MikaStars39/nano-eval huggingface dataset:
What kind of criticism in China is referred to as "pin" (appreciation) and as "wu" (comprehension)?

Options:
A. Philosophical criticism.
B. Aesthetic criticism.
C. Literary criticism.
D. Environmental criticism.
E. Historical criticism.
F. Cultural criticism.
G. Political criticism.
H. Social criticism.
I. Ethical criticism.
J. Economic criticism.
Answer: B
In the process of literary reception, after we finish reading a novel or a poem, the characters and scenes from the work may linger in our minds, the thoughts and emotions may continue to resonate within us, and the charm and artistic conception may lead us to repeatedly savor the experience. This can even influence our speech, behavior, and aesthetic pursuits, consciously or unconsciously, for a considerable period of time. This phenomenon is known as what in the context of literary reception?

Options:
A. Emotional resonance.
B. Residual impact.
C. Lasting impression.
D. Aesthetic afterglow.
E. Cognitive echo.
F. Literary shadow.
G. Poetic reverberation.
H. Lingering effect.
I. Reflective persistence.
J. Narrative imprint.
Answer: H
The posthumous works of Chinese musician Xian Xinghai in the Soviet Union were sent back to China in _____.

Options:
A. 1949
B. 1955
C. 1950
D. 1951
E. 1946
F. 1947
G. 1953
H. 1954
I. 1952
J. 1948
Answer: C
Since 1935, Mai Xin has actively participated in the national salvation singing movement and became the backbone of progressive music organizations such as the "Song Research Society", "People's Singing Society", and "_______".

Options:
A. People's Music Alliance
B. Harmony for Change Initiative
C. Amateur Choir
D. Hopeful Singers Guild
E. National Music Coalition
F. Progressive Musicians Society
G. United Voices Collective
H. Cultural Harmony Association
I. Revolutionary Sound League
J. nternal server error
Answer: C
According to historical records, the earliest Chinese-run new-style band was after ____.

Options:
A. Xinhai Revolution
B. Sino-Japanese War
C. Chinese Civil War
D. Boxer Rebellion
E. Long March
F. Opium War
G. Second Sino-Japanese War
H. Great Leap Forward
I. Cultural Revolution
J. Taiping Rebellion
Answer: B
Xian Xinghai's _______ composed in Paris is one of the earliest modern Chinese orchestral works performed abroad.

Options:
A. Concerto for Orchestra
B. Symphony in C major
C. Overture in E minor
D. Symphony for Winds
E. Sonata in D minor
F. Rhapsody for Piano
G. Suite for Strings
H. Concerto for Strings
I. Nocturne for Flute
J. Fantasia for Violin
Answer: E
Zeng Zhitai's ______ published in 1904 is the earliest monograph on music education in modern China, and is also Zeng Zhitai's representative article on music theory.

Options:
A. "Theoretical Approaches to Music Learning"
B. "A Guide to Music Teaching"
C. "Essentials of Music Education"
D. "Music Theory and Practice"
E. "Innovations in Music Education"
F. "Principles of Music Instruction"
G. "Music Education in the Modern Era"
H. "Foundations of Musical Pedagogy"
I. "The Art of Music Teaching"
J. "On Music Education"
Answer: J
Suzhou tanci artists ______ and ________ created the Xiaoyang tune, which uses both true and false voices and is crisp and clear, as well as the Xia tune of "high-pitched and loud singing" and "fast-pitched and slow-singing" by singing and talking about "Painting the Golden Phoenix" and other songs.

Options:
A. Lan Xiaofang, Feng Yusheng
B. Sun Yunqing, Peng Qingsheng
C. Qin Haiyan, Xu Zeming
D. Yang Xiaoting, Xia Hesheng
E. Liu Ning, Zhang Shuheng
F. Jiang Yuwei, Sun Leiheng
G. Chen Xiaoyun, Li Haisheng
H. Wu Yuejing, Zhou Wei
I. Wang Jingmei, Du Fenglan
J. Zhao Mingzhu, Liang Chengshun
Answer: D
What are the earliest opera schools in Italy?

Options:
A. Bologna opera school, Genoa opera school, Parma opera school
B. Reggio Emilia opera school, Lecce opera school, Ravenna opera school
C. Florentine opera school, Milan opera school, Turin opera school
D. Siena opera school, Bari opera school, Modena opera school
E. Pisa opera school, Verona opera school, Palermo opera school
F. Perugia opera school, Trieste opera school, Lucca opera school
G. Bergamo opera school, Messina opera school, Vicenza opera school
H. Ferrara opera school, Livorno opera school, Trento opera school
I. Venetian opera school, Roman opera school, Naples opera school
J. Ancona opera school, Cagliari opera school, Brescia opera school
Answer: I
Who is the author of the song "Yu Guang Qu"?

Options:
A. John Williams
B. David Guetta
C. Lady Gaga
D. Taylor Swift
E. Jay Chou
F. Kanye West
G. Lionel Richie
H. Adele
I. Song Yang
J. Bruno Mars
Answer: I
What does Lasso represent?

Options:
A. Pop art
B. Surrealist art
C. Abstract expressionism
D. Impressionist movement
E. Cubist style
F. Renaissance art
G. Baroque period
H. Realism
I. Modernism
J. Flemish school
Answer: J
The works "The First Collection of the Uncanny" and "The Second Collection of the Uncanny," compiled by ( ), have already become a personal anthology of vernacular novel creations.

Options:
A. Zhang Wei
B. Chen Yuming
C. Liu Xiaodong
D. Li Hong
E. Ling Yangchu
F. Sun Qiang
G. Xu Feng
H. Zhao Ming
I. Wang Jianhua
J. Guo Lin
Answer: E
Ancient Egyptian literature is one of the oldest literatures in the world, primarily consisting of poetry and ( ).

Options:
A. Novel
B. Tale
C. Myth
D. Drama
E. Legend
F. Essay
G. Journal
H. Short Essay
I. Fable
J. Chronicle
Answer: B
According to the degree of interconnectivity among channel members in a channel, it can be divided into why and vertical channel systems( ).

Options:
A. Dynamic channel configurations
B. Horizontal network subsystems
C. Contemporary channel editions
D. Standardized transmission approaches
E. Progressive channel networks
F. Integrated network structures
G. Traditional channels
H. Conventional flow methods
I. Modern distribution lines
J. Linear communication paths
Answer: G
The Activity Film Department of the Commercial Press was established in ( ).

Options:
A. 1931
B. 1923
C. 1899
D. 1913
E. 1905
F. 1897
G. In 1920
H. 1910
I. 1902
J. 1918
Answer: J
The "interlude" in the aria was formed during _____;

Options:
A. Milanese opera school
B. Viennese opera school
C. Roman school
D. Florentine opera school
E. Venetian opera school
F. Neapolitan opera school
G. Parisian opera school
H. Genoese opera school
I. Venetian school
J. Bavarian opera school
Answer: E
If a certain structural unit in a piece of music ends completely with the main function of its own main tonality, then the structural unit is called _______.

Options:
A. Transitional structure
B. Cadential structure
C. Expository structure
D. Divergent structure
E. Binary structure
F. Ternary structure
G. Convergent structure
H. Sequential structure
I. Modulatory structure
J. Periodic structure
Answer: G
Which option briefly describes the five aesthetic qualities of war film texts?

Options:
A. War films and the desire to attack. War films and heroic plots. War films and tragic consciousness. War films and humanitarianism. War films and philosophical sublimation.
B. War films and suspense. War films and dramatic irony. War films and visual metaphors. War films and character motivations. War films and thematic consistency.
C. War films and realism. War films and symbolism. War films and cinematography. War films and editing. War films and production design.
D. War films and character development. War films and narrative structure. War films and visual storytelling. War films and sound design. War films and emotional impact.
E. War films and action sequences. War films and dramatic tension. War films and visual aesthetics. War films and pacing. War films and dialogue.
F. War films and narrative complexity. War films and visual effects. War films and soundtracks. War films and character interactions. War films and plot development.
G. War films and historical context. War films and character arcs. War films and plot twists. War films and emotional resonance. War films and thematic depth.
H. War films and political messages. War films and cultural representation. War films and moral dilemmas. War films and psychological depth. War films and thematic exploration.
I. War films and storytelling techniques. War films and emotional storytelling. War films and visual symbolism. War films and character studies. War films and narrative pacing.
J. War films and romantic subplots. War films and comedic relief. War films and musical scores. War films and historical accuracy. War films and special effects.
Answer: A
The two films written by the famous female writer Zhang Ailing in the 1940s are ____.

Options:
A. "Lights in Thousands of Houses" and "New Complaints of the Boudoir"
B. "Long Live Madam" and "Lights in Thousands of Houses"
C. "New Complaints of the Boudoir" and "Love Without End"
D. "Love Without End" and "Lights in Thousands of Houses"
E. "Long Live Madam" and "New Complaints of the Boudoir"
F. "Spring Light That Cannot Be Confined" and "Long Live Madam"
G. "Love Without End" and "Spring Light That Cannot Be Confined"
H. "Spring Light That Cannot Be Confined" and "Lights in Thousands of Houses"
I. "New Complaints of the Boudoir" and "Spring Light That Cannot Be Confined"
J. "Love Without End" and "Long Live Madam"
Answer: J
Who directed the 1949 film "The White-Haired Girl"?

Options:
A. Xu Wei
B. Jin Yue
C. Zhou Hua
D. Li Han
E. Wang Bin
F. Lu Yang
G. Ge Ping
H. Chen Lu
I. Sun Tao
J. Zhao Ming
Answer: E
Which film features the famous martial arts choreography by Yuen Woo-ping?

Options:
A. House of Flying Daggers
B. Fist of Fury
C. The Matrix
D. Crouching Tiger, Hidden Dragon
E. The Grandmaster
F. Kung Fu Panda
G. Ip Man
H. Rush Hour
I. Enter the Dragon
J. Once Upon a Time in China
Answer: C
Which film won the Best Director Award at the 2016 Hong Kong Film Awards?

Options:
A. From Vegas to Macau III
B. The Monkey King 2
C. The Taking of Tiger Mountain
D. Monkey King 2
E. Port of Call
F. Trivisa
G. Cold War II
H. The Mermaid
I. Ten Years
Answer: H
Who directed the 1994 film "The Lovers," known for its portrayal of historical romance?

Options:
A. Tsui Hark
B. Stanley Kwan
C. Ang Lee
D. Hou Hsiao-hsien
E. Zhang Yimou
F. Chen Kaige
G. John Woo
H. Peter Chan
I. Wong Kar-wai
J. Edward Yang
Answer: A
What is the title of the 2009 film by director Chen Kaige that depicts historical figures from ancient China?

Options:
A. The Celestial Empire
B. The Eternal Throne
C. The Emperor's Shadow
D. The Ancient Warriors
E. The Dynasty's Secret
F. The Imperial Tale
G. The Last Dynasty
H. The Promise
I. The Forbidden Kingdom
J. The Royal Legends
Answer: H
Who directed the 2019 film "The Wandering Earth," which became a major box office hit in China?

Options:
A. Li Weiran
B. Guo Fan
C. Feng Xiaogang
D. Frant Gwo
E. Lou Ye
F. Wang Xiaoshuai
G. Zhang Yimou
H. Chen Kaige
I. Jiang Wen
J. Jia Zhangke
Answer: D
What is filigree enamel commonly known as?

Options:
A. Plinth-lacquer
B. Cloisonné
C. Basse-taille
D. Champlevé
E. Repoussé
F. Tesserae-glaze
G. Niello
H. Plique-à-jour
I. Sgraffito
J. Guilloché
Answer: B
Which Chinese dynasty is known for its production of intricate woodblock prints?

Options:
A. Zhou Dynasty
B. Yuan Dynasty
C. Liao Dynasty
D. Song Dynasty
E. Qing Dynasty
F. Han Dynasty
G. Ming Dynasty
H. Jin Dynasty
I. Sui Dynasty
J. Tang Dynasty
Answer: G
Which dynasty is known for its advancements in silk weaving and textile arts?

Options:
A. Liao Dynasty
B. Ming Dynasty
C. Song Dynasty
D. Tang Dynasty
E. Xia Dynasty
F. Zhou Dynasty
G. Qing Dynasty
H. Yuan Dynasty
I. Han Dynasty
J. Jin Dynasty
Answer: D
Which dynasty is noted for the creation of "Baimiao" white porcelain?

Options:
A. Zhou Dynasty
B. Han Dynasty
C. Ming Dynasty
D. Qing Dynasty
E. Tang Dynasty
F. Shang Dynasty
G. Jin Dynasty
H. Yuan Dynasty
I. Sui Dynasty
J. Song Dynasty
Answer: C
The "Liao" porcelain is known for its distinctive use of which type of glaze?

Options:
A. Blue glaze
B. Orange glaze
C. Pink glaze
D. White glaze
E. Green glaze
F. Purple glaze
G. Black glaze
H. Celadon glaze
I. Yellow glaze
J. Red glaze
Answer: G
What is a representative culture of the Shandong region?

Options:
A. Xia Culture
B. Half-slope Culture
C. Erlitou Culture
D. Liangzhu Culture
E. Dawenkou Culture
F. Hongshan Culture
G. Majiayao Culture
H. Hemudu Culture
I. Yangshao Culture
J. Longshan Culture
Answer: J
What is known for firing porcelain with powder-blue glaze, and was an important kiln site during the Song Dynasty?

Options:
A. Wuyuan Kiln
B. Tongren Kiln
C. Bainiu Kiln
D. Longquan Kiln
E. Taolou Kiln
F. Jingmen Kiln
G. Huizhou Kiln
H. Dingzhou Kiln
I. Caozhou Kiln
J. Xingren Kiln
Answer: D
The French Renaissance movement clearly formed two factions of __.

Options:
A. Royalist sector and Populist sector
B. Monarch section and Citizen section
C. High-class bloc and Low-class bloc
D. Aristocratic faction and Democratic faction
E. Royalist assembly and Populist assembly
F. Upper echelon and Commoner echelon
G. Noble group and Commoner group
H. Noble class and Peasant class
I. Elite faction and Masses faction
J. Elite division and Public division
Answer: D
Sophocles is _____ .

Options:
A. Thucydides in the Art of Drama
B. Plato in the Philosophy of Tragedy
C. Socrates in the Art of Drama
D. Pindar in the Craft of Epic
E. Euripides in the Philosophy of Tragedy
F. Virgil in the Craft of Epic
G. Herodotus in the Poetics of Theater
H. Aeschylus in the Art of Drama
I. Aristotle in the Poetics of Theater
J. Homer in the Art of Drama
Answer: J
How to understand the criticism of the idealistic explanations from various disciplines on the origin of music?

Options:
A. In earlier periods of societal growth, the bond between music and spirituality gets intricate and remains always ambiguous as seen in archaic cultures. In feudal states, aspects molding the progression and type of musical expressions, beyond spiritual import, encompass class
B. In earlier periods of societal growth,the relationship between music and labor becomes complex and is no longer as direct and clear as in primitive times. In class societies, factors influencing the development and nature of musical art, besides labor production, class is not included
C. During later stages of societal maturation, the interplay between music and commerce becomes intricate and invariably less distinct as noted in ancient societies. In class-based systems, elements affecting the formation and essence of musical styles, beyond economic activity, involve class
D. In earlier periods of societal growth,the relationship between music and labor becomes complex and is no longer as direct and clear as in primitive times. In class societies, factors influencing the development and nature of musical art, besides labor production, include class
E. At a more advanced stage of social development,the connection between music and rituals becomes evident and is constantly straightforward as observed in early societies. In tribal communities, elements shaping the growth and character of musical forms, apart from ritual significance, involve class
F. At a more advanced stage of social development, the relationship between music and labor becomes complex and is no longer as direct and clear as in primitive times. In class societies, factors influencing the development and nature of musical art, besides labor production, include class
G. Throughout the advanced periods of social evolution, the linkage between music and politics gets complex and maintains a clear yet indirect manner as seen in early civilizations. In societal classes, aspects guiding the advancement and form of musical genre, aside from political engagement,
H. At the initial phase of cultural evolution, the connection between music and rituals becomes evident and is constantly straightforward as observed in early societies. In tribal communities, elements shaping the growth and character of musical forms, apart from ritual significance, involve class
I. At the primary phase of social emergence, the tie between music and religion becomes complicated and continually vague as detected in archaic cultures. In theocratic systems, factors affecting the progression and essence of musical art, beyond religious practices, involve class
J. At the initial phase of cultural evolution, the bond between music and spirituality gets intricate and remains always ambiguous as seen in archaic cultures. In feudal states, aspects molding the progression and type of musical expressions, beyond spiritual import, encompass class
Answer: F
What is Drum Lyrics?

Options:
A. During the late Yuan era, alongside choral hymns, a type of harmonic music that surfaced in the eastern provinces came into existence. Initially, it mainly addressed broad and organized compositions.
B. After the early Ming era, along with theatrical acts, a type of dramatic music that flourished in the southern district appeared. In its initial phase, it particularly concentrated on comprehensive and orderly pieces.
C. After the mid-Ming dynasty, alongside ballad singing, a form of narrative singing that spread through the northern region emerged. In its early days, it primarily focused on extensive and formal compositions.
D. During the early Qing period, together with instrumental music, a mode of rhythmic music that developed in the western zone appeared. At first, it mainly emphasized intricate and planned melodies. Nevertheless, owing to the difficulty in playing these extended tunes.
E. Following the early Ming period, with the rise of drum performances, a genre of percussive music that expanded in the central provinces began. Initially, it targeted complex and arranged rhythms. However, the obstacles in maintaining these extended sessions.
F. During the late Tang dynasty, with folklore recitals, a type of storytelling music that spread in the eastern areas surfaced. Initially, it aimed at detailed and systematic stories. Yet, due to the challenge of presenting these broad narratives.
G. Before the late Ming dynasty, in conjunction with drum music, a type of rhythmic performance that spread in the northern regions emerged. Initially, it emphasized grand and formal arrangements.
H. Before the late Ming era, combined with traditional dance, a style of expressive dance common in the southern areas arose. Initially, it concentrated on elaborate and structured routines. Consequently, because of challenges in executing these expansive dances.
I. During the mid-Ming dynasty, along with storytelling, a genre of narrative dance that developed in the southern sector arose. At first, it primarily emphasized complicated and polished performances.
J. Following the early Ming era, together with poetry recitations, a style of lyric poetry that spread in the western regions developed. Initially, it specifically aimed at broad and strategic structures.
Answer: C
What is a flower drum?

Options:
A. Flower Drum is a mainly singing-centered folk tune and dance of the Han Chinese ethnicity. It emerged from the Yangge dance and is also referred to as Playing Flowers.
B. Flower Drum is a traditional painting style that focuses on botanical subjects, often used in classical Chinese art.
C. Flower Drum is a historically significant novel about the life and trials of a young gardener in ancient China.
D. Flower Drum is a predominantly vocal-driven folk melody and movement of the Han Chinese ethnicity. It originated from the Yangge dance and is equally known as Playing Flowers.
E. Flower Drum is a primarily percussion-based musical instrument crafted by the Han Chinese ethnicity. It was derived from the Yangge dance and is also recognized as Playing Flowers.
F. Flower Drum is a widely celebrated instrument made from petals and stems, used primarily in traditional Chinese ceremonies.
G. Flower Drum is a predominantly chanting-based folk narrative and dance of the Han Chinese ethnicity. It arose from the Yangge dance and is similarly termed Playing Flowers.
H. Flower Drum is a predominantly singing-based folk song and dance of the Han Chinese ethnicity. It evolved from the Yangge dance and is also known as Playing Flowers.
I. Flower Drum is a mostly drumming-based folk genre originating from the Han Chinese group. It developed from the Tao dance and is also called Blossom Beats.
J. Flower Drum is an ancient type of Chinese poetry that uses floral imagery to symbolize beauty and decay.
Answer: H
The ___refers to the layer between the surface of the earth and the first discontinuity.

Options:
A. biosphere
B. crust
C. lithosphere
D. sediment
E. mesosphere
F. ozone
G. mantle
H. stratosphere
I. hydrosphere
J. core
Answer: B
Inland seas include: (1) bays, straits, estuaries; (2) marine areas between the ____ and ____; (3) marine areas surrounded by land or connected to the ocean through narrow channels.

Options:
A. midpoints of estuary regions; the waterfronts
B. outer boundary of coral reefs; oceanic frontiers
C. baseline of territorial waters; the coastline
D. edge of continental shelves; the riverbanks
E. fringe of wetland areas; the coastal barriers
F. perimeter of freshwater lakes; the seacoasts
G. limit of aquatic reserves; the seabeds
H. centerline of rivers; the shoreline
I. boundary of coastal zones; the beachfronts
J. boundary of marine sectors; the coastlines
Answer: C
Solar activity is primarily manifested as variations in solar phenomena such as sunspots, faculae, plages, flares, solar prominences, and ____.

Options:
A. solar gravitational pulls
B. interstellar dust concentrations
C. stellar absorption rates
D. solar wind intensities
E. atmospheric pressure changes
F. solar lunar cycles
G. cosmic ray intensities
H. solar radio emissions
I. planetary alignments
J. lunar magnetic effects
Answer: H
The______refers to the area surrounding a continent, extending from the low tide shoreline to where the seabed slope becomes dramatically steep.

Options:
A. continental shelf
B. coastal perimeter
C. continental ridge
D. coastal terrace
E. maritime basin
F. seaside escarpment
G. oceanic plateau
H. underwater plain
I. suboceanic incline
J. littoral zone
Answer: A
Meridians, also known as ____, are great circles that pass through a certain point on the Earth's surface and both poles, indicating the local north-south direction.

Options:
A. hemisphere arches
B. equatorial lines
C. secondary meridians
D. polar routes
E. global pathways
F. cardinal loops
G. celestial equators
H. prime meridians
I. longitudinal belts
J. axial circles
Answer: H
On the outer edge of the continental shelf, there often lie elevated ridges called ______.

Options:
A. continental peak boundary zones
B. continental crust boundary points
C. continental slope boundary hills
D. continental divide elevation levels
E. continental plate border lines
F. continental shelf margin banks
G. continental basin edge mounts
H. continental shelf edge elevations
I. continental ridge boundary ridges
J. continental drift barrier reefs
Answer: F
The ____is a celestial body resembling a cloud of mist, composed of gases and dust materials within the Milky Way Galaxy, similar to the Orion Nebula and others.

Options:
A. Hanoi Nebula
B. Cassiopeia Cluster
C. Lyra Shroud
D. Hydra Veil
E. Falcon Nebula
F. Barnard's Star
G. Andromeda Halo
H. Jupiter Cloud
I. Draco Mist
J. Gemini Dust
Answer: A
____is generally found in mountainous areas lacking vegetation cover and is a type of non-zonal soil formed primarily by soil erosion.

Options:
A. Laterite soil
B. Alluvial soil
C. Loamy soil
D. Podzol soil
E. Peaty soil
F. Sandy soil
G. Rough soil
H. Chalky soil
I. Silty soil
J. Clay soil
Answer: G
The complete process of descending from a geosyncline, returning, and folding to form a fold belt is called a ____.

Options:
A. sedimentary pattern
B. metamorphic phase
C. tectonic cycle
D. orogenic event
E. crustal shift
F. continental drift
G. volcanic arc
H. geological sequence
I. rock formation
J. seismic activity
Answer: C
_____ refers to the difficulty in observing flat cleavage planes when a crystal breaks, often resulting in irregular fracture surfaces, as seen in cassiterite and apatite.

Options:
A. Fragmented cleavage
B. Irregular cleavage
C. Broken cleavage
D. Uneven cleavage
E. Partial cleavage
F. Disrupted cleavage
G. Disjointed cleavage
H. Faulty cleavage
I. Skewed cleavage
J. Incomplete cleavage
Answer: J
After the "Crisis of the Third Century", Roman rulers utilized Christianity and made it the spiritual pillar of imperial rule. Which council marked the convergence of the Church and the imperial authority?

Options:
A. Council of Ephesus
B. Council of Chalcedon
C. Nisian Conference
D. Synod of Laodicea
E. Synod of Hippo
F. Latran Conference
G. Sadika Conference
H. Diet of Worms
I. Council of Arles
J. Synod of Elvira
Answer: C
The "Pyramid Age" of ancient Egypt refers to ().

Options:
A. First Intermediate Period
B. Middle Kingdom Period
C. Old Kingdom Period
D. New Kingdom Period
E. Early Dynastic Period
F. Second Intermediate Period
G. Late Period
H. Third Intermediate Period
I. Ancient Dynasty Period
J. Ptolemaic Period
Answer: I
What marked the peak of the English bourgeois revolution?

Options:
A. The English Civil War
B. Equality Faction Uprising
C. Glorious Revolution
D. The Signing of the Magna Carta
E. Establishment of the English Republic
F. The Battle of Naseby
G. The Act of Settlement
H. The Establishment of the Protectorate of Cromwell
I. The Restoration of Charles II
J. The Petition of Right
Answer: E
What was the main purpose of the establishment of the "European Community" by Western European countries in 1958?

Options:
A. Establishing a common currency for all member countries
B. Promoting environmental sustainability across Europe
C. Developing a unified European diplomatic strategy
D. Facilitating free trade agreements with non-European countries
E. Integrate the allocation and use of European economic resources
F. Countering the U.S. and the Soviet Union, strengthening economic cooperation.
G. Enhancing cultural exchanges and educational programs
H. Achieve political and military unification in Europe
I. Creating a European defense force to combat external threats
J. Promoting the Process of Global Economic Integration
Answer: F
The "Eastern Conference" held in Japan from June 27 to July 7, 1927, Who hosted it?

Options:
A. Giichi Tanaka
B. Makoto Saito
C. Nobusuke Kishi
D. Terauchi Masatake
E. Shigeru Yoshida
F. Tetsu Katayama
G. Kijyuro Shidehara
H. Eisaku Sato
I. Fumimaro Konoe
J. Hiranuma Kiichiro
Answer: A
The bourgeois revolutionaries' concept of democracy was more progressive than the reformists' idea of civil rights, mainly reflected in ().

Options:
A. Class essence of the state
B. Strengthening of labor rights
C. Emphasis on individual liberties
D. Promotion of economic equality
E. Expansion of educational access
F. Organization of state power
G. Advocacy for religious freedom
H. Support for universal suffrage
I. Oppose national oppression
J. Oppose feudal land ownership
Answer: F
What was the effect of the Homestead Act on the development of American capitalism at that time?

Options:
A. It shifted America's economic center of gravity to the west
B. It resulted in increased immigration from Europe to the western territories
C. It created a significant decline in agricultural productivity
D. It accelerated the development of the western region and expanded the domestic market
E. It had no significant impact on the economic landscape of the country
F. It encouraged the rise of monopolies in the agricultural sector
G. It has accelerated the transformation of science and technology into productive forces
H. The plantation economy was replaced by a small peasant economy
I. It facilitated the growth of urban centers in the eastern states
J. It led to the establishment of large corporate farms in the Midwest
Answer: H
What is the significant difference between the establishment of the Second International and the establishment of the first International?

Options:
A. There is a struggle between different factions within the international community
B. Loosely organized, is a federation without a central authority
C. The membership included a greater number of socialist parties
D. It was established in a more militarized political climate
E. It focused primarily on economic issues rather than political ones
F. The backbone is well-known workers' leaders and activists
G. It included a significant number of non-working class members
H. More emphasis was placed on national identity and governance
I. The form of the activity is mainly to hold a congress
J. The founding document was written by a single individual
Answer: B
Which of the following legal documents makes the Cabinet responsible to the monarch?

Options:
A. The Treaty of Versailles
B. The Articles of Confederation
C. Constitution of France, 1875
D. The United States Constitution of 1787
E. Constitution of the German Empire
F. The Magna Carta of 1215
G. The Federalist Papers
H. The Act of Settlement, 1701
I. The Declaration of Independence
J. English Bill of Rights, 1689
Answer: E
What is an example of how defeat in an international war often gives rise to revolutionary movements at home?

Options:
A. The Russo-Japanese War
B. The American Civil War
C. The Spanish-American War
D. The Greco-Turkish War
E. The Franco-Prussian War
F. Napoleonic Wars
G. The Italian-Egyptian War
H. The French-Indochina
I. The British-Zulu War
J. The Sino-Indian War
Answer: E
What difficulties did the United States face compared to France during the first Industrial Revolution?

Options:
A. There are many small and medium-sized enterprises and their management is scattered
B. There was constant war and political chaos
C. Lack of skilled labor and technological knowledge
D. Frequent natural disasters disrupting production
E. Excessive government regulation on industries
F. High levels of illiteracy among the workforce
G. Inadequate transportation infrastructure to support industrial growth
H. The unification of the internal market has not been completed
I. Scarce resources and narrow market
J. Over-reliance on agricultural exports
Answer: H
To find the differential equation satisfied by a curve, where the tangent line at any point on this curve forms a triangle with the coordinate axes, and the area of this triangle is equal to the constant $a^2$, the corresponding equation is ().

Options:
A. $$
\left| \left( y-x y^{\prime} \right) \left( x-\frac{y} {y^{\prime}} \right) \right|=2 a^{2}
$$
B. $$
\left| \left( 3y-x y^{\prime} \right) \left( x-\frac{y} {2y^{\prime}} \right) \right|=3 a^{2}
$$
C. $$
\left| \left( y-x y^{\prime} \right) \left( x-\frac{y} {y^{\prime}} \right) \right|=3 a^{2}
$$
D. $$
\left| \left( 2y-x y^{\prime} \right) \left( 3x-\frac{y} {y^{\prime}} \right) \right|=3 a^{2}
$$
E. $$
\left| \left( 2y-x y^{\prime} \right) \left( x-\frac{y} {y^{\prime}} \right) \right|=3 a^{2}
$$
F. $$
\left| \left( y-x y^{\prime} \right) \left(2 x-\frac{y} {y^{\prime}} \right) \right|=3 a^{2}
$$
G. $$
\left| \left( y-2x y^{\prime} \right) \left( x-\frac{y} {y^{\prime}} \right) \right|=3 a^{2}
$$
H. $$
\left| \left( y-x y^{\prime} \right) \left( x-\frac{y} {3y^{\prime}} \right) \right|=3 a^{2}
$$
I. $$
\left| \left( 2y-x y^{\prime} \right) \left( 2x-\frac{y} {y^{\prime}} \right) \right|= 2a^{2}
$$
J. $$
\left| \left( 3y-2x y^{\prime} \right) \left( 2x-\frac{y} {y^{\prime}} \right) \right|=3 a^{2}
$$
Answer: A
Given that the function $f ( x )$ is continuous on $(-\infty,+\infty)$, and $f ( x )=( x+1 )^{2}+2 {\int_{0}^{x}} f ( t ) \mathrm{d} t$, then for $n \geqslant2$ ,$f^{( n )} \left( 0 \right)=$ ( ).

Options:
A. $5 \cdot2^{n-1}$
B. $6 \cdot2^{n-1}$
C. $3 \cdot2^{n-2}$
D. $4 \cdot2^{n+1}$
E. $4 \cdot2^{n+2}$
F. $7 \cdot2^{n+1}$
G. $3 \cdot2^{n-3}$
H. $3 \cdot2^{n+1}$
I. $8 \cdot2^{n-1}$
J. $10 \cdot2^{n-1}$
Answer: A
Given the differential equation
$$
\frac{\mathrm{d} y}{\mathrm{d} x}=4 \mathrm{e}^{-y} \sin x-1
$$
, Which of the following represents the general integral (solution) to this differential equation()?

Options:
A. $$
e^{x}=C e^{-x}+3 ( \operatorname{s i n} x-\operatorname{c o s} x )
$$
B. $$
e^{x}=C e^{-x}+3 ( \operatorname{s i n} -4x\operatorname{c o s} x )
$$
C. $$
e^{x}=C e^{-x}+4 ( \operatorname{s i n} x-3\operatorname{c o s} x )
$$
D. $$
e^{x}=C e^{-x}+4 ( \operatorname{s i n} x+\operatorname{c o s} x )
$$
E. $$
e^{x}=C e^{-x}+4 ( \operatorname{s i n} x-2\operatorname{c o s} x )
$$
F. $$
2e^{x}=C e^{-x}+3 ( \operatorname{s i n} x+\operatorname{c o s} x )
$$
G. $$
e^{x}=C e^{-x}+2 ( \operatorname{s i n} x-\operatorname{c o s} x )
$$
H. $$
e^{x}=C e^{-x}+3 ( \operatorname{s i n} x+\operatorname{c o s} x )
$$
I. $$
e^{x}=C e^{-x}+3 ( 5\operatorname{s i n} x-2\operatorname{c o s} x )
$$
J. $$
2e^{x}=C e^{-x}+3 ( \operatorname{s i n} x-\operatorname{c o s} x )
$$
Answer: G
Let $y_{1}=2 x-\mathrm{e}^{x}, y_{2}=2 x+\mathrm{e}^{x}$ be two particular solutions for the differential equation $y^{\prime}+a \left( x \right) y=b \left( x \right)$, then () is right.

Options:
A. $$a \left( x \right)=-1, b \left( x \right)=2 x-\mathrm{e}^{x}$$
B. $$a \left( x \right)=1, b \left( x \right)=2+2 \mathrm{e}^{x}$$
C. $$a \left( x \right)=1, b \left( x \right)=2+2 x$$
D. $$a \left( x \right)=-1, b \left( x \right)=2+2 x$$
E. $$a \left( x \right)=-1, b \left( x \right)=2+2 \mathrm{e}^{x}$$
F. $$a \left( x \right)=1, b \left( x \right)=2-2 x$$
G. $$a \left( x \right)=-1, b \left( x \right)=2-2 \mathrm{e}^{2x}$$
H. $$a \left( x \right)=-1, b \left( x \right)=2-2 \mathrm{e}^{x}$$
I. $$a \left( x \right)=-1, b \left( x \right)=2-2 x$$
J. $$a \left( x \right)=-1, b \left( x \right)=\mathrm{e}^{x}-2 x$$
Answer: I
The interval of existence for the solution of the equation $\mathbf{y}'=\frac{y^{2}-1}{2}$ passing through the point $(\ln 2, -3)$ is _____.

Options:
A. $$(-\infty, 0)$$
B. $$(-\infty, +\infty)$$
C. $$(-3, 3)$$
D. $$( 0,+\infty)$$
E. $$(-\infty, -1)$$
F. $$[0, +\infty)$$
G. $$[-1, 1]$$
H. $$(1, +\infty)$$
Answer: D
Set $\mathbf{y}=\mathbf{f} \ \ ( \mathbf{x} )$ is $\mathrm{y^{\prime\prime}-2 y^{\prime}+4 y=0}$ a solution, If $f( \mathrm{x}_{0} ) \ > 0$ and
$$
\mathrm{f}^{\prime} ( \mathrm{x}_{0} ) \ =0
$$
, f (x) in some $\mathbf {x} _ {0}$ place ().

Options:
A. Achieve maximum value
B. Attain breaking point
C. Monotonically decreasing within a certain neighborhood
D. Monotonically increasing within a certain neighborhood
E. Maintain constant value
F. Accomplish steady state
G. Achieve minimum value
H. Obtain threshold level
I. Reach equilibrium point
J. Reach critical point
Answer: A
If the slope of the tangent line at any point on the curve is $- 2 \mathbf{x} / \mathbf{y}$, then this curve is ______.

Options:
A. Square
B. Circle
C. Trapezoid
D. Equilateral triangle
E. Parabola
F. Hyperbola
G. Rectangle
H. Ellipse
I. Straight line
J. Semicircle
Answer: H
If f (x) is differentiable and f $(0) \ =1$, for any simple closed curve L,
$$
\int_{L} y f \left( x \right) \! \mathrm{d} x+\! \left[ \, f \left( x \right) \!-\! x^{2} \, \right] \! \mathrm{d} y=0
$$
Then $\int_{0}^{1} x f \left(x \right) \! \mathrm{d} x=\left( \begin{array} {l l} {{}} & {{}} & {{}} \\ \end{array} \right)$.

Options:
A. $$2 / 5$$
B. $$1 / 3$$
C. $$1 / 2$$
D. $$3 / 5$$
E. $$3 / 4$$
F. $$2 / 3$$
G. $$6 / 5$$
H. $$4 / 3$$
I. $$5 / 3$$
J. $$7 / 4$$
Answer: H
Let the functions f (x), g $(\mathbf{x})$satisfy the following conditions: $\mathrm{f}^{\prime} \ \ ( \mathrm{x} ) \ =\mathrm{g} \ \ ( \mathrm{x} ) \ \, \ \ \mathrm{g}^{\prime} \ \ ( \mathrm{x} ) \ =2 e^{\mathrm{x}}-\mathrm{f} \ \ ( \mathrm{x} )$ ,f (0) = 0, and g (0) = 2, Then $\int_{0}^{\pi} \left[ \frac{g \left( x \right)} {1+x}-\frac{f \left( x \right)} {\left( 1+x \right)^{2}} \right] \mathrm{d} x$ =().

Options:
A. $$\frac{1-\mathrm{e}^{\pi}} {1+\pi}$$
B. $$\frac{1+\mathrm{e}^{-\pi}} {1+2\pi}$$
C. $$\frac{1+\mathrm{e}^{-\pi}} {1-2\pi}$$
D. $$\frac{1-\mathrm{e}^{-\pi}} {1+\pi}$$
E. $$\frac{1+\mathrm{e}^{\pi}} {1+\pi}$$
F. $$\frac{1-\mathrm{e}^{\pi}} {1-\pi}$$
G. $$\frac{1-\mathrm{e}^{\pi}} {1+2\pi}$$
H. $$\frac{1+\mathrm{e}^{\pi}} {1-\pi}$$
Answer: E
$\widehat{O A}$For $\widehat{O A}$For $\widehat{O A}$for $\widehat{o a}$for each point $P \left(x, y \right)$, the area enclosed by curve arc $\widehat{O P}$and line segment $\overline{{{O P}}}$is $x^{2}$, and the equation of curve arc $\widehat{O A}$is ().

Options:
A. $$y=-4 x \operatorname{l n} y + y$$
B. $$y=-4 x \operatorname{l n} y + y-4$$
C. $$y=-4 x \operatorname{l n} x+x$$
D. $$y=-4 x \operatorname{l n} y + y+2$$
E. $$y=4x\operatorname{l n}x-3x$$
F. $$y=-4 x \operatorname{l n} y + 2xy$$
G. $$y=-4x\operatorname{l n}x+2x$$
H. $$y=-4 x \operatorname{l n} y + y+4$$
I. $$y=-4 x \operatorname{l n} y + y-2$$
J. $$y=4 x \operatorname{l n} x + x$$
Answer: C
The cannon fires a projectile at an elevation angle $\alpha$ and an initial speed $v_{0}$. Assuming no air resistance, the trajectory curve is ().

Options:
A. $$\left\{ \begin{array}{l}
x = v_{0} \cos \alpha \cdot 2t, \\
y = v_{0} \sin \alpha \cdot t - \frac{g}{2} t^{2}.
\end{array} \right.$$
B. $$\left\{ \begin{array}{l}
x = v_{0} \cos \alpha \cdot 3t, \\
y = v_{0} \sin \alpha \cdot t - \frac{g}{2} t^{3}.
\end{array} \right.$$
C. $$\left\{ \begin{array}{l}
x = v_{0} \cos \alpha \cdot t, \\
y = v_{0} \sin \alpha \cdot t - \frac{g}{2} t^{}.
\end{array} \right.$$
D. $$\left\{ \begin{array}{l}
x = v_{0} \cos \alpha \cdot t, \\
y = v_{0} \sin \alpha \cdot2 t - \frac{g}{2} t^{2}.
\end{array} \right.$$
E. $$\left\{ \begin{array}{l}
x = v_{0} \cos \alpha \cdot t, \\
y = v_{0} \sin \alpha \cdot t + \frac{g}{2} t^{3}.
\end{array} \right.$$
F. $$\left\{ \begin{array}{l}
x = v_{0} \cos \alpha \cdot 3t, \\
y = v_{0} \sin \alpha \cdot t - \frac{g}{2} t^{2}.
\end{array} \right.$$
G. $$\left\{ \begin{array}{l}
x = v_{0} \cos \alpha \cdot 2t, \\
y = v_{0} \sin \alpha \cdot 2t - \frac{g}{2} t^{2}.
\end{array} \right.$$
H. $$\left\{ \begin{array}{l}
x = v_{0} \cos \alpha \cdot t, \\
y = v_{0} \sin \alpha \cdot t - \frac{g}{2} t^{2}.
\end{array} \right.$$
I. $$\left\{ \begin{array}{l}
x = v_{0} \cos \alpha \cdot t, \\
y = v_{0} \sin \alpha \cdot t - \frac{3g}{2} t^{3}.
\end{array} \right.$$
J. $$\left\{ \begin{array}{l}
x = v_{0} \cos \alpha \cdot t, \\
y = v_{0} \sin \alpha \cdot t - \frac{g}{2} t^{3}.
\end{array} \right.$$
Answer: H
Satisfy the differential equation of $y^{\prime\prime}-y=\mathrm{e}^{x}+4 \operatorname{c o s} x,$L is( ), make the curve at the point of $(0, 1)$and curve $y=x^{2}-x+1$ tangent.

Options:
A. $$y={\frac{3} {5}} \mathrm{e}^{x}+{\frac{9} {4}}\mathrm{e}^{-x}+{\frac{1} {2}} x \mathrm{e}^{x}-2 \operatorname{cos} 2x$$
B. $$y={\frac{3} {5}} \mathrm{e}^{x}+{\frac{9} {4}}\mathrm{e}^{-x}+{\frac{1} {2}} x \mathrm{e}^{x}+2 \operatorname{cos} x$$
C. $$y={\frac{3} {4}} \mathrm{e}^{x}+{\frac{9} {4}}\mathrm{e}^{-x}+{\frac{1} {2}} x \mathrm{e}^{x}-2 \operatorname{c o s} x$$
D. $$y={\frac{3} {4}} \mathrm{e}^{x}+{\frac{9} {4}}\mathrm{e}^{-x}+{\frac{1} {2}} x \mathrm{e}^{x}-2 \operatorname{sin} 2x$$
E. $$y={\frac{3} {5}} \mathrm{e}^{x}+{\frac{9} {4}}\mathrm{e}^{-x}+{\frac{1} {2}} x \mathrm{e}^{x}$$
F. $$y={\frac{3} {4}} \mathrm{e}^{x}+{\frac{9} {4}}\mathrm{e}^{-x}+{\frac{1} {2}} x \mathrm{e}^{x}-2 \operatorname{sin} x$$
G. $$y={\frac{3} {5}} \mathrm{e}^{x}+{\frac{9} {4}}\mathrm{e}^{-x}+{\frac{1} {2}} x \mathrm{e}^{x}-2 \operatorname{sin} x$$
H. $$y={\frac{3} {5}} \mathrm{e}^{x}+{\frac{9} {4}}\mathrm{e}^{-x}+{\frac{1} {2}} x \mathrm{e}^{x}-3 \operatorname{cos} 2x$$
I. $$y={\frac{3} {5}} \mathrm{e}^{x}+{\frac{9} {4}}\mathrm{e}^{-x}+{\frac{1} {2}} x \mathrm{e}^{x}-2 \operatorname{cos} x$$
J. $$y={\frac{3} {4}} \mathrm{e}^{x}+{\frac{9} {4}}\mathrm{e}^{-x}+{\frac{1} {2}} x \mathrm{e}^{x}-2 \operatorname{sin3} x$$
Answer: C
The rate of change of the base radius and height of a cylinder with time is $2 \mathrm{c m/s},-3 \mathrm{c m/s}$, respectively. When the base radius is 10cm and the height is 5cm, the change rate of the volume and surface area of the cylinder with time is (), respectively.

Options:
A. $$ - 3 0 \pi\mathrm{c m}^{3} / s \,, \, \, \, 4 0 \pi\mathrm{c m}^{2} / \mathrm{s}. $$
B. $$ - 1 0 0 \pi\mathrm{c m}^{3} / s \,, \, \, \, -4 0 \pi\mathrm{c m}^{2} / \mathrm{s}. $$
C. $$ 1 0 0 \pi\mathrm{c m}^{3} / s \,, \, \, \, -4 0 \pi\mathrm{c m}^{2} / \mathrm{s}. $$
D. $$ - 2 0 \pi\mathrm{c m}^{3} / s \,, \, \, \, -4 0 \pi\mathrm{c m}^{2} / \mathrm{s}. $$
E. $$ - 2 0 \pi\mathrm{c m}^{3} / s \,, \, \, \, 4 0 \pi\mathrm{c m}^{2} / \mathrm{s}. $$
F. $$ 2 0 \pi\mathrm{c m}^{3} / s \,, \, \, \, 4 0 \pi\mathrm{c m}^{2} / \mathrm{s}. $$
G. $$ - 1 0 0 \pi\mathrm{c m}^{3} / s \,, \, \, \, 4 0 \pi\mathrm{c m}^{2} / \mathrm{s}. $$
H. $$ 2 0 \pi\mathrm{c m}^{3} / s \,, \, \, \, -4 0 \pi\mathrm{c m}^{2} / \mathrm{s}. $$
I. $$ - 6 0 \pi\mathrm{c m}^{3} / s \,, \, \, \, 4 0 \pi\mathrm{c m}^{2} / \mathrm{s}. $$
J. $$ 1 0 0 \pi\mathrm{c m}^{3} / s \,, \, \, \, 4 0 \pi\mathrm{c m}^{2} / \mathrm{s}. $$
Answer: G
Let $D$ be a circular sheet of radius $R$, $L$be a tangent line of $D$, the point density of any point $P$ of $D$ is proportional to the square of the distance $d$from $P$ to $L$, the scaling coefficient $k > 0$, and the position of the mass center of the sheet is ().

Options:
A. $$ (R, 0 ) $$
B. $$ ( \frac{3} {4} R, 0 ) $$
C. $$ ( \frac{1} {3} R, 0 ) $$
D. $$ ( \frac{2} {5} R, 0 ) $$
E. $$ ( \frac{2} {3} R, 0 ) $$
F. $$ ( \frac{3} {5} R, 0 ) $$
G. $$ ( \frac{1} {4} R, 0 ) $$
H. $$ ( \frac{4} {5} R, 0 ) $$
I. $$ ( \frac{1} {2} R, 0 ) $$
J. $$ ( \frac{1} {5} R, 0 ) $$
Answer: D
Let the function $y \left(x \right) ~ ~ (x \geqslant0)$be second-order derivable, $y^{\prime} \left( x \right) > 0 \, \,, \, \, \, \, y \left( 0 \right)=1$, Cross the curve $y=y \left(x \right)$each point $P \left(x, y \right)$ as tangent to the curve and perpendicular to the $x$ axis. The area of the triangle enclosed by the above two lines and the $x$ axis is denoted as $S_{1}$ In the interval $[ 0, x ]$ $y=y \left( x \right)$ for the area of the curved trapezoid remember $S_ {2}$, and $2S_ {1} - S_ {2} = 1$, $y \left( x \right)=()$.

Options:
A. $$ \mathrm{e}^{x+1} $$
B. $$ 2\mathrm{e}^{3x} $$
C. $$ \mathrm{e}^{2x} $$
D. $$ \mathrm{e}^{x^2} $$
E. $$ 3\mathrm{e}^{x/2} $$
F. $$ \mathrm{e}^{x^4} $$
G. $$\sqrt{e^{x}} $$
H. $$\mathrm{e}^{2x-1} $$
I. $$ \mathrm{e}^{x} $$
J. $$ 2\mathrm{e}^{x-1} $$
Answer: I
The general solution of the difference equation $\Delta y_{t}=t$ is $y_{t}=()$.

Options:
A. $\frac{} {} 3t \left( t+1 \right)+C$, where $\left( C \right)$ is an arbitrary constant.
B. $\frac{1} {2} t \left( 3t+1 \right)+C$, where $\left( C \right)$ is an arbitrary constant.
C. $\frac{1} {2} t \left( t+2 \right)+C$, where $\left( C \right)$ is an arbitrary constant.
D. $\frac{1} {2} t \left( t+1 \right)+C$, where $\left( C \right)$ is an arbitrary constant.
E. $\frac{1} {2} t \left(2 t-1 \right)+C$, where $\left( C \right)$ is an arbitrary constant.
F. $\frac{1} {2} t \left( t-2 \right)+C$, where $\left( C \right)$ is an arbitrary constant.
G. $\frac{1} {2} t \left( t-1 \right)+C$, where $\left( C \right)$ is an arbitrary constant.
H. $\frac{} {} t \left( t+1 \right)+C$, where $\left( C \right)$ is an arbitrary constant.
I. $\frac{} {} t \left(2 t-3 \right)+C$, where $\left( C \right)$ is an arbitrary constant.
J. $\frac{1} {2} t \left(2 t-3 \right)+C$, where $\left( C \right)$ is an arbitrary constant.
Answer: G
Find the particular solution of the differential equation $y''[x+(y')^{2}] = y'$ that satisfies the initial conditions $y(1) = y'(1) = 1$ is().

Options:
A. $$
y=\frac{2} {3} x^{3}+\frac{1} {3}
$$
B. $$
y=\frac{2} {3} x^{\frac{3} {2}}-1
$$
C. $$
y=\frac{2} {3} x^{\frac{3} {2}}
$$
D. $$
y=\frac{2} {3} x^{4}+\frac{1} {3}
$$
E. $$
y=\frac{2} {3} x^{2}+\frac{1} {3}
$$
F. $$
y=\frac{2} {3} x^{\frac{} {}}+\frac{1} {3}
$$
G. $$
y=\frac{2} {3} x^{\frac{3} {2}}+\frac{2} {3}
$$
H. $$
y=\frac{2} {3} x^{\frac{3} {2}}+\frac{1} {3}
$$
I. $$
y=\frac{2} {3} x^{\frac{3} {2}}+2
$$
J. $$
y=\frac{2} {3} x^{\frac{3} {2}}+3
$$
Answer: H
Let the function $f \left(x \right)$ satisfy $x f^{\prime} \left(x \right) − 2 f \left(x \right)= − 4 x$and curved
A plane graph bounded by the line $y=f \left(x \right)$, the line $x=1$, and the $x$ axis will have the smallest volume of rotation if it is rotated around the x axis once, then $f \left(x \right)=()$.

Options:
A. $$3 x^{2} - 4 x^3$$
B. $$- 5 x^{2} - 4 x$$
C. $$- 5 x^{2}+4 x$$
D. $$-5 x^{2} + 4 x^3$$
E. $$5 x^{2} + 4 x^3$$
F. $$3 x^{2} + 4 x$$
G. $$-5 x^{2} - 4 x^3$$
H. $$- 3 x^{2}+4 x$$
I. $$5 x^{3} + 4 x$$
J. $$- 5 x^{2} - 4 x + 1$$
Answer: C
Find a curve $L: y \left(x \right)$such that $y (x)=()$ is continuously differentiable on $(-\infty,+\infty)$such that at every point on the curve $L$the intersection of the tangent line with the horizontal axis is equal to half the abscission of the tangent point.

Options:
A. $y = Cx^{2}+2x$, where $C$ is any nonzero constant
B. $y = Cx^{4}$, where $C$ is any nonzero constant
C. $y = Cx^{3}$, where $C$ is any nonzero constant
D. $y = Cx^{2}-2$, where $C$ is any nonzero constant
E. $y = Cx^{2}$, where $C$ is any nonzero constant
F. $y = Cx^{}$, where $C$ is any nonzero constant
G. $y = C \sin(x)$, where $C$ is any nonzero constant
H. $y = Ce^{x}$, where $C$ is any nonzero constant
I. $y = Cx^{2}+2$, where $C$ is any nonzero constant
J. $y = Cx^{2}+x$, where $C$ is any nonzero constant
Answer: E
Let the curve $L$ lie in the first quadrant of the plane $x O y$, the tangent line at any point $M$on $L$ always intersects the $y$ axis, and the intersection point is denoted as $A$. Known $\left| \overline{{{M A}}} \right|=\left| \overline{{{O A}}} \right|$, and A little $\left( \frac{3} {2}, \frac{3} {2} \right)$, find the equation for $L$ is ().

Options:
A. $$ y=\sqrt{5x-6x^2} (0 < x < 3) $$
B. $$ y=\sqrt{3x-5x^3} (0 < x < 4) $$
C. $$ y=\sqrt{5x-2x^4} (0 < x < 3) $$
D. $$ y=\sqrt{3 x-2x^{2}} ( 0 < x < 3 ) $$
E. $$ y=\sqrt{2 x-x^{2}} ( 0 < x < 2 ) $$
F. $$ y=\sqrt{3 x-x^{2}} ( 0 < x < 3 ) $$
G. $$ y=\sqrt{5 x-x^{2}} ( 0 < x < 5 ) $$
H. $$ y=\sqrt{3 x+x^{2}} ( 0 < x < 3 ) $$
I. $$ y=\sqrt{3 x-2x^{3}} ( 0 < x < 3 ) $$
J. $$ y=\sqrt{4 x-x^{2}} ( 0 < x < 4 ) $$
Answer: F
The melting speed of half of the spherical snowdrift is directly proportional to the surface area of the hemisphere, and the proportional coefficient is $k > 0$. Suppose that the shape remains unchanged during the melting process, and suppose that the volume of the snowdrift with radius $r_{0}$is the original $\frac{1} {8}$after melting for 3 hours, and the time required for full melting is ().

Options:
A. $6$ hours
B. $9$ hours
C. $24$ hours
D. $15$ hours
E. $3$ hours
F. $1$ hours
G. $12$ hours
H. $18$ hours
I. $2$ hours
J. $21$ hours
Answer: A
Suppose the demand function of a product is $Q=Q \left(p \right)$, and its elasticity to price $p$ is $\xi_{p}= 0.2$, then when the quantity demanded is 10000, an increase of $1$ in price will increase the revenue of the product by () yuan.

Options:
A. $3000$
B. $12000$
C. $2000$
D. $5500$
E. $18000$
F. $22000$
G. $8000$
H. $5000$
I. $10000$
J. $15000$
Answer: G
Suppose the diameter of the bottom surface of the cylindrical buoy is $0.5 \mathrm{m}$, put it straight in the water and suddenly release it when it presses down slightly. The period of the buoy's vibration in the water is $2 \mathrm{s}$, and the mass of the buoy is calculated as ().

Options:
A. $$1 7 0 \mathrm{k g}$$
B. $$1 9 0 \mathrm{k g}$$
C. $$2 1 5 \mathrm{k g}$$
D. $$1 7 5 \mathrm{k g}$$
E. $$2 0 0 \mathrm{k g}$$
F. $$1 8 0 \mathrm{k g}$$
G. $$2 2 5 \mathrm{k g}$$
H. $$2 1 0 \mathrm{k g}$$
I. $$150 \mathrm{k g}$$
J. $$1 9 5 \mathrm{k g}$$
Answer: J
Let the probability density function f(x) of the random variable X satisfy f(1+x)=f(1-x), and $$\int_{0}^{2} f \left( x \right) \mathrm{d} x=0. 6$$ then P{X<0}=().

Options:
A. 0.45
B. 0.4
C. 0.35
D. 0.15
E. 0.3
F. 0.25
G. 0.2
H. 0.5
I. 0.0
J. 0.1
Answer: G