractive index modulation amplitude and the fiber length?

Options:
A. proportional to the refractive index offset and inversely proportional to the fiber thickness
B. proportional to the refractive index and inversely proportional to the optical length
C. proportional to both the refractive index modulation amplitude and the fiber length
D. proportional to the refractive index modulation product and inversely proportional to fiber diameter
E. independent of the refractive index modulation amplitude and proportional to fiber length
F. inversely proportional to the refractive index modulation amplitude and proportional to the fiber length
G. independent of the refractive index modulation amplitude and inversely proportional to the fiber length
H. proportional to the refractive index modulation amplitude and inversely proportional to the fiber length
I. inverse to the refractive index modulation amplitude and proportional to the optical length
J. inversely proportional to both the refractive index modulation amplitude and the fiber length
Answer: H
In photonics, to achieve high-precision measurements in a fiber optic gyroscope, it is generally necessary to:

Options:
A. decrease the coherence length of the light
B. adjust the physical length of the fiber
C. increase the dynamic range of the system
D. lower the frequency of the optical pulses
E. reduce the impact of environmental temperature
F. maximize the exposure to ambient lighting
G. enhance the response time of detection sensors
H. increase the nonlinear coefficient of the fiber
I. enhance the optical density of the material
Answer: E
In photonics, the wavelength selectivity of a Fiber Bragg Grating (FBG) is related to which parameters of the grating?

Options:
A. width and depth
B. depth and spacing
C. length and material
D. spacing and length
E. depth and material
F. width and material
G. period and length
H. refractive index and spacing
I. period and refractive index
J. period and depth
Answer: I
The "Record of Music" systematically discusses Confucian thoughts on rites and music, summarizing their functions and interrelations. Which of the following is not a related viewpoint?

Options:
A. "Harmony is achieved through music, while order is achieved through rites."
B. "Rites are the guiding principles of behavior, whereas music is the expression of inner emotions."
C. "When society is chaotic, music brings balance; when society is in harmony, rites maintain stability."
D. "Emotions are cultivated through music, whereas behavior is regulated through rites."
E. "All sounds arise from the human heart; the movements of the heart are influenced by external factors."
Answer: E
Which model would be most appropriate for analyzing logistical support in military operations?

Options:
A. SWOT analysis
B. Cost-benefit analysis
C. Game theory
D. Inventory control
E. Queuing theory
F. Decision tree
G. Bayesian model
H. Portfolio theory
I. Principal component analysis
J. Linear regression model
Answer: E
Wei Changsheng was an outstanding actor of which type of flower role during the Qianlong period?

Options:
A. Nankun Opera
B. Jinju Opera
C. Yiyang Opera
D. Huangmei Opera
E. Nanguan Opera
F. Kunshan Opera
G. Haiyan Opera
H. Bangzi Opera
I. Huai Opera
J. Ping Opera
Answer: H
An 18-year-old, lying in bed in the morning, unresponsive, with profuse sweating, drooling, and difficulty breathing. Physical examination reveals: confusion, pinpoint pupils, both lungs filled with moist rales, heart rate 60 beats per minute, muscle fasciculations, and convulsions. The most likely diagnosis is __.

Options:
A. Acute parathion exposure poisoning
B. Acute ethanol toxicity poisoning
C. Acute narcosis poisoning
D. Acute strychnine poisoning
E. Acute organophosphate poisoning
F. Acute digoxin poisoning
G. Acute carbon monoxide poisoning
H. Acute chlorpromazine poisoning
I. Acute diazepam poisoning
J. Acute opioid overdose poisoning
Answer: E
In the humic substance components, the substances that are soluble in both acid and alkali are ().

Options:
A. Acidic peptides
B. Humic acid + Fulvic acid
C. Alkaline proteins
D. Water-soluble polymers
E. Lignin components
F. Organic matter
G. Folic acid
H. Humic substances
I. Base-soluble fibers
Answer: G
What are the main measures to prevent rebar corrosion in concrete?

Options:
A. Treat the surface of the rebar with alkali
B. Add corrosion inhibitors to the concrete
C. Modify the pH level of the concrete
D. Use galvanized steel for the rebar
E. Embed sacrificial anodes in the concrete
Answer: B
Which of the following belongs to surface drainage facilities for road subgrade?

Options:
A. water culvert
B. surface well
C. filtration trench
D. seepage well
E. watering pipe
F. drainage ditch
Answer: F
Which aspect of the pipeline is most affected by pressure fluctuations in oil and gas pipelines?

Options:
A. Pipeline distribution
B. Conveyor speed
C. Material degradation
D. Pipeline lifespan
E. Flow rate efficiency
F. Transport timing
G. Energy allocation
H. Oil Product Quality
I. Operating Costs
J. Pressure monitoring
Answer: D
Compared to longitudinal fractures, transverse fractures are more likely to cause what?

Options:
A. Cerebrospinal fluid leakage
B. Bone deformity, mainly affecting limb alignment
C. Conductive hearing loss and low-frequency tinnitus
D. Mixed hearing loss
E. Limited range of motion, particularly in adjacent joints
F. Chronic pain and muscle spasms, often localized around the fracture site
G. Severe infection, with symptoms of redness and swelling
H. Numbness and tingling, predominantly in extremities
I. Dural tear
J. Sensorineural hearing loss, with tinnitus often being high-frequency
Answer: J
Which of the following statements is incorrect regarding the compensatory phase of brain herniation?

Options:
A. Blood pressure increases
B. Pulse rate increases
C. Vision becomes significantly impaired
D. Coma
Answer: B
Middle ear infection accompanied by ipsilateral limb weakness or loss of muscle tone, ataxia, and a positive finger-to-nose test is most commonly seen in ()

Options:
A. Otogenic cerebellar abscess
B. Otogenic occipital lobe abscess
C. Sigmoid sinus thrombophlebitis
D. Labyrinthitis-induced vertigo
E. Transverse sinus thrombosis
F. Mastoiditis with cranial neuropathy
G. Otogenic frontal lobe abscess
H. Temporal bone cholesteatoma
I. Otogenic temporal lobe abscess
J. Epidural abscess
Answer: A
What was the cause of the "Decapolis disaster"?

Options:
A. migration of local villagers due to economic crisis
B. suppression of the newspaper industry by the Yuan Shikai authorities
C. assassination of key political figures sparking riots
D. implementation of harsh trade policies by foreign entities
E. discovery of ancient ruins leading to regional conflicts
F. establishment of agricultural communes by the national government
G. outbreak of a pandemic causing mass evacuations
H. collapse of the local dam resulting in widespread flooding
I. rise of separatist movements leading to civil unrest
J. introduction of new tax regulations causing protests
Answer: B
In a fiber grating, what parameter determines the reflected wavelength of the grating?

Options:
A. Fiber Diameter
B. Core Refractive
C. Optical Couplers
D. Core Thickness
E. Light Detectors
F. Fiber Length
G. Light Intensity
H. Material Density
I. Signal Amplitude
Answer: E
In a Fresnel lens, by what method is the lens thickness reduced?

Options:
A. Formed by melting layers
B. Ground to a knife edge
C. Cut into multiple loops
D. Reduced using air gaps
E. Compressed under pressure
F. Sliced into thin discs
G. Tilted at various angles
H. Etched with precise lasers
I. Molded with varying depths
Answer: C
Which substance is most commonly used as an energy supplement during exercise?

Options:
A. Anabolic steroids
B. Creatine
C. Taurine
D. Coenzyme Q10
E. Beta-alanine
F. Ribose
G. Fish oil
H. Dietary fiber
I. Carnitine
J. L-arginine
Answer: B
A fluid flows through a vertical variable diameter pipe that is thin at the top and thick at the bottom. Now notice that the pressure gauges at the thick and thin sections installed at a certain distance from the variable diameter have the same readings. So what can we conclude about the fluid in the pipe?

Options:
A. externally heated
B. magnetically driven
C. influenced by gravity
D. flowing downward
E. flowing in cycles
F. compressible fluid
G. remaining stagnant
H. flowing upward
I. having high viscosity
J. changing density
Answer: D
The orifice flow coefficient $C_{0}$ of the orifice flowmeter, when Re increases, its value ().

Options:
A. Constantly increasing without limit
B. Increasing exponentially as Re increases
C. Remaining constant, then decreasing slowly
D. Fluctuating unpredictably with Re
E. Showing no significant change with Re
F. Decreasing first, then maintaining a constant value
G. Dropping to zero and staying constant
H. Maintaining a constant value throughout
I. Increasing first, then decreasing steadily
J. Fluctuating slightly, then stabilizing
Answer: F
When a suspension medium is filtered by a straight-flow air filter, the positive force can be ignored. If the concentration of the filter pulp decreases for some reason, the ratio of the volume of the filter cake to the volume of the obtained filtrate becomes $80\\%$ of the original (assuming that the specific resistance of the filter cake remains unchanged). If the other operating conditions remain unchanged, how many times will the production capacity of the filter (in terms of filtrate per hour) be increased? How many times will the thickness of the filter cake be increased?

Options:
A. 1.118;1.1
B. 1.250;0.8
C. 1.050;1.0
D. 1.118;0.8
E. 1.200;0.85
F. 1.118;0.85
G. 1.200;1.0
H. 1.150;0.9
I. 1.118;0.9
J. 1.050;0.95
Answer: I
What is the two-layer model that represents the analogy between momentum transfer and heat transfer?

Options:
A. Clausius statement of the second law
B. Navier-Stokes equations
C. Joule's law of heating
D. Fick's first law of diffusion
E. Fourier's heat law
F. Kirchhoff's current law
G. Pascal's principle of fluids
H. Ohm's law of conduction
I. Bernoulli's principle
J. Poiseuille's equation
Answer: B
A certain piglet pen with windows in the Wuhan area adopts a brick-concrete structure and a flat roof. The span is 7.5 meters, the length is 50.4 meters, and the eave height is 4 meters. The four walls (originally the north and south side walls) are 240mm thick brick walls, with an inner layer of 3.5cm thick cement expanded perlite, and a 20mm thick cement mortar plaster on the outside. Each side wall has 14 single-layer wooden frame windows sized 1500×1500mm, and each of the two end walls has a single-layer wooden door sized 1500×2700mm. The roof consists of 200mm thick aerated concrete slabs, with a double felt and three-layer waterproof coating on top. The pen houses 250 piglets (9kg each), with a ventilation rate of 1500m³/h in winter. Calculate the temperature that can be maintained in the pen without heating. If an indoor temperature of 20°C needs to be maintained, how much heating power is required? (The outdoor calculation temperature for heating in the Wuhan area is -2°C.)

Options:
A. 92.4 W/m²
B. 95.2 W/m²
C. 115.9 W/m²
D. 97.6 W/m²
E. 128.3 W/m²
F. 103.6 W/m²
G. 120.8 W/m²
H. 125.0 W/m²
I. 110.4 W/m²
J. 130.2 W/m²
Answer: F
A liquid passes through a sand pipe of diameter D = 10 cm and length L = 30 cm. It is known that φ = 0.2, μ₀ = 0.65 mPa-s, Δp = 0.7 MPa, S_{wc} = 0.3, and K₀ = 0.2 μm², but what is the yield Q?

Options:
A. 5.1 cm³/s
B. 5.0 cm³/s
C. 4.6 cm³/s
D. 5.3 cm³/s
E. 4.9 cm³/s
F. 5.6 cm³/s
G. 6.2 cm³/s
H. 6.0 cm³/s
I. 6.8 cm³/s
J. 4.8 cm³/s
Answer: F
Under what conditions can economic overheating factors be recognized and assets be valued at historical cost in order to improve economic efficiency?

Options:
A. Reduced consumer confidence
B. Enhanced trade barriers
C. High inflation rates
D. Rising unemployment
E. Stagnant market growth
F. Declining market shares
G. Decreasing interest rates
H. Volatile commodity prices
I. Continuing operations
J. Increasing debt levels
Answer: I
When the Qiong Opera was performed in Thailand, how many times did Princess Sirindhorn attend the show?

Options:
A. Seven times
B. Four times
C. Five times
D. Once
E. Six times
F. Three times
G. Nine times
H. Twice
I. Ten times
J. Eight times
Answer: F
A car dealership entered into a written agreement with an eight-year-old child in which the dealership would sell the child a used sedan for \$10,000, as long as the child paid \$2,000 up front. The child paid the $2,000 up front but then refused to accept delivery of the vehicle and refused to pay the additional \$8,000. Both the dealership and the child brought suit against one another for damages.
Which party is most likely to prevail?

Options:
A. The child, because the child was induced by unfair practices.
B. The dealership, because the contract terms were completely clear.
C. The dealership, because the child showed bad faith in negotiations.
D. The dealership, because the child breached the contract by refusing to pay the $8,000.
E. The child, because the dealership was in breach of the contract.
F. The child, because the child did not complete the entire payment.
G. The child, because the child partially performed and the contract was voidable.
H. The child, because the contract was never legally binding.
I. The dealership, because the dealership incurred a significant loss.
J. The dealership, because the dealership had performed its part of the contract.
Answer: G
A sulfate-reducing organism oxidizes formate to CO2 while reducing sulfate to sulfide.
What are the two half-reactions and the balanced complete reaction assuming the appropriate species at pH=9.4?
Hint: look up the dissociation constants for hydrogen sulfide, formate, carbonic acid and sulfuric acid from the table to determine the appropriate species at a pH of 9.4 (pKa of formic acid $< ->$ formate is 3.74)

Options:
A. $$
1/2 \ HO_{3}^{-}+H^{+}+2e^{-}=1/2 \ HCOO^{-}+ 1/2 \ H_{2}O
$$
$$
pe^{0}=-1.34
$$
B. $$
1/2 \ {H CO_{3}}^{-}+H^{+}+e^{-}=1/2 \ HCOO^{-}+ 1/4 \ H_{2}O
$$
$$
pe^{0}=-1.31
$$
C. $$
1/2 \ {HC O}_{3}^{-}+2H^{+}+e^{-}=1/3 \ HCOO^{-}+ 1/2 \ H_{2}O
$$
$$
pe^{0}=-1.33
$$
D. $$
1/2 \ {H C O_{3}}^{-}+H^{+}+e^{-}=1/2 \ H C O O^{-}+ 1/2 \ H_{2} O
$$
$$
p e^{0}=-1. 3 2
$$
E. $$
1/2 \ HC O_{3}^{-}+H^{-}+e^{-}=1/2 \ H CO O^{-}+ 1/2 \ H_{2}O
$$
$$
pe^{0}=-1.29
$$
F. $$
1/2 \ HO_{3}^{-}+2H^{+}+e^{-}=1/2 \ HCOO^{-}+ 1/2 \ H_{2}O
$$
$$
p e^{0}=-1.30
$$
G. $$
1/3 \ HC O_{3}^{-}+H^{+}+e^{-}=1/2 \ H CO O^{-}+ 1/2 \ H_{2}O
$$
$$
pe^{0}=-1.39
$$
H. $$
1/2 \ {HC O}_{3}^{-}+H^{+}+e^{-}=1/2 \ HCO O^{-}+ 1/2 \ H_{2}O
$$
$$
pe^{0}=-1.36
$$
I. $$
1/2 \ {HC O}_{3}^{-}+H^{2+}+e^{-}=1/2 \ HOCOO^{-}+ 1/2 \ H_{2}O
$$
$$
pe^{0}=-1.35
$$
J. $$
1/2 \ HC O_{3}^{-}+H^{2+}+e^{-}=1/4 \ HCOO^{-}+ 1/2 \ H_{2}O
$$
$$
pe^{0}=-1.28
$$
Answer: D
The study of outcrop dimensions doesn't involve which of the following aspect?

Options:
A. Crystal lattice structures
B. Rock composition and type
C. Glacier advance measurements
D. Magma chamber depth analysis
E. Soil erosion and patterns
F. Sedimentary basin thickness
G. Global climate models
H. Solar radiation effects
I. Sea level fluctuations
J. Tectonic plate movement
Answer: B
Neutron shielding is typically divided into two steps: moderation and absorption. Among the following materials, the most suitable for moderating neutrons is ___

Options:
A. Copper block
B. Lead plate
C. Glass
D. Silver slab
E. Graphite rod
F. Gold sheet
G. Iron plate
H. Aluminum plate
I. Nickel alloy
J. Water
Answer: J
In a certain project network plan, the total float of task C is 7 days, and the free float is 4 days. When checking the actual progress, it is found that the duration of this task has been extended by 5 days, indicating that the actual progress of task C has delayed the earliest start time of its succeeding task by ().

Options:
A. Delay inadvertently accelerates preliminary phase.
B. Delay ostensibly shifts deliverable submission timeline.
C. Delay unexpectedly advances future stage kickoff.
D. Delay noticeably affects preliminary budget estimates.
E. Delay marginally alters upcoming resource allocation.
F. Delay significantly impacts overall task dependencies.
G. Delay indirectly postpones next milestone event.
H. Delay does not affect the overall construction schedule.
I. Delay potentially modifies stakeholder communication points.
J. Delay directly influences project end date by days.
Answer: H
Eccentricity $e < 0.1 \text{m}$ for a strip foundation with a base width $b = 3 \text{m}$ and a foundation depth $d = 1.5 \text{m}$. The soil layer is silty clay, with an average unit weight of soil above the foundation base of $\gamma_{\mathrm{m}} = 18.5 \text{kN/m}^{3}$. Below the foundation base, the unit weight of soil is $\gamma = 19 \text{kN/m}^{3}$, and the saturated unit weight is $\gamma_{\mathrm{sat}} = 20 \text{kN/m}^{3}$. The standard value of the internal friction angle is $\varphi_{\mathrm{k}} = 20°$, and the standard value of cohesion is $c_{\mathrm{k}} = 10 \text{kPa}$. When the groundwater rises from a deep point below the foundation base to the foundation surface (meanwhile, disregarding the impact of groundwater level on shear strength parameters) $( M_{\mathrm{b}} = 0.51 \,, \; \; M_{\mathrm{d}} = 3.06 \,, \; \; M_{\mathrm{c}} = 5.66 \,)$, the foundation is ().

Options:
A. 13.89%
B. 7.12%
C. 5.45%
D. 11.25%
E. 6.78%
F. 4.21%
G. 2.37%
H. 8.98%
I. 10.53%
J. 9.47%
Answer: H
We now define an algorithm: The definition of a(n) is the number of meaningful differential operations of the n-th order on the space R^7 in the context of differential geometry. Given the input x_list (a series of values): [23, 24, 25, 26, 27, 28, 29, 30, 31, 32], determine the corresponding output sequence y_list.

Options:
A. [7169141, 13474506, 25322371, 47592653, 89441620, 168100326, 315917523, 593742591, 1115852901, 2097145322]
B. [7169140, 13474500, 25322350, 47592660, 89441620, 168100330, 315917530, 593742590, 1115852900, 2097145310]
C. [7169150, 13474509, 25322373, 47592658, 89441628, 168100322, 315917525, 593742595, 1115852920, 2097145305]
D. [7169140, 13474501, 25322376, 47592654, 89441624, 168100329, 315917526, 593742598, 1115852916, 2097145306]
E. [7169149, 13474502, 25322378, 47592661, 89441623, 168100321, 315917528, 593742593, 1115852912, 2097145314]
F. [7169143, 13474503, 25322380, 47592659, 89441627, 168100325, 315917524, 593742590, 1115852915, 2097145312]
G. [7169148, 13474507, 25322370, 47592655, 89441622, 168100320, 315917522, 593742592, 1115852902, 2097145308]
H. [7169156, 13474508, 25322379, 47592662, 89441630, 168100328, 315917521, 593742599, 1115852910, 2097145319]
I. [7169145, 13474502, 25322375, 47592650, 89441626, 168100324, 315917527, 593742597, 1115852904, 2097145320]
J. [7169145, 13474502, 25322375, 47592650, 89441626, 168100324, 315917527, 593742597, 1115852904, 2097145317]
Answer: J
We now define an algorithm: The definition of a(n) is: Number of tilings of a 4 X 2n rectangle with L tetrominoes. L tetrominoes are Tetris-like pieces consisting of 4 squares that form an "L" shape. Given the input x_list (a series of values): [15, 16, 17, 18, 19, 20, 21, 22, 23, 24], determine the corresponding output sequence y_list.

Options:
A. [1898026232, 8248853134, 35849651070, 155803171860, 677123141810, 2942788286798, 12789406189672, 55582969192486, 241564496305670, 1049843265359828]
B. [1898026236, 8248853140, 35849651076, 155803171869, 677123141818, 2942788286790, 12789406189679, 55582969192481, 241564496305679, 1049843265359837]
C. [1898026229, 8248853133, 35849651073, 155803171866, 677123141815, 2942788286801, 12789406189676, 55582969192484, 241564496305676, 1049843265359834]
D. [1898026234, 8248853138, 35849651074, 155803171863, 677123141813, 2942788286802, 12789406189674, 55582969192490, 241564496305674, 1049843265359832]
E. [1898026233, 8248853131, 35849651072, 155803171865, 677123141814, 2942788286803, 12789406189675, 55582969192485, 241564496305675, 1049843265359833]
F. [1898026235, 8248853136, 35849651075, 155803171864, 677123141811, 2942788286797, 12789406189670, 55582969192489, 241564496305673, 1049843265359831]
G. [1898026228, 8248853139, 35849651068, 155803171867, 677123141816, 2942788286788, 12789406189677, 55582969192483, 241564496305677, 1049843265359835]
H. [1898026230, 8248853132, 35849651071, 155803171862, 677123141812, 2942788286800, 12789406189673, 55582969192488, 241564496305672, 1049843265359830]
I. [1898026231, 8248853135, 35849651069, 155803171861, 677123141809, 2942788286799, 12789406189671, 55582969192487, 241564496305671, 1049843265359829]
J. [1898026238, 8248853130, 35849651067, 155803171868, 677123141817, 2942788286789, 12789406189678, 55582969192482, 241564496305678, 1049843265359836]
Answer: A
We now define an algorithm: The definition of a(n) is the number of ways to bend a piece of wire of length n+1 into non-overlapping, non-intersecting shapes, where configurations that can only be made to coincide by turning the figure over are counted as different. Given the input x_list (a series of values): [19, 20, 21, 22, 23, 24, 25, 26, 27, 28], determine the corresponding output sequence y_list.

Options:
A. [581140575, 1743421825, 5230206129, 15690618368, 47071677997, 141215033980, 423644570452, 1270933711370, 3812799539600, 11438398618500]
B. [581140572, 1743421720, 5230206123, 15690618382, 47071677984, 141215033975, 423644570444, 1270933711355, 3812799539630, 11438398618245]
C. [581140570, 1743421730, 5230206125, 15690618388, 47071677990, 141215033930, 423644570450, 1270933711365, 3812799539640, 11438398618335]
D. [581140574, 1743421727, 5230206125, 15690618379, 47071677989, 141215033932, 423644570448, 1270933711380, 3812799539610, 11438398618035]
E. [581140573, 1743421723, 5230206129, 15690618375, 47071677988, 141215033945, 423644570455, 1270933711320, 3812799539620, 11438398618655]
F. [581140578, 1743421721, 5230206127, 15690618368, 47071677993, 141215033970, 423644570449, 1270933711315, 3812799539680, 11438398618555]
G. [581140580, 1743421728, 5230206124, 15690618370, 47071677985, 141215033990, 423644570440, 1270933711330, 3812799539650, 11438398618960]
H. [581140575, 1743421725, 5230206126, 15690618378, 47071677987, 141215033961, 423644570442, 1270933711326, 3812799539655, 11438398618965]
I. [581140576, 1743421726, 5230206128, 15690618380, 47071677980, 141215033965, 423644570443, 1270933711300, 3812799539700, 11438398618445]
J. [581140577, 1743421722, 5230206122, 15690618376, 47071677983, 141215033947, 423644570447, 1270933711340, 3812799539670, 11438398618825]
Answer: H
We now define an algorithm: The definition of a(n) is the coordination sequence for the Cairo or dual-3.3.4.3.4 tiling with respect to a trivalent point, representing the number of vertices that are at a distance n from a given trivalent vertex in a specific type of vertex-centered non-orthogonal tiling. Given the input x_list (a series of values): [48, 49, 50, 51, 52, 53, 54, 55, 56, 57], determine the corresponding output sequence y_list.

Options:
A. [188, 193, 198, 201, 204, 209, 214, 217, 220, 225]
B. [191, 196, 201, 204, 207, 212, 217, 220, 223, 228]
C. [195, 200, 205, 208, 211, 216, 221, 224, 227, 232]
D. [196, 201, 206, 209, 212, 217, 222, 225, 228, 233]
E. [194, 199, 204, 207, 210, 215, 220, 223, 226, 231]
F. [193, 198, 203, 206, 209, 214, 219, 222, 225, 230]
G. [190, 195, 200, 203, 206, 211, 216, 219, 222, 227]
H. [187, 192, 197, 200, 203, 208, 213, 216, 219, 224]
I. [192, 197, 202, 205, 208, 213, 218, 221, 224, 229]
J. [189, 194, 199, 202, 205, 210, 215, 218, 221, 226]
Answer: B
We now define an algorithm: The definition of a(n) is the number of unrooted nonseparable planar maps with n edges and a distinguished face. Given the input x_list (a series of values): [15, 16, 17, 18, 19, 20, 21, 22, 23, 24], determine the corresponding output sequence y_list.

Options:
A. [68864089, 391120039, 2246122577, 13025721604, 76194378045, 449155863871, 2666126033853, 15925105028688, 95664343622237, 577651490729533]
B. [68864087, 391120037, 2246122575, 13025721602, 76194378043, 449155863869, 2666126033851, 15925105028686, 95664343622235, 577651490729531]
C. [68864083, 391120033, 2246122571, 13025721598, 76194378039, 449155863865, 2666126033847, 15925105028682, 95664343622231, 577651490729527]
D. [68864081, 391120031, 2246122569, 13025721596, 76194378037, 449155863863, 2666126033845, 15925105028680, 95664343622229, 577651490729525]
E. [68864085, 391120035, 2246122573, 13025721600, 76194378041, 449155863867, 2666126033849, 15925105028684, 95664343622233, 577651490729529]
F. [68864084, 391120034, 2246122572, 13025721599, 76194378040, 449155863866, 2666126033848, 15925105028683, 95664343622232, 577651490729528]
G. [68864088, 391120038, 2246122576, 13025721603, 76194378044, 449155863870, 2666126033852, 15925105028687, 95664343622236, 577651490729532]
H. [68864090, 391120040, 2246122578, 13025721605, 76194378046, 449155863872, 2666126033854, 15925105028689, 95664343622238, 577651490729534]
I. [68864086, 391120036, 2246122574, 13025721601, 76194378042, 449155863868, 2666126033850, 15925105028685, 95664343622234, 577651490729530]
J. [68864082, 391120032, 2246122570, 13025721597, 76194378038, 449155863864, 2666126033846, 15925105028681, 95664343622230, 577651490729526]
Answer: I
We now define an algorithm: The definition of a(n) is: Third tetrahedral coordinate, i.e., tetrahedron with \\( T(t,n,k) = k \\); succession of growing finite triangles with increasing values towards bottom right. Consider the numbers in the context of triangular number arrangements within a tetrahedral structure. Given the input x_list (a series of values): [95, 96, 97, 98, 99, 100, 101, 102, 103, 104], determine the corresponding output sequence y_list.

Options:
A. [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
B. [1, 2, 3, 4, 0, 1, 2, 3, 4, 5]
C. [6, 7, 8, 9, 2, 3, 4, 5, 6, 7]
D. [3, 4, 5, 0, 1, 2, 3, 4, 5, 6]
E. [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
F. [8, 7, 6, 5, 4, 3, 2, 1, 0, 9]
G. [7, 8, 9, 0, 1, 5, 6, 7, 8, 9]
H. [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
I. [4, 3, 2, 1, 0, 4, 3, 2, 1, 0]
J. [5, 6, 7, 8, 1, 2, 3, 4, 5, 6]
Answer: B
We now define an algorithm: The definition of a(n) is Schroeder's second problem (generalized parentheses); also called super-Catalan numbers or little Schroeder numbers. These numbers enumerate certain types of paths in the plane or the number of ways to insert parentheses into a sequence. Given the input x_list (a series of values): [14, 15, 16, 17, 18, 19, 20, 21, 22, 23], determine the corresponding output sequence y_list.

Options:
A. [372693519, 1968801519, 10463578353, 55909013009, 300159426963, 1618362158587, 8759309660445, 47574827600981, 259215937709463, 1416461675464871]
B. [372693522, 1968801523, 10463578356, 55909013012, 300159426966, 1618362158590, 8759309660448, 47574827600984, 259215937709469, 1416461675464877]
C. [372693516, 1968801517, 10463578350, 55909013006, 300159426960, 1618362158584, 8759309660442, 47574827600978, 259215937709466, 1416461675464874]
D. [372693519, 1968801519, 10463578353, 55909013009, 300159426963, 1618362158587, 8759309660445, 47574827600981, 259215937709462, 1416461675464871]
E. [372693524, 1968801525, 10463578358, 55909013014, 300159426968, 1618362158592, 8759309660450, 47574827600986, 259215937709471, 1416461675464879]
F. [372693518, 1968801520, 10463578352, 55909013008, 300159426962, 1618362158586, 8759309660444, 47574827600980, 259215937709464, 1416461675464872]
G. [372693521, 1968801522, 10463578355, 55909013011, 300159426965, 1618362158589, 8759309660447, 47574827600983, 259215937709468, 1416461675464876]
H. [372693517, 1968801518, 10463578351, 55909013007, 300159426961, 1618362158585, 8759309660443, 47574827600979, 259215937709465, 1416461675464873]
I. [372693523, 1968801524, 10463578357, 55909013013, 300159426967, 1618362158591, 8759309660449, 47574827600985, 259215937709470, 1416461675464878]
J. [372693520, 1968801521, 10463578354, 55909013010, 300159426964, 1618362158588, 8759309660446, 47574827600982, 259215937709467, 1416461675464875]
Answer: A
We now define an algorithm: The definition of a(n) is the number of asymmetric planted projective plane trees with n+1 nodes; alternatively, it is the number of bracelets (reversible necklaces) containing n black beads and n-1 white beads in combinatorial enumeration. Given the input x_list (a series of values): [20, 21, 22, 23, 24, 25, 26, 27, 28, 29], determine the corresponding output sequence y_list.

Options:
A. [886543210, 3292345678, 12409876543, 45787654321, 170543210987, 646876543210, 2434567890123, 9195678901234, 34765432109876, 131894567890123]
B. [882901234, 3278901234, 12367890123, 45909876543, 171012345678, 644234567890, 2441209876543, 9181234567890, 34821987654321, 132765432109876]
C. [887654321, 3286543211, 12276543210, 45723456789, 171345678900, 645987654321, 2432198765432, 9192345678901, 34754321098765, 132123456789012]
D. [883585406, 3281967832, 12232957152, 45740929104, 171529130786, 644950721584, 2430970600576, 9183671335776, 34766765428852, 131873955816880]
E. [883765432, 3281234567, 12387654321, 45890987654, 171432109876, 643456789012, 2443456789012, 9186789012345, 34789012345678, 132678901234567]
F. [882345678, 3276543210, 12309876543, 45687654320, 171123456789, 643219876543, 2439087654321, 9171234567890, 34787654321098, 131567890123456]
G. [885876543, 3309876542, 12123456789, 45876543210, 170987654321, 648765432101, 2431234567890, 9176543209876, 34712345678901, 131234567890123]
H. [888765432, 3291234567, 12299876543, 45798765431, 172109876543, 646345678901, 2427654321098, 9170987654321, 34798765432123, 131345678901234]
I. [881234567, 3271234567, 12187654320, 45843210987, 170876543219, 645123456789, 2445678901234, 9181234567890, 34876543210123, 132345678901234]
J. [884123456, 3298765432, 12456789123, 45987654321, 172345678901, 645678910111, 2435678901234, 9198765432101, 34890123456789, 132987654321987]
Answer: D
We now define an algorithm: The definition of a(n) is: Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by upward antidiagonals. In other words, arrange the binomial coefficients in a two-dimensional array where each element T(n,k) represents the binomial coefficient "n choose k". Read these elements by traversing the array along the upward diagonals starting from the lower-left corner. Given the input x_list (a series of values): [84, 85, 86, 87, 88, 89, 90, 91, 92, 93], determine the corresponding output sequence y_list.

Options:
A. [1, 0, 0, 0, 0, 1, 0, 1, 12, 53]
B. [2, 1, 0, 0, 0, 0, 0, 1, 11, 54]
C. [1, 1, 0, 0, 0, 0, 0, 1, 12, 54]
D. [1, 0, 0, 0, 0, 0, 0, 1, 12, 55]
E. [1, 0, 1, 0, 0, 0, 0, 1, 10, 55]
F. [1, 0, 0, 1, 0, 0, 0, 0, 12, 54]
G. [1, 0, 0, 0, 1, 0, 0, 1, 13, 55]
H. [1, 0, 0, 0, 0, 0, 0, 2, 13, 55]
I. [1, 0, 0, 0, 0, 1, 0, 1, 11, 52]
J. [0, 0, 0, 0, 0, 0, 0, 1, 13, 56]
Answer: D
We now define an algorithm: The definition of a(n) is the total number of moves required to optimally solve the Magnetic Tower of Hanoi puzzle with three posts, where each disk is pre-colored either RED, NEUTRAL, or BLUE, and disks must be placed on top of disks of the same or a different color following specific rules. Given the input x_list (a series of values): [20, 21, 22, 23, 24, 25, 26, 27, 28, 29], determine the corresponding output sequence y_list.

Options:
A. [1000000000, 3000000000, 9010000000, 27010000000, 81030000000, 243090000000, 729270000000, 2187810000000, 6563430000000, 19690290000000]
B. [1267924528, 3803769261, 11411301184, 34233893527, 102701665332, 308104972769, 924314883004, 2772944595283, 8318833704088, 24956500987925]
C. [1122443556, 2244665778, 3366887990, 4488110112, 5609333234, 6730556356, 7851779478, 8973002600, 9104235722, 10252658844]
D. [1122334455, 3344556677, 5566778899, 7788990011, 9900112233, 11223344554, 3344556677, 5566778899, 7788990011, 9900112233]
E. [1234567890, 2345678901, 3456789012, 4567890123, 5678901234, 6789012345, 7890123456, 8901234567, 9012345678, 12345678909]
F. [1234432110, 2333345677, 3444456788, 4555567899, 5666679000, 6777780112, 7888891223, 8999902234, 9101113345, 1032224456]
G. [998877665, 2998877668, 8998877669, 26996433082, 80989299235, 243094943786, 729284831759, 2187854790538, 6563564371039, 1969069311312]
H. [1221122334, 3333344455, 5545566677, 7757788899, 9969900111, 11120112232, 33223333443, 55333455654, 77444577865, 99555699076]
I. [1199887766, 2911998877, 8219988778, 24329988789, 7298996639, 2189698896, 6569698897, 19708988789, 59128898899, 17738988790]
J. [987654321, 2976654322, 8976654323, 26929963234, 80789963235, 2423698896, 7271996888, 21765993037, 65297979128, 195893749388]
Answer: B
We now define an algorithm: The definition of a(n) is a triangle in which the k-th item in the n-th row (both starting from 1) represents the number of ways to add 2 distinct integers from 1 to n such that their sum is divisible by k. Given the input x_list (a series of values): [80, 81, 82, 83, 84, 85, 86, 87, 88, 89], determine the corresponding output sequence y_list.

Options:
A. [36, 28, 18, 17, 11, 11, 8, 8, 7, 6]
B. [32, 26, 17, 14, 12, 12, 9, 9, 7, 6]
C. [37, 27, 18, 15, 13, 11, 9, 7, 6, 8]
D. [36, 25, 18, 15, 12, 11, 9, 8, 7, 8]
E. [35, 27, 18, 16, 13, 10, 8, 7, 8, 7]
F. [33, 26, 19, 16, 12, 10, 9, 9, 6, 6]
G. [35, 25, 17, 16, 11, 11, 8, 8, 7, 6]
H. [34, 24, 19, 15, 12, 11, 9, 8, 8, 7]
I. [36, 26, 18, 16, 12, 12, 9, 8, 7, 7]
J. [36, 25, 17, 16, 13, 12, 9, 8, 6, 7]
Answer: I
We now define an algorithm: The definition of a(n) is: If in a line of n persons every n-th person is eliminated until only one person is left, which position P should one assume in the original lineup to avoid being eliminated? P is the output for position n in the sequence. Given the input x_list (a series of values): [73, 74, 75, 76, 77, 78, 79, 80, 81, 82], determine the corresponding output sequence y_list.

Options:
A. [70, 4, 8, 18, 62, 16, 80, 2, 74, 76]
B. [71, 3, 7, 19, 61, 17, 79, 1, 73, 77]
C. [68, 6, 10, 16, 64, 14, 82, 3, 76, 74]
D. [73, 1, 5, 21, 59, 19, 77, 3, 71, 79]
E. [72, 1, 7, 21, 58, 20, 76, 4, 70, 80]
F. [73, 3, 8, 20, 59, 18, 79, 7, 72, 82]
G. [74, 1, 6, 23, 56, 22, 74, 6, 68, 82]
H. [69, 5, 9, 17, 63, 15, 81, 1, 75, 75]
I. [72, 2, 6, 20, 60, 18, 78, 2, 72, 78]
J. [73, 2, 5, 22, 57, 21, 75, 5, 69, 81]
Answer: I
We now define an algorithm: The definition of a(n) is the number of partitional matroids on n elements, where a partitional matroid is a matroid that can be represented by a partition of the ground set into independent sets such that the union of any subfamily of these sets is also independent. The first few values of the sequence are 1, 2, 5, 16, 62, 276, 1377, 7596, 45789, 298626. Given the input x_list (a series of values): [12, 13, 14, 15, 16, 17, 18, 19, 20, 21], determine the corresponding output sequence y_list.

Options:
A. [123897413, 1038535174, 9165475893, 84886111212, 822648571314, 8321077557124, 87648445601429, 959450073912136, 10894692556576613, 128114221270929646]
B. [133897413, 1038535174, 8165475893, 84886111212, 922648571314, 7321077557124, 87648445601429, 859450073912136, 10894692556576613, 118114221270929646]
C. [123897413, 2038535174, 9165475893, 74886111212, 722648571314, 7321077557124, 77648445601429, 859450073912136, 9894692556576613, 118114221270929646]
D. [123897413, 2038535174, 9165475893, 94886111212, 722648571314, 8321077557124, 87648445601429, 859450073912136, 10894692556576613, 118114221270929646]
E. [123897413, 2038535174, 8165475893, 94886111212, 722648571314, 8321077557124, 87648445601429, 759450073912136, 10894692556576613, 998114221270929646]
F. [113897413, 1038535174, 9165475893, 74886111212, 922648571314, 8321077557124, 97648445601429, 859450073912136, 10894692556576613, 128114221270929646]
G. [133897413, 1038535174, 8165475893, 94886111212, 922648571314, 7321077557124, 87648445601429, 859450073912136, 9984692556576613, 128114221270929646]
H. [133897413, 1038535174, 9165475893, 74886111212, 822648571314, 8321077557124, 77648445601429, 959450073912136, 10894692556576613, 118114221270929646]
I. [113897413, 1138535174, 9165475893, 84886111212, 822648571314, 8321077557124, 87648445601429, 759450073912136, 10894692556576613, 128114221270929646]
J. [123897413, 1138535174, 9165475893, 94886111212, 822648571314, 7321077557124, 97648445601429, 959450073912136, 9984692556576613, 128114221270929646]
Answer: A
We now define an algorithm: The definition of a(n) is the sequence generated by starting with the initial term '0' and repeatedly applying the following substitution rules: 0 -> 0012, 1 -> 12, 2 -> 012, at each step. Given the input x_list (a series of values): [95, 96, 97, 98, 99, 100, 101, 102, 103, 104], determine the corresponding output sequence y_list.

Options:
A. [0, 1, 1, 2, 2, 0, 2, 0, 1, 1]
B. [1, 1, 1, 0, 2, 0, 2, 2, 1, 0]
C. [2, 0, 0, 1, 2, 1, 1, 0, 2, 1]
D. [0, 1, 2, 0, 0, 1, 2, 1, 2, 0]
E. [1, 0, 1, 2, 0, 2, 0, 1, 0, 1]
F. [2, 1, 1, 2, 0, 0, 0, 2, 1, 1]
G. [1, 0, 2, 1, 0, 0, 2, 1, 0, 1]
H. [2, 1, 0, 0, 1, 1, 2, 2, 0, 2]
I. [0, 2, 0, 1, 2, 2, 1, 0, 0, 2]
J. [0, 2, 1, 1, 0, 1, 2, 0, 0, 2]
Answer: D
We now define an algorithm: The definition of a(n) is the ternary tribonacci word; also known as a Rauzy fractal sequence. It is defined as the fixed point of the morphism where 1 maps to 12, 2 maps to 13, and 3 maps to 1, starting from a(1) = 1. Given the input x_list (a series of values): [96, 97, 98, 99, 100, 101, 102, 103, 104, 105], determine the corresponding output sequence y_list.

Options:
A. [2, 1, 2, 3, 1, 3, 2, 1, 1, 2]
B. [1, 3, 1, 2, 1, 3, 1, 2, 1, 2]
C. [1, 2, 1, 3, 2, 1, 3, 1, 2, 1]
D. [3, 1, 1, 2, 3, 2, 1, 1, 2, 3]
E. [2, 1, 3, 1, 2, 1, 1, 2, 1, 3]
F. [3, 2, 1, 2, 3, 1, 3, 2, 1, 3]
G. [2, 1, 3, 2, 2, 1, 3, 1, 3, 1]
H. [2, 3, 1, 1, 2, 1, 2, 1, 3, 2]
I. [1, 2, 1, 2, 1, 3, 1, 3, 1, 2]
J. [3, 1, 2, 1, 1, 2, 1, 3, 2, 1]
Answer: E
We now define an algorithm: The definition of a(n) is the smallest positive integer not occurring earlier in the sequence such that Sum_{k=1..n} a(k) written in binary contains binary n as a substring. The context involves finding consecutive terms that satisfy this binary representation criterion. Given the input x_list (a series of values): [62, 63, 64, 65, 66, 67, 68, 69, 70, 71], determine the corresponding output sequence y_list.

Options:
A. [79, 71, 73, 76, 68, 136, 100, 113, 67, 93]
B. [73, 65, 67, 70, 62, 130, 94, 107, 61, 87]
C. [77, 69, 71, 74, 66, 134, 98, 111, 65, 91]
D. [78, 70, 72, 75, 67, 135, 99, 112, 66, 92]
E. [72, 64, 66, 69, 61, 129, 93, 106, 60, 86]
F. [80, 72, 74, 77, 69, 137, 101, 114, 68, 94]
G. [75, 67, 69, 72, 64, 132, 96, 109, 63, 89]
H. [76, 68, 70, 73, 65, 133, 97, 110, 64, 90]
I. [81, 73, 75, 78, 70, 138, 102, 115, 69, 95]
J. [74, 66, 68, 71, 63, 131, 95, 108, 62, 88]
Answer: E