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Asked: December 30, 2024In:
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Explain Fundamental Forces in Nature (Class 11 – Physics) – Notes

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  1. Saralyn
    Saralyn Begginer

    Fundamental Forces The most beautiful phenomenon that can be seen in physics is that how universe is so disciplined and synced together. The force has kept the universe bind together. Forces have always played an important role in the human existence, but it is not realized by humans. Human beings cRead more

    Fundamental Forces

    The most beautiful phenomenon that can be seen in physics is that how universe is so disciplined and synced together. The force has kept the universe bind together. Forces have always played an important role in the human existence, but it is not realized by humans. Human beings constantly experience some force acting on them like gravitational force, etc.  There are some forces that naturally exist in the universe, they are known as Fundamental Forces. Let’s learn about them in some detail.

    Force

    Force is an interaction, either with contact or without contact. When there is no opposition given to the Force, It can result in changing the motion, shape, position, of a body. Whenever some interaction occurs between two objects, there is a certain force acting upon them. There are many types of Forces present, For instance, Applied Force, Gravitational Force, Frictional Force, Tension Force, etc.

    Fundamental Forces in nature

    These forces are so well-defined that they cover the macroscopic and microscopic forces present in nature. The forces learned or seen by humans in everyday life, from frictional force, pull, push, thrust, etc. are known as derived forces, and they are not considered the fundamental forces. The derived forces are actually derived from the fundamental forces in some way or the other. Some Fundamental Forces are,

    • Gravitational Force
    • Electromagnetic Force
    • Strong Nuclear Force
    • Weak Nuclear Force

    These above-mentioned forces are responsible for all the observations obtained in forces present in the nature.

    Gravitational Force

    This force exists by the virtue of the masses of any objects. Gravitational force is the mutual force of attraction between two masses. Attraction between any mass and Earth is called Gravity. Isaac Newton first gave the concept of gravity. Gravity is the most intuitive and the weakest force present in nature. The Irony is that Gravity actually holds the planet, Solar system, Entire Universe together, yet it is known to be the weakest force present in nature.

    The Force of Gravitation is given as,

    Formula for Gravitational Force,

    F1=F2=G\frac{M1.M2}{r^2}

    Where, F = Force of Gravitation

    M1, M2 = Masses 1 and 2

    r = Distance between the masses

    G = Gravitational Constant (6.67× 10-11m3kg-1s-2)

    Electromagnetic Force

    Charges when they are at rest exert a force at each other known as the Electric force of attraction/repulsion. Like charges repel each other while unlike charges attract each other. When charges start to move and become dynamic, they develop magnetic field lines around and have magnetic force, these two forces combined are known as Electromagnetic forces present in nature.

    Magnetic force produced by current (moving charge)

    Combining the above two forces which are always perpendicular to each other will give rise to Electromagnetic Force. The force is produced by massless bosons and photons present in the charges, Electromagnetic force exists in nature and is responsible for many derived forces we experience every day, for example, Friction Force, Normal Force, Elasticity, and so on.

    Strong Nuclear Force

    It is the force of attraction between Protons and Neutrons. The force is the same whether protons and protons are present or neutrons and neutrons are present or protons and neutrons are looked at. In short, a Strong nuclear force exists between all nucleons. In short Ranges, this Force is the strongest among all the forces. It is important to note that at a distance of 10-13 cm, this force vanishes.

    Weak Nuclear Force 

    This Force is seen In the β Decay of a nucleus. Scientist named Wolfgang Pauli First predicted a particle named Neutrino. The Neutrino is an uncharged Particle that is released along with the electron in the β Decay process. During β Decay, when Beta Particle is ejected from an Atom, it tends to accelerate away from the atom and some force is required to accelerate the particle known as Weak Nuclear Force. Weak Nuclear Force is stronger than gravitational force but weaker than a strong nuclear force. 

    Table to represent Range and Relative Strength of Different Forces:

    Forces Range Relative strength
    Gravitational Force ∞ 10-38
    Electromagnetic Force ∞ 10-2
    Strong nuclear force < 10-15m 1
    Weak nuclear Force < 10-18m 10-13

    Conceptual Questions

    Question 1: Which Fundamental Force is the strongest and weakest among the fundamental forces present in nature?

    Answer:

    The strongest force present in nature is the Strong Nuclear Force and the weakest force present in nature at atomic scale is Gravity.

    Question 2: Which of the following forces are Fundamental, and which are derived in nature?

    Weak Nuclear Force, Friction Force, Gravity, Elasticity, Electromagnetic Force, Push

    Answer:

    Fundamental Forces ⇢ Weak Nuclear Force, Gravity, Electromagnetic Force.

    Derived Force ⇢ Friction Force, Elasticity, Push.

    Question 3: A statement is being used now “Gravity is not a force” Throw light on this statement.

    Answer:

    Isaac Newton initially discovered Gravity and Gravitational Force. It was then stated that gravity is a Force. Later on, with the help of Theory of Relativity, Einstein stated that Gravity is actually not a force but a result of space-time orientation. It is a consequence of masses moving along a geodesic lines in space time.

    Question 4: If the masses of 2 objects are doubled and the space between them is also doubled. How will the gravitational Force between them change?

    Answer:

    Gravitational Force is given as,

    F_G=G\frac{M_1.M_2}{r^2}

    When, Mass 1 and Mass 2 is doubled, M1’=2M1, M2’=2M2

    Distance between the masses is doubled, r’= 2r

    New Gravitational Force Between them,

    F_G'=G\frac{M_1'.M_2'}{r'^2}=G\frac{2M_1.2M_2}{4r^2} \\=G\frac{M_1.M_2}{r^2}=F_G

    Hence, The new value of gravitational Force will be same as the old Gravitational Force.

    Question 5: What are Pseudo Forces? Give Examples.

    Answer:

    Pseudo Forces are also known as Inertial Force or Fictitious Force. These forces actually do not exist and are the apparent forces that are seen due to fact that they are defined from a non-inertial frame.

    Example: A man sees another man going in a car and realized that some force is acting on the man in the car. This type of force seen is real as it is seen from a non-accelerated or inertial frame. However, the man in the car if looks at the man standing would feel that some force is acted upon the man and he is going backwards, this force is pseudo force, Since this force is seen from a non-inertial frame or an accelerated frame.

    Question 6: Which two forces have infinite range?

    Answer:

    The two fundamental forces having infinite range are Gravitational force and Electromagnetic force.

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Asked: December 27, 2024In:
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Explain – Biological Classification (NCERT Class 11 Chapter 2 Biological Classification).

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  1. Saralyn
    Saralyn Begginer

    Notes for NCERT Class 11 Chapter 2 Biological Classification: Biological classification is the process by which biologists group living organisms which, are classified on the basis of their similarity. Classification is essential for the convenient study of living organisms. It is required to identiRead more

    Notes for NCERT Class 11 Chapter 2 Biological Classification: Biological classification is the process by which biologists group living organisms which, are classified on the basis of their similarity. Classification is essential for the convenient study of living organisms. It is required to identify different varieties of organisms. It helps in the correct identification of many organisms. It leads to the evolution of organisms. It also establishes phylogenetic relationships among organisms. Carolus Linneuas was one of the scientists to classify organisms.

    NCERT Class 11 Biology Chapter 02 Biological Classification: The practice of classifying organisms based on shared characteristics is known as biological classification. Linnaeus proposed two areas of classification. He divided organisms into two kingdoms: the animal kingdom (Animalia) and the plant kingdom (Plantae). The classification of the two kingdoms had some disadvantages, such as the impossibility of distinguishing between eukaryotes and prokaryotes, unicellular and multicellular species, and photosynthetic and non-photosynthetic organisms. As a result, the field continued to grow and served as a primary example of R.H. Whittaker’s classification of the five domains or kingdoms.

    Biological Classification

    Two Kingdom Classification

    Two kingdom classification was given by a biologist, Carolus Linnaeus. He classified organisms into two kingdoms, i.e. Plantae (included all plants) and Animalia (included all animals).

    Disadvantages of Two Kingdom Classification

    This system didn’t distinguish between the following types of organisms-

    1. Eukaryotes and prokaryotes
    2. Unicellular and multicellular organisms
    3. Photosynthetic (green algae) and non-photosynthetic (fungi) organisms

    Five Kingdom Classification

    In 1969, R.H. Whittaker proposed the five-kingdom classification. He classified those five kingdoms as Monera, Protista, Fungi, Plantae, and Animalia. He primarily used the following criteria for classification:

    1. Cell structure
    2. Body organisation
    3. Mode of nourishment
    4. Reproduction
    5. Phylogenetic linkages or relationships
    Five Kingdom Classification

    Kingdom Monera

    Bacteria are the main members of this kingdom. Kingdom Monera is further divided into:

    1. Archaebacteria 
    2. Eubacteria or true bacteria
    Classification of Bacteria on the basis of Shape

    Archaebacteria

    They are special bacteria as they can withstand extreme environmental conditions because of their different cell wall structure. They can be:

    • Thermoacidophiles: They are found in the hot springs
    • Halophiles: They are found in the salty areas
    • Methanogens: They are found in the marshy areas/ gut of ruminant animals (production of biogas)

    Eubacteria or True Bacteria

    They have rigid cell walls and flagellum (locomotion), if motile. They can be photosynthetic autotrophs, chemosynthetic autotrophs and heterotrophs.

    • Photosynthetic Autotrophs: Cyanobacteria (blue-green algae, have chlorophyll a), Nostoc and Anabaena are their common examples. They are surrounded by a gelatinous sheath or mucilaginous covering, which protects them from wetting. They fix atmospheric nitrogen in specialised cells called heterocysts (significance)
    • Chemosynthetic Autotrophs: These are the bacteria which oxidise inorganic substances, e.g. nitrates, nitrites and ammonia and use the released energy for ATP production. They recycle nutrients, e.g. nitrogen, phosphorous, iron and sulphur (significance).
    • Heterotrophs: They are decomposers. Some of them are pathogens and some are beneficial as they are helpful in making curd from milk, producing antibiotics, and fixing atmospheric nitrogen in leguminous plants (significance).

    Heterocyst

    Reproduction in Bacteria

    They reproduce by asexual mode- binary fission, sexual mode- transfer of DNA and spore formation in unfavourable conditions.

    Binary Fission

    Mycoplasma

    They are the smallest organisms which lack cell walls. They can survive in the absence of oxygen (anaerobic). They cause diseases (pathogens).

    Kingdom Protista

    They are single-celled eukaryotes. They include:

    1. Chrysophytes
    2. Dinoflagellates
    3. Euglenoids
    4. Slime moulds
    5. Protozoans
    Classification of Protista Characteristic Features Examples
    Chrysophytes (chief producers in oceans) Their cell walls form two overlapping shells, which are fit together and embedded with silica which, makes them indestructible. So, cell wall deposits and their accumulation leads to ‘diatomaceous earth’. This soil can be used to polish things, and filter oils and syrups. Diatoms and golden algae (desmids)
    Dinoflagellates They show rapid multiplication and make the appearance of sea red (bioluminescence). Toxins released by them can kill other aquatic animals. Red dinoflagellates (Example: Gonyaulax)
    Euglenoids They have a pellicle protein-rich layer) which keeps them flexible Euglena
    Slime Moulds During suitable conditions, they form plasmodium and during unfavourable conditions,
    plasmodium differentiates and forms fruiting bodies (spores inside)    		 Acrasia, Plasmodiophorina
    Protozoans They are heterotrophs and live as predators or parasites. They are classified into four types Plasmodium

    Types of Protozoans and their Features/ Diseases Caused

    Protozoans Features/Diseases Caused Examples
    Amoeboid Protozoans They form pseudopodia to capture their prey. Some of them are parasites Amoeba, Entamoeba
    Flagellated Protozoans Sleeping sickness, a disease caused by the parasitic forms Trypanosoma
    Ciliated Protozoans Cilia (locomotion) and gullet, a cavity is present on the body Paramoecium
    Sporozoans Some species cause malaria Plasmodium

    Kingdom Fungi

    Fungi are multicellular and the how heterotrophic mode of nutrition (saprophytes/parasites/symbiotic- mycorrhiza). Some fungi are unicellular, e.g. yeast.

    Fungi

    Some Useful Fungi

    Mushrooms and yeast are the most valuable fungi. Mushrooms are edible and are a good source of proteins. Yeast is used to make bread and cheese. Penicillium fungi are used to produce antibiotics.

    Some Harmful Fungi

    Some fungi cause diseases in both plants and animals, e.g. wheat rust disease is caused by Puccinia fungus.

    Reproduction in Fungi

    There are three modes of reproduction in fungi, i.e. vegetative, asexual and sexual.

    • Vegetative Propagation: It takes place by fragmentation, fission and budding.
    • Asexual Reproduction: It takes place by conidia or sporangiospores or zoospores.
    • Sexual Reproduction: It takes place by oospores, ascospores and basidiospores.

    Stages of Sexual Reproduction in Fungi

    1. Plasmogay- It is the fusion of protoplasms between two motile or non-motile gametes.
    2. Karyogamy- It is the fusion of two nuclei.
    3. Meiosis in zygote, gives rise to haploid spores.

    In ascomycetes and basidiomycetes, the dikaryotic stage (n + n, i.e., two nuclei per cell) is formed, known as dikaryon and the phase is dikaryophase.

    Four Major Groups of Fungi

    Classification of Fungi Characteristic Features Examples
    Phycomycetes They grow on decaying wood in moist sites and obligate parasites on plant bodies Mucor, Rhizopus (bread
    mould fungi) and Albugo (parasitic fungi
    on mustard)
    Ascomycetes (sac-fungi) Neurospora is used in biochemical and genetic work. Some are edible, e.g. morels and truffles Penicillium, yeast, Aspergillus, Claviceps and Neurospora
    Basidiomycetes Some are edible, e.g. mushrooms. Mushrooms are rich in protein Agaricus (mushroom), Ustilago (smut) and Puccinia (rust
    fungus), Mushrooms, bracket fungi, puffballs
    Deuteromycetes They are known as ‘Imperfect Fungi’ because in this group, only asexual or vegetative phases are seen. Some fungi of this group are saprophytes or parasites while the majority are decomposers of litter, which aid in mineral cycling Alternaria, Colletotrichum and Trichoderma

    Kingdom Plantae

    All eukaryotic organisms that contain chlorophyll, usually known as plants, are classified as Plantae. A few species, like parasites and plants that feed on insects, are partially heterotrophic. Insectivorous plants include bladderwort and Venus fly traps, and parasites like Cuscuta feed on them. The eukaryotic structure of plant cells has large chloroplasts and a cell wall comprised primarily of cellulose. Algae, bryophytes, pteridophytes, gymnosperms, and angiosperms are all part of the plant kingdom.

    Alternation of Generation

    The haploid gametophytic and the diploid sporophytic phases of a plant’s life cycle alternate with one another. Various plant families have different haploid and diploid phase lengths and whether they are independent or reliant on others.

    Kingdom Plantae

    Kingdom Animalia

    They are multicellular and heterotrophic (show the holozoic mode of nutrition) eukaryotes. They lack cell walls. Almost, all the animals show locomotion. Sexual reproduction occurs by the fusion of male and female gametes which give rise to an embryo followed by repeated cell divisions.

    Viruses, Viroids, Prions And Lichens

    The differences between viruses, viroids and prions are given below:

    Viruses Viroids Prions
    They are oblique intracellular agents They are oblique intracellular agents They are the abnormal form of a cellular protein
    They have either DNA or RNA which is surrounded by a protein coat They consist of only RNA. The protein coat is absent They don’t possess DNA or RNA. Only protein coat is present

    Bacteriophage

    Bacteriophages are also known as phages. These are the viruses which infect and replicate in the bacterial cells.

    Bacteriophage

    Tobacco Mosaic Virus

    The tobacco mosaic virus (TMV) consists of single-stranded RNA. It infects tobacco plants and members of the family Solanaceae. The infection can cause some patterns like a mosaic, which shows mottling and discolouration on the surface of the leaves.

    Tobacco Mosaic Virus

    Lichens

    The close association of fungus and algae form lichens. They are found in a pollution-free environment. Lichens are used in deodorant, pH papers, insense-sticks, toothpaste and perfumes. The fungal component is known as mycobiont and the algal component is known as phycobiont.

    FAQs on Biological Classification

    Q1: What are the Commercial Applications for Heterotrophic Bacteria and Archaea?

    Answer:

    Heterotrophic Bacteria: They help with nitrogen fixation, ammonification and nitrification. In addition, Rhizobium bacteria, they maintain soil fertility. Other members produce dairy products such as cheese and cottage cheese. Archaebacteria: Methanogens in animal feces produce biogas.

    Q2: Write Some Plant like and Animal-like Features of Euglena.

    Answer:

    Plant-like features are:

    • Euglena has plastids which help in photosynthesis
    • Some of the species of euglena have carotenoid pigments, which give it red colour

    Animal-like features are:

    • Euglena doesn’t have a cell wall
    • Flagella are present for locomotion

    Q3: What Function Do Fungi Play in Our Daily Lives?

    Answer:

    Mushroom and yeast are the most useful fungi. Mushrooms are edible and are a good source of proteins. Yeast is used to make bread and cheese. Penicillium fungi is used to produce antibiotics.

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Asked: December 26, 2024In:
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The Living World – Introduction, Classification, Characteristics, FAQs (Class 11 – Biology)

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  1. Saralyn
    Saralyn Begginer

    The living world is a complex network of interconnected organisms that engage in metabolism, reproduction, and response to environmental cues. We are aware of how intricately connected everything in the living world is. The diversity of living forms on earth gives it a wonderful environment to liveRead more

    The living world is a complex network of interconnected organisms that engage in metabolism, reproduction, and response to environmental cues. We are aware of how intricately connected everything in the living world is. The diversity of living forms on earth gives it a wonderful environment to live and thrive. The abundance of diversity suggests the presence of numerous species with unique characteristics. The fact that an organism is either a living thing or a non-living entity is its most striking characteristic. As a result, in order to distinguish between a living item and a non-living one, we first need to define what a “living being” actually is.

    What is ‘Living’?

    Any organism that breathes and moves is considered ‘Living’. Any life form that exhibits or possesses the qualities of life or being alive is referred to as a living thing. The basic traits include having an organized structure, requiring energy, reacting to stimuli and changing their surroundings, and having the ability to reproduce, grow, move, metabolize, and die. The three Domains that make up the current classification of living things are Bacteria, Archaea, and Eucarya.

    Characteristics of Living World

    All living organisms grow and increase in mass and number of individuals. Growth, reproduction, ability to sense the environment and mount a suitable response is unique features of living organisms. Given below are some characteristic features of the Living world:

    Respiration

    • Aerobic respiration: Aerobic respiration is a chemical process in which oxygen is used to make energy from sugars. Aerobic respiration is also known as aerobic metabolism and cell respiration.
    • Anaerobic respiration: Anaerobic respiration takes place in the absence of oxygen. examples include alcohol fermentation and lactic acid fermentation.

    Nutrition

    • Autotrophic Nutrition: It is a type of nutrition in which plants make their own food .they are interdependent on themselves. example- plants. Autotrophic nutrition is of two types: phototrophic, and chemotrophic.
    • Heterotrophic Nutrition: It is a type of nutrition in which an organism is dependent on another organism for food. example -humans. Heterotrophic nutrition is of three types: herbivorous, carnivorous, and omnivorous.

    Excretion

    The process of moving out waste material from the body is known as excretion.

    Locomotion/Movement

    Locomotion is a term used to describe a movement of an organism from one place to another.

    Reproduction

    • Asexual Reproduction: A process where a single gamete is responsible for reproduction to take place i.e., new offspring is produced from a single parent. Examples: hydra and paramecium.
    • Sexual Reproduction: Process where both the gametes take part in reproduction. Examples: fishes, and mammals.

    Structural Organisation

    • Unicellular: It is also known as a single-celled organism and only single cells perform all the functions needed for an organism to live. example- protozoa and Protista.
    • Multicellular: Multicellular organisms consist of many cells to perform different functions. example-Dogs, cows.

    Diversity

    A large variety of anything is known as diversity. Diversity is a vast term to include different species, genes, and ecosystem levels. Thomas Lovejoy introduced the term biological diversity in 1980.

    Biodiversity

    A large variety of organisms or terms used to refer to the number of varieties of plants and animals on earth is termed biodiversity. there are three types of biodiversity: genetic, species, and ecological diversity. There are over 15 Lakh species in the world of which 10 Lakh are animals(8 Lakh of insects and 2 Lakh of others) and 5 Lakh of plants.

    Nomenclature

    The scientific naming of organisms is known as nomenclature. Nomenclature is defined as the language of sculpture. The scientific name of mango is written as Mangifera indica.

    Rules of Nomenclature

    • Latinised names are used.
    • The first word represents the genus and the second word is the species name.
    • Printed in italics, if handwritten then underline separately.
    • The first word starts with a capital letter while the species name is written in small letters.

    ICBN  International Code of Botanical  Nomenclature (This is for giving scientific names to plants).

    ICZN International Code of Zoological Nomenclature(This is for giving scientific names to animals).

    Classification

    Grouping organisms into categories on the basis of similarities and differences is known as classification. classification is the process by which anything is grouped into systematic categories based on some easily observable characteristics. For example, we easily recognize groups such as plants or animals, dogs or cats, insects, or reptiles.

    Need of Classification

    Classification is done to organize the vast number of plants and animals into categories that could be named, remembered, studied, and understood. classification avoids confusion among the different varieties of organisms. Moreover, it makes the study of organisms easier.

    Given below are some scientist’s contributions to biology

    • Carolus Linnaeus (Father of Taxonomy): He gives the 2 kingdoms system.
    • Hackel: He gave the 3 kingdom systems.
    • Copeland: He gave the 4 kingdom systems.
    • R.H Whittaker: He gave the 5 kingdom system which is the popular one.
    • Carl Woese: He gave the 6 kingdom system and is the latest.

    Taxonomy

    The study of principles and procedures of classification is termed taxonomy. Based on characteristics, all living organisms can be classified into different taxa. This process of classification is taxonomy.

    Taxonomy

    Taxonomic Categories

    A. P. Candolle is credited with coining the term “taxonomy,” which refers to the seven main taxonomic categories. It is the listing of categories from the top-most kingdom to the bottom-most species, either in ascending or declining orders. There are two kinds in the hierarchy: intermediate and mandatory. From kingdoms to species, Obligate is rigidly adhered to, yet Intermediate is the exact reverse.

    • Species: The smallest and most fundamental distinction in classification is the species. It describes a population that is comparable in terms of form, shape, and reproductive characteristics. Similar reproductive characteristics can lead to the formation of fertile siblings.
    • Genus: This is the grouping of a number of closely related species that share linked features and are thought to have shared ancestors. For instance, the genus Panthera is where the leopard and cat belong.
    • Family: Families are associations of connected genera. The vegetative and reproductive characteristics are used to categorize the families. The Felidae family includes animals like tigers and lions as examples.
    • Order: It is the combination of one or more common families, which is regarded as a higher category. Felidae family members participate in the Carnivora order.
    • Class: A class designates a division in a phylum made up of one or more orders. All mammals, including gorillas, monkeys, humans, and gibbons, are included in the Mammalia class.
    • Phylum: It contains a group of related classes. Mammalia, along with reptiles, fish, amphibians, and birds, make up the phylum Chordata.
    • Kingdom: The highest taxonomic classification known as a kingdom is given to every animal that belongs to various phyla. The kingdom Animalia and Plantae encompasses all living things, including both plants and animals. A taxon is a classification that identifies an organismal group based on external characteristics.

    FAQs on Living World

    Q1: Define the following terms: Phylum, and Class.

    Answer:

    • Phylum– Classes comprising animals like fishes, amphibians, reptiles, and birds along with mammals constitute the higher category called phylum. All these, based on the common features like the presence of notochord and dorsal hollow neural system, are included in phylum Chordata.
    • Class– This category includes related orders. For example- the order primate comprising monkey, gorilla, and gibbon is placed in class Mammalia along with the order Carnivora which includes animals like tiger, cat, and dog.

    Q2: How is a key helpful in the identification and classification of organisms?

    Answer:

     The key is defined as the taxonomical aid used to identify and classify plants and animals based on their similarities and differences. Keys are generally analytical in nature.

    Q3: Define a taxon.

    Answer:

     Taxon is plural of taxa, it is the taxonomic unit of any rank. ARISTOTLE is known as the father of taxonomy.

    Q4: Why are living organisms classified?

    Answer:

    Living organism are classified due to the following reasons:

    • To make study of organism easy.
    • To avoid confusion.
    • To learn the interrelationship among the various organisms.
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Asked: December 26, 2024In:
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What is Physics? Definition, History, Importance, Scope (Class 11)

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  1. Saralyn
    Saralyn Begginer

    The most curious mind out of all the species is the mind of homosapiens. Humans are always curious about the nature around them and the magic laws on which it functions. The sun always rises in the east and sets in the west, the moon appears at night and the sun appears in the day, and so on. All thRead more

    The most curious mind out of all the species is the mind of homosapiens. Humans are always curious about the nature around them and the magic laws on which it functions. The sun always rises in the east and sets in the west, the moon appears at night and the sun appears in the day, and so on. All these questions not on make humans curious but make them think and discover about the different theories of nature and by doing so, humans soon started discovering physics in order to discover the world and its mystery. Let’s learn what is physics in more detail,

    What is Physics?

    The word “science” has been originated from a word in the Latin dictionary named “Scientia” which means “to know”. Therefore, in one way, it can be said that science is nothing but to know the working of everything, from nature to machines. Under science, a category well known is nature science, which is the study of the physical world around humans. Physics, chemistry, biology, geology, all these fields lie under nature science.

    A basic discipline of nature sciences is physics. Physics is also a word taken from the Latin dictionary which means nature. In Sanskrit, it is known as “Bhautiki” which is the physical world around. The definition of physics is not accurately present but it can be said that physics is the study of all basic laws of nature and their manifestation in a different phenomenon.

    Physics as a whole explains the diverse physical phenomenon with respect to concepts and laws. For instance, from the falling off an apple on the ground and the law associated with it to the revolving of planets around the sun, to electromagnetism and its effects, physics defines it all. The major concept involved in physics is the use of basic approaches for bigger and complex problems, the process of solving a complex problem by breaking them into smaller parts is called reductionism. Then the act of unifying different laws is called unification.

    History of Physics

    The word science has been originated from a Latin word named “Scientia” which means “to know”. The word “Physics” has been originated from a Greek word named “Phusike” which means nature. In Sanskrit, physics is called “Vigyaan” which means “knowledge”, all of these words simply tell that physics is as old as the human species. Early civilizations like Egypt, India, Greece, etc, made a significant contribution in the field of physics. From the 16th century, Europe participated heavily and contributed. By the mid-twentieth century, science became an international enterprise and the rapid growth in the very field is on. The two major approaches in physics are already described above, they are unification and reductionism.

    Importance and application of physics

    • The complex and bigger magnitude identities are explained using simpler theories.
    • New devices are invented using the basic physics laws.
    • The observations and experiments can be used to create new laws or to modify the existing laws.
    • The ultimate aim is to find a unified set of laws that govern matter, energy, motion at both microscopic and macroscopic levels.

    Scope and Excitement of Physics

    The scope of physics can be majorly understood by looking at its sub-divisions. There are basically two types of studies in physics, macroscopic physics, and microscopic physics. Macroscopic physics deals with phenomena on a terrestrial, astronomical scale, while microscopic physics deals with the phenomenon on an atomic, molecular, or nuclear scale. The macroscopic study is done mostly in classical physics that includes subjects like mechanics, thermodynamics, etc. The microscopic study is the study of the structure of the atom, etc. Classical physics is unable to contribute in this field and currently, quantum theory is referred for the microscopic level studies.

    Therefore, it can be said that the scope of physics is really very vast. The study covers a plethora of physical quantities like length, mass, time, energy, etc. From the study of smallest quantities (ranging up to 10-30 or less) to the study of the quantities on an astronomical level (ranging up to 1020 or more).

    Fundamental forces in Nature

    Force is seen and experienced on a daily basis and is available on both macroscopic and microscopic levels. At a macroscopic level, apart from gravitational force, several kinds of forces are experienced, for instance, muscular force, contact forces, the elongation or compression of elastics, etc. On a microscopic level, there are electric and magnetic forces, nuclear forces, etc. Although, it was further observed that most of the forces defined or explained are derived from four fundamental forces. The four fundamental forces in nature are,

    • Gravitational Force: It is the mutual force that occurs between two objects by the virtue of their masses. Gravitational force is a universal force. The formula for gravitational force is,

    FG = (G M1M2)/r2

    FG = Gravitational force

    M1, M2 = Masses1 and 2.

    r = distance between the center of the masses.

    • Electromagnetic force: It is the force that occurs between the charged particles. If the charges are at rest, the phenomenon of electric field occurs and if the charges are moving, both electric and magnetic field phenomenon occurs. Therefore, it is named electromagnetic force.
    • Strong nuclear force: It is the strongest force among all four fundamental forces. This force binds the protons and neutrons in a nucleus. This force is charge independent, that is, it acts on proton-proton, proton-neutron, etc.
    • Weak nuclear force: Weak nuclear force is not the weakest force among fundamental forces. It is not as weak as a gravitational force but is weaker than the electromagnetic force. This force is observed in only some nuclear processes, for example, β-decay of the nucleus.

    Conceptual Questions

    Question 1: Which of the four fundamental forces is the weakest and the strongest?

    Answer: 

    The weakest force in nature is the gravitational force and the strongest force in nature is the strong nuclear force.

    Question 2: What are the laws of conservation in nature?

    Answer:

    Following are the laws of conservation in nature:

    1. Law of conservation of mass.
    2. Law of conservation of energy.
    3. Law of conservation of momentum.
    4. Law of conservation of charge.

    Question 3: On what two things the scope of physics is defined?

    Answer:

    The two things on which the scope of physics is defined are unification and reductionism. Unification is the physics of unifying all laws. Whereas, reductionism is the process of solving complex problems by breaking them into simpler parts.

    Question 4: What part of the study is not handled by the classical study of physics?

    Answer:

    The microscopic study of the physical world is not handled by classical physics. A new field termed quantum theory handles the study of physics at the microscopic level.

    Question 5: Give an example of a weak nuclear force.

    Answer:

    The weak nuclear force is observed in a few nuclear processes. An example of a weak nuclear force is the β-decay of the nucleus.

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Asked: January 17, 2025In:
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Please Explain System of Units (Class 11 – Physics).

class 11physicssciencesystem of units
  1. Saralyn
    Saralyn Begginer

    Measurement forms the fundamental principle to various other branches of science, that is, construction and engineering services. Measurement is defined as the action of associating numerical with their possible physical quantities and phenomena. Measurements find a role in everyday activities to aRead more

    Measurement forms the fundamental principle to various other branches of science, that is, construction and engineering services. Measurement is defined as the action of associating numerical with their possible physical quantities and phenomena. Measurements find a role in everyday activities to a large extent. Therefore, it is necessary to study and explore the associated elements along with their theoretical foundations, conditions as well as limitations. It defines the units to be chosen for the measurement of various commodities. It also caters to the comparison of plausible units with the ones already existing of a similar kind.

    Measurement defined the new standards as well as form transductions for the quantities which do not have any possible access for direct comparison. These physical quantities can be converted into analogous measurement signals.

    Measurements may be made by unaided human senses, generally termed as estimates. It can also be estimated by the use of instruments, which may range in complexity from simple rules for measuring lengths to highly complex analogous systems to handle and design the commodities beyond the capabilities of the senses. Thus, the measurements may range from buying some quantity of milk (in L) or to the highly complex mechanisms, such as radio waves from a distant star or the nuclear bomb radiations. Therefore, we can consider that a measurement, always involves a transfer of energy or interaction between the object and the observer or observing instrument.

    Measurement of Height of a person

    Unit

    The unit of a specified physical quantity can be considered as an arbitrarily chosen standard that can be used to estimate the quantities belonging to similar measurements. The units are well accepted and recognized by the people and well within all guidelines.

    A physical quantity is measured in terms of the chosen standards of measurement.

    The chosen standard is recognized as the unit of that corresponding physical quantity. A standard unit, in short, is a definite amount of a physical quantity. These standard units can be quickly reproduced to create a wide variety of units and are internationally accepted and accessible.

    The measurement of any physical quantity is based on a formula, nu,

    where, n = numerical value of the measure of the quantity,

    u = unit of the quantity.

    Standard

    The actual physical embodiment of the unit of a physical quantity is termed as a standard of that physical quantity. The standard is expressed in terms of the numerical value (n) and the unit (μ).

    Measurement of physical quantity = Numerical value × Unit

    For example: Length of a rod = 12 m. Here 12 is its numerical segment and m (meter) is the unit.

    Fundamental Units

    Fundamental units are elementary in nature, that is, they can be expressed independently without any dependence on any other physical quantity. This implies that it is not possible to resolve it further in terms of any other physical quantity. It is also termed as a basic physical quantity. Fundamental quantities have their own values and units.

    Fundamental Quantities Fundamental Units Symbol
    Length meter m
    Mass kilogram kg
    Time second s
    Temperature kelvin k
    Electric current ampere A
    Luminous intensity candela cd
    Amount of substance mole mol

    Supplementary Fundamental Units

    There are two other supplementary fundamental units, namely Radian and steradian are two supplementary which measures plane angle and solid angle respectively.

    Supplementary Fundamental Quantities Supplementary Unit
    Plane angle radian
    Solid angle steradian
    • Radian (rad)
      One radian is equivalent to an angle subtended at the center of a circle by an arc of length equal to the radius of the circle. It is the unit represented for the plane angle.

    θ = 1 radian

    dθ=\left(\frac{ds}{r}\right)\ radian

    • Steradian (sr)
      One steradian is equivalent to the solid angle subtended at the center of a sphere by its surface. Its area is equivalent to the square of the radius of the sphere.It is the unit represented for the solid angle. Solid angle in steradian,

    Ω = 1 steradian

    dΩ =\frac{Area\ cut\ out\ from\ the\ surface\ of\ sphere}{(Radius)^2}\\ dΩ =\left(\frac{dA}{r^2}\right)\ steradian

    Properties of Fundamental Units

    Any standard unit should have the following two properties:

    • Invariability
      The standard unit must be invariable. Thus, defining distance between the tip of the middle finger and the elbow as a unit of length is not invariable.
    • Availability
      The standard unit should be easily made available for comparing with other quantities.

    The seven fundamental units of S.I. have been defined as under.

    • Meter (m)
      Defined as 1650763.73 times the wavelength, in vacuum of the orange light emitted in transition from 2p10­  to 5d5.
    • Kilogram (kg) 
      Defined as the mass of a platinum-iridium cylinder kept at Serves.
    • Second (s) 
      Time taken by 9192631770 cycles of the radiation from the hyperfine transition in cesium – 133 when unperturbed by external fields.
    • Ampere (A)
      The constant current which, if maintained in each of two infinitely long, straight, parallel wires of negligible cross-section placed 1 m apart, in vacuum, produces between the wires a force of 2×10-7 newton per meter length of the wires.
    • Kelvin (K)
      Temperature is measured with absolute zero as the zero and the triple point of water as the upper fixed point on the thermodynamic scale. The interval is divided into 273.15 divisions and each division is considered to be unit temperature.
    • Candela (cd)
      The luminous intensity in the perpendicular direction of a surface of \frac{1}{600000} square meter of a full radiator at the temperature of freezing platinum under a pressure of 101325 newtons per square meter.
    • Mole (mol)
      The mole is the amount of any substance which contains as many elementary entities as there are atoms in 0.012 kg of the carbon isotope \frac{12}{6} C.

    Derived units

    The derived units are in usage for the commodities where the units are obtained from a combination of fundamental units. Derived units are sometimes assigned names. For instance, the S.I unit of force is kg ms-2 , termed as Newton (N). The unit of power is kg m2 s-3 , termed as watt (W).

    Steps to find Derived Units

    • Fetch the formula for the quantity whose unit is to be derived.
    • Substitute units of all the involved quantities. The chosen units should all belong to one system on units in their fundamental or standard form.
    • Simplify for the derived unit of the quantity to compute its final unit.

    Example: Compute the unit of velocity.

    Since, we know velocity is a derived quantity, obtained from distance and time(fundamental quantities).

    Mathematically ,

    velocity =  displacement/time

    S.I. unit of velocity = \frac{S.I.\ unit\ of\ displacement}{ S.I.\ unit\ of\ time}  = m/s

    Thus S.I. unit of velocity is m/s.

    Some Important derived units

    Some of the derived units have been given specific names, depending on the increase in their usage , though they are not recognized in S.I units.

    • Micron (mm) = 10-6 m
    • Angstrom (Å)  = 10-10 m
    • Fermi (fm) = 10-15 m
    • Barn (b) = 10-28 m2

    Systems of Units

    Any system of units contains the entire set of both fundamental as well as derived units, for all kinds of physical quantities. The preferred system of units are the following :

    • CGS System  (Centimeter Gram Second)
      The unit of length is centimeter, the unit of mass is gram and the unit of time is second according to the guidelines of this system.
    • FPS System  (Foot Pound Second)
      The unit of length is foot, the unit of mass is pound and the unit of time is second according to the guidelines of this system.
    • MKS System (Meter Kilogram Second)
      The unit of length is meter, the unit of mass is kilogram and the unit of time is second according to the guidelines of this system.
    • SI System 
      The System Internationale d’ Units, that is S.I system contains seven fundamental units and two supplementary fundamental units.

    Note:

    While computation of values for any physical quantity, the units for the involved derived quantities are treated as algebraic quantities till the desired units are obtained.

    Advantages of S.I Unit System

    The S.I unit of measurement is preferred over other units of measurement, because,

    • It is internationally accepted.
    • It is a metric system.
    • It is a rational and coherent unit system,
    • Easy conversion between CGS and MKS systems of units.
    • Uses decimal system, which is easy to understand and apply.

    Other Important Units of Length

    The distances can be infinitely larger in magnitude, which cannot be depicted in terms of meters or kilometers. For instance, the distances of planets and stars etc. Therefore, it is necessary to use some larger units of length such as ‘astronomical unit’, ‘light year’, parsec’ etc. while making such calculations, some of which are :

    • Astronomical Unit – The average separation between the Earth and the sun.
      1 AU = 1.496 x 1011 m.
    • Light Year – The distance travelled by light in vacuum in one year.
      1 light year = 9.46 x 1015 m.
    • Parsec – The distance at which an arc of length of one astronomical unit subtends an angle of one second at a point.
      1 parsec = 3.08 x 1016 m
    • Fermi – Size of a nucleus is expressed in ‘fermi’.
      1 fermi = If = 10-15 m
    • Angstrom – Size of a tiny atom
      1 angstrom = 1A = 10-10 m

    Sample Problems

    Problem 1. Convert the unit of G, which is gravitational constant, G = 6.67 x 10-11Nm2/kg2 in CGS system.

    Solution: 

    Since, we have

    G = 6.67 x 10-11 Nm2/kg2

    Converting kg into grams, 1 kg = 1000 gms

    = 6.67 x 10-11 x 108 x 103 cm3/g1 s2

    = 6.67 x 108  cm3/g1 s2

    Problem 2. Name the S.I units of the following commodities : 

    a. Pressure

    b. Solid angle

    c. Luminous intensity.

    Solution: 

    a. Pascal

    b. Steradian

    c. Candela

    Problem 3. Derive the S.I unit of latent heat. 

    Solution: 

    Latent heat = \frac{Heat energy}{Mass}

    Latent\space Heat = \frac{Q}{m} \\ =\frac{ kg m^2 s^{-2}}{kg} \\ = m^2 s^{-2}

    Problem 4: How are A0 and A.U related? 

    Solution: 

    Describing both quantities in terms of meters,

    Ao = 10-10m

    and 1 A.U. = 1.4961011m.

    Therefore,

    1 A.U. =  1.496 x 1011 x 1010 A0

    1 A.U = 1.496 x 1021 A0

    Problem 5: Describe 1 light-year in meters. 

    Solution: 

    A light-year is a distance travelled by light in 1 year with the speed of light :

    = 9.46 x 1011 m

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Asked: December 30, 2024In:
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Explain Diversity In The Living World (Class 11 – Biology) – Notes.

biologyclass 11living world
  1. Saralyn
    Saralyn Begginer
    This answer was edited.

    Diversity In The Living World Each residing life form will in general share highlights like development, upkeep of homeostasis, propagation, utilization of energy, adaption, and so forth. These highlights help to recognize various species and furthermore prove to be useful in laying out a connectionRead more

    Diversity In The Living World

    Each residing life form will in general share highlights like development, upkeep of homeostasis, propagation, utilization of energy, adaption, and so forth. These highlights help to recognize various species and furthermore prove to be useful in laying out a connection between organic entities with a typical hereditary part.

    Biodiversity: Biodiversity is every one of the various types of life you’ll track down in one region — the range of creatures, plants, growths, and even microorganisms like microbes that make up our normal world. Every one of these animal categories and living beings cooperates in environments, similar to a multifaceted web, to keep up with equilibrium and back life. Biodiversity upholds everything in nature that we want to get by food, clean water, medication, and asylum.

    • Taxonomy: Taxonomy is the area of science that manages the recognizable proof, terminology, and grouping of creatures.
    • Identification: Identification is the acknowledgment of the fundamental person of a life form.
    • Nomenclature: Nomenclature is the naming of life forms. Latinized names are utilized to allude to various types of plants and creatures.

    Features of Living World 

    • Development: The expansion in cells’ number and mass through cell division.
    • Material sense: It is the capacity to detect the climate.
    • Digestion: A progression of biochemical responses happening in the body to shape and change substance organization.
    • Proliferation: The method involved creating posterity and proceeding with the progeny.
    • Organization: The very characterizing qualities of every living organic entity.
    • Cognizance: The feeling of monitoring one’s environmental factors, activities, and aims.

    Diversity in the Living World

    Diversity in Living Organism

    The world is overwhelmed by plenty of living organic entities living in the land, water, ice, sweets, and so forth. Each living organic entity is one of a kind of structure, body capabilities, hereditary make-up, etc. The living life forms found in various natural surroundings have different primary organs or capabilities created according to the states of their environment. Organic entities have advanced to adjust to their evolving surroundings. Various sorts and classes of life forms possessing various conditions are known as biodiversity. Districts that are warm and damp have more different organic entities and are called super biodiversity.

    People have advanced from primates. However, presently they don’t appear to be comparative in any capacity. Likewise, every individual is not quite the same as the other. Each individual has an alternate skin tone, hair tone, and eyes, and generally significant of everything is hereditary cosmetics. And that implies that the qualities of each and every individual are unique.

    In this manner, to recognize better, we have made gatherings of creatures that in some way seem to be comparative and have a few utilitarian and primary similitudes. This is known as order. There are different variables that impact the order of creatures. It is significantly done based on the accompanying models

    • Presence of core
    • Body plan which infers the make-up of cells or the presence of single or numerous cells
    • Food creation
    • Level of the association in groups of creatures completing photosynthesis
    • In creatures – an association of one’s body parts, advancement of body, particular organs for various capabilities, organs frameworks.

    Classification System

    The grouping of life forms is finished by two techniques. One is characterizing them into plants and creatures and the other one which is a five-realm framework is a more nitty-gritty and coordinated characterization of living beings:

    • Two-Kingdom Classification- It was proposed via Carolus Linnaeus. He ordered organic entities into two classifications, plants, and creatures.
    • Five-Kingdom Classification- It was proposed by Whittaker. He separated the life forms into five distinct classes.
      • Monera
      • Protista
      • Fungi
      • Plantae
      • Animalia

    Hierarchy of Classification

    Carolus Linnaeus additionally organized the organic entities into various scientific classifications at various levels. These scientific classifications in a chronic request are as per the following

    • Kingdom
    • Phylum
    • Class
    • Order
    • Family
    • Genus
    • Species

    Characteristics of Five Kingdoms

    Kingdom Monera

    These are unicellular prokaryotes. The life forms come up short on the evident nucleus. They might contain a cell wall. They might be heterotrophic or autotrophic in nature. For instance Bacteria, Cyanobacteria.

    Kingdom Protista

    Protista are unicellular and eukaryotic organic entities go under this group. They display an autotrophic or heterotrophic method of nutrition. They show the presence of pseudopodia, cilia, or flagella for headway. For instance one-celled critter, paramecium.

    Kingdom Fungi

    These are multicellular, eukaryotic organisms. They have a saprophytic method of nourishment which includes chemoheterotrophic extracellular processing. The cell wall in these organic entities is comprised of chitin. They live in a cooperative relationship with blue-green growth. For instance Yeast, Aspergillus

    Kingdom Plantae

    These are multicellular, eukaryotic organisms. The cell mass of these creatures is comprised of cellulose. They are heterotrophs and set up their own food through photosynthesis. Kingdom Plantae is partitioned into Thallophyta, Bryophyta, Pteridophyta, Gymnosperms, and Angiosperms. For instance Pines, plants, palm trees, mango trees, and so on.

    Kingdom Animalia

    Kingdom Animalia is multicellular, eukaryotic living beings yet they don’t show the presence of cell walls. They are heterotrophs or creatures who can’t set up their own food. Both straightforward and complex life forms are found in this gathering and it’s an extremely general gathering of organisms. The organic entities are hereditarily diverse. They display an organ-framework level of organization. It is partitioned into various phyla like Porifera, Coelenterata, Echinodermata, Chordata, Annelids, and so on. For instance Earthworms, Hydra, and so on.

    FAQs on Diversity In The Living World

    Question 1: Why are living creatures arranged?

    Answer:

    A colossal assortment of plants, creatures, and organisms are tracked down on the planet. This multitude of living creatures varies in size, shape, variety, natural surroundings, and numerous different attributes. As there is an enormous number of living organic entities on the planet, concentrating on every one of them is unimaginable. Accordingly, researchers have concocted systems to arrange every single living creature. These strategies for arrangement depend on decisions and rules that permit recognizable proof, terminology, and lastly characterization of an organic entity.

    Question 2: Why are the order frameworks changing occasionally?

    Answer:

    Huge quantities of plants, creatures, and microorganisms are tracked down on the planet. A significant number of these have been recognized by researchers while numerous new species are as yet being found all over the planet. In this manner, to order these newfound species, new frameworks of the arrangement must be determined from time to time. This makes the necessity to change the current frameworks of order.

    Question 3: What various measures could you decide to group individuals that you meet frequently?

    Answer:

    The different standards that might be decided to arrange individuals whom we meet frequently incorporate a way of behaving, geological area, morphology, relatives, family members, companions, and so forth.

    Question 4: What do we gain from distinguishing proof of people and the populace?

    Answer:

    The information on attributes of an individual or its entire populace helps in recognizable proof of similitudes and dissimilarities among the people of a comparative kind or between various sorts of life forms. It assists us with grouping living beings into different classes relying on these similitudes and dissimilarities.

    Question 5: Given underneath is the logical name of Mango. Recognize the accurately composed name. Mangifera Indica

    Answer:

    In the binomial arrangement of terminology, the conventional name of an animal group generally begins with a capital letter though the particular name begins with a little letter. Accordingly, the right logical name for Mango is Mangifera indica.

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Asked: December 27, 2024In:
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Explain – Representation of a Set (Class 11 – Maths). Please also Provide Some examples.

class 11examplemathssetsolution
  1. Saralyn
    Saralyn Begginer

    Imagine a very haphazard world where no categories are divided to memorize and classify things separately, a world like this will be full of chaos and mess, this is why humans prefer to categorize things and classify them to neatly understand and remember them. The same case happens in mathematics,Read more

    Imagine a very haphazard world where no categories are divided to memorize and classify things separately, a world like this will be full of chaos and mess, this is why humans prefer to categorize things and classify them to neatly understand and remember them. The same case happens in mathematics, studying math involves dealing with a lot of data, and when the data can be grouped, it is preferred to group them and categorize them, hence, Sets come into play.

     

    What are the Sets in Mathematics?

    Sets are defined as the collection of well-defined data. In Math, a Set is a tool that helps to classify and collect data belonging to the same category, even though the elements used in sets are all different from each other, they all are similar as they belong to one group. For instance, a set of different outdoor games, say set A= {Football, basketball, volleyball, cricket, badminton} all the games mentioned are different, but they all are similar in one way as they belong to the same group (outdoor games).

    The set is denoted as a capital letter, for example, set A, set B, etc., and the elements belonging to the set are denoted as a small letter, and they are kept in curly brackets {}, for example, set A= {a, b, c, d}, as it is clear that a, b, c, d belong to set A, it can be written a ∈ A, do p belong to set A? No. Therefore, it will be written as, p∉ A.

    Representation of Sets

    Sets can be represented in two ways, one is known as the Roster form and the other is famous as the Set-Builder form, these two forms can be used to represent the same data, but the style varies in both cases.

    Roster Form

    In Roster Form, the elements are inside {}⇢ Curly brackets. All the elements are mentioned inside and are separated by commas. Roster form is the easiest way to represent the data in groups. For example, the set for the table of 5 will be, A= {5, 10, 15, 20, 25, 30, 35…..}.

    Properties of Roster Formrelations of Sets:

    • The arrangement in the Roster form does not necessarily to be in the same order every time. For example, A= {a, b, c, d, e} is equal to A= {e, d, a, c, b}.
    • The elements are not repeated in the set in Roster form, for example, the word “apple” will be written as, A= {a, p, l, e}
    • The Finite sets are represented either with all the elements or if the elements are too much, they are represented as dots in the middle. The infinite sets are represented with dots in the end.

    Set-Builder Form

    In Set-builder form, elements are shown or represented in statements expressing relations among elements. The standard form for Set-builder, A= {a: statement}. For example, A = {x: x = a3, a ∈ N, a < 9}

    Properties of Set-builder form:

    • In order to write the set in Set- builder form, the data should follow a certain pattern.
    • Colons (:) are necessary in Set-builder form.
    • After colon, the statement is to be written.

    Order of the Set

    The order of the Set is determined by the number of elements present in the Set. For example, if there are 10 elements in the set, the order of the set becomes 10. For finite sets, the order of the set is finite, and for infinite sets, the order of the set is infinite.

    Sample Problems

    Question 1: Determine which of the following are considered assetsin and which are not.

    1. All even numbers on the number line.
    2. All the good basketball players from class 9th.
    3. The bad performers from the batch of dancers.
    4. All prime numbers from 1 to 100.
    5. Numbers that are greater than 5 and less than 15.

    Answer: 

    Sets are not those bunches or groups where some quality or characteristic comes in the picture. Therefore,

    1. “All even numbers on the number line” is a set.
    2. “All the good basketball players from class 9th” is not a Set as “good” is a quality which is involved.
    3. “The bad performers from the batch of dancers” cannot be a Set since “bad” is a characteristic.
    4. “All prime numbers from 1 to 100” is a Set.
    5. “Numbers that are greater than 5 and less than 15” is a Set.

    Question 2: Represent the following information inSet-Builder the Roster form.

    1. All Natural numbers.
    2. Numbers greater than 6 and less than 3.
    3. All even numbers from 10 to 25.

    Answer:

    The Roster form for the above information,

    1. Set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11……}
    2. Set B = {} ⇢ Null set, since there are no numbers greater than 6 and less than 3.
    3. Set C = {10, 12, 14, 16, 18, 20, 22, 24}

    Question 3: Express the given information in the Set-Builder form.

    1. Numbers that are greater than 10 and less than 20.
    2. All Natural numbers greater than 25.
    3. Vowels in English Alphabet.

    Answer: 

    The Set-Builder form for the above information,

    1. A = {a: a∈ N and 10 < a < 20}
    2. B = {b: b∈ N and b > 25}
    3. C = {c: c is the vowel of English Alphabet}

    Question 4: Convert the following Sets given in Roster form into Set-Builder form.

    1. A = {b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z}
    2. B = {2, 4, 6, 8, 10}
    3. C = {5, 7, 9, 11,13, 15, 17, 19}

    Answer: 

    The Set- builder form for the above Sets,

    1. A = {a: a is a consonant of the English Alphabet}
    2. B = {b: b is an Even number and 2 ≤ b ≤10}
    3. C = {c: c is an odd number and 5 ≤ c ≤ 19}

    Question 5: Give an example of the following types of Sets in both Roster form and Set-builder form.

    1. Singular Set.
    2. Finite Set.
    3. Infinite Set.

    Solution:

    The Examples can be taken as per choice since there can be a infinite number of examples for any of the above Sets,

    • Singular Set

    Roster Form: A = {2}

    Set- builder form: A= {a: a∈N and 1<a<3}

    • Finite Set

    Roster Form: B = {0,1, 2, 3, 4, 5}

    Set-builder form: B = {b: b is a whole number and b<6}

    • Infinite Set

    Roster Form: C = {2, 4, 6, 8, 10, 12, 14, 16…..}

    Set- builder form: C= {c: c is a Natural and Even number}

    Question 6: What is the order of the given sets,

    1. A = {7, 14, 21, 28, 35}
    2. B = {a, b, c, d, e, f, g….x, y, z}
    3. C = {2, 4, 6, 8, 10, 12, 14……}

    Answer:

    The order of the set tells the number of element present in the Set.

    1. The order of Set A is 5 as it has 5 elements.
    2. The order of set B is 26 as the English Alphabet have 26 letters.
    3. The order of set C is infinite as the set has the infinite number of elements.

    Question 7: Express the given Sets in Roster form,

    1. A = {a: a = n/2, n ∈ N, n < 10}
    2. B = {b: b = n2, n ∈ N, n ≤ 5}

    Answer:

    Representing the above Set-builder sets in Roster form,

    1. A = {1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 9/2}
    2. B = {1, 4, 9, 16, 25}
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