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1. Explain in brief why birds that walk on the leaves floating on the surface of water have wide feet.

Answer:

Birds that walk on leaves floating on the surface of the water have wide feet. This is because wide feet increase the area of contact with the leaves. So, they exert less pressure on the leaves, allowing them to walk on these leaves.

1. Explain why the wall of a dam is made thicker at the bottom.
   Answer:
   The wall of a dam is made thicker at the bottom because of the following reasons:
   a. A dam has a massive weight and thus, applies a large force on the ground. In order to reduce the pressure exerted by it on the ground, its area of contact with the ground is increased by making its base broad. So, a broad base supports the weight of the dam.

1. Moreover, the pressure of water increases with depth. So, it is greater at the base than at the top. So, the base is broad to withstand the huge pressure of the water.

1. When the nozzle of a syringe is dipped in a liquid and its piston is withdrawn, the liquid pushes up into the syringe. Give a reason.

Answer:

When the nozzle of a syringe Is dipped in a liquid and its piston is withdrawn, a region of low pressure is created in the syringe. The atmospheric pressure acting on the surface of the liquid is greater and hence forces the liquid to rise in the syringe.

1. Why do the pillars of a bridge have a broader base than the top?

Answer:

Pillars of a bridge have a broader base than the top. This is done to reduce the pressure exerted on the ground by the enormous weight of the bridge. As pressure is inversely proportional to the area of contact, so if the base is broader, the area of the contact increases, reducing the pressure on the ground due to the weight of the bridge.

1. Where is the pressure of the sea water greater : 5 m below the surface of the sea or 10 m below the surface of the sea? Why?

Answer:

Pressure is greater at 10 m below the surface of the sea as compared to that at 5 m below the surface of the sea. This is because pressure exerted by a liquid increases with depth.

1. Why is water not used as a barometric liquid?

Answer:

Water is not used as a barometric fluid as it has less density due to which it will have to rise to a height of 10.5 m to balance the atmospheric pressure. Moreover, it vaporizes in vacuum and thus, never records the true atmospheric pressure.

1. Two women are of the same weight. One of them wears sandals with pointed heels, while the other woman wears sandals with flat soles. Which one of them would feel more comfortable while walking on a sandy beach? Also, give reasons for your answer.

Answer:

Although both women’s heights are the same, they also carry the same weight when they walk. But the woman wearing the sandal with flat heels will be more comfortable than the woman wearing sandals with pointed heels while walking on a sandy beach. This is because the flat soles have a larger surface area as compared to sandals with pointed heels. Also, the pressure exerted by the woman with pointed heels will be greater as compared to that of the woman wearing sandals with flat soles. This increased pressure will make walking on sand in sandals with pointed soles difficult.

1. Why do safety pins and drawing pins have narrow and sharp tips?

Answer:

Safety pins and drawing pins have narrow and sharp tips because the smaller surface area of the tip causes a high pressure and, therefore, makes it easier for these objects to pierce through a given material.

1. The hand flour grinder ¡s provided with a handle near its rim. Give reasons why.

Answer:

The hand flour grinder is provided with a handle near its rim to increase the moment arm so that even a small force applied can produce a large turning effect.

1. How are force, area and pressure related to each other?

Answer:

Force, area and pressure are related by the following expression.

If the force applied is doubled for the same area, then the pressure will also double.

1. Why is it easier to walk on soft sand if we have flat shoes rather than shoes with sharp heels (or pencil heels)?

Answer:

A flat shoe has a greater area in contact with the soft sand and exerts less pressure on the soft ground. Due to this the ‘flat’ shoes do not sink much in soft sand and it is easy to walk on it. On the other hand, a sharp heel has a small area in contact with the soft sand and exerts a greater pressure on the sand. Due to this, the sharp heels sink deep into soft sand making it difficult for the wearer to walk on it.

1. We know that there is a huge amount of atmospheric pressure on us. But we do not experience its effect why?

Answer:

The pressure of air inside our body is the same as that of the atmosphere. Therefore, we do not experience its effect.

1. Why do sea divers wear specially designed suits?

Answer:

Since the pressure of liquid increases with the increasing depth of sea. Specially designed suits protect scuba divers from the huge pressure of the water underneath.

1. An archer shoots an arrow in the air horizontally. However, after moving some distance, the arrow falls to the ground. Name the initial force that sets the arrow in motion. Explain why the arrow ultimately falls down.

Answer:

The initial force is muscular force which sets the arrow in motion. The force of gravity that acts on the arrow in the downward direction brings it to the ground.

1. Two rods: A and B, having same weight and equal length have different thickness. Rod A is thinner while Rod B is thicker. They are held vertically on the surface of sand. Which one of them will sink more? Why?

Answer:

Rod A will go deeper as it has a smaller area of contact, therefore the same force produces more pressure. In case of rod B the same force produces less pressure.

1. It is difficult to cut cloth using a pair of scissors with blunt blades. Explain.

Answer:

Blunt blades have a larger area compared to the sharp-edged blades. Thus, the applied force produces a lower pressure in case of blunt blades, which makes it difficult to cut the cloth.

1. Observe the figures given below carefully.

Volume of water in each vessel is shown above. Arrange them in order of decreasing pressure at the base of each vessel. Explain the reason.

Answer:

Pressure of a liquid column depends upon the height of the liquid column and not on volume of the liquid. Decreasing order of pressure at the base of each vessel is B > D > A > C.

1. On Lokesh’s birthday Shreya was given charge to amuse children with some little tricks. Shreya stuck balloons to the wall by just rubbing them in her clothes. She bent the water stream from a tap without touching it. She did so by bringing a big balloon near the flowing water. All the children were very happy to see this little magic. Everybody praised Shreya.

How do balloons stick to walls?

How Shreya bent the water stream by bringing a big balloon near it and without touching it?

What values of Shreya are shown here?

Answer:

On rubbing the balloon with hair or clothes, it acquires negative charges. The negative charges are attracted to the positive charges on the wall and balloon sticks to the wall.

Negative charge on the balloon attracts positive charge on water molecules. Thus, bent the water molecules.

Shreya is dutiful, friendly with scientific aptitude.

1. Explain why, snow shoes stop you from sinking into snow.

Answer: The snow shoes have large, flat soles so they exert less on the soft snow and stop the wearer from sinking into it.

1. What happens to the springs fixed to the seat of a bicycle when we sit on it?

Answer: When we sit on the seat of a bicycle, the force exerted by the body weight compresses the spring and changes its shape.

1. Why do balloons expand when filled with air?
   Or
   Why does the balloon get inflated?
   Or
   What makes a balloon get inflated when air is filled in it?

Answer: Air exerts pressure on the inner walls of the balloon causing it to expand and get inflated.

1. Explain why, a wide steel belt is provided over the wheels of an army tank.

Answer: The wide belts increase the area and reduce the pressure. This avoids sinking of the tank into the ground.

1. Why do the shape and size of balloon change when filled with air or water?

Answer: The high pressure produced by the gas or water molecules on the walls of the balloon causes it to expand and get inflated.

1. Why does water come out more slowly from an upstairs tap than from a similar tap downstairs?

Answer: This is so because water pressure is less in the upstairs tap due to lesser depth.

1. Why are we not crushed by atmospheric pressure?
   Or
   If the pressure due to the atmosphere is so great, then why are we not crushed by it?

Answer: We do not get crushed because the atmospheric pressure acting on our body from outside is balanced by the blood pressure acting from inside.

1. Why does a sharp knife cut better than a blunt knife?

Ans. Lesser the area, larger the pressure for the same force applied. Therefore, it is easier to cut with sharp knives than blunt ones, with same force.

1. Why do the tools meant for cutting and piercing always have sharp edges?

Answer: The cutting edges of tools like blades, knives etc., are provided with sharp edges to cut the things easily because the smaller the area, larger the pressure on a surface for the same force.

1. Explain why, the tip of a sewing needle is sharp.

Answer: The tip of the sewing needle is sharp so that due to its sharp tip, the needle may put the force on a very small area of the cloth, producing a large pressure sufficient to pierce the cloth being stitched.

1. Explain why, porters place a thick, round piece of cloth on their heads when they have to carry heavy loads.

Answer: By this they increase the area of contact of the load with their head. So, the pressure on their head is reduced and they find it easier to carry the load.

1. Explain now why shoulder bags are provided with broad straps and not thin straps?
   Or
   Why are the straps of school bags made broader?
   Or
   Why is it more comfortable to lift a school bag with broad straps than thin straps?

Answer: Shoulder bags are provided with broad straps and not thin strap so that the weight of the bag may fall over a large area of the shoulder of the child producing less pressure on the shoulder.

1. A rocket has been fired upwards to launch a satellite in its orbit. Name the two forces acting on the rocket immediately after leaving the launching pad.

Answer: The two forces acting on the rocket are the force of gravity, which pulls the rocket towards the ground, and the force of friction due to earth’s atmosphere, which opposes its motion.

1. Why a fountain of water is created at the leaking joints or holes of pipes of the main water supply line?

Answer: Many times we see a fountain of water rushing out of the leaking joints (or holes) in the pipes of main water supply line. It is due to the very high pressure exerted by water on the sides (or walls) of the pipes that such a fountain of water is formed.

1. Why does the liquid rise in a syringe when its piston is pulled up?
   Or
   How does a liquid medicine enter a syringe?

Answer: When the nozzle of a syringe is dipped in a liquid and its piston is withdrawn, the pressure inside the syringe is lowered. The greater atmospheric pressure acting on the surface of the liquid pushes the liquid up into the syringe.

1. Why does nose bleeding occur at high altitudes?
   Or
   Why do mountaineers suffer from nose bleeding at high altitudes?

Answer: At high altitudes, the atmospheric pressure becomes much less than our blood pressure. Since, our blood is at higher pressure than outside pressure, therefore, some of the blood vessels in our body burst and nose bleeding takes place at high altitudes.

1. Name the forces acting on a plastic bucket containing water held above ground level in your hand. Discuss why the forces acting on the bucket do not bring a change in its state of motion.

Answer: In this case, muscular force is acting in upward direction and the force of gravity is acting in downward direction. The two forces are equal in magnitude but opposite in direction. Therefore, the net force on the bucket is zero. Hence, there is no change in its state of motion.

1. Why atmospheric pressure decreases as we go higher up above the earth’s surface?

Answer: The pressure at any level in the atmosphere may be interpreted as the total weight of the air above a unit area at any elevation. Since most of the atmosphere’s molecules are held close to the earth’s surface by the force of gravity, air pressure decreases as we go higher up above the earth’s surface.

1. Why does a plastic comb rubbed with dry hair attract tiny pieces of paper?

Answer: When a plastic comb is rubbed in dry hair, the comb gets electric charges by friction. And when this electrically charged comb is brought near tiny pieces of paper, it exerts an electrostatic force of attraction on them. Due to this electrostatic force, the tiny pieces of paper move towards the comb and stick to it.

1. If the area of my head were 10 cm × 10 cm, how much weight of air would I be carrying on my head? Why don’t we feel the weight of such a huge amount of air on us?

Answer: The weight of air in a column of the height of the atmosphere and area 10 cm × 10 cm is as large as 1000 kg. The reason we are not crushed under this weight is that the pressure inside our bodies is also equal to the atmospheric pressure and cancels the pressure from outside.

1. If a vacuum is created between two Magdeburg hemispheres joined together, they cannot be separated easily. Give reason.
   Or
   Why do Magdeburg hemispheres stick together?

Answer: This is due to the fact that since there is no air inside, the unopposed atmospheric pressure acting over the whole surface of the hemispheres from outside presses them very, very hard and does not allow them to be separated.

1. Explain why, when a person stands on a cushion, the depression is much more than when he lies down on it.

Answer: When a man stands on a cushion then only his two feet are in contact with the cushion. Due to this, the weight of man falls on a small area of cushion producing a large pressure. This large pressure causes a big depression in the cushion. On the other hand, when the same man is lying on the cushion, then his whole body is in contact with the cushion. In this case, the weight of man falls on a much larger area of the cushion producing much smaller pressure. And this smaller pressure produces a very little depression in the cushion.

1. Some facts:
1. Skis have a large surface in order to reduce the pressure on snow.
2. Wooden sleepers are placed under railway tracks to reduce the pressure on the ground.
3. Pressure is directly proportional to the force applied.
4. If the force acting on an area is increased, pressure will increase.
5. The straps and handles of travel bags are made broad to reduce the pressure on our shoulders.
6. An object exerts a pressure of 2 Pa on the ground. If another object of the same weight is kept above it, then the net pressure will become 4 Pa.
7. The pressure exerted by a liquid at a given depth of the liquid same is in all directions.
8. If the height above the sea level increases, atmospheric pressure will decrease.
9. Army tanks are provided with caterpillar tracks under their wheels in order to decrease pressure on the ground.
10. School bags have broad straps to reduce the pressure on our shoulders.
11. Smaller the area on which a force acts, greater is the effect of force.
12. Pressure exerted on a surface depends upon thrust and area of contact.
13. If the thrust acting on a surface decreases, then the pressure decreases.
14. A long spanner is used to loosen a tight nut. This is because by increasing the length of the spanner, the moment arm gets increased and even a small force can produce a large turning effect.
15. The hand flour grinder is provided with a handle near its rim to increase the moment arm so that even a small force applied can produce a. large turning effect.
16. It is easier to open a door by applying the force at its handle than at the hinged end because the moment of force is large when the force is applied at the handle as the moment arm is larger as compared to when the force is applied at the hinged end.
17. Nose bleeding may occur at a high altitude because the atmospheric pressure decreases.

In my opinion, most of the students would have done great in maths in childhood (say 1st to 4th STD), not because they were studying well, it might be because the concepts were easy.

But what happens after that is slight shift in focus. It's not that they are bad now. It's just that now they start feeling the effect of weak basics. 

It all starts with LCM, HCF, Decimals and goes on to find x and y, solving equations. 

People who are good with this, can actually focus more on only concepts from here on, whereas the weak student has to focus on both concepts as well as the process to solve.

This gap in understanding continues and student with good basics scores good marks only studying 30minutes a day and a student with weak basics struggles to score average marks even after spending 2-3 hours.

This makes most of the students say, 'I hate Mathematics'

                      HEREDITY

Important concepts of Heredity:

There are different terms in this chapter that need to be understood well to get what exactly heredity is!

1. GENETICS; It is the branch of biology where you will study about genes , human genome, characteristics features and everything about the DNA.
2. HEREDITY: Heredity is nothing but gaining the characteristics features from the parent. It is the flow of genes in the generation that defines the similarity and differences.
3. MONOHYBRID CROSS: Crossing between organisms that have atleast one different character.
4. MONOHYBRID=> Phenotypic ratio = 3:1

             Genotypic ratio=> 1:2:1

• DIHYBRID CROSS: Crossing the organisms that have two different characters.
• Phenotypic ratio=> 9:3:3:1
• PRINCIPLES OF DOMINANCE; When there are two different characters with two different factors, there only the dominant characters are expressed over recessive character. 

LAWS OF HEREDITY: 

1. LAW OF SEGREGATION;  Only one form of character can be carried by a gamete in one factor.
2. LAW  OF INDEPENDENT ASSORTMENT; Gamet formation allows the factors to separately move and express.

• DNA: Francis and Crick in the year 1953 explained the double helix model of the DNA. Which is then studied further to understand the concept of genome.
• DNA Replication: The chromosomes are duplicated with equally distributing the genes this process is called DNA replication. It's an important life process responsible for formation of offspring.

SIGNIFICANCE OF DNA; 

• It Controls the cells directly or indirectly.
• Ensures it's equal distribution of genetic material to offsprings.
• ItRIt helps insin the RNA synthesis.
• DNAUDNA mutations and combinations which leads to change in the existing characters.

GENES: It carries genetic information to help in the making of protein.

VARIATION: Difference in characteristics or genetic information from parents to offsprings.

BIOTECHNOLOGY: The application of technological procedures on organisms  used to bring out the best from the existing creatures and modifying the lacking capacity.

RNA FINGERPRINTING Technology: It is the technology used for comparing the different DNA segments and analysing the result under gel electrophoresis.

GENETIC ENGINEERING: This is the technique used with the modern technology to bring out the desired change in the genome.

For example: To get the desired growth in plant species genetic engineering helps.

CLONING: Developing the clones in the laboratory that have similarities with the template. It is nothing but producing a copy of an original.

Willmut was successful scientist whonwho first cloned a sheep.

LIMITATIONS OF BIOTECHNOLOGY: 

• The seeds of the modified plants are sterile in nature, as they are grown with the lab techniques.
• It's a threat to original species of the plants.

• These plants are less likely live longer .
• The food we get from these plants is hazardous for the human beings.
• Ecology is disturbed by applying biotechnological processes.

*Fraction addition :

When denominator is not same

Question:

Solve: [(2/5)+(3/7)]

Ans:

Using the rule 

[(a/b)+(c/d)]

[(a×d)+(b×c)]/(b×d)

(ad+bc)/bd

By using this formula 

We can solve 

[(2/5)+(3/7)]

[(2×7)+(3×5)]/(5×7)

(14+15)/35

[(2/5)+(3/7)] = (29/35)

This is final answer.

Hi Mahima I wouldn't disclose my locality but I also live here and according to my experience it's upto the background of the family as well as their  the requirements from you.

If you are a beginner then start from 200/hr to 300/hr it would be easy for you to convert the parents.

You can also manipulate the fee but not less than +/- 50₹/hr.

Best wishes.

Are you scared of numerical? Do you think you don't understand them? If yes, then read ahead.

See, it might be any exam, but numerical won't leave your back.

So let's talk about common problems and their solutions:

Problem 1: Sir, I am not able to understand what the numerical is saying!

Solution: It's simple, read again, find the meaning of the word and see again and again for words you don't understand. It's a problem of vocabulary or non-understanding of concepts.

Let me give you an example:

Force is mass multiplied by acceleration. So if I want to ask you to find the force and frame it like "Find force when mass is 5kg, and acceleration is 8 m/s²", I don't think anybody would have a problem. Now the same question when I frame it like " Find the rate at which momentum changes for a 5kg body moving with a constant rate of 8 m/s²" is the same question why did you feel it to be difficult? Firstly, because you might not know that the rate of momentum is a force as per Newtons 2nd law, nowhere does it mention mass or acceleration, and you might not know its units. So we can't get hold of a numerical either if we don't understand the words that the paper setter is using or simply are not aware of the concept.

I'll tell you a fun fact. Many times teachers interpret questions differently. So it is okay, and eventually, you will get the hang of it.

Problem 2: I make a lot of silly mistakes.

Solution: Practice! Practice! Practice! And work on your focus because we have Netflix, amazon prime, IPL, Anime and many more things in our life to distract us. BTW I have learned how to balance, so if I can, you can too! Find your distractions work on them learn to focus.

Know what everyone does is eventually stop doing numerical, and they avoid practice which is quitting. Don't do that. Tell yourself you can do it, and humans make errors. Be happy the next time you make a mistake and make sure you work on it and never repeat it.

How to approach numerical?

1) Find the concept hidden like in the above example; the concept is of force.

2) Identify the formula or formulas related to the concept. (While practising, it is okay if you look at the formulas rather than memorizing). In the example, the formula is F =M x A.

3) Try to fit the given data in the formula and see how you can get the asked data. So in the above example, since M and A are given, it's a matter of just putting the values. But what if instead of A, they give you U, V and S. As I can see, these are variables from the kinematic equations, and if A is constant, I can use them and find A and hence F.

4) Remember Units. I can't emphasize enough on this enough. Sometimes units will give you a helping hand.

PRACTICE! PRACTICE! PRACTICE!

Expected Utility: Theorems
The theory of expected utility was developed by the founders of game theory, namely John von Neumann and Oskar Morgenstern, in their 1944 book Theory of Games and Economic Behavior.
In a rather unconventional way, we shall first (in this section) state the main result of the theory (which we split into two theorems) and then (in the following section) explain the assumptions (or axioms) behind that result. The reader who is not interested in understanding the conceptual foundations of expected utility theory, but wants to understand what the theory says and how it can be used, can study this section and skip the next. Let O be a set of basic outcomes. Note that a basic outcome need not be a sum of money: it could be the state of an individual’s health, or whether the individual under consideration receives an award, or whether it will rain on the day of her planned outdoor party, etc. Let L (O) be the set of simple lotteries (or probability distributions) over O. We will assume throughout that O is a finite set: O = {o1,o2,..., om} (m ≥ 1). Thus, an element of L (O) is of the form  o1 o2 ... om p1 p2 ... pm  with 0 ≤ pi ≤ 1, for all i = 1,2,...,m, and p1 + p2 +...+ pm = 1. We will use the symbol L (with or without subscript) to denote an element of L (O), that is, a simple lottery. Lotteries are used to represent situations of uncertainty.
For example, if m = 4 and the individual faces the lottery L =  o1 o2 o3 o4 2 5 0 1 5 2 5  , then she knows that, eventually, the outcome will be one and only one of o1,o2,o3,o4, but does not know which one; furthermore, she can quantify her uncertainty by assigning probabilities to these outcomes. We interpret these probabilities either as objectively obtained from relevant (past) data or as subjective estimates by the individual.
For example, an individual who is considering whether or not to insure her bicycle against theft for the following 12 months knows that there are two relevant basic outcomes: either the bicycle will be stolen, or it will not be stolen. Furthermore, she can look up data on past bicycle thefts in her area and use the proportion of stolen bicycles as an “objective” estimate of the probability that her bicycle will be stolen.
Alternatively, she can use a more subjective estimate: she might use a lower probability of theft than suggested by the data because she knows herself to be very conscientious and – unlike other people – always to lock her bicycle when left unattended.
The assignment of zero probability to a particular basic outcome is taken to be an expression of belief, not impossibility: the individual is confident that the outcome will not arise, but she cannot rule out that outcome on logical grounds or by appealing to the laws of nature.