MikaStars39/nano-eval huggingface dataset:
What is the underlying reason for literary production, despite the fact that life is the only source of literature and materials are the starting point of literary creation?

Options:
A. Educational reforms.
B. Strengthening international relations.
C. The development of art.
D. The economic benefit of publishing.
E. Increasing global communication.
F. Advancement of technological tools.
G. Reflection on societal changes.
H. Historical documentation needs.
I. Public demand for entertainment.
J. Exploration of human emotions.
Answer: C
What identities does the literary audience possess based on the characteristics of literature, such as cognitive, aesthetic, and cultural aspects?

Options:
A. Reader, critic, and scholar.
B. Participant, observer, and critic.
C. Participant, connoisseur, and evaluator.
D. Learner, judge, and inventor.
E. Imaginer, reflector, and appraiser.
F. Observer, thinker, and creator.
G. Explorer, reviewer, and artist.
H. Spectator, analyst, and designer.
I. Admirer, commentator, and expert.
J. Cognizer, aesthete, and interpreter.
Answer: J
Lyricism is a special form of reflection. Firstly, the object of lyrical reflection primarily involves ______ aspects of social life. Secondly, emotions reflect the specific relationship between the subject and the object.

Options:
A. The environmental aspects.
B. The cultural aspects.
C. The political aspects.
D. The technological aspects.
E. The recreational aspects.
F. The educational aspects.
G. The economic aspects.
H. The historical aspects.
I. The geographic aspects.
J. The spiritual aspects.
Answer: J
Due to the rich tradition of lyrical literature in China, what theories have emerged?

Options:
A. The Theory of Poetic Literature.
B. The Theory of Historical Context.
C. The Theory of Emotion in Art.
D. The Theory of Narrative Structure.
E. The Theory of Cultural Exchange.
F. The Theory of Symbolic Imagery.
G. The Theory of Artistic Conception.
H. The Theory of Revolutionary Aesthetics.
I. The Theory of Intertextuality.
J. The Theory of Ethereal Beauty.
Answer: G
From the development of the left-wing music movement to the climax of the national salvation singing movement, a new path was opened up for the construction and development of modern _________ in my country.

Options:
A. Folk music genre
B. Opera tradition
C. Choral harmony
D. Classical symphony
E. Traditional theater
F. Jazz influence
G. Modern dance form
H. Artistic revival
I. Cultural renaissance
J. New music career
Answer: J
Xinghai's "Yellow River Cantata" is linked together with ______ and the orchestra as the background.

Options:
A. Visual Arts
B. Dance
C. Literature
D. Film
E. Photography
F. Recitation
G. Storytelling
H. Sculpture
I. Poetry
J. Theatre
Answer: F
"March of the Volunteers" and "The Singer Under the Iron Hoof" are interludes of the movie "________".

Options:
A. Tales of Valor
B. Echoes of Tomorrow
C. Whispers in the Dark
D. Shadows of the Past
E. Paths of Destiny
F. Legends of the East
G. Guardians of Time
H. Winds of Change
I. Children of the Storm
J. Songs of the Revolution
Answer: I
The ______ led by Ye Chunshan and Xiao Changhua has always maintained the relatively comprehensive and strict art education tradition of Peking Opera.

Options:
A. Changsheng Society
B. Honghua Association
C. Wujiaban Troupe
D. Yisuo Troupe
E. Tianqiao Theatre Group
F. Shengping Society
G. Longzaitian Opera Club
H. Qianmen School
I. Mianhua Lane Troupe
J. Fuliancheng Class
Answer: J
The works collected in ______ are Zhao Yuanren's most representative artistic creations. These works are all written in the new vernacular poetry style.

Options:
A. "Progressive Poetry Series"
B. "Contemporary Poetic Works"
C. "Vernacular Verse Compilation"
D. "Traditional Poem Anthology"
E. "Emerging Poets Collection"
F. "Modern Verse Anthology"
G. "Classic Poetry Selections"
H. "Innovative Poetic Expressions"
I. "New Poetry Collection"
J. "Experimental Verse Collection"
Answer: I
The five-tone drum, which is widely spread in rural Hebei, was later named ______.

Options:
A. Tianjin Erhu
B. Jiangsu Yangqin
C. Sichuan Guzheng
D. Beijing Qinshu
E. Shandong Pipa
F. Hunan Suona
G. Liaoning Sheng
H. Inner Mongolia Morin Khuur
I. Shanxi Dizi
J. Hebei Guqin
Answer: D
The violin and piano piece "Night Scene" and the piano piece "______" written by Mr. Sang Tong are the earliest representative works in the history of modern Chinese music that fully use atonal composition techniques.

Options:
A. The Forgotten Path
B. Journey Through the Mist
C. Reflections of Time
D. Dreaming in Colors
E. Chasing the Stars
F. In that distant place
G. Echoes of Silence
H. Beneath the Moonlight
I. The Last Serenade
J. Whispering Shadows
Answer: F
Who is the author of "Yuefu Transmission"?

Options:
A. Su Shi
B. Wang Wei
C. Han Yu
D. Du Fu
E. Xu Dachun
F. Lu You
G. Ouyang Xiu
H. Bai Juyi
I. Li Bai
J. Liu Zongyuan
Answer: E
Around 1600, opera art was born in Florence, Italy. What is the name of the first opera?

Options:
A. Euridice
B. The Magic Flute
C. Rigoletto
D. Tosca
E. Orfeo
F. Carmen
G. Aida
H. Daphne
I. nternal server error
J. La Traviata
Answer: H
During the Dali period, which poet considered himself the "Great Wall of Five-Character Poems"?

Options:
A. Du Fu
B. Qu Yuan
C. Li Shangyin
D. Liu Changqing
E. Bai Juyi
F. Su Shi
G. Meng Haoran
H. Xue Tao
I. Li Bai
J. Wang Wei
Answer: D
Under the influence of the Sturm und Drang spirit, Schiller wrote his famous work "The Robbers" and ( ) plays.

Options:
A. "The Visit"
B. "Don Carlos"
C. "Faust"
D. "The Seagull"
E. "The Wild Duck"
F. "The Merchant of Venice"
G. "A Midsummer Night's Dream"
H. "The Broken Jug"
I. "Conspiracy and Love"
J. "The Count of Ory"
Answer: I
What methods should be used to distribute unique products such as antiques, antiques, celebrity calligraphy and paintings( ).

Options:
A. Long term storage facilities
B. Permanent collection points
C. Annual trade conventions
D. Short term circulation channels
E. Continuous online auctions
F. Seasonal display centers
Answer: D
The first feature film in New China was( ).

Options:
A. The Eastern Gate
B. The Ancient Town
C. The Bridge
D. The White Haired Girl
E. The Yellow River
F. The Spring Dawn
G. The Great Wall
H. Chinese Daughter
I. The Mountain Road
J. The Red Star
Answer: C
In 1597, the ________ with a script by Rinuccini and music by Peri was performed. Since only fragments of the score of this work remain, people usually regard the ________ performed in 1600, which is complete and written by Rinuccini and composed by Peri and Caccini, as the earliest opera.

Options:
A. Daphne, Orpheus
B. Daphne, Apollo
C. Orpheus, Apollo
D. Orpheus, Daphne
E. Eurydice, Daphne
F. Orpheus, Eurydice
G. Apollo, Eurydice
H. Daphne, Eurydice
I. Eurydice, Orpheus
J. Apollo, Daphne
Answer: H
Famous composers of the Burgundian school during the Renaissance include ______ and _______.

Options:
A. Benchois, Dufay
B. Lassus, Victoria
C. Gabrieli, Schutz
D. Machaut, Landini
E. Palestrina, Josquin
F. Dunstable, Power
G. Monteverdi, Gesualdo
H. Ockeghem, Obrecht
I. Tallis, Byrd
J. Des Prez, Isaac
Answer: A
Paragraphs may also overlap at the beginning and end, which is called _______.

Options:
A. Boundary merging
B. Paragraph blending
C. Paragraph fusion
D. Intersecting paragraphs
E. Convergent ending
F. Overlap initiation
G. Overlapping closure
H. Intrusion termination
I. Overlap conclusion
J. Textual intersection
Answer: H
The first film that Chen Qiang and Chen Peisi collaborated on was ____.

Options:
A. "Family Ties"
B. "Our Happy Days"
C. "Look at This Family"
D. "Him and Her"
E. "Sweet Business"
F. "A Day in the Life"
G. "The Great Adventure"
H. "Journey Together"
I. "The Big Reunion"
J. "Father and Son's Classic Car"
Answer: C
Hou Yao was deeply influenced by Ibsen's comedy views and advocated the use of art to _____, _____, _____, _____.

Options:
A. Capture essence, critique structures, enhance reality, balance complexities
B. Show reality, debate ideologies, transform lives, promote peace
C. Visualize concepts, dispute traditions, inspire beauty, cultivate harmony
D. Depict truth, contest beliefs, uplift spirits, foster unity
E. Express life, criticize life, beautify life, reconcile life
F. Portray circumstances, question ethics, enrich experiences, harmonize cultures
G. Reflect society, challenge norms, improve life, enlighten audience
H. Represent humanity, confront issues, perfect existence, bridge differences
I. Explore emotions, engage people, beautify art, resolve conflicts
J. Illustrate life, oppose injustice, refine perspectives, support progress
Answer: E
Which 1987 film by director Chen Kaige won the Palme d'Or at the Cannes Film Festival?

Options:
A. The Blue Kite
B. King of the Children
C. The Promise
D. Temptress Moon
E. The Emperor and the Assassin
F. Together
G. The Assassin's Tale
H. Life on a String
I. Farewell My Concubine
J. Yellow Earth
Answer: I
Which film directed by Feng Xiaogang became one of China's highest-grossing films of all time?

Options:
A. Aftershock
B. The Great Revival
C. The Warlords
D. Forever Enthralled
E. The Painted Veil
F. Lost in Thailand
G. Mountain Patrol
H. The Banquet
I. Red Cliff
J. The Assembly
Answer: J
What film did John Woo direct that is considered a landmark in Hong Kong action cinema?

Options:
A. Project A
B. Bullet in the Head
C. Hard Boiled
D. Once a Thief
E. Dragon Inn
F. City on Fire
G. Fist of Fury
H. A Better Tomorrow
I. The Killer
J. Police Story
Answer: H
Which 2016 film by director Zhang Yimou features a young girl who becomes a hero during the Second Sino-Japanese War?

Options:
A. Hero's Dawn
B. The Red Sorgh
C. The Brave Blossom
D. The Silent Sentinel
E. The Warrior's Path
F. The Hidden Dragon
G. The Great Wall
H. The Last Fortress
I. The Eastern Shield
J. The Crimson Defender
Answer: G
Which 2011 film directed by Andrew Lau and Alan Mak focuses on the Chinese police and organized crime?

Options:
A. The Secret Dynasty
B. The Last Tycoon
C. The Criminal Code
D. The Final Stand
E. The Silent Force
F. The Shadow League
G. The Hidden War
H. The Eastern Dawn
I. The Eastern Syndicate
J. The Lost Empire
Answer: B
Which period did the earliest specialized work on craftsmanship in China, "Kao Gong Ji" appear?

Options:
A. Song Dynasty
B. Zhou Dynasty
C. Han Dynasty
D. Three Kingdoms Period
E. Warring States Period
F. Sui Dynasty
G. Qing Dynasty
H. Ming Dynasty
I. Yuan Dynasty
J. Tang Dynasty
Answer: E
In which Chinese dynasty did the art of porcelain carving achieve its peak?

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

Options:
A. Qing Dynasty
B. Yuan Dynasty
C. Han Dynasty
D. Tang Dynasty
E. Ming Dynasty
F. Sui Dynasty
G. Xia Dynasty
H. Song Dynasty
I. Liao Dynasty
J. Jin Dynasty
Answer: A
The "Guangcai" porcelain technique is associated with which Chinese dynasty?

Options:
A. Jin Dynasty
B. Qing Dynasty
C. Song Dynasty
D. Tang Dynasty
E. Xia Dynasty
F. Han Dynasty
G. Shang Dynasty
H. Ming Dynasty
I. Zhou Dynasty
J. Yuan Dynasty
Answer: H
Which art form uses a technique involving "cutting away" to create detailed designs?

Options:
A. Stone Etching
B. Marble Chipping
C. Ice Sculpting
D. Fabric Trimming
E. Paper Cutting
F. Silk Painting
G. Wood Carving
H. Canvas Printing
I. Glass Blowing
J. Metal Shaping
Answer: E
In the history of calligraphy, who is known as the "Little Sage"?

Options:
A. Ouyang Xun
B. Sun Guoting
C. Wang Xizhi
D. Wei Shuo
E. Zhong Yao
F. Huaisu
G. Zhong Hui
H. Yan Zhenqing
I. Wang Xianzhi
J. Zhang Xu
Answer: I
What is a scroll shed roof?

Options:
A. For a type of roof with a segmented ridge, it is characterized by a dual-slope system with the main ridge segmented into various angles. This design is commonly used in southern residential homes or in architectural structures such as museums.
B. For a type of roof with an angular ridge, it is characterized by a dual-slope system with the main ridge formed into a sharp angle. This design is commonly used in urban residential homes or in architectural structures such as museums.
C. For a type of roof with a curved ridge, it is characterized by a dual-slope system with the main ridge bent into a curved shape. This design is commonly used in midwestern residential homes or in architectural structures such as parks.
D. For a type of roof with a rounded ridge, it is characterized by a dual-slope system with the main ridge formed into an arched curve. This design is commonly used in northern residential homes or in architectural structures such as gardens.
E. For a type of roof with a tiered peak, it is characterized by a dual-slope system with the main ridge layered into multiple levels. This design is commonly used in mountainous residential homes or in architectural structures such as lodges.
F. For a type of roof with a sloped ridge, it is characterized by a dual-slope system with the main ridge inclined into a gradual slope. This design is commonly used in suburban residential homes or in architectural structures such as libraries.
G. For a type of roof with a softened peak, it is characterized by a dual-slope system with the main ridge smoothed into a gentle curve. This design is commonly used in coastal residential homes or in architectural structures such as resorts.
H. For a type of roof with a flat top, it is characterized by a dual-slope system with the main ridge extended into a flat surface. This design is commonly used in western residential homes or in architectural structures such as marketplaces.
I. For a type of roof with a pointed peak, it is characterized by a dual-slope system with the main ridge elevated into a pointed peak. This design is commonly used in southern residential homes or in architectural structures such as villas.
J. For a type of roof with a rounded peak, it is characterized by a dual-slope system with the main ridge folded into a rounded peak. This design is commonly used in eastern residential homes or in architectural structures like temples.
Answer: D
French Classical drama reached its peak across Europe in the 17th century.What are the names of three outstanding playwrights?

Options:
A. J. Racine, M. de Scudéry, Corneille
B. A. Camus, G. Flaubert, Molière
C. A. Camus, T. Corneille, Voltaire
D. M. Proust, E. Zola, Molière
E. H. Balzac, V. Hugo, Molière
F. J. Racine, V. Hugo, Corneille
G. J. Racine, T. Corneille, Voltaire
H. J. Racine, A. Dumas, Corneille
I. P. Gaonaiyi, J. Laxin, Molière
J. H. Balzac, A. Dumas, Molière
Answer: I
Ancient Greek Drama can be devided into __.

Options:
A. Tragedy, Ly
B. Tragedy, Fable, Satyr Play
C. Tragedy, Comedy, Epic Play
D. Tragedy, Opera, Satyr Play
E. Tragedy, Comedy, Satyr Dance
F. Drama, Epic, Lyric Work
G. Tragedy, Lyric, Satyr Play
H. Tragedy, Drama, Satyr Play
I. Tragedy, Romance, Satyr Play
J. Myth, Tragedy, Comedy
Answer: H
The representative works of Euripides are __.

Options:
A. "Bacchae" and "Phaedra"
B. "Electra" and "Ajax"
C. "Medea" and "Orestes"
D. "Hippolytus" and "Heracles"
E. "The Clouds" and "The Wasps"
F. "Lysistrata" and "Cyclops"
G. "The Frogs" and "The Birds"
H. "Andromache" and "Cassandra"
I. "Alcestis" and "Prometheus"
J. "Antigone" and "Philoctetes"
Answer: C
What is palace yan music?

Options:
A. Addresses directly the melodies utilized in royal engagements. The sovereign engagement music of the Liao dynasty was filled with several bands and two squads of dancers.
B. Pertains mostly to the music utilized by the king during festivities. The court festivity music of the Sui dynasty included numerous orchestras and two troupes of dancers.
C. Refers specifically to the music used by the ruler when hosting guests. The court banquet music of the Tang dynasty was composed of multiple orchestras and two troupes of performers.
D. Addresses mainly the melodies created for the monarch during receptions. The imperial reception music of the Han dynasty was delivered by several bands and two teams of performers. It arose from the musical roots of the Zhao, Qin, and Jin.
E. Relates mainly to the music performed by the subjects for their king. The festival music of the Song dynasty featured multiple bands and multiple dancing groups.
F. Refers mainly to the songs performed by the queens for their subjects. The court gathering music of the Yuan dynasty featured various orchestras and two circles of performers.
G. Pertains solely to the songs sung by the emperor to his subjects. The royal serenade music of the Ming dynasty was performed by varied choirs and two circles of dancers.
H. Pertains exclusively to the soundtracks used in royal processions. The parade music of the Qing dynasty featured multiple bands and two groups of dancers.
I. Refers generally to the entertainment during royal ceremonies. The Sovereign's celebration music of the Zhou dynasty was played by several ensembles and two dance teams. It originated from the music basics of the Ming, Shang, and Zhou dynast
J. Concerns mainly the tunes played for the monarch at feasts. The regal feast music of the Yuan dynasty was performed by numerous orchestras and two groups of dancers.
Answer: C
What is the Northern Song miscellaneous drama?

Options:
A. An ancient style of folk dance characterized by an amalgamation of various dance forms
B. A form of opera (or drama). It evolved from various comic performances, songs, dances, and miscellaneous plays, mainly consisting of three parts: Yan Duan, Zheng Zaji, and Hou San Duan.
C. A narrative storytelling approach that merges diverse thematic elements, commonly involving distinct sections like introduction, development, and conclusion phases.
D. A synthesis of theatrical acts stemming from multiple humorous acts, songs, dances, and mixed plays, often divided into three components: Yan Duan, Zheng Zaji, and Hou San Duan.
E. A type of musical entertainment incorporating multiple performance styles, featuring a sequence of acts including courtship, battle, and harvest celebrations.
F. A style of painting that integrated diverse artistic elements, primarily featuring landscape, figure, and bird-and-flower compositions. The scenes depicted often include folk life and natural settings.
G. A type of dramatic entertainment that evolved from different comedic sketches, songs, movements, and various dramas, usually including three stages: Yan Duan, Zheng Zaji, and Hou San Duan.
H. A genre of literature integrating a mix of stories, poetry, and theatrical scripts, typically segmented into three main parts: opening, middle, and closing scenes.
I. A blend of theatrical performances originating from diverse comedy routines, vocalizations, dance interludes, and assorted theatricals, generally consisting of three segments: Yan Duan, Zheng Zaji, and Hou San Duan.
J. A theater practice that originated from a variety of humorous acts, melodies, dance routines, and assorted theaters, typically divided into three segments: Yan Duan, Zheng Zaji, and Hou San Duan.
Answer: B
Residual parent material refers to the___ that remain in place for a long time after the weathering of rocks.

Options:
A. heavy matter
B. rough particles
C. strong contents
D. sticky residues
E. firm features
F. solid aggregates
G. dense components
H. compact elements
I. sharp objects
J. loose substances
Answer: J
In regions where leaching is more pronounced, there is a dual effect combining both residual and sedimentary accumulation and ____.

Options:
A. amplification
B. adaptation
C. arbitration
D. aggregation
E. acculturation
F. assimilation
G. agglutination
H. appreciation
I. acceleration
J. annexation
Answer: G
A ____ is the total area of surface and underground catchment areas of rivers or lakes that are enclosed by the watershed divide.

Options:
A. estuary
B. watershed
C. riverbank
D. reservoir
E. watercourse
F. aquifer
G. water table
H. wetland
I. drainage basin
J. floodplain
Answer: B
The geographical environment refers to the Earth's surface on which humans depend for survival. It is comprised of the ___, ___ and ___ environments that overlap and interconnect with each other to form a whole.

Options:
A. natural, financial, social
B. natural, economic, social-cultural
C. contemporary, ancient, futuristic
D. biological, technological, ideological
E. human, animal, microbial
F. physical, ecological, demographic
G. urban, rural, coastal
H. native, economic, community
I. organic, commercial, societal
J. atmospheric, land, marine
Answer: B
The_____ is the line of intersection between the axial plane and the horizontal plane.

Options:
A. fold axis
B. layer intersection
C. fold line
D. bend axis
E. fault line
F. plane junction
G. horizontal line
H. fold point
I. axial line
J. junction axis
Answer: A
The continental shelf is a gently sloping submerged seabed plain (flat surface) extending into the sea, but it descends in steps and is also known as an _____.

Options:
A. aquatic bench
B. oceanic stairway
C. aquatic stair
D. marine table
E. underwater terrace
F. submarine ledge
G. oceanic plateau
H. marine ledge
I. sea level shelf
J. coastal flat
Answer: E
Quartz sandstone should be formed by deposition after prolonged weathering, sorting, and___.

Options:
A. accumulation
B. sedimentation
C. cementation
D. crystallization
E. fossilization
F. calcification
G. compaction
H. solidification
I. erosion
J. fragmentation
Answer: I
The ___is a land classification unit derived from the commonality and basic characteristics of those land units in occurrence.

Options:
A. variety block
B. sector space
C. land group
D. classification layer
E. type unit
F. zone area
G. category range
H. terrain division
I. region part
J. division section
Answer: E
The ____ is the mode of succession for mountain vertical zones. It reflects the spatial distribution pattern of natural complexes in mountain areas and is a special form of regional structure.

Options:
A. vertical zonation spectrum
B. vertical stratification sequence
C. vertical segmentation spectrum
D. vertical zonation sequence
E. horizontal segmentation spectrum
F. horizontal division spectrum
G. horizontal stratification sequence
H. horizontal zonation sequence
I. vertical division spectrum
J. horizontal zonation spectrum
Answer: A
In the presence of unfrozen, water-bearing thawsol, plastic deformation occurs under the dual pressures of the upper seasonal frost and the lower permafrost layer, leading to various types of folding known as ____.

Options:
A. frost cracking
B. thaw flowing
C. thaw tilting
D. thaw slumping
E. permafrost bending
F. frost heaving
G. ice wedging
H. ice settling
I. permafrost shifting
J. freeze buckling
Answer: D
The Persian Empire was the first empire in the ancient world to span three continents: Europe, Asia, and Africa. Its downfall marked the end of ancient civilizations in Western Asia and North Africa. Which country replaced the Persian Empire?

Options:
A. Byzantine Empire
B. Macedonian Empire
C. Spartan Empire
D. Peacock Empire
E. Carthaginian Empire
F. Egyptian Empire
G. Ottoman Empire
H. Roman Empire
I. Alexander Empire
J. Assyrian Empire
Answer: I
Since the 1960s, after gaining independence, African countries have been striving to explore their own development paths. What is the economic system of most countries?

Options:
A. Feudal Economy
B. Market economy
C. Command Economy
D. Subsistence Economy
E. Planned Economy
F. Mixed Economy
G. Barter Economy
H. Socialist Economy
I. Traditional Economy
J. Tribal Economy
Answer: B
What is the sign that the war between Egypt and the Hittites for supremacy has basically come to an end?

Options:
A. Hittite Defeat
B. Battle of Kadesh
C. Treaty of Kadesh
D. Diplomatic Agreement
E. Battle of Carrhae
F. Peace Conference
G. The two countries conclude a treaty.
H. Hittite Victory
I. Egypt's Defeat
J. Egyptian Victory
Answer: E
Japan used the League of Nations' refusal to recognize "Manchukuo" as an excuse to withdraw from the League. When did this withdrawal take place?

Options:
A. September 1931
B. March 1933
C. December 1932
D. January 1934
E. October 1934
F. June 1933
G. November 1933
H. May 1933
I. February 1933
J. April 1932
Answer: I
Which period is referred to as the "relative stability" of capitalist countries?

Options:
A. 1928~1933
B. 1926~1931
C. 1930~1935
D. 1925~1930
E. 1929~1934
F. 1924~1928
G. 1923~1928
H. 1924~1929
I. 1923~1929
J. 1927~1932
Answer: H
The Hubei Military Government established after the Wuchang Uprising was a ().

Options:
A. A bourgeois regime dominated by constitutionalists
B. A military dictatorship led by the Qing loyalists
C. A monarchy reinstated by foreign powers
D. An anarchist commune with no central leadership
E. A regime in which the bourgeois revolutionaries are in complete control
F. A theocratic state governed by religious leaders
G. A federal republic with equal power-sharing among provinces
H. A coalition of revolutionaries, constitutionalists and old bureaucrats
I. The first local revolutionary power established by the bourgeois revolutionaries
J. A socialist state with worker control
Answer: H
When was the vast and abundant continent of Africa almost completely carved up?

Options:
A. During the Age of Enlightenment
B. After World War I
C. During the Renaissance
D. During the Cold War
E. After the opening of the new route
F. Early 19th century
G. Early 20th century
H. Early 17th century
I. Mid 19th century
J. Late 18th century
Answer: G
In the late 19th and early 20th centuries, opportunism emerged in the European labor movement. What is the immediate cause?

Options:
A. Development of democratic politics in capitalist countries
B. The theory of scientific socialism has not yet come into being
C. Rise of nationalist movements
D. Increased literacy among the working class
E. The life of people in capitalist countries has improved
F. Economic depression in Europe
G. Emergence of new political parties
H. Unprecedented strengthening of the police and military machinery by the bourgeoisie
I. Migration of workers to industrial centers
J. Expansion of colonial empires
Answer: A
What triggered the outbreak of the American Civil War?

Options:
A. Enactment of the Homestead Act
B. The South declared its independence
C. States' rights were increasingly challenged
D. The publication of Uncle Tom's Cabin
E. The expansion of slavery into new territories
F. The Emancipation Proclamation was issued
G. The Dred Scott decision was announced
H. Lincoln was elected President
I. The abolitionist movement was on the rise
J. Secession of Southern states began
Answer: H
What is the sign that the North began to take the initiative in the American Civil War?

Options:
A. Lincoln is elected President
B. Enactment of the Homestead Act
C. Sherman's March to the Sea
D. Signing of the Treaty of Paris
E. Battle of Gettysburg
F. The Siege of Vicksburg
G. Establishment of Confederate Capital in Richmond
H. The Emancipation Proclamation came into effect
I. The Formation of the Union Pacific Railroad
J. Introduction of the Cotton Gin
Answer: E
Which class was the leader of the Indian National uprising?

Options:
A. Soldiers
B. Tribal chiefs
C. Religious leaders
D. Local businessmen
E. Colonial administrators
F. Farmers
G. University professors
H. The bourgeoisie
I. Feudal princes
J. Industrial workers
Answer: I
The second-order approximate solution for the equation ${\frac{\mathrm{d} y} {\mathrm{d} x}}=x+y^{2}$ passing through the origin $(0, 0)$ is _____.

Options:
A. $y_{2} \left( x \right)=\frac{3} {7} x^{}+\frac{1} {1 0} x^{3}$
B. $y_{2} \left( x \right)=\frac{1} {3} x^{}+\frac{1} {2 0} x^{3}$
C. $y_{2} \left( x \right)=\frac{1} {5} x^{}+\frac{1} {2 0} x^{30}$
D. $y_{2} \left( x \right)=\frac{1} {10} x^{}+\frac{1} {1 0} x^{3}$
E. $y_{2} \left( x \right)=\frac{1} {4} x^{}+\frac{1} {2 0} x^{3}$
F. $y_{2} \left( x \right)=\frac{} {} x^{}+\frac{1} {2 0} x^{3}$
G. $y_{2} \left( x \right)=\frac{1} {8} x^{}+\frac{1} {3 0} x^{3}$
H. $y_{2} \left( x \right)=\frac{1} {2} x^{}+\frac{1} {3 0} x^{4}$
I. $y_{2} \left( x \right)=\frac{1} {2} x^{2}+\frac{1} {2 0} x^{3}$
J. $y_{2} \left( x \right)=\frac{5} {6} x^{}+\frac{1} {1 0} x^{3}$
Answer: I
Given a particular solution of a certain second-order linear non-homogeneous differential equation, $y_{1}=x, \; y_{2}=\sin x, \; y_{3}=\cos 2x$, then the general solution of this equation is ____.

Options:
A. $y=c_{1} ( x+\operatorname{s i n} 2 x )+c_{2} ( x-\operatorname{c o s} x )+x$
B. $y=c_{1} ( x+\operatorname{t a n} 2 x )+c_{2} ( x-\operatorname{s i n} x )+\cos x$
C. $y=c_{1} ( x-\operatorname{s i n} x )+c_{2} ( x+\operatorname{s i n} 2 x )+\cos x$
D. $y=c_{1} ( x+\operatorname{s i n} x )+c_{2} ( x-\operatorname{c o s} x )+2x$
E. $y=c_{1} ( x-\operatorname{s i n} 2 x )+c_{2} ( x+\operatorname{c o s} x )+x$
F. $y=c_{1} ( x-\operatorname{t a n} x )+c_{2} ( x+\operatorname{s i n} 2 x )+\cos x$
G. $y=c_{1} ( x+\operatorname{c o s} x )+c_{2} ( x-\operatorname{t a n} 2 x )+\sin x$
H. $y=c_{1} ( x-\operatorname{s i n} 2 x )+c_{2} ( x+\operatorname{c o s} 2 x )+\sin x$
I. $y=c_{1} ( x-\operatorname{s i n} x )+c_{2} ( x-\operatorname{c o s} 2 x )+x$
J. $y=c_{1} ( x+\operatorname{t a n} x )+c_{2} ( x-\operatorname{c o s} 2 x )+\sin x$
Answer: I
Consider the differential equation
$$(1 + \mathrm{e}^{\frac{x}{y}}) \, \mathrm{d}x + \mathrm{e}^{\frac{x}{y}} \, \left(1 - \frac{x}{y}\right) \, \mathrm{d}y = 0$$
Which of the following represents the general solution to this differential equation()?

Options:
A. $$
3y e^\frac{x} {y}+2x=C
$$
B. $$
3y e^\frac{x} {2y}+x=C
$$
C. $$
3y e^\frac{x} {y}+4x=C
$$
D. $$
y e^\frac{x} {2y}+2x=C
$$
E. $$
y e^\frac{x} {y}+x=C
$$
F. $$
2y e^\frac{x} {y}+3x=C
$$
G. $$
y e^\frac{2x} {y}+x=C
$$
H. $$
y e^\frac{x} {y}+2x=C
$$
I. $$
2y e^\frac{3x} {2y}+3x=C
$$
J. $$
2y e^\frac{x} {y}+x=C
$$
Answer: E
Let the continuous function $f(x)$ satisfy: $f(x) - \int_{0}^{x} f(x-t) \, dt = e^x$, then
$f(x) = ()$.

Options:
A. $$\left( x^2+1 \right) \mathrm{e}^{x}$$
B. $$\left( x+1 \right) \mathrm{e}^{x}$$
C. $$\left( x+1 \right)^2 \mathrm{e}^{x}$$
D. $$\left( 2x+1 \right) \mathrm{e}^{x}$$
E. $$\left( x-2 \right) \mathrm{e}^{x}$$
F. $$\left( x+2 \right) \mathrm{e}^{x}$$
G. $$\left( x+3 \right) \mathrm{e}^{x}$$
H. $$\left( x+5 \right) \mathrm{e}^{x}$$
I. $$\left( x-1 \right) \mathrm{e}^{x}$$
J. $$\left( x+4 \right) \mathrm{e}^{x}$$
Answer: B
The maximum interval of existence for the solution of the Cauchy problem $\left\{\begin{matrix} {{{\frac{\mathrm{d} y} {\mathrm{d} x}}=1+y^{2}}} \\ {{{y ( 0 )=0}}} \\ \end{matrix} \right.$ is().

Options:
A. $$\left(-\frac{\pi} {2}, \frac{\pi} {2} \right)$$
B. $$\left(-\frac{\pi}{8}, \frac{\pi}{8}\right)$$
C. $$\left(-\frac{3\pi}{4}, \frac{3\pi}{4}\right)$$
D. $$\left(-\frac{\pi} {3}, \frac{\pi} {3} \right)$$
E. $$\left(-\frac{5\pi}{12}, \frac{5\pi}{12}\right)$$
F. $$\left(-\frac{3\pi}{2}, \frac{3\pi}{2}\right)$$
G. $$\left(-\pi, \pi\right)$$
H. $$\left(-\frac{2\pi}{3}, \frac{2\pi}{3}\right)$$
I. $$\left(-\frac{\pi}{6}, \frac{\pi}{6}\right)$$
J. $$\left(-\frac{\pi}{4}, \frac{\pi}{4}\right)$$
Answer: A
Linear homogeneous differential equations with ${\frac{\mathrm{d} {\boldsymbol{x}}} {\mathrm{d} t}}=\mathbf{A} ( t ) and x {\frac{\mathrm{d} {\boldsymbol{x}}} {\mathrm{d} t}}=\mathbf{B} ( t )$, have each basic solutions group, is A (t) and B (t) meet ().

Options:
A. $$A ( t ) > B ( t )$$
B. $$A ( t ) =2 B ( t )$$
C. $$A ( t ) \equiv -B ( t )$$
D. $$A ( t ) \neq 2B ( t )$$
E. $$A ( t ) \equiv B ( t )$$
F. $$A ( t ) \neq B ( t )$$
G. $$B ( t ) \equiv -A ( t )$$
H. $$2B ( t ) \neq A ( t )$$
I. $$B ( t ) > A ( t )$$
J. $$B ( t ) \equiv 2A ( t )$$
Answer: E
If the tangent to the plane curve C at every point is perpendicular to the line connecting the tangent point and the origin, then the equation of this curve is ().

Options:
A. $$x^{3}+y^{3}=c$$
B. $$x^{2}+y^{3}=c$$
C. $$x^{2}+y^{2}=c$$
D. $$y^{2}-x^{2}=c$$
E. $$x+y=c$$
F. $$x^{2}+3y^{2}=c$$
G. $$x^{2}+2y^{2}=c$$
H. $$xy=c$$
I. $$x^{2}-y^{2}=c$$
J. $$x^{2}+y=c$$
Answer: C
If $\psi$(x) has a continuously differentiable function and $\psi\ (0) \ =1$, And set the curvilinear integral $A=\int_{( 0, 0 )}^{\left( \frac{\pi} {4}, \frac{\pi} {4} \right)} y \psi\left( x \right) \operatorname{t a n} x \mathrm{d} x-\psi\left( x \right) \mathrm{d} y$ Independent of the path, then $A=$().

Options:
A. $$- \frac{\sqrt{2}} {8}$$
B. $$\frac{\sqrt{2} \pi} {4}$$
C. $$- \frac{\sqrt{2} \pi} {8}$$
D. $$\frac{\sqrt{2} \pi} {8}$$
E. $$- \frac{2 \pi} {8}$$
F. $$\frac{\pi^2} {8}$$
G. $$-\frac{\sqrt{2} \pi} {4}$$
Answer: C
Differential equation of $\left\{\begin{matrix} {{y^{\prime\prime}+y=x}} & {{x \leq\pi}} \\ {{y^{\prime}+y=\operatorname{c o s} x}} & {{x > \pi}} \\ \end{matrix} \right.$ ,$\mathrm{y ~ \ ( 0 ) ~}=0 \,, \mathrm{y^{\prime} ~ \ ( 0 ) ~}=0$ , And continuous at $\mathbf{x}=\pi$, the solution is ().

Options:
A. $$
y=\left\{\begin{aligned} {{{x-\operatorname{s i n} x,}}} & {{{} {{x \leq\pi}}}} \\ {{{{\left( \pi+\frac{1} {2} \right) e^{\pi-x}+\frac{1} {2} \operatorname{c o s} x+\frac{1} {2} \operatorname{s i n} 2x,}}}} & {{{} {{x > \pi}}}} \\ \end{aligned} \right.
$$
B. $$
y=\left\{\begin{aligned} {{{x-\operatorname{s i n} x,}}} & {{{} {{x \leq\pi}}}} \\ {{{{\left( 3\pi+\frac{1} {2} \right) e^{\pi-x}+\frac{1} {2} \operatorname{c o s} x+\frac{1} {2} \operatorname{s i n} x,}}}} & {{{} {{x > \pi}}}} \\ \end{aligned} \right.
$$
C. $$
y=\left\{\begin{aligned} {{{2x-\operatorname{s i n} 2x,}}} & {{{} {{x \leq\pi}}}} \\ {{{{\left( \pi+\frac{1} {2} \right) e^{\pi-x}+\frac{1} {2} \operatorname{c o s} x+\frac{1} {2} \operatorname{s i n} x,}}}} & {{{} {{x > \pi}}}} \\ \end{aligned} \right.
$$
D. $$
y=\left\{\begin{aligned} {{{2x-\operatorname{s i n} x,}}} & {{{} {{x \leq\pi}}}} \\ {{{{\left( \pi+\frac{1} {2} \right) e^{\pi-x}+\frac{1} {2} \operatorname{c o s} x+\frac{1} {2} \operatorname{s i n} x,}}}} & {{{} {{x > \pi}}}} \\ \end{aligned} \right.
$$
E. $$
y=\left\{\begin{aligned} {{{x-\operatorname{s i n} x,}}} & {{{} {{x \leq\pi}}}} \\ {{{{\left( \pi+\frac{1} {2} \right) e^{\pi-2x}+\frac{1} {2} \operatorname{c o s} x+\frac{1} {2} \operatorname{s i n} x,}}}} & {{{} {{x > \pi}}}} \\ \end{aligned} \right.
$$
F. $$
y=\left\{\begin{aligned} {{{x-\operatorname{s i n} x,}}} & {{{} {{x \leq\pi}}}} \\ {{{{\left( \pi+\frac{1} {2} \right) e^{\pi-x}+\frac{1} {2} \operatorname{c o s} x+\frac{1} {2} \operatorname{s i n} x,}}}} & {{{} {{x > \pi}}}} \\ \end{aligned} \right.
$$
G. $$
y=\left\{\begin{aligned} {{{x-\operatorname{s i n} x,}}} & {{{} {{x \leq\pi}}}} \\ {{{{\left(2 \pi+\frac{1} {2} \right) e^{\pi-x}+\frac{1} {2} \operatorname{c o s} x+\frac{1} {2} \operatorname{s i n} x,}}}} & {{{} {{x > \pi}}}} \\ \end{aligned} \right.
$$
H. $$
y=\left\{\begin{aligned} {{{x-\operatorname{s i n} 2x,}}} & {{{} {{x \leq\pi}}}} \\ {{{{\left( \pi+\frac{1} {2} \right) e^{\pi-x}+\frac{1} {2} \operatorname{c o s} x+\frac{1} {2} \operatorname{s i n} x,}}}} & {{{} {{x > \pi}}}} \\ \end{aligned} \right.
$$
I. $$
y=\left\{\begin{aligned} {{{x-\operatorname{s i n} 3x,}}} & {{{} {{x \leq\pi}}}} \\ {{{{\left( \pi+\frac{1} {2} \right) e^{\pi-x}+\frac{1} {2} \operatorname{c o s} x+\frac{1} {2} \operatorname{s i n} x,}}}} & {{{} {{x > \pi}}}} \\ \end{aligned} \right.
$$
J. $$
y=\left\{\begin{aligned} {{{x-\operatorname{s i n} x,}}} & {{{} {{x \leq\pi}}}} \\ {{{{3\left( \pi+\frac{1} {2} \right) e^{\pi-x}+\frac{1} {2} \operatorname{c o s} x+\frac{1} {2} \operatorname{s i n} x,}}}} & {{{} {{x > \pi}}}} \\ \end{aligned} \right.
$$
Answer: F
According to the equation
$$
(2x+y-4) dx + (x+y-1) dy = 0
$$
find the original equation as ______.

Options:
A. $$x^{2}-4 x+x y+\frac{y^{2}} {2}-y=C$$
B. $$x^{2}-4 x-x y+\frac{y^{2}}{2}+2y=C$$
C. $$x^{2}-8 x-x y+\frac{y^{2}}{2}+y=C$$
D. $$x^{2}-3 x-x y+\frac{y^{2}}{2}+y=C$$
E. $$x^{2}-4 x-x y+\frac{y^{2}}{2}+y=C$$
F. $$x^{2}-4 x-x y+\frac{y^{2}}{2}-y=C$$
G. $$3x^{2}-4 x-x y+\frac{y^{2}}{2}+y=C$$
H. $$x^{2}+4 x+x y+\frac{y^{2}}{2}-y=C$$
I. $$x^{2}-4 xy-x +\frac{y^{2}}{2}+y=C$$
J. $$2x^{2}-4 x-x y+\frac{y^{2}}{2}+y=C$$
Answer: A
Known homogeneous equation $\left( x-1 \right) y^{\prime\prime}-x y^{\prime}+y=0$ and the general solution $Y \left( x \right)=C_{1} x+C_{2} \mathrm{e}^{x}$ , non-homogeneous equation
$\left( x-1 \right) y^{\prime\prime}-x y \prime+y=\left( x-1 \right)^{2}$the general solution is ().

Options:
A. $$y=x^{2}+C_{2} \mathrm{e}^{x}+C_{4} x+1$$
B. $$y=-2x^{4}+C_{2} \mathrm{e}^{x}+C_{4} x+3$$
C. $$y=-2x^{2}+C_{2} \mathrm{e}^{x}+C_{4} x+1$$
D. $$y=-2x^{2}+C_{2} \mathrm{e}^{2x}+C_{4} x-2$$
E. $$y=-x^{3}+C_{2} \mathrm{e}^{x}+C_{4} x-2$$
F. $$y=-2x^{2}+C_{2} \mathrm{e}^{x}+C_{4} x+2$$
G. $$y=-2x^{2}+C_{2} \mathrm{e}^{x}+C_{4} x-1$$
H. $$y=-2x^{3}+C_{2} \mathrm{e}^{x}+C_{4} x-2$$
I. $$y=-x^{2}+C_{2} \mathrm{e}^{x}+C_{4} x-1$$
J. $$y=-2x^{3}+C_{2} \mathrm{e}^{x}+C_{4} x+2$$
Answer: I
Differential equations of $\left\{\begin{matrix} {{\frac{\mathrm{d} y} {\mathrm{d} x}=3 y-2 z,}} \\ {{\frac{\mathrm{d} z} {\mathrm{d} x}=2 y-z.}} \\ \end{matrix} \right.$ is ().

Options:
A. $$\left\{ \begin{array}{l}
y = \frac{1}{2}(2C_{1} + C_{2} + 2C_{2}x)\mathrm{e}^{2x} \\
z = (C_{1} + C_{2}x)\mathrm{e}^{3x}
\end{array} \right.$$
B. $$\left\{ \begin{array}{l}
y = \frac{1}{2}(2C_{1} + C_{2} + 2C_{2}x)\mathrm{e}^{-2x} \\
z = (C_{1} + C_{2}x)\mathrm{e}^{-3x}
\end{array} \right.$$
C. $$\left\{ \begin{array}{l}
y = \frac{1}{2}(2C_{1} + C_{2} + 2C_{2}x)\mathrm{e}^{x} \\
z = (C_{1} + C_{2}x)\mathrm{e}^{x}
\end{array} \right.$$
D. $$\left\{ \begin{array}{l}
y = \frac{1}{2}(2C_{1} + C_{2} - 2C_{2}x)\mathrm{e}^{x} \\
z = (C_{1} + C_{2}x)\mathrm{e}^{x}
\end{array} \right.$$
E. $$\left\{ \begin{array}{l}
y = \frac{1}{2}(2C_{1} + C_{2} + 2C_{2}x)\mathrm{e}^{x} \\
z = (C_{1} - C_{2}x)\mathrm{e}^{x}
\end{array} \right.$$
F. $$\left\{ \begin{array}{l}
y = \frac{}{}(2C_{1} + C_{2} + 2C_{2}x)\mathrm{e}^{x} \\
z = (C_{1} + C_{2}x)\mathrm{e}^{x}
\end{array} \right.$$
G. $$\left\{ \begin{array}{l}
y = \frac{1}{2}(2C_{1} + C_{2} + 2C_{2}x)\mathrm{e}^{x} \\
z = (C_{1} + C_{2}x)\mathrm{e}^{2x}
\end{array} \right.$$
H. $$\left\{ \begin{array}{l}
y = \frac{1}{2}(2C_{1} + C_{2} + 2C_{2}x)\mathrm{e}^{x} \\
z = (C_{1} + C_{2}x^2)\mathrm{e}^{-x}
\end{array} \right.$$
I. $$\left\{ \begin{array}{l}
y = \frac{1}{2}(2C_{1} + C_{2} - 4C_{2}x)\mathrm{e}^{x} \\
z = (C_{1} + C_{2}x)\mathrm{e}^{x}
\end{array} \right.$$
J. $$\left\{ \begin{array}{l}
y = \frac{1}{2}(2C_{1} + C_{2} + 2C_{2}x)\mathrm{e}^{2x} \\
z = (C_{1} + C_{2}x)\mathrm{e}^{x}
\end{array} \right.$$
Answer: C
Given the curve $L: y=\frac{4} {9} x^{2} \left(x \geqslant0 \right)$, point
$O \left(0, 0 \right)$, point $A \left(0, 1 \right)$Let $P$ be the moving point on $L$, $S$ is the area of the graph enclosed by the straight line $O A$, the straight line $A P$ and the curve $L$. If $P$ moves to the point $(3, 4)$ along the axis of $x$, the rate of change of $S$ with respect to time $t$ is ().

Options:
A. $9$
B. $14$
C. $13$
D. $12$
E. $8$
F. $10$
G. $15$
H. $11$
I. $7$
J. $6$
Answer: F
A ball with a radius of $R$ sinks into water, the top of the sphere is exactly tangent to the water, the density of the ball is $1$, and what is the amount of work required to remove the ball from the water?

Options:
A. $$ \frac{4} {5} \pi g R^{4} $$
B. $$ \frac{1} {3} \pi^{2} g R^{4} $$
C. $$ \frac{3} {4} \pi g R^{4} $$
D. $$ \frac{4} {3} \pi g R^{4} $$
E. $$ \frac{5} {3} \pi g R^{4} $$
F. $$ \frac{4} {3} \pi^{2} g^{3} R^{3} $$
G. $$ \frac{5} {4} \pi g R^{4} $$
H. $$ \frac{2} {3} \pi g R^{4} $$
I. $$ \frac{4} {3} \pi^{2} g^{2} R^{4} $$
J. $$ \frac{5} {3} \pi^{2} g R^{4} $$
Answer: D
Let the curve $y=y \left(x \right)$have a second order continuous derivative, $y^{\prime\prime} \left(x \right) > 0$, any point on it $ (x, y) curvature at $K=\frac{1} {2 y^{2} \operatorname{c o s} \alpha} \left(\operatorname{c o s} \alpha> 0 \right)$, Where $\alpha$is the inclination of the tangent of the curve at the corresponding point, and the curve obtains the minimum value at the point $(1, 1)$, and the curve is ().

Options:
A. $$y=\frac{1} {5} \left( x-1 \right)^{2}+1$$
B. $$y=\frac{1} {3} \left( x-2 \right)^{3}+4$$
C. $$y=\frac{1} {3} \left( x-2 \right)^{2}+4$$
D. $$y=\frac{1} {6} \left( x-1 \right)^{2}+1$$
E. $$y=\frac{1} {4} \left( x-1 \right)^{2}+1$$
F. $$y=\frac{2} {3} \left( x-2 \right)^{2}+2$$
G. $$y=\frac{1} {3} \left( x-2 \right)^{2}+3$$
H. $$y=\frac{1} {3} \left( x-2 \right)^{2}+2$$
I. $$y=\frac{} {} \left( x-2 \right)^{2}+2$$
J. $$y=\frac{1} {3} \left( x-2 \right)^{3}+2$$
Answer: E
It is known that a high temperature object is placed in a low medium, and the temperature of the object at time $t$is $T (t)^{\circ} \mathrm{C}$. The change rate of $\operatorname* {m i n}$is proportional to the temperature difference between the object and the medium at time t$(T > T_{0}$), and the proportional coefficient is k, k > 0$, and the change rate of $\operatorname* {m I n}$is proportional to the temperature difference $T- t _{0}$. Let us cool an object with an initial temperature of $120 ^{\circ} \mathrm{C}$ in a constant temperature medium of $20 ^{\circ} \mathrm{C}$. $3 0 \operatorname* {m i n}$ the object after the temperature dropped to $3 0^{\circ} \mathrm{C}$, then $T ( t )=\underline{{{{}}}}()$.

Options:
A. $$ 9 0 \mathrm{e}^{-\frac{\operatorname{l n} 10} {3 0} t}+4 0 $$
B. $$ 9 0 \mathrm{e}^{-\frac{\operatorname{l n} 8} {3 0} t}+3 0 $$
C. $$10\mathrm{e}^{-\frac{\operatorname{l n} 10} {3 0} t}+2 0 $$
D. $$ 9 0 \mathrm{e}^{-\frac{\operatorname{l n} 8} {2 0} t}+3 0 $$
E. $$1 0 0 \mathrm{e}^{-\frac{\operatorname{l n} 1 0} {3 0} t}+2 0 $$
F. $$ 130 \mathrm{e}^{-\frac{\operatorname{l n} 10} {3 0} t}+2 0 $$
G. $$ 1 0 \mathrm{e}^{-\frac{\operatorname{l n} 9} {3 0} t}+2 0 $$
H. $$ 9 0 \mathrm{e}^{-\frac{\operatorname{l n} 8} {3 0} t}+4 0 $$
I. $$9 0 \mathrm{e}^{-\frac{\operatorname{l n} 8} {2 0} t}+2 0 $$
J. $$9 0 \mathrm{e}^{-\frac{\operatorname{l n} 8} {3 0} t}+2 0 $$
Answer: E
Differential equation $\begin{array} {l l} {{x \mathrm{d} y+}} & {{( x-2 y ) \, \mathrm{d} x=0}} \\ \end{array}$ a solution $y=y \left(x \right)$ such that from the curve $y=y \left(x \right)$and the line $x=1$, The smallest volume of a plane graph bounded by $x=2$ and the $x$ axis is ().

Options:
A. $$ y=2x-\frac{7 0} {1 5 2} x^{2} $$
B. $$ y=4x-\frac{7 8} {1 5 5} x^{3} $$
C. $$ y=x-\frac{7 5} {1 2 4} x^{2} $$
D. $$ y=2x-\frac{7 7} {1 5 6} x^{3} $$
E. $$ y=3x-\frac{7 4} {1 5 6} x^{2} $$
F. $$ y=2x-\frac{7 4} {1 5 6} x^{3} $$
G. $$ y=x-\frac{7 4} {1 5 5} x^{2} $$
H. $$ y=2x-\frac{7 7} {1 5 8} x^{4} $$
I. $$ y=3x-\frac{7 4} {1 5 6} x^{3} $$
J. $$ y=3x-\frac{7 5} {1 6 6} x^{3} $$
Answer: C
Let $y=y \left(x \right)$be a second-order linear differential equation with constant coefficients $y^{\prime\prime}+2 m y^{\prime}+n^{2} y=0$ satisfy $y \left( 0 \right)=a \; \overset{\!} and\, y^{\prime} \left( 0 \right)=b$ special solution, where $m > n > 0$, then $\int_{0}^{+\infty} y \left( x \right) \mathrm{d} x=()$.

Options:
A. $$\frac{1} {m^{2}} ( n a+2 b^2 )$$
B. $$\frac{1} {n^{2}} ( 2 m a+3b )$$
C. $$\frac{2} {n^{2}} ( m a+2 b )$$
D. $$\frac{1} {n^{2}} ( 2 m a+4b )$$
E. $$\frac{2} {n^{2}} ( 2 m^2 a+3b )$$
F. $$\frac{2} {m^{2}} ( 2 n a+b )$$
G. $$\frac{2} {n^{2}} ( 2 m a+b )$$
H. $$\frac{1} {n^{2}} ( 2 m a^2+b )$$
I. $$\frac{1} {n^{2}} ( 2 m a+b )$$
J. $$\frac{1} {n^{2}} ( a+2 m b )$$
Answer: I
Let $y=y \left(x \right)$be such that $y^{\prime}+2 \left(\operatorname{l n} x+1 \right) y=0, y \left(1 \right)=1$, Then the maximum value of $y (x)$ on (0, 1] is ( ).

Options:
A. $$3\mathrm{e}^{\frac{2} {\mathrm{e}}}.$$
B. $$\mathrm{e}^{\frac{3} {\mathrm{2e}}}.$$
C. $$\mathrm{e}^{\frac{3} {\mathrm{e}}}.$$
D. $$2\mathrm{e}^{-\frac{2} {\mathrm{e}}}.$$
E. $$\mathrm{e}^{\frac{3} {\mathrm{4e}}}.$$
F. $$\mathrm{e}^{\frac{2} {\mathrm{e}}}.$$
G. $$3\mathrm{e}^{-\frac{2} {\mathrm{e}}}.$$
H. $$\mathrm{e}^{-\frac{2} {\mathrm{e}}}.$$
I. $$\mathrm{e}^{\frac{5} {\mathrm{2e}}}.$$
J. $$2\mathrm{e}^{\frac{2} {\mathrm{e}}}.$$
Answer: F
The motor boat moves at a speed of $5 m/s$ in still water, and the engine stops at full speed. After $20$ seconds, the speed of the boat is reduced to $v_{1}=3$ m/s. Determine the speed of the boat after $2$ minutes of engine stop as (). The resistance of the water is assumed to be proportional to the speed of motion of the boat.

Options:
A. $$0.48 m/s$$
B. $$2 m/s$$
C. $$0.75 m/s$$
D. $$0.23424 m/s$$
E. $$0.23328 m/s$$
F. $$0.60 m/s$$
G. $$0.25329 m/s$$
H. $$0.30 m/s$$
I. $$1 m/s$$
J. $$0.15 m/s$$
Answer: E
A particle with mass $1 g$ moves in a straight line under the action of an external force, which is directly proportional to time and inversely proportional to the velocity of the particle. When $t=1 0 s$, the velocity is equal to $5 0 \mathrm{c m} /$s, and the external force is $39.2 \mathrm{c m/s^{2}}$ What is the velocity $1min$ after the start of the movement?

Options:
A. $$\sqrt{6 8 8 5 0 0} \mathrm{c m / s}.$$
B. $$\sqrt{7 8 8 5 0 0} \mathrm{c m / s}.$$
C. $$\sqrt{5 1 3 0 0 0} \mathrm{c m / s}.$$
D. $$\sqrt{7 9 8 5 0 0} \mathrm{c m / s}.$$
E. $$\sqrt{6 8 8 6 0 0} \mathrm{c m / s}.$$
F. $$\sqrt{7 0 0 0 0 0} \mathrm{c m / s}.$$
G. $$\sqrt{6 8 8 5 1 0} \mathrm{c m / s}.$$
H. $$\sqrt{7 5 0 0 0 0} \mathrm{c m / s}.$$
I. $$\sqrt{6 8 8 5 3 9} \mathrm{c m / s}.$$
J. $$\sqrt{6 8 8 5 2 5} \mathrm{c m / s}.$$
Answer: A
Given that the fixed cost of producing a good is $a \left(a > 0 \right)$, the difference between the marginal cost and the average cost of producing $x$units is $\frac{x} {a}-\frac{a} {x}$and the total cost is $2 a$ when the output is equal to A, Then the function relationship between total cost $C$and output $x$ is given by ().

Options:
A. $$
C \left( x \right)=\frac{1} {a} x^{2}+a, \left( a > 0 \right)
$$
B. $$
C \left( x \right)=\frac{1} {a} x + a, \left( a > 0 \right)
$$
C. $$
C \left( x \right)=\frac{1} {a} x^{3}+a, \left( a > 0 \right)
$$
D. $$
C \left( x \right)=\frac{2} {a} x^{2}+a, \left( a > 0 \right)
$$
E. $$
C \left( x \right)=\frac{1} {a} x^{2}+2a^2, \left( a > 0 \right)
$$
F. $$
C \left( x \right)=\frac{1} {a} x^{2}+a^2, \left( a > 0 \right)
$$
G. $$
C \left( x \right)=\frac{1} {a} x^{2}\left( a > 0 \right)
$$
H. $$
C \left( x \right)=\frac{2} {a} x^{2}+3a, \left( a > 0 \right)
$$
I. $$
C \left( x \right)=\frac{2} {a} x^{3}+a, \left( a > 0 \right)
$$
J. $$
C \left( x \right)=\frac{1} {a} x^{3}-a, \left( a > 0 \right)
$$
Answer: A
Let an object with mass $m$ fall from rest in the air. If the air resistance $R=c v$ (where $c$ is a constant and $v$ is the speed of the object movement), try to find the function relationship between the distance $s$ of the object falling and the time $t$ as ().

Options:
A. $$
s \left( t \right)=\frac{m g} {c} t-\frac{m^{2} g} {c^{2}} \left( \mathrm{e}^{-\frac{c} {m} t}-2 \right)
$$
B. $$
s \left( t \right)=\frac{m g} {c} t-\frac{m^{2} g^2} {c^{2}} \left( \mathrm{e}^{-\frac{c} {m} t}-1 \right)
$$
C. $$
s \left( t \right)=\frac{m g} {c} t-\frac{m^{2} g} {c^{2}} \left( \mathrm{e}^{-\frac{c} {m} t}-1 \right)
$$
D. $$
s \left( t \right)=\frac{m g} {c} t+\frac{m^{2} g} {c^{2}} \left( \mathrm{e}^{-\frac{c} {m} t}-1 \right)
$$
E. $$
s \left( t \right)=\frac{m g} {c} t+\frac{m^{2} g} {c^{2}} \left( \mathrm{e}^{-\frac{c} {m} t}-2 \right)
$$
F. $$
s \left( t \right)=\frac{m^2 g^2} {c} t+\frac{m^{2} g} {c^{2}} \left( \mathrm{e}^{-\frac{c} {m} t}-1 \right)
$$
G. $$
s \left( t \right)=\frac{m g^2} {c} t+\frac{m^{2} g} {c^{2}} \left( \mathrm{e}^{-\frac{c} {m} t}-1 \right)
$$
H. $$
s \left( t \right)=\frac{m g} {c} t+\frac{m^{2} g} {c^{2}} \left( \mathrm{e}^{-\frac{c} {m} t^2}-1 \right)
$$
I. $$
s \left( t \right)=\frac{m g} {c} t+\frac{m^{2} g} {c^{2}} \left( \mathrm{e}^{-\frac{c^2} {m} t}-1 \right)
$$
Answer: D
Let A, B and C be three random events, and P(A)=P(B)=P(B)=P(C) =1/4, P (AB) =0, P(AC)=P(BC)=1/12, then the probability that exactly one event among A, B, and C occurs is ().

Options:
A. 1/3
B. 3/4
C. 1/2
D. 3/8
E. 5/12
F. 2/5
G. 2/3
H. 1/6
I. 7/12
J. 1/4
Answer: E
Let the random variables $( \mathbf{X}, \ \mathbf{Y} )$ follow a two-dimensional normal distribution $\mathrm{N} \ ( 0, \ 0 ; \ 1, \ 4 ; \ -1 / 2 )$. Which of the following random variables follows a standard normal distribution and is independent of $X$?

Options:
A. ${\frac{1}{2}} ( X + 2Y )$
B. ${\frac{\sqrt{5}} {5}} ( X+Y )$
C. ${\frac{1}{\sqrt{7}}} ( 3X - Y )$
D. ${\frac{\sqrt{2}} {2}} ( X - Y )$
E. ${\frac{\sqrt{3}} {3}} ( X-Y )$
F. ${\frac{\sqrt{6}} {6}} ( 2X + Y )$
G. ${\frac{1}{\sqrt{3}}} ( X + 3Y )$
H. ${\frac{\sqrt{5}} {5}} ( X-Y )$
I. ${\frac{\sqrt{3}} {3}} ( X+Y )$
J. ${\frac{1}{2}} ( 2X - Y )$
Answer: I
Out of 10 Go stones, there are 2 black stones and 8 white stones. If these 10 stones are randomly divided into two piles, each containing 5 stones, the probability that each pile contains one black stone is____.

Options:
A. 4/7
B. 5/12
C. 2/5
D. 6/11
E. 5/9
F. 1/2
G. 3/8
H. 7/10
I. 1/4
J. 9/14
Answer: E