Dwarf planets are heavenly bodies that are too small to be considered a planet but too large to fall under smaller categories. The International Astronomical Unit defines a planet as something that obeys the following criteria:

1. To be in orbit around the Sun
2. Has enough gravity to pull its own mass into a round shape
3. Has cleared its orbit of smaller objects

• Equation For Position - Velocity Relation:

From the velocity-time graph, the distance s travelled by the object in time t, moving under uniform acceleration a is given by the area enclosed within the trapezium OABC under the graph. That is,

s = area of the trapezium OABC = (OA + BC) X OC/2

Substituting OA = u, BC = v and OC = t,

We get

s= (u+v) t/2

From the velocity-time relation

We get

t= v - u/a

We have

s = (v + u) x (v – u)/2a

or 2as = v² – u²

Grandmother was an old and short lady. Her face was covered with wrinkles. She always wears white dress and take beads of rosary in her hands. She was a polite and kind lady. She was a very religious woman. When narrator live with her in village. She always feed dogs with stale chapattis. But after coming in city she was unable to feed dogs with chapattis. Because in city there are no dogs.

Also she cannot help the narrator in her studies because she don't know about science and English. She was sad to hear that there was no teaching about God and scriptures in narrator's school. She also think that music was not meant for gentle folk.

But when narrator went to abroad for his further studies. She felt very sad. Now, she spent most of her time by spinning at the wheel and praying. She feed the sparrows in her spare time. When she feed the sparrows they sat on her head, hand etc. and start chapping like they are talking with her.

When the narrator came from the abroad. She felt happy and collect all the women of her neighborhood and start singing the homecoming of warriors. Due to overwork, she developed fever. She told her family members that her end was near. But the doctor said she would recover soon. She don't spend time with her family members, instead she continued praying; till she breathed her last.

The production possibilities curve (PPC) is a graph that shows all of the different combinations of output that can be produced given current resources and technology. Sometimes called the production possibilities frontier (PPF), the PPC illustrates scarcity and tradeoffs.  The PPF is extremely important in describing a range of economic phenomena. The PPF can be used to explain the concept of opportunity cost: Rather than measuring costs in dollars which are rather arbitrary (and change with inflation), we can measure the cost of producing one good in terms of not producing other goods.

Mass spectrometry is an analytical method to find the molecular mass of a compound and indirectly helped to prove the identity of isotopes.
A mass spectrometer generates multiple ions from the sample being investigated, then separates them by their specific mass-to-charge ratio (m/z) and then records the relative abundance of each type of ion.

The first law has already given us a qualitative definition of force. Now we are interested in finding out its magnitude. According to Newton’s second law of motion, the net force experienced by a body is directly proportional to the rate of change of momentum of the body. It can be written as:

f ∝ dP/dt
⇒f ∝ (mv−mu)/t
⇒f∝m(v−u)/t
⇒f∝ma
⇒f=kma
Where k is the constant of proportionality and it comes out to be 1 when the values are taken in SI unit. Hence the final expression will be,

F = ma

limits is bascially tending certain value to an impossible value, i use the word tending as it is not practically achievable but theoritically is. for eg. Velocity is. A limit tells us the value that a function approaches as that function's inputs get closer and closer to some number. The idea of a limit is the basis of all calculus.

The earliest hunter-gatherers in southern Africa were the San people. Hunter-gatherer societies hunt, fish and gather wild plants to survive. They also move around from place to place, following a nomadic way of life. A hunter-gatherer is a human living in a society in which most or all food is obtained by foraging (collecting wild plants and pursuing wild animals). Following the invention of agriculture, hunter-gatherers who did not change have been displaced or conquered by farming or pastoralist groups in most parts of the world.

Motion:-A body is said be in a state of motion if it changes its position continuously with respect to its surroundings with the passage of time.
E.g A bus running on a road, a flying bird etc

Rest:- A body is said to be at rest if it does not changes its position continuously with respect to its surroundings with the passage of time.
Eg A book lying on a table.

Amino acids are molecules used to build proteins. All amino acids have a central carbon atom surrounded by a hydrogen atom, a carboxyl group (COOH), an amino group (NH2), and an R-group. An amino acid is a carboxylic acid-containing an aliphatic primary amino group in the α position to the carboxyl group and with a characteristic stereochemistry. Proteins are biosynthesized from 20 amino acids in a system involving strict genetic control. Thus, amino acids are the basic unit of proteins. The general linear formula of an amino acid is R-CH(NH2)-COOH. The 20 common amino acids are grouped in classes according to their side chains: Click here for IMGT classes of the 20 common amino acids 'Physicochemical' properties. Twenty Amino acids can be grouped according to the characteristics of the side chains as follows: Aliphatic – alanine, glycine, isoleucine, leucine, proline, valine. Aromatic – phenylalanine, tryptophan, tyrosine. Acidic – aspartic acid, glutamic acid.

Entity: Entity means a reality that has a definite individual existence.

Business entity: It means a specifically identifiable business enterprise like Super Bazaar, Hira Jewellers, ITC Limited, etc. An accounting system is always devised for a specific business entity (also called accounting entity).