Exponents rules


Exponents are shorthand for repeated multiplication of the same thing by itself. For instance, the shorthand for multiplying three copies of the number 5 is shown on the right-hand side of the “equals” sign in (5)(5)(5) = 53. The “exponent”, being 3 in this example, stands for however many times the value is being multiplied. The thing that’s being multiplied, being 5 in this example, is called the “base”.
This process of using exponents is called “raising to a power”, where the exponent is the “power”. The expression “53” is pronounced as “five, raised to the third power” or “five to the third”.




The Cell,(comes from Latin word cella,meaning “small room”) is the smallest unit of life. It is basic structural,functional, and biological unit of all living organisms.
Cell was discovered by Robert Hooke in 1665.
Cells are often called the “building blocks of life”.
All plants and animals are made of cells.
Organisms are classified as Unicellular (consisting of single cell,such as bacteria) and Multicellular (consisting of multiple cells,such as Plants and Animals).
Number of cells are varies from species to species.Human contains more than 10 trillion cells.
Most of cells are visible only under microscope.

Types of cells
There are two types of cells:
Prokaryotic cells: Single celled organisms.
Doesn’t contains Nucleus.
Eukaryotic cells: Single or multi cellular organisms.
Contains Nucleus.

Prokaryotic cells
The first form of life on Earth.
Prokaryotic cell is a unicellular organism lacking membrane bound organelles.
Most of prokaryotic cells are unicellular.They are generally small in size.
There Nucleur region is not well defined as they lack a Nucleus but it is known as Nucleoid.

Eukaryotic cells
Eukaryot are those organisms whose cells have a Nucleus and other organelles enclosed within membrane.
Eukaryotic organisms may be unicellular or multi-cellular and only Eukaryotes form multi-cellular organisms consists of many kinds of tissue made up of different types of cells.
They are generally larger in size.
Plants and animals cells are Eukaryotic cells.
Contains more than one chromosomes.


All cells posses DNA except for red blood cells.




A microprocessor is a computer processor which incorporates the functions of a computer’s central processing unit (CPU) on a single integrated circuit (IC), or at most a few integrated circuits.

The first use of the term “microprocessor” is attributed to Viatron Computer Systems describing the custom integrated circuit used in their System 21 small computer system announced in 1968. The microprocessor, also known as the Central Processing Unit (CPU), is the brain of all computers and many household and electronic devices.

The computer you are using to read this page uses a microprocessor to do its work. The microprocessor is the heart of any normal computer, whether it is a desktop machine, a server or a laptop. The microprocessor you are using might be a Pentium, a K6, a PowerPC, a Sparc or any of the many other brands and types of microprocessors, but they all do approximately the same thing in approximately the same way.


How Microprocessor work

A microprocessor executes a collection of machine instructions that tell the processor what to do. Based on the instructions, a microprocessor does three basic things:

A microprocessor can make decisions and jump to a new set of instructions based on those decisions.

2. Using its ALU (Arithmetic/Logic Unit), a microprocessor can perform mathematical operations like addition, subtraction, multiplication and division. Modern microprocessors contain complete floating point processors that can perform extremely sophisticated operations on large floating point numbers.

3.A microprocessor can move data from one memory location to another.

Crops and production (II)


Manure is an organic substance. Manure is made by decomposing organic matter like animal waste and plant residue.
To prepare manure, farmers dump animal wastes like cow dung and plant wastes like hay and leaves in pits at open places. These wastes are decomposed by micro-organisms and get converted into manure.


1. Manure makes the soil porous and increases the water holding capacity of soil
2. It improves the texture of the soil.
3. Manure increases the number of useful microbes in the soil. Hence it is considered better than fertilizers.


Fertilizers are inorganic salts made in factories.


1. Fertilizers are rich in a specific plant nutrient such as nitrogen, phosphorous or potassium
2. Fertilizers are more soluble in water and can be quickly absorbed by plants.


1.Excessive use of chemical fertilisers reduces soil fertility.
2. Fertilisers reduce porous nature of soil which leads to water logging.
3.When fertilisers are washed away by rain water, it leads to water pollution.

Advantages of Manure over fertilizers

When compared, organic manure is more desirable and effective than fertilisers. Because:
1. Manure increases the soil capacity allowing to hold it water in large quantity.
2. The interchange of gases becomes easy since manure has made the soil penetrable.
3. The number of friendly microorganisms are increased.
4. The smoothness of the soil has also been increased due to addition of manure.


IRRIGATION:-  is the method in which a controlled amount of water is supplied to plants at regular intervals for agriculture. It is used to assist in the growing of agricultural crops, maintenance of landscapes, and revegetation of disturbed soils in dry areas and during periods of inadequate rainfall. Additionally, irrigation also has a few other uses in crop production, which include protecting plants against frost,[1] suppressing weed growth in grain fields[2] and preventing soil consolidation.[3] In contrast, agriculture that relies only on direct rainfall is referred to as rain-fed or dry land farming


Traditional methods:-

irrigation often include pulley systems that are used to deliver water to soil, vegetation, flowers, and/or other forms of plant life. For many farmers who can’t afford expensive spray systems that are pre-timed for near-perfect results, lower-priced, traditional methods of irrigation, such as ra-hats, chain pumps, or lever systems (also known as Dhe Kli) can be very cost-effective. Here is a look at the most common methods of low-tech irrigation:

Pulley Systems

• Pulleys are used to carry buckets of water where they are needed. Much like clotheslines that use pulleys to move clothes nearer or further away, pulley systems for irrigation are designed to cut down on the amount of manual labour needed to take care of gardens or farmland. Since pulleys automate part of the process, they are a cheap and useful way to carry water to plants and soil. Pulleys must be installed aboveground – they may be tied to stakes that are buried in the earth – strong rope will hold the pulley-based irrigation system together.

Chain Pumps

• These ancient Chinese irrigation systems use round metal discs and a long loop of metal chain to water soil and plants. Each metal disc runs through a pool of liquid, and each disc collects some water during this process. When the chain is pulled, the metal disc rises up to the top, and the water held inside pours out, hydrating the earth and flora. This low-cost method of traditional irrigation has been practised for centuries.

Lever Systems

• Lever systems allow the user to control the speed of irrigation by choosing slow, medium or fast water flow; however, the lever system method is not as ancient, or inexpensive, as other methods mentioned here.

Traditional irrigation systems allow farmers or hobbyists to keep their plants and soil moist, which creates the right atmosphere for the growth of healthy plants.

MODERN METHODS of irrigation help save water. They are given below:

This system is more useful on uneven land, having fewer water supplies. In this method,water is supplied using pipes to one or more central locations within the field. When water is allowed to flow under high pressure with the help of a pump, it gets sprinkled on the crops.


In this system , water delivered at or near the roots of plants , drop by drop . This is the most efficient method of irrigation as there is no wastage of water at all. This method is important in areas where water availability is poor.

The Weed Problem

Weeds grow in gardens, whether we like it or not. They compete with plants and lawn grass for water and nutrients and they grow everywhere, making the garden less attractive. To solve this problem, they must be removed.
However, for various reasons, weeds often grow back. Here are some of the most common reasons:
• They were not removed completely and part of their roots stayed in the soil. The left-over roots allow them to grow again.
• The garden is surrounded by woods or non-landscaped areas that contain a lot of weeds, and their seeds get carried by wind or birds to residential yards.
• If they were not completely removed (all the weeds and all their roots), this makes it easier for them to return.
• They might reappear because the lawn is not dense enough and the empty spots invite weeds to settle down and spread.

Removing Weeds

Digging out plants: Plants with bulbs, tubers and corms must be completely removed from the soil by digging out. Often these plants will reproduce from broken off pieces.
• You will need to prepare the area by removing as much ground vegetation as possible (such as mulch or ground debris)
• Using a small trowel, dig a narrow channel next to the stem until you reach the main bulb, then dig the main bulb up.
• Check the soil for any adjoining or loose bulbets. These must also be removed with a substantial amount of soil and bagged.
• Follow up on a regular basis.


This technique is useful for weeds such as asparagus fern, which have their growing points below the surface of the soil. (corms, rhizomes or tufted fibrous root systems).
• Grasp the leaves or stems of the plant and hold them firmly so that the base of the plant is visible. Any weeds with sharp leaves or stems should be cut back first.
• Insert a knife close to the base of the plant at an angle, with the tip well under the root system.
• Cut through the roots close to the base of the plant. Make sure that the hard crown or base of the plant where the roots begin is completely removed. It may require several cuts.
• Hang the crowned plant matter up off the ground.
• Follow up on a regular basis.

Hand pulling:

This requires holding the plant stem as close as possible to the base of the plant. Gently tug the plant. This will loosen the soil and allow the plant to come free. The plant may be hung up off the ground or piled in a heap.
Winding up: This process is suitable for plants with surface or climbing runners such as Morning glory.
• You need to locate a runner, gently pull it along the ground towards you. Roll the runners up for easy removal. Continue doing this until all the runners have been rolled up. Small fibrous roots growing from the runners can be cut with a knife.
• You should locate the main root system whilst removing the runners. When you do, remove it manually.
• Do not leave any bits of stem or large roots, as these may reshoot.
• Bag or compost the runners/roots.
• Follow up on a regular basis.



is the process of gathering a ripe crop from the fields. Reaping is the cutting of grain or pulse for harvest, typically using a scythe, sickle, or reaper. On smaller farms with minimal mechanization, harvesting is the most labor-intensive activity of the growing season. On large mechanized farms, harvesting utilizes the most expensive and sophisticated farm machinery, such as the combine harvester. The term “harvesting” in general usage may include immediate postharvest handling, including cleaning, sorting, packing, and cooling.
• The completion of harvesting marks the end of the growing season, or the growing cycle for a particular crop, and the social importance of this event makes it the focus of seasonal celebrations such as harvest festivals, found in many religions


Food storage

allows food to be eaten for some time (typically weeks to months) after harvest rather than solely immediately. It is both a traditional domestic skill and, in the form of food logistics, an important industrial and commercial activity. Food preservation, storage, and transport, including timely delivery to consumers, are important to food security, especially for the majority of people throughout the world who rely on others to produce their food. Food is stored by almost every human society and by many animals. Storing of food has several main purposes:
• Storage of harvested and processed plant and animal food products for distribution to consumers

• Enabling a better balanced diet throughout the year
• Reducing kitchen waste by preserving unused or uneaten food for later use
• Preserving pantry food, such as spices or dry ingredients like rice and flour, for eventual use in cooking
• Preparedness for catastrophes, emergencies and periods of food scarcity or famine
• Religious reasons (Example: LDS Church leaders instruct church members to store food)
• Protection from animals or theft


Animal source foods

Animal source foods : include many food item that comes from an animal source such as meat, milk, eggs, cheese and yogurt. Many individuals do not consume or consume little by either personal choice or necessity as may not be accessible or available to these people.





Rational Numbers and its Properties

Q. What is Rational Number ?
Ans. A Rational Number is a real number that can be written as a simple fraction (i.e. as a ratio).
A rational number is a number that can be in the form p/q
where p and q are integers and q is not equal to zero.
So, a rational number can be:

Where q is not zero

Q. What are Positive rational numbers ?

Ans. A rational number is said to be positive if its numerator and denominator are either both positive integers or both negative integers.
In other words, a rational number is positive, if its numerator and denominator are of the same sign.

Q. What are Negative rational numbers ?

Ans. A rational number is said to be negative if its numerator and denominator are of opposite signs such that, one of them is positive integer and another one is a negative integer.
In other words, a rational number is negative, if its numerator and denominator are of the opposite signs.

Q. what is lowest term of a rational number ?

Ans. A rational expression has been reduced to lowest terms if all common factors from the numerator and denominator have been canceled.
Some solved example

1) Write in lowest form : i) 17 / 79 ii) -60 / 72
Solution : i) 17 / 79

As HCF of 17 and 79 is 1 so 17 / 79 is in the lowest form.

ii) -60 / 72

HCF of 60 and 72 is 12.

-60 ÷ 12 = – 5 and 72 ÷ 12 = 6.

∴ -60 / 72 = – 5 / 6.

Q. What is Standard form of a Rational Number ?

Ans. A rational number is in standard or simplest or lowest form when following two conditions are fulfilled:
• Numerator and denominator have only 1 as its highest common factor.
• Denominator is a positive integer.

Lets study some examples on this –

Example : Is rational number 6/7 is in standard form ?
Solution : This proceeds in the following ways:

First find the HCF of denominator and numerator i.e. 6 & 7 and we get:
HCF of 6 & 7 = 1

Since, Numerator and denominator have only 1 as its highest common factor; so as explained above first condition is fulfilled.

Now check second condition ?

Here we can see that denominator is 7, which is a positive integer. So this fulfills second condition also.

Now, since both the conditions are fulfilled, we can say that given rational number 6/7 is in standard form.

Q. What are Equivalent Rational Numbers ?

Ans. The equivalent rational numbers are numbers that have same value but are represented differently.
*The equivalent rational number defines the equivalence of fractions in math and the equivalent ratio for the numbers.

The ratios of the two numbers have equivalent ratio for the ratios of the other two numbers. Here, we are going to see about the equivalent forms of rational numbers for the two numbers.
Two rational numbers are said to be equivalent if we divide each decimal value will be the same



Ans. Among the positive rational numbers with the same denominator, the number with the greatest numerator is the largest. It is easy to compare the rational numbers with same denominators.
e.g. 2830 > 2630 > 2130 .

A negative rational number is to the left of zero whereas a positive rational number is to the right of zero on a number line. So, a positive rational number is always greater than a negative rational number.

To compare two negative rational numbers with the same denominator, their numerators are compared ignoring the minus sign. The number with the greatest numerator is the smallest.
e.g. – 710 < – 310 ; – 6 7 < – 4 7

To compare rational numbers with different denominators, they are converted into equivalent rational numbers with the same denominator, which is equal to the LCM of their denominators.

There are unlimited number of rational numbers between two rational numbers. To find a rational number between the given rational numbers, they are converted to rational numbers with same denominators


Rational numbers are terminating or recurring decimal numbers written in the form of fraction p/q In which ‘p’ and ‘q’ are integers and the denominator ‘q’ not equal to zero.

Let a,b,c be three rational numbers and the properties of rational numbers are given below:

Rational numbers are commutative and associative under addition and multiplication.

Commutative law:
a + b = b + a
a x b = b x a

Associative law:
a + (b + c) = (a + b) + c
a x (b x c) = (a x b) x c

Rational numbers holds true for closure law under addition, subtraction and multiplication.
a + b = a rational number
a – b = a rational number
a x b = a rational number
a/b = not a rational number

Rational numbers have an additive identity of 0 and multiplicative identity of 1.
a + 0 = a
a x 1 = a

Rational numbers holds true for distributive property also.
a + (b x c) = (a + b) x (a + c)
(a + b) x c = (a x c) + (b x c)



Tyndall effect

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Tyndall effect

The Tyndall effect, also known as Willis-Tyndall scattering, is light scattering by particles in a colloid in a very fine suspension. It is named after the 19th-century physicist John Tindall.


The Tyndall effect is the scattering of light as a light beam passes through a colloid. The individual suspension particles scatter and reflect light, making the beam visible.


Tyndall Effect Examples

1.The Tyndall effect is used in commercial and lab settings to determine particle size of aerosols.

2.Shining a flashlight beam into a glass of milk.                           

3.The visible beam of headlights in fog is caused by the Tyndall effect. The water droplets scatter the light, making the headlight beams visible.

Note: The blue color of the sky results from light scattering, but this is called Rayleigh scattering and not the Tyndall effect because the particles involved are molecules in air, which are smaller than particles in a colloid.



What Is a Solution?

A solution is a type of homogeneous mixture that is made up of two or more substances.

Two main parts of a solution are:

1.Solute: this is the part that is dissolved.

example: salt water, the solute is the salt.

2.Solvent: This is the part where the solute is dissolved.

example: salt water, the solvent is water.


Crops and its type

A crop is “a plant or animal or plant or animal product that can be grown and harvested extensively for profit or subsistence. Crop may refer either to the harvested parts or to the harvest in a more refined state (husked, shelled, etc.). Most crops are cultivated in agriculture or aquaculture.

Types of crops

1 Kharif
2 Rabi
3. Zaid


1. The kharif crops are associated with the monsoon season. They are sown in the month of June and July and harvested in autumn months i.e.in September and October
2. Important kharif crops are rice, jowar,maize,cotton,ragi,bajra,sugarcane and jute


1. The rabi crops are sown in the period between October and December and harvested in April and May .
2. Important Rabi crops are wheat,peas,pulses,mustard and rapeseed.


1. Zaid crops are sown in the summer season .
2. Important zaid crops are rice , maize , sunflower and groundnut.


Various tasks; which a farmer needs to do during cultivation of crops are collectively called agricultural practices. Activities which are part of agricultural practices are as follows:
i. Preparation of soil
ii. Sowing
iii. Adding manure and fertilizer
iv. Irrigation
v. Protecting from weeds
vi. Harvesting
vii. Storage

Preparation of Soil

The first step of cultivation is preparation of soil. This is done by loosening and turning the soil. A plough is used for this purpose. If the soil becomes too hard then farmer may resort to watering the soil before ploughing.
Traditionally, animal-drawn ploughs have been used by farmers. Now-a-days, tractor-drawn ploughs are used for this purpose. A tractor helps in saving time and labour.
The soil may contain many big lumps even after ploughing. The lumps are broken with the help of a hoe. Sometimes the farmer may add manure before ploughing; in order to properly mix the manure with soil.
Significance of Ploughing:
• Loosening the soil allows the roots to penetrate deep into the soil.
• It allows the root tips to breathe easily when they go deep into the soil.
• Nutrients from humus get properly mixed into the soil.
• It brings nutrients and minerals to the top and thus plants are able to utilize these minerals in a better way.

Tilling or ploughing

1. Tilling or ploughing allows the roots not only to penetrate deep inside the soil but also to breathe easily even deep inside the soil because loosened soil has enough space in which air is trapped.

2. It also increases the water retaining capacity of the soil.

3. It also helps the growth of the earth worms and microbes which further turn and loosen the soil and add humus.

4. It gives a good texture to the soil and allows more air to circulate through the soil by increasing the air space

5. The nutrients present in the dead plants and animals are released back into soil by decomposition by these soil organisms and are again absorbed by plants.

6. As only a few centimeters of the top soil support plant growth, turning and loosening of the soil brings the nutrient-rich soil to the top so that plants can use these nutrients.
7. The manure gets mixed properly with the soil.

The big pieces of soil called crumbs are required to be broken with the help of plank. This process is called pulverization. Then the soil is leveled with the help of leveler and made ready for sowing. Hence, preparation of soil plays a great role for cultivation. The yield becomes less if the preparation of soil is not proper. So there is a great need of good preparation of soil as “well begun is half done”.


A. Sowing is the most important part of cultivation. Before sowing, selection of clean and healthy high-breed or high yield seeds is important. Healthy seeds are separated from damaged seeds by floatation method. The healthy seeds which sink in water are separated from the damaged ones which float on water. The separated healthy seeds are then treated with fungicides. Then they are sown uniformly at proper distances and depths. An appropriate distance between the seeds is important to avoid overcrowding of plants. It allows plants to get sufficient sunlight, nutrients and water from the soil otherwise there will be a competition among the seedlings for space, water, nutrients and sunlight. Sometimes a few plants have to be removed to prevent overcrowding. Hence, now-a-days traditional sowing tools are replaced with seed drills which sow the seeds uniformly at proper distances and depths. After sowing, the seeds need to be covered by the soil to prevent damage caused by the birds.

Some of the methods of sowing are:

a) Broadcasting: This is traditional method of sowing seeds. In this method, the seeds are thrown (scattered) with force in a particular direction by hand.

b) Drilling: In this method seeds are sown uniformly at proper distances and depths with the help of a machine called Seed Drill.

c) Planting: Generally, crops which need a wide spacing and whose seeds are big are sown manually. This method is called planting. Maize, Kidney beans, potato, sugar cane are sown in this method.

d) Transplantation: The process of removing the seedlings from the nursery bed and planting them in the field is called transplantation. The seedlings which have healthy leaves are transplanted.