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November 5, 2023
LIGHT | Study
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Light
Light is the natural agent that stimulates sight and makes things visible. Light is reflected from all surfaces. It is a form of energy.
Reflection of Light: Bouncing back of light after striking any surface such as a rough surface, Smooth surfce, shiny surface or polished surface, into the same medium, is called reflection of light. (Scroll down to continue …)
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luminous objects: Objects that give out light on their own are called luminous objects.
Examples: Flame, Sun, Glowing bulb
Non-luminous objects: Objects that do not give out light on their own are called non-luminous objects.
Examples: Rocks, Plasic Toys, Walls of room.
The Non – Luuminous objects, reflect light that falls on them.
When the reflected light enters into our eyes from the objects we could see them.
Types of Reflection:
(i) Regular Reflection: When a beam of parallel light rays is incident on a smooth and plane surface, the reflected rays will also be parallel. This type of reflection is called Regular Reflection.
The reflection from a plane mirror is an example of regular reflection.
(ii) Diffused or Irregular Reflection: When a parallel beam of light is incident upon a rough or uneven surface, it is reflected in many directions due to presence of irregularities on that.
multiple reflections: If a reflected light ray is reflected again on being incident on another surface, it is termed as multiple reflections.
Multiple reflections are used in periscope, kaleidoscope etc.
Periscopes are used in submarines, war tanks and by soldiers in bunkers to see objects.
In a kaleidoscope, beautiful patterns are formed due to multiple reflections.
Laws of reflection of light:
(i) The angle of incidence is equal to the angle of reflection.
(ii) Incident ray, reflected ray and the normal drawn at the point of incidence to the reflecting surface, lie in the same plane.
Lateral inversion: Lateral inversion is the effect produced by a plane mirror in reversing images from left to right.
Example: Our left hand will appear as right and vice versa.
Characteristics of the image formed by a plane mirror
Size the image formed by a plane mirror is equal to the siz of the object.
The image formed by the plane mirror is left-right inverted.
The image formed by the plane mirror erect and virtual formed behind the mirror.
Since the distance of the object in front of the mirror two mirrors inclined to each other give multiple images.
Sunlight: Sunlight, called white light, consists of seven colours.
dispersion: Splitting of light into its constituent colours is known as dispersion.
Human Eye:
A normal eye can see nearby and distant objects clearly.
Visually challenged persons can read and write using Braille system.
Visually challenged persons develop their other senses more sharply to improve their interaction with their environment.
Parts of Human Eye:
(i) Cornea: Transparent bulge on the front surface of the eyeball which protects the eye andhelps in refraction of light.
(ii) Iris: Coloured diaphragm behind the cornea which controls the amount of light
entering the eye.
(iii) Pupil: Dark hole in the middle of iris through which light enters the eye. (iv) Eye lens: Transparent, crystalline structure behind pupil and iris. (v) Ciliary muscles: Hole the eye lens in position and control the focal length of the eye lens.
(vi) Retina: Surface of the rear part of the eyeball where the light entering the eye is focused.
(vii) Rods and Cones: Rod cells respond to the brightness of light while cone cells.

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November 5, 2023
COAL AND PETROLEUM | Study
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Natural Resources: Resources include everything provide by the nature. They form the wealth of a country.
Types of Natural Resources:
(i) Inexhaustible: There are some resources that are present unlimited in nature and will not be exhausted even if used continuously.
Example: Sunlight, Air. (Scroll down to continue …)
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(ii) Exhaustible: These resources are limited and can soon get exhausted because of Coal, petroleum and natural gas are fossil fuels.
Fossil fuels were formed from the dead remains of living organisms millions of yearsago.
Fossil fuels are exhaustible resources.
Coke, coal tar and coal gas are the products of coal.
Petroleum gas, petrol, diesel, kerosene, paraffin wax, lubricating oil are
obtained by refining petroleum.
Coal and petroleum resources are limited.
We should use them judiciously.
Petroleum is mixture of various constituents such as petroleum gas, petrol, diesel, lubricating oil, paraffin wax, etc.
Refining: Refining is the process of refracting the various constituents / fractions of petroleum.
It carried out in a petroleum refinery.
Natural Gas: A very important fuel as it easy to transport through pipes and can be compressed and stored under high pressure as Compressed Natural Gas (CNG).
It causes no pollution and has high calorific value.

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November 5, 2023
COMBUSTION AND FLAME | Study
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Combustion and Flame
Combustion: The process of burning a substance in the presence of air (oxygen) andundergoes a chemical reaction to produce heat and light. The substances which burn in air are called combustible.
Oxygen (in air) is essential for combustion. During the process of combustion, heat and light are given out. Ignition temperature is the lowest temperature at which a combustible substancecatches fire.
Types of combustion: The type of combustion differs depending on the type of fuel. (Scroll down to continue)
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Based on nature and intensity combustions are classified into three types. They are:
(i) Rapid combustion
(ii) Spontaneous combustion
(iii) Explosion
Flame: It is a zone or burning vapour. The substances which vaporise during
burning give flames.
Example: Kerosene oil and molten wax. Inflammable substances have very low ignition temperature. Fire can be controlled by removing one or more requirements essential for producing fire. Water is commonly used to control fires. Water cannot be used to control fires involving electrical equipments or oils.
There are three different zones of a flame – dark zone, luminous zone and non-luminous zone.
Fuel is any material that is burned to obtain energy that can be used to heat or
A good fuel must:
Be readily
available. Be cheap. Burn easily at a moderate rate.
Produce a large amount of heat. • Not leave behind any undesirable
Fuels differ in their efficiency and cost. Fuel efficiency is expressed in terms of its calorific value which is expressed in
units of kilo joule per kg.
Types of Fuels:
(i) Solid Fuels: Combustible substances which are solid at room
temperature.Example: coal, coke, wood, charcoal, etc. (ii) Liquid fuels: Volatile liquids which produce combustible vapour. Example:
Petrol,kerosene, alcohol, diesel, etc. (iii) Gaseous fuels: Combustible gases or mixture of combustible gases. Example:
Effects of Burning of Fuels:
(i) Carbon fuels like wood, coal petroleum release un burnt carbon particles. Theseare dangerous pollutants causing respiratory diseases, such as asthma.
(ii) Incomplete combustion of carbon fuels gives carbon monoxide which
is apoisonous gas.
(iii) Increased concentration of carbon dioxide in the air is believed to cause
globalwarming.
(iv) Oxides of Sulphur and nitrogen dissolve in rain water and form acids. Such
rain is Un burnt carbon particles in air are dangerous pollutants causing respiratoryproblems.
Incomplete combustion of a fuel gives poisonous carbon monoxide gas. Increased percentage of carbon dioxide in air has been linked to global warming.
Oxides of sulphur and nitrogen produced by the burning of coal, diesel and
petrol cause Acid rain which is harmful for crops, buildings and soil.
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November 5, 2023
CONSERVATION OF PLANTS AND ANIMALS | Study
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Conservation of Plants and Animals
Biodiversity: Occurrence of innumerable types of organisms and the whole range of their varieties (biotypes) adapted to different climates, environments and areas. Wildlife sanctuary, national park and bio-sphere reserve are names given to the areas meant for conservation and preservation of forest and wild animals. (Scroll down to continue …)
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Biodiversity refers to the variety of living organisms in a specific area.
Plants and animals of a particular area are known as the flora and fauna of that area.
Endemic species are found only in a particular area.
Endangered species are those which are facing the danger of extinction.
Red Data Book contains a record of endangered species.
Migration is the phenomenon of movement of a species from its own habitat to some other habitat for a particular time period every year for a specific purpose like breeding.
We should save, reuse and recycle paper to save trees, energy and water.
Reforestation is the restocking of destroyed forests by planting new trees.
Flora: Different types of plants belonging to an area.
Example: Silver ferns, sal, teak, mango, etc.
Fauna: All animals found in an area.
Example: dog, frog, insects, bull, jackal, etc.
Endemic Species: Species of plants and animals found exclusively in a particular area.
These are not naturally found anywhere else.
Extinct Species: Species of plants and animals which have already been lost.
Type of Threatened Species:
(ii) Vulnerable Species: A vulnerable species is a species of animals or plants which are likely to become endangered unless something changes.
Example: Chinkara deerand black buck, golden langur, etc
(iii) Rare Species: Species whose population are originally small and scattered in the National Parks: Protective areas reserved exclusively for the betterment of the wildlife. These are established at the approval of legislature.
Example: Hazaribagh National Park in Jharkhand, Desert National Park in Rajasthan.
Sanctuaries: Hunting prohibited areas set up by government are known as sanctuaries. These are only for the protection of wild animals.
Example: Jaldapara in Madarihat (West Bengal), Keoladeo Ghana in Bharatpur (Rajasthan)
igration: The regular, periodic, two way movements of birds and some animals from their place of residence to some other place along well defined routes. It is linked to seasonal factors, breeding, shortage of foods, etc.
The sanctuary is known for the migratory birds.

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November 5, 2023
REPRODUCTION IN ANIMALS | Study
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Reproduction in Animals
Reproduction is a process in which the organisms produce the young ones of their own kind. There are two modes by which animals reproduce.
These are: (i) Sexual reproduction, and (ii) Asexual reproduction (Scrolldown to continue …)
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Sexual Reproduction
Reproduction resulting from the fusion of male and female gametes is called sexual reproduction.
The reproductive organs in the female include ovaries, oviducts and uterus.
The reproductive organs in male include testes, sperm ducts and penis.
The ovary produces female gametes called ovum and the testes produce male gametes called sperms. The fusion of ovum and sperm is called fertilization.
zygote: The fertilized egg is called a zygote.
internal fertilization: Fertilization that takes place inside the female body is called internal fertilization. This is observed in human beings and other animals such as hens, cows and dogs.
external fertilization: Fertilization that takes place outside the female body is called external fertilization. This is observed in frogs, fish, starfish, etc.
The zygote divides repeatedly to give rise to an embryo. The embryo gets embedded in the wall of the uterus for further development.
The stage of the embryo in which all the body parts are identifiable is called foetus.
Animals such as human beings, cows and dogs which give birth to young Ones.
Asexual Reproduction: The type of reproduction in which only a single parent is involved is called asexual reproduction. The transformation of the larva into adult through drastic changes is called Asexual Reproduction
budding: In hydra, new individuals develop from buds. This method of asexual reproduction is called budding.
binary fission.: Amoeba reproduces by dividing itself into two. This type of asexual reproduction is called binary fission.

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November 5, 2023
REACHING THE AGE OF ADOLESCENCE | Study
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Reaching The Age of Adolescence
Humans become capable of reproduction after puberty. Puberty sets in between the ages of 11 years and 19 years. These children are called adolescents.
The onset of puberty brings about growth of the reproductive organs. Hairs grow at various places on the body.
Breasts develop in girls.
Facial hair (moustache and beard) appear in boys.
Voice of boys become hoarse as voice box enlarges during adolescence.
Children gain height during adolescence.
Puberty: It is the time when sex organs begin to work.
It brings about growth in reproductive organs and changes in the body.
Puberty starts at the beginning of adolescence.
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Reaching the age of Adolescence
The onset of puberty starts much earlier in girls, between 8 and 13 years of age, whereas it starts between 10 and 14 years of
age in boys and lasts upto 2 to 4 years.
Changes during Puberty:
(i) Increase in Height: The bones of the legs and arms elongate and the individual becomes tall and lanky.
(ii) Changes in Body Shape: In boys, the body becomes more muscular, the shoulder becomes wider.
In girls, the body shows curves in certain parts and the region below the waist become wider and broader.
(iii) Change in Voice: In boys, the voice becomes hoarse and heavy due to the extra growth of larynx (voice box).
In girls, the voice becomes high pitched and shriller.
(iv) Sweat and sebaceous glands: They become more active and secrete more.
(v) Emotional aspects develop.
Periodic cycle of 28 days. The onset of puberty and maturity of reproductive parts are controlled by hormones.
Hormones are secretions of endocrine glands which pour them directly into the blood stream.
Pituitary gland secretes hormones which include growth hormone and hormones that make other glands such as the testes, ovaries, thyroids and adrenals, secrete hormones.
Pancreas secretes insulin, thyroid produces thyroxin and adrenals produce adrenalin.
Testosterone is the male hormone and estrogens, the female hormone.
The uterine wall in females prepares itself to receive the developing fertilised egg.
Menstruation: In case there isno fertilisation, the thickened lining of the uterine wall breaks down and goes out of the body along with blood.This is called menstruation.
Sperm and Ovum fuses together to form a zygote.
Sex chromosomes in sperms determine the baby’s gender. Humans have 23 pairs of chromosomes in each cell.
A pair of chromosome forms the sex chromosomes. Males carry XY and females carry XX chromosomes.
If a sperm carrying X fertilises the ovum with X chromosome, then the resulting baby is a girl.
If a sperm carrying Y chromosome fertilises the ovum with X chromosome, then the resulting baby is a boy.
Hence, males are responsible for the gender of the newly formed babies, Not Women.
Reproductive Health:
It is important to eat balanced food and maintain personal hygiene during adolescence.
Cleaning of private parts is important to prevent possible infections.
The activity of sweat glands increases in puberty and releases bad odour from the body.
Thus frequent bathing is necessary. Physical exercise keeps the body fit and healthy as it releases lot of sweat.
Peer pressure is best addressed by self-confidence and a healthy lifestyle.

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November 5, 2023
FORCE AND PRESSURE | Study
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Force And Pressure
Force: A push or a pull, that changes or tends to change the state of rest or of uniform motion of an object or changes its direction or shape.
A force arises due to the interaction between two objects.
Force has magnitude as well as direction.Therefore force is a vector quantity.
The SI unit of force is newton. (Scroll down to continue …)
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A change in the speed of an object or the direction of its motion or both implies a change in its state of motion.
Force acting on an object may cause a change in its state of motion or a change in its shape.
Contact Non Contact Forces:
A force can act on an object with or without being in contact with it. Based on Contact the forces are classclassified as Contact Forces and Non Contact Forces.
Contact Forces: The forces act on a body when the source of force touches the body directly.
The point where the force is applied on an object is called the point of application of force (or point of contact).
Examples of Contact Forces:
(i) Muscular Force: The force exerted by the muscles of the body.
We use force acted by muscles of animals like Humans, bullocks, horses and camels to get our activities done.
(ii) Mechanical Force: The force acted by a machine.
Non-Contact Forces:
Non-Contact Forces: Forces which do not involve physical contact between two bodies on which they act.
Examples of Non-Contact Forces:
(i) Magnetic Force: A magnet exerts a non-contact force on objects made of iron, steel, cobalt or nickel.
(ii) Electrostatic Force: The force which result due to repulsion of similar charges or attraction of opposite charges.
(iii) Gravitational Forces: The force that exists between any two bodies by virtue of
Pressure
Pressure: Thrust acting per unit surface area is called pressure.
Thrust
Thrust is the force acting on an object perpendicular to its surface.
In SI system, pressure is measured in newton per square metre which is equal to 1 pascal (Pa).
Like solids, fluids (liquids and gases) also exert pressure.
A solid exerts pressure only in the downward direction due to its weight, whereas liquids and gases exert pressure inall directions.
Hence liquids and gases exert pressure on the walls of their container.
Atmospheric Pressure
Ttmosphere: The thick blanket of air that covers the earth is termed atmosphere.
The pressure exerted by the atmosphere is called atmospheric Pressure.
The tremendous atmospheric pressure surrounding us is not felt by us because the fluid pressure inside our bodies counter-balances the atmospheric pressure around us.

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November 5, 2023
FRICTION | Study
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Friction:
Friction is the force that resists the motion of one object against another. It is the force felt between two surfaces when one attempts to slide against the other.
Causes of Friction: Friction exists between two surfaces due to irregularities on the surfaces of the objects in contact, interlocking of micro-level irregularities of the two surfaces and ploughing of harder surfaces into smoother surfaces.
Factors Affecting Friction:
(i) Roughness of the surface.
(ii) The extent to which the two surfaces press against each other.
(iii) Nature of the surface· (Scroll doen to continue …)
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Types of Friction: Friction is classified into three types as: Static Friction, Sliding Friction, Rolling Friction.
(i) Static Friction: When a body is at rest, the force of friction is called the static friction and is always equal and opposite to the applied force.
limiting friction: The force of friction which acts when the body is just at the verge of sliding on the surface is called limiting friction.
Motion between two contacting surfaces
(ii) Sliding friction: The friction force which opposes the actual relative sliding motion between two contact surfaces.
Sliding friction is smaller than static friction.
(iii) Rolling Friction: The frictional force that exists between two surfaces when a body rolls over the other.
Rolling friction is smaller than sliding friction.
Static friction > Sliding friction > Rolling friction
Effects of Friction
(i) Friction produces heat.
(ii) Friction causes wear and tear.
(iii) Friction opposes motion.
Advantages of Friction
(i) Friction between pen and paper enables us to write on the paper.
(ii) Friction between our feet and the ground allows our movements like standing, walking and running.
(iii) Friction between the surface of the road and tyres of our vehicles allow the vehicles to move without slipping.
Disadvantages of Friction:
(i) Friction causes moving objects to stop or slow down.
(ii) Friction produces heat causing wastage of energy in machines.
(iii) Friction causes wear and tear of moving parts of machinery, soles of shoes, etc.
Friction is a necessary Evil:
As friction is advantageous to us it is considered as a friend but, due to its disadvantages it is a foe.
Depending on the circumstance, friction can be a help or a hindrance.
Thus it is a necessary evil.
Increasing Friction: By pressing the surfaces together more strongly.
For example, when brakes are applied on a bicycle or car, the brake pads press against a moving part of the wheel and the force of friction increases.
Friction can be increased by increasing the roughness of the surfaces in contact.
For example, treading of shoes and tyres is done to increase friction.
Reducing Friction: Friction between the sliding surfaces of two objects can be reduced by making the surfaces in contact smooth by polishing them.
Sliding friction between the moving parts of vehicles and machinery can be reduced by introducing oil, grease, graphite or any other lubricant.
Lubricant: A lubricant is a substance that reduces friction between surfaces in contact. This reduces the heat generated when the surfaces move. Lubricants can also transmit forces, transport foreign particles, or heat or cool the surfaces.
Rolling friction is less than sliding friction. Hence, sliding friction is replaced by rolling friction by using rollers, like ball bearings between the hub and the axles in the moving parts of machines and vehicles.
Friction is reduced by providing wheels,
Examples: suitcase, school bags of kids, etc.
Streamlined shape: Aeroplanes, boats, fishes and birds which move through fluids have bodies of special shape, called streamlined shape, The streamlined shape reduces the friction due to fluid and reduces the energy usage.

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November 5, 2023
SOUND | Study
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Sound: Vibrations that travel through the air or another medium and can be heard
when they reach a person’s or animal’s ear. Musical Sound: The sound which produce a pleasing effect on the ear.
Noise: The sounds which produce a jarring or unpleasant effect. (Scroll down to contue …)
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Types of Sound:
(i) Audible Sound: Vibrations whose frequency lies between 20 Hz to 20,000 Hz (20
kHz) are heard by human ear.
(ii) Inaudible Sound: The sounds having frequencies above 20,000 Hz and below
20 Hz cannot be heard by the normal human ear.
Low frequency sounds which cannot be heard are called infrasonics.
High frequency sounds which cannot be heard are called ultrasonics.
In human beings, the vibration of the vocal cords produces sound.
Sound travels through a medium (gas, liquid or solid). It cannot travel in
vacuum.
The eardrum senses the vibrations of sound. It sends vibrations to the inner ear. From
there, the signal goes to the brain.
That is how we hear. Higher the frequency of vibration, the higher is the pitch, and shriller is the
sound. Unpleasant sounds are called noise.
Excessive or unwanted sounds lead to noise pollution. Noise pollution may pose health problems for human beings. Lack of sleep, hypertension (high bloodpressure), anxiety and many more health disorders may be caused by noise pollution.
A person who is loud sound continuously may get temporary or even permanent impairment of hearing.
Attempts should be made to minimise noise pollution. Silencing devices must be installed in air craft engines, transport vehicles, industrial machines and home appliances. Plantation on the roadside and elsewhere can reduce noise pollution.
Amplitude: The maximum extent of vibration of the vibrating body from its mean position is known as its amplitude.
Time Period: One complete to and fro movement of the pendulum around its mean positionis called one oscillation.
The time taken by the vibrating particle to complete one oscillation is called time period.
Frequency: The number of vibrations made by the vibrating body in one second is known as its frequency. The SI unit of frequency is the hertz (Hz).
Characteristics of Sounds:
(i) Loudness: The sensation produced in the ear which enables us to distinguish between a loud and a faint sound. Larger the amplitude of vibration, the louder is the sound produced. It is proportional to square of the amplitude.
(ii) Pitch: The characteristics of sound which distinguishes between a shrill sound and a soft sound.
Higher the frequency of vibration, higher is the pitch and shrillness.
(iii) Quality: Characteristic which enables us to distinguish between musical notes emittedby different musical instruments or voices even though they have the same.

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November 5, 2023
CHEMICAL EFFECTS OF ELECTRIC CURRENT | Study
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Chemical Effects of Electric Current
Materials through which electric current can pass through easily are called electric conductors or conductors of electricity.
Electrical conductivity Or Electric Conductivity: Electrical conductivity is a measure of the ability of a substance to allow the flow of electric current.
Among solids metals and graphite are good conductors which have high electrical conductivity.
Some liquids are also good conductors.
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Pure water or distilled water is a poor conductor of electricity. But the presence of even small amount of impurities(salts and minerals) makes water a good conductor as it contains ions through which conduction takes place.
Hence water from taps, wells, lakes, etc. conduct electricity as they contain impurities.
Most liquids that conduct electricity are solutions of acids, bases and salts.
When electricity is passed through a conducting solution, the molecules of the solution dissociate into ions.
Ions are atoms or group of atoms with a positive or a negative charge.
These ions cause electrical conduction through the liquid.
Electrolyte: A liquid That conducts electricity is called an electrolyte.
Electrolysis:
The process of chemical decomposition compound in a solution when an electric current passes through it is called electrolysis.
Electrolysis, is due to the chemical effect of electric current.
electrolytic cell: Two electrodes are inserted in the solution and are connected to the terminals of a battery with a switch in between them.
This arrangement is called an electrolytic cell.
anode: The electrode that is connected to the positive terminal of the battery is called the anode,
cathode: The electrode that is connected to the negative terminal of the battery is called the cathode.
Electrolysis is used in refining, electroplating and extraction of metals from impure samples.
electrorefining: This process of refining and extraction of metals from impure samples is called electrorefining.
electroplating: electroplating is the process of coating a useful metal with another metal.
chemical effect of electric current: The process of passing an electric current through a conducting solution to cause chemical reactions is known as the chemical effect of electric current.
Chemical effects of electric current:
(i) Formation of bubbles of a gas on the electrodes.
(ii) Deposition of metal on electrodes.
(iii) Change in colour of solutions.
Electroplating: The process of depositing a layer of any desired metal on another material by means of electricity is called electroplating. The object to be electroplated is made the cathode (negative electrode) by connecting it to thenegative terminal of the battery.
The metal which has to be deposited is made the anode (positive electrode) by connecting it to the positive terminal of the battery. Usually a salt solution of the metal to be coated is made as anode.
Application of Electroplating:
(i) Metals that rust are often coated with other metals to prevent rusting.
(ii) Chromium plating is found on bath taps, car bumpers, etc. to give a bright attractive appearance and resist scratches and wear.
(iii) Silver plating is done on cutlery and jewellery items.
(iv) Tin cans, used for storing food, are made by electroplating tin onto iron.
Tin is less reactive than iron. Thus, food does not come into contact with iron and is protected from getting spoilt.

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November 5, 2023
SOME NATURAL PHENOMENA | Study
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Some Natural Phenomena
Some objects can be charged by rubbing with other
objects. There are two kinds of charges — positive charge and negative charge Like charges repel and unlike charges attract each other.
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Static Electric Charges: The electric charges produced due to rubbing are called static electric charges. The electric charges constitute electric current during their motion.
An electroscope may be used to detect whether a body is charged or not.
An electroscope is a deviced used to detect the presence of electric charge.
earthing: The process of transfer of charge from a charged object to the earth is called earthing.
Lightning
Lightning is a sudden, natural and violent phenomenon of creating bright flashes during a thunderstorm.
Lightning occurs due to a high-voltage electric discharge between two clouds or a cloud and the ground, or within a single cloud during a thunderstorm.
The formation of clouds involves friction between water droplets in the atmosphere.
The friction charges the particles in the atmosphere. The negative charges accumulate at the bottom of the cloud and the positive charges at the top.
As the accumulation of the charges increases, the cloud will induce positive charges on the ground nearby.
As the amount of charge increases. This causes an imbalance of charges between a region of a cloud and gorund or another cloud (or in a cloud itself). This imbalance is significant enough to break through air resistance.
Lightning releases an average of one gigajoule of energy.
Lightning strike could destroy life and property.
Protective measures are of utmost importance during lightning strikes.
Taking shelter in interiors (house or other closed places) and vehicles (closed e.g. cars) are the most preferred measures.
Lightning conductors can protect buildings from the effects of lightning.
Earth Quake
A natural phenomenon that cannot be predicted is an earthquake.
The earth consists of three major layers, called the crust, the mantle and the core.
The core is further divided into the inner core and the outer core.
The mantle consists of semi-solid material above which the crust floats.
The crust consists of oceans and continents.
The crust is divided into several parts, called tectonic plates.
The regions where one tectonic plate slides against another are referred to as fault zones, and these are the regions where an earthquake is likely to occur.
Hence, these zones are referred to as seismic zones.
The place in the interior of the earth where an earthquake occurs is the focus, and the region on the surface of the earth that is the closest to focus is likely to experience the largest damage.
This region is called the epicenter of the earthquake.
The instrument that measures the severity of an earthquake is a seismograph.
It basically consists of a drum that rolls and a pendulum with a stylus that traces the waves of an earthquake on a sheet like a graph paper.
The energy released at the focus propagates outwardly in form of waves known as seismic waves. Destructive energy of an earthquake is measured on the Richter scale.
It is a logarithmic scale, ranging from 1 to 10 for indicating the intensity of an earthquake.
The earthquake measuring 7 or more on Richter scale can cause severe damage to life and property. Protective measures for earthquake:
If you are at home:
Take shelter under a table and stay there till shaking stops.Stay away from tall and heavy objects that may fall on you. If you are in bed, do not get up. Protect your head with a pillow.
If you are outdoors: Find a clear spot, away from buildings, trees and overhead power lines. Drop to the ground. If you are in a car or a bus, do not come out. Ask the driver to drive slowly to a clear spot. Do not come out till the tremors stop. Moreover, it is advisable to make the structure of buildings simple so that they are ‘Quake Safe’.

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November 5, 2023
CROP PRODUCTION AND MANAGEMENT | Study
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Crop Production and Management
In order to provide food for a large population – regular production, proper management and distribution of food is necessary. (Scroll down to continue …)
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Crop : When plants of the same kind are grown and cultivated at one place on a large scale,
it is called a crop.
In India, crops can be broadly categorised into two types based on seasons – Rabi and Kharif crops. Sowing of seeds at appropriate depths and distances gives good yield.
Good variety of seeds are sown after selection of healthy seeds.
Sowing is done by seed drills.
Soil needs replenishment and enrichment through the use of organic manure introduction of new crop varieties.
Basic practices of crop production:
(i) Preparation of Soil: One of the most important tasks in agriculture is to
turn the soil and loosen it.
The process of loosening and turning of the soil is
called tilling or ploughing.
(ii) Sowing: Sowing of seeds at appropriate depths and distances gives good yield.
Good variety of seeds is sown after selection of healthy seeds. Sowing is done by seed
drills.
(iii) Adding Manure and Fertilisers Soil needs replenishment and enrichment through the use of organic manure and fertilisers.
Use of chemical fertilisers
fertilisers has increased tremendously with the introduction of new crop varieties.
Fertiliser: The inorganic compounds containing nutrients such as nitrogen, potassium and phosphorus. They are made in the factories.
Example: ammonium sulphate, potash, etc.
Manure: A natural substance prepared from decomposition of plant and animal wastes (cow dung, animal bones, dead leaves, dead insects and vegetable wastes) by t(he action of microbes.
iv) Irrigation : Supply of water to crops at appropriate intervals is called
irrigation. Method of Irrigation:
(a)Tradition methods of Irrigation: Moat, Chain pump, Dheki, Rahat.
(b) Modern methods of Irrigation: Sprinkler system, Drip
(v) Protection from Weeds: Weeding involves removal of unwanted and
uncultivated plants called weeds.
(vi) Harvesting: Harvesting is the cutting of the mature crop manually or by
machines.
(vii) Storage Proper storage of grains is necessary to protect them from pests
and microorganisms.
Harvested food grains normally contain more moisture than
required for storage.
Large scale of storage of grains is done in silos and granaries to
pest like rats and insects.
Farmers store grains in jute bags or metallic bins.
Food is also obtained from animals for which animals are reared.

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November 5, 2023
MICROORGANISMS : FRIEND AND FOE | Study
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Micro-organisms: Micro-organisms are too small and are not visible to the un aided eye.
They can survive under all types of environment, ranging from ice cold climate to hot springs and deserts to marshy lands.
They are also found inside the bodies of animals including humans. (Scroll down to continue …)
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Micro-organisms are found in air, water and in the bodies of plants and animals.They may be unicellular or multicellular.
Micro-organisms are classified into four major groups. These groups are bacteria,fungi, protozoa and some algae.
Viruses are quite different from other micro-organisms. They reproduce only inside
Micro-organisms: Friend and Foe
Based on the significance, micro-organisms can be useful or harmful.
Uses Of Microorganisms
Protozoan cause serious diseases like dysentery and malaria.
Some bacteria and blue green algae present in the soil fix nitrogen from the atmosphere and convert into nitrogenous compounds.
Certain bacteria convert compounds of nitrogen present in the soil into nitrogen gas which is released to the atmosphere.
Pathogens: Some of the microorganisms cause diseases animals. Such disease causing microorganisms are called pathogens.
Cleaning of Environment: The microorganisms decompose dead organic waste
of plants and animals converting them into simple substances. These substances are again used by other plants and animals.
Microorganisms can be used to degrade theharmful and smelly substances and thereby clean up the environment.

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Mensuration | Study
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Perimeter: Length of boundary of a simple closed figure.
Perimeter of Rectangle = 2(l +b)
Perimeter of Square = 4a
Perimeter of Parallelogram = 2(sum of two adjacent sides)
Area: The measure of region enclosed in a simple closed figure.
Area of a trapezium = half of the sum of the lengths of parallel sides × perpendiculardistance between them.
Area of a rhombus = half the product of its diagonals. (Scroll down to continue …)
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November 5, 2023

Understanding Quadrilaterals | Study

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https://www.youtube.com/watch?v=5Wi9JTYOblw&list=PLEuUy4TjqFeAD5Xcp85qBGE8VHxrYIu7F&pp=gAQBiAQB

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A quadrilateral has 10 parts – 4 sides, 4 angles and 2 diagonals. Five measurements can determine a quadrilateral uniquely. (Scroll down to continue …)

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Curve: Curve is a figure formed on a plane surface by joining a number of non linear points without lifting a pencil.

Open Curve: An open curve is a curve which does not end at the same starting point or which does not intersect itself.

Closed Curve: Closed curve is a curve which intersects itself or which starts and ends at the same point.

Simple Closed Curve: A simple closed curve is a closed curve that does not intersect itself.

Polygon: Polygon is a closed figure bounded by three or more line segments such that each line segment intersects the other two line segements at exactly two other points (vertices) as shown in the following figures.

Polygons are classified into two types on the basis of interior angles: as (i) Convex polygon (ii) Concave polygon

(a) Convex Polygon: In this case, each angle is either acute or obtuse (angle < 180 ^o) as shown in the following figures.

Concave Polygon: In this case, any one angle is reflex (angle > 180°) and one diagonal is outside the polygon as shown in the following figures.

On the basis of sides, there are two types of polygons :

(a) Regular Polygon: A convex polygon is called a regular polygon, if all its sides and angles are equal as shown in the following figures.

Each angle of a regular polygon of n-sides =

Important results on polygon :

For a regular polygon of n sides (n > 2).

(b) Irregular Polygon: A polygon in which all the sides are unequal as shown in the following figures,

Triangle :

A simple closed figure bounded by three line segments is called a triangle, it has three sides as AB, BC and AC; three vertices as A, B and C and three interior angles A, ZB and ZCand the sum of all angles is 180°.

i.e., <A + <B + <C = 180°

Quadrilateral:

A simple closed figure bounded by four line segments is called a quadrilateral, it has four sides i.e.,

AB, BC, CD and AD and four vertices as A, B, Can d D and the sum of all angles of a quadrilateral is 360.

Practical Geometry

Five measurements can determine a quadrilateral uniquely.

A quadrilateral can be constructed uniquely if the lengths of its four sides and a diagonal is given.

A quadrilateral can be constructed uniquely if its two diagonals and three sides are

known.

A quadrilateral can be constructed uniquely if its two adjacent sides and three angles

are known.

A quadrilateral can be constructed uniquely if its three sides and two included angles

are given.

Quadrilateral

Quadrilateral is a closed figure with four sides.

Characteristics of a quadrilateral

Angle Sum Property of a Quadrilateral:

Qudrilateral is a four sided closed figure.

Sum of all angles of a quadrilateral is 360°.

Types Of Quadrilaterals

Quadrilaterals are broadly classified into three categories as:

(i) Kite

(ii) Trapezium

(ii) Parallelogram

Kite:

Kite

(i) Kite has no parallel sides

(ii) Kite has a pair of equal adjacent sides.

(ii) It is not a parallelogram

Characteristics Of Kite:

Perimeter Of Square

Area Of Kite

Trapezium:

Trapezium is a quadrilateral with the following characteristics:

(i) One pair of opposite sides is parallel to each other.

(ii) The other pair of opposite sides may not be parallel to each other.

Characteristics Of Trapezium

(i) Sum of all angles of a quadrilateral is 360°.

(ii) One pair of opposite sides is parallel to each other.

(iii) The other pair of opposite sides need not be parallel to each other.

Types Of Trapezium:

Quadrilaterals are broadly classified into two categories as:

(i) Isosceles Trapezium.

(ii) Scalene Trapezium.

(i) Right Trapezium.

Isosceles Trapezium:

Isosceles Trapezium is a quadrilateral with the following characteristics:

(i) One pair of opposite sides is parallel to each other.

(ii) The other pair of opposite sides are equal.

(iii) The other pair of opposite sides need not be parallel to each other.

Isosceles Trapezium is a trapezium with the following characteristics:

(i) One pair of opposite sides is parallel to each other.

(ii) The other pair of opposite sides are equal.

(iii) The other pair of opposite sides need not be parallel to each other.

Characteristics Of Isosceles Trapezium

(i) Sum of all angles of a quadrilateral is 360°.

(ii) One pair of opposite sides is parallel to each other.

(iii) The other pair of opposite sides are equal.

(iv) The other pair of opposite sides need not be parallel to each other.

Scalene Trapezium:

Scalene trapezium: Classified by the length of the legs or the measurement of their angles.

Characteristics Of Scalene Trapezium

Right Trapezium:

Right trapezium: Has one pair of parallel sides and one pair of right angles.

Characteristics Of Right Trapezium

Perimeter Of Trapezium

Area Of Trapezium

Parallelogram:

Parallelogram is a quadrilateral with the following characteristics:

(i) Two pairs of opposite sides are parallel to each other.

(ii) Two pairs of opposite sides are equal in length.

Characteristics of a parallelogram

(i) Sum of all angles of a Parallelogram is 360°.

(ii) Two pairs of opposite sides are parallel to each other.

(ii) Two pairs of opposite sides are equal in length.

(ii) Two pairs of opposite angles are equal.

(iii) Diagonals bisect each other.

(iv) Diagonals need not be equal to each other.

(v) Diagonals divide it into two congruent triangles.

Types Of Parallelogram

Parallelograms are broadly classified into three categories as:

(i) Rectangle

(ii) Rhombus

(iii) Square

Perimeter Of Parallelogram

Area Of Parallelogram

Rectangle:

Rectangle is a quadrilateral with the following characteristics:

(i) Two pairs of opposite sides are parallel to each other.

(ii) Two pairs of opposite sides are equal in length.

(iii) All four angles are right angles. (each angle is 90 ^o).

Characteristics Of Rectangle

(i) Sum of all angles of a quadrilateral is 360°.

(ii) Two pairs of opposite sides are parallel to each other.

(ii) Two pairs of opposite sides are equal in length.

(iii) All four angles are right angles. (each angle is 90 ^o).

(iii) Diagonals bisect each other.

(iv) Diagonals are equal to each other.

(v) Diagonals of a rectangle divide it into two congruent triangles.

Conclusions:

Every Rectangle is a Parallelogram. But Every Parallelogram need not to be a Rectangle.

Condition for a rhombus to be a square:

If all four angles of a parallelogram are right angles. (each angle is 90 ^o), the parallelogram becomes a Rectangle.

Perimeter Of Rectangle

Area Of Recatangle

Rhombus:

Rhombus is a quadrilateral with the following characteristics:

(i) Two pairs of opposite sides are parallel to each other.

(ii) All four sides are equal in length.

Characteristics Of Rhombus

(i) Sum of all angles of a quadrilateral is 360°.

(ii) Two pairs of opposite sides are parallel to each other.

(ii) All four sides are equal in length.

(ii) Two pairs of opposite angles are equal.

(iii) Diagonals bisect each other.

(iv) Diagonals need not be equal to each other.

(v) Diagonals divide a Rhombus into two congruent triangles.

Conclusions:

Every Rhombus is a Parallelogram. But Every Parallelogram need not to be a Rhombus.

Condition for a rhombus to be a square:

If all the sides of a parallelogram are equal, the parallelogram becomes a Rhombus.

Perimeter Of Rhombus

Area Of Rhombus

Square:

Square is a quadrilateral with the following characteristics:

(i) Two pairs of opposite sides are parallel to each other.

(ii) All four sides are equal in length.

(iii) All four angles are right angles. (each angle is 90 ^o).

Characteristics Of Square

(i) Sum of all angles of a quadrilateral is 360°.

(ii) Two pairs of opposite sides are parallel to each other.

(iii) All four sides are equal in length.

(iv) All four angles are right angles. (each angle is 90 ^o).

(v) Diagonals bisect each other.

(vi) Diagonals need not be equal to each other.

(vii) Diagonals divide a Rhombus into two congruent triangles.

Conclusions:

Every square is a Rhombus. But Every Rhombus need not to be a square.

Condition for a rhombus to be a square:

If all the angles of a rhombus are right angles (euqal to 90^o), the rhombus becomes a square.

2. Every Square is a prallelogram. But Every prallelogram need not to be a square.

Condition for a prallelogram to be a square:

(i) If all the angles of a parallelogram are right angles (euqal to 90^o), and all the sides of a parallelogram are equal in length, the parallelogram becomes a square.

3. Every Square is a rectangle. But Every Rectangle need not to be a square.

Condition for a Rectangle to be a square:

If all the sides of a Rectangle are equal in length, the Rectangle becomes a square.

If all the sides of a parallelogram are equal, the parallelogram becomes a Rhombus.

Perimeter Of Square

Area Of Square

Important Points To Remember

The diagonals of a parallelogram are equal if and only if it is a rectangle.
If a diagonal of a parallelogram bisects one of the angles of the parallelogram then it also bisects the opposite angle.
In a parallelogram, the bisectors of any two consecutive angles intersect at a right angle.
The angle bisectors of a parallelogram form a rectangle.

Mid Point Theorem

A line segment joining the mid points of any two sides of a triangle is parallel to the third side and length of the line segment is half of the parallel side.

Converse Of Mid Point Theorem

A line through the midpoint of a side of a triangle parallel to another side bisects the third side.

Intercept Theorem

If there are three parallel lines and the intercepts made by them on one transversal are equal then the intercepts on any other transversal are also equal.

svg+xml;nitro-empty-id=ODUyOjUzOA==-1;base64,PHN2ZyB2aWV3Qm94PSIwIDAgMSAxIiB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==

Angle Sum Property of a Quadrilateral

The sum of the four angles of a quadrilateral is 360°

If we draw a diagonal in the quadrilateral, it divides it into two triangles.

And we know the angle sum property of a triangle i.e. the sum of all the three angles of a triangle is 180°.

The sum of angles of ∆ADC = 180°.

The sum of angles of ∆ABC = 180°.

By adding both we get ∠A + ∠B + ∠C + ∠D = 360°

Hence, the sum of the four angles of a quadrilateral is 360°.

Example

Find ∠A and ∠D, if BC∥ AD and ∠B = 52° and ∠C = 60° in the quadrilateral ABCD.

Solution:

Given BC ∥ AD, so ∠A and ∠B are consecutive interior angles.

So ∠A + ∠B = 180° (Sum of consecutive interior angles is 180°).

∠B = 52°

∠A = 180°- 52° = 128°

∠A + ∠B + ∠C + ∠D = 360° (Sum of the four angles of a quadrilateral is 360°).

∠C = 60°

128° + 52° + 60° + ∠D = 360°

∠D = 120°

∴ ∠A = 128° and ∠D = 120 °.

Types of Quadrilaterals

Remark: A square, Rectangle and Rhombus are also a parallelogram.

Properties of a Parallelogram

Theorem 1: When we divide a parallelogram into two parts diagonally then it divides it into two congruent triangles.

∆ABD ≅ ∆CDB

Theorem 2: In a parallelogram, opposite sides will always be equal.

Theorem 3: A quadrilateral will be a parallelogram if each pair of its opposite sides will be equal.

Here, AD = BC and AB = DC

Then ABCD is a parallelogram.

Theorem 4: In a parallelogram, opposite angles are equal.

In ABCD, ∠A = ∠C and ∠B = ∠D

Theorem 5: In a quadrilateral, if each pair of opposite angles is equal, then it is said to be a parallelogram. This is the reverse of Theorem 4.

Theorem 6: The diagonals of a parallelogram bisect each other.

Here, AC and BD are the diagonals of the parallelogram ABCD.

So the bisect each other at the centre.

DE = EB and AE = EC

Theorem 7: When the diagonals of the given quadrilateral bisect each other, then it is a parallelogram.

This is the reverse of the theorem 6.

The Mid-point Theorem

1. If a line segment joins the midpoints of the two sides of the triangle then it will be parallel to the third side of the triangle.

If AB = BC and CD = DE then BD ∥ AE.

2. If a line starts from the midpoint of one line and that line is parallel to the third line then it will intersect the midpoint of the third line.

If D is the midpoint of AB and DE∥ BC then E is the midpoint of AC.

Example

Prove that C is the midpoint of BF if ABFE is a trapezium and AB ∥ EF.D is the midpoint of AE and EF∥ DC.

Solution:

Let BE cut DC at a point G.

Now in ∆AEB, D is the midpoint of AE and DG ∥ AB.

By midpoint theorem, G is the midpoint of EB.

Again in ∆BEF, G is the midpoint of BE and GC∥ EF.

So, by midpoint theorem C is the midpoint of BF.

Hence proved.

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November 5, 2023

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November 5, 2023
Factorisation | Study
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Factorisation: Representation of an algebraic expression as the product of two or more expressions is called factorization. Each such expression is called a factor of the given algebraic expression. (Scroll down to continue …)
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When we factorise an expression, we write it as a product of factors. These factors may be numbers, algebraic variables or algebraic expressions.
An irreducible factor is a factor which cannot be expressed further as a product of factors.
A systematic way of factorising an expression is the common factor method. It consists of three steps:
Write each term of the expression as a product of irreducible factors
Look for and separate the common factors and
Combine the remaining factors in each term in accordance with the distributive law.
Sometimes, all the terms in a given expression do not have a common factor; but the terms can be grouped in such a way that all the terms in each group have a common factor. When we do this, there emerges a common factor across all the groups leading to the required factorisation of the expression. This is the method of regrouping.
In factorisation by regrouping, we should remember that any regrouping (i.e., rearrangement) of the terms in the given expression may not lead to factorisation. We must observe the expression and come out with the desired regrouping by trial and error.
A number of expressions to be factorised are of the form or can be put into the form: a²+ 2ab + b², a²– 2ab + b², a²– b²and x² + (a + b)x + ab. These expressions can be easily factorised using Identities I, II, III and IV
a²+ 2ab + b²= (a + b)²
a²– 2ab + b²= (a – b)²
a²– b²= (a + b) (a – b)
Factorisation
x² + (a + b)x + ab = (x + a)(x + b)
In expressions which have factors of the type (x + a) (x + b), remember the numerical term gives ab.
Its factors, a and b, should be so chosen that their sum, with signs taken care of, is the coefficient of x.
We know that in the case of numbers, division is the inverse of multiplication. This idea is applicable also to the division of algebraic expressions.
In the case of division of a polynomial by a monomial, we may carry out the division either by dividing each term of the polynomial by the monomial or by the common factor method.
In the case of division of a polynomial by a polynomial, we cannot proceed by dividing each term in the dividend polynomial by the divisor polynomial. Instead, we factorise both the polynomials and cancel their common factors.
In the case of divisions of algebraic expressions that we studied in this chapter, we have Dividend = Divisor × Quotient.
In general, however, the relation is Dividend = Divisor × Quotient + Remainder
Thus, we have considered in the present chapter only those divisions in which the remainder is zero.
There are many errors students commonly make when solving algebra exercises.
You should avoid making such errors.
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November 5, 2023
Introduction to Graphs | Study
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Graphical presentation of data is easier to understand.
A bar graph is used to show comparison among categories.
A pie graph is used to compare parts of a whole.
A Histogram is a bar graph that shows data in intervals. (Scrol down to continue …)
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Introduction to Graphs
A line graph displays data that changes continuously over periods of time. A line graph which is a whole unbroken line is called a linear graph.
For fixing a point on the graph sheet we need, x-coordinate and y-coordinate.
The relation between dependent variable and
through a graph.
independent variable is shown
A Bar Graph: A pictorial representation of numerical data in the form of bars (rectangles) of uniform width with equal spacing. The length (or height) of each bar
represents the given number.
A Pie Graph: A pie graph is used to compare parts of a whole. The various
observations or components are represented by the sectors of the circle.
A Histogram: Histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars (rectangles) show the frequency of the class interval, but there is no gap between the bars as there is no gap between the
class intervals.
Linear Graph: A line graph in which all the line segments form a part of a single line. Coordinates: A point in Cartesian plane is represented by an ordered pair of numbers.
Ordered Pair: A pair of numbers written in specified order.
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Variations: If the values of two quantities depend on each other in such a way that a change in one causes corresponding change in the other, then the two quantities are said to be in variation. (Scroll down to continue …)
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Direct Variation or Direct Proportion:
Extra:
Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains
constant. That is if
=k [k is a positive number, then x and y are said to vary directly.
In such a case if y₁, y₂are the values of y corresponding to the values x₁, x of x
respectively then = .
If the number of articles purchased increases, the total cost also increases. More than money deposited in a bank, more is the interest earned.
Quantities increasing or decreasing together need not always be in direct proportion, same in the case of inverse proportion.
When two quantities x and y are in direct proportion (or vary directly), they are
written as
. Symbol
stands for ‘is proportion to’.
Inverse Proportion: Two quantities x and y are said to be in inverse proportion if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant. That is, if xy
= k, then x and y are said to vary inversely. In this case if y₁, y₂are the values of y
corresponding to the values x₁, x₂of x respectively then
^x1^{, Y}1 = ^x2^{, y}2 or
=
When two quantities x and y are in inverse proportion (or vary inversely), they are
written as x
. Example: If the number of workers increases, time taken to finish
the job decreases. Or If the speed will increase the time required to cover a given distance decreases.

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Numbers with exponents obey the following laws of exponents.
Very small numbers can be expressed in standard form using negative exponents. (Scroll down to continue …)
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Use of Exponents to Express Small Number in Standard form:
Very large and very small numbers can be expressed in standard form.
Standard form is also called scientific notation form.
(iii) A number written as number such that is said to be in standard form if m is a decimal and n is either a positive or a negative integer.
Examples: 150,000,000,000 = 1.5 x 10¹¹.
Exponential notation is a powerful way to express repeated multiplication of the same number.
For any non-zero rational number ‘a’ and a natural number n, the product a x a x a x x a(n times) = aⁿ.
It is known as the nth power of ‘a’ and is read as ‘a’ raised to the power n’.
The rational number a is called the base and n is called exponent.
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Data Handling: Deals with the process of collecting data, presenting it and getting result.
Data mostly available to us in an unorganised form is called raw data. (Scroll down to continue …)
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Grouped data can be presented using histogram. Histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars show the frequency of the class interval. Also, there is no gap between the bars as there is no gap between the class intervals.
In order to draw meaningful inferences from any data, we need to organise the data systematically.
Frequency gives the number of times that a particular entry occurs.
Raw data can be ‘grouped’ and presented systematically through ‘grouped frequency distribution’.
Statistics: The science which deals with the collection, presentation, analysis and interpretation of numerical data.
Observation: Each entry (number) in raw data.
Range: The difference between the lowest and the highest observation in a given data.
Array: Arranging raw data in ascending or descending order of magnitude. Data can also presented using circle graph or pie chart. A circle graph shows the relationship between a whole and its part.
There are certain experiments whose outcomes have an equal chance of occurring. A random experiment is one whose outcome cannot be predicted exactly in advance. Outcomes of an experiment are equally likely if each has the same chance of occurring.
Frequency: The number of times a particular observation occurs in the given data.
Class Interval: A group in which the raw data is condensed.
(i) Continuous: The upper limit of a class interval coincides with the lower limit of the next class.

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Squares And Square Roots | Study
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Square: Number obtained when a number is multiplied by itself. It is the number raised to the power 2. 2²= 2 x 2=4(square of 2 is 4).
If a natural number m can be expressed as n², where n is also a natural number, then m is a square number. (Scroll down to continue …)
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All square numbers end with 0, 1, 4, 5, 6 or 9 at unit’s place. Square numbers can only have even number of zeros at the end. Square root is the inverse operation of square.
There are two integral square roots of a perfect square number.
Positive square root of a number is denoted by the symbol For example, 3²=9 gives
Perfect Square or Square number: It is the square of some natural number. If m=n², then m is a perfect square number where m and n are natural numbers. Example: 1=1 x 1=12, 4=2 x 2=2².
Properties of Square number:
A number ending in 2, 3, 7 or 8 is never a perfect square. Example: 152, 1028, 6593 etc.
A number ending in 0, 1, 4, 5, 6 or 9 may not necessarily be a square number. Example: 20, 31, 24, etc.
Square of even numbers are even. Example: 2²= 4, 4²=16 etc.
Square of odd numbers are odd. Example: 5²= 25, 9²= 81, etc.
A number ending in an odd number of zeroes cannot be a perferct square. Example: 10, 1000, 900000, etc.
The difference of squares of two consecutive natural number is equal to their sum. (n + 1)²– n²= n+1+n. Example: 4²– 3²=4 + 3=7. 12²– 11²=12+11 =23, etc.
A triplet (m, n, p) of three natural numbers m, n and p is called Pythagorean
triplet, if m²+ n²= p²: 3²+ 4²= 25 = 5²
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Cubes And Cube Roots | Study
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Cube number: Number obtained when a number is multiplied by itself three times. 2³= 2 x 2 x 2 = 8, 3³= 3 x 3 x 3=27, etc.
Numbers like 1729, 4104, 13832, are known as Hardy – Ramanujan Numbers. They
can be expressed as sum of two cubes in two different ways.
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Numbers obtained when a number is multiplied by itself three times are known as cube numbers. For example 1, 8, 27, … etc.
If in the prime factorisation of any number each factor appears three times, then the
number is a perfect cube.
The symbol
denotes cube root. For example
Perfect Cube: A natural number is said to be a perfect cube if it is the cube of some natural number. Example: 8 is perfect cube, because there is a natural number 2 such that 8 = 2³, but 18 is not a perfect cube, because there is no natural number whose cube is 18.
The cube of a negative number is always negative.
Properties of Cube of Number:
Cubes of even number are even.
Cubes of odd numbers are odd.
The sum of the cubes of first n natural numbers is equal to the square of their sum.
Cubes of the numbers ending with the digits 0, 1, 4, 5, 6 and 9 end with digits 0, 1, 4, 5, 6 and 9 respectively.
Cube of the number ending in 2 ends in 8 and cube of the number ending in 8 ends in 2.
Cube of the number ending in 3 ends in 7 and cube of the number ending in 7
ends in 3.
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November 5, 2023

S No.	Quadrilateral	Property	Image
1.	Kite	a. No Parallel Sides b. Two pairs of adjacent sides are equal.
2.	Trapezium	One pair of opposite sides is parallel.
3.	Parallelogram	Both pairs of opposite sides are parallel.
3.	Rectangle	a. Both the pair of opposite sides are parallel. b. Opposite sides are equal.c. All the four angles are 90°.
4.	Square	a. All four sides are equal. b. Opposite sides are parallel. c. All the four angles are 90°.
5.	Rhombus	a. All four sides are equal. b. Opposite sides are parallel. c. Opposite angles are equal.d. Diagonals intersect each other at the centre and at 90°.

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