PREFACEWhat is Knowledge Bytes ?Knowledge Bytes is a collection of riddles, intersting facts, mnemonics, and puzzles that will make your learning fun and engaging.We want you to be delighted about studying. Knowledge Bytes helps you to know more about the subject in a fun, motivating and educational way and helps to implement what you learn in a creative way.

Benefits

Leads to Increased comprehension

EXPLOREEXPLORE1. Puzzle 12. MEANS AM, GM & HM 33. Facts on Electricity 64. Myths About Electricity 75. Compositions of Various Alloys 86. Control and Coordination 127. Brainstormer 16

Saves Time

Develops Learning Skills

Stimulates Interest

Cheat code:

Here, a1 = 16, a2 = 50, a3 = 84

Second 1 2 3 4 5 6 Total height

Height 16 50 84 – – – –

Cheat code:

Adding 5 minutes to the daily jogging time creates the sequence10, 15, 20 minutes ......

Day No. 1 2 3 – – n

Minutes of 10 15 20 – – 90 jogging each day

After knee transplantation, Arun’s doctor told him to return to his jogging program gradually. He suggested jogging for 10 minutes on first day. Thereafter, he suggested to increase jogging time by 5 minutes per day.

In how many days jogging time will become 90 minutes?

1

Puzzle

Rohan visits the Grand Canyon and drop a coin from the edge of a cliff. The depth of the coin falling in 1st, 2nd, 3rd seconds and so on is 16 feet, 50 feet, 84 feet and so on respectively. What is the total depth the coin would fall in total 6 seconds?

(in 6 sec)

10, 15, 20 ......

This sequence is arithmetic progression.

[where, a1 is the first term and d is the common difference]

⇒

⇒

∴

an = 10 + (n – 1)5

90 = 10 + (n – 1)5

n = 17 days

an = a1 + (n – 1)d

This forms an A.P.

a1 = 16, a2 = 50, a3 = 84

[where, a1 is the first term and d is the common difference]

d = a2 – a1 = (50 – 16) = 34

a6 = 16 + (n – 1)34

a6 = 16 + (6 – 1)34

a6 = 186

S6 = 606 feet

⇒

⇒

Now, Sn = (a1 + an)

an = a1 + (n – 1)d

n2

S6 = (16 + 186)62

Solutions

2

1.

2.

3

MEANS AM, GM & HM

Let a1, a2, a3...., an are group of values, then arithmetic mean is given by the formula.

Let a1, a2, a3...., an are values of the set, then geometric mean is given by the formula.

1A.M . (x) = ai

i=1n

n1 2 3 nGM= a × a × a ....a

( )1 2 3 na × a × a ....a=

∑

Arithmetic Mean (AM)

Geometric Mean (GM)

Geometric mean is defined as the nth root of product of ‘n’ valuesof the set.

1n

n

The arithmetic mean is the sum of all the values of the set divided by the quantity of numbers in the set. It is commonly referred as average.

1 2 na + a + ... + a=

nA.M .

GM =

1n ∏

n

i=1ai

4

1 2 3 n

nHM= 1 1 1 1+ + +...+a a a a

Let a1, a2, a3...., an be the values, the Harmonic Mean is given by

It is defined as the number of values divided by the sum of the reciprocal of the values of the set

Harmonic Mean (HM)

MEANS AM, GM & HM

HM=∑

n

i=1

n1ai

5

What is the relationship between AM, GM & HM?

Let us consider two positive values ‘a’ and ‘b’

2H.M= 1 1+a b

⇒a + bA.M= 2(A.M) = a + b ...(4)

2

⇒ 2G.M= ab (G.M) = ab ...(5)

( )

⇒

⇒

⇒

2 1 1 2H.M= + =1 1 a b H.M+a b

b + a 2=ab H.M

a + b2 = ...(6)H.M ab

( )( )2

2 A.M2 =H.M G.M

a + bA.M=2

G.M= ab

...(1) (Arithmetic Mean)

...(2) (Geometric Mean)

...(3) (Harmonic Mean)

Squaring on both sides

using equation (4) and (5)⇒

⇒

∴ G2 = AH

(G.M)2 = A.M × H.M

6

Electricity

A spark of static electricity can measure upto 3000 volts.

Thomas Edison built the first power plant, and in 1882 his pearl street power station in New York sent electricity to 85 buildings.

1.

2.

Sun radiates more energy in 15 minutes than 1 year of global human energy consumption.

3.

A single bolt of lightning can contain upto 30,00,000 volt thats enough electricity to serve over 200000 homes.

4.

Electricity causes muscle cells in your heart to contract. Electrocardiogram (ECG) machines measure the electricity going through heart.

5.

CURRENT EFFECT

1 mA Barely noticeable

16 mA Maximum amps before you can’t let go

20 mA Paralysis of respiratory muscles

Ventricular fibrillation starts100 mA

2 Amps Cardiac standstill and organ damage

Effect of current on human body (For 50/60 Hz AC)

Facts

7

Myths About Electricity

Power lines are insulated 90 percent of power lines are not insulated that means they are never safe to touch.

The wire is safe because it is not high voltage Actually voltage is not what will kill you, amperage will. It takes 1amp to cause total heart irregularities.

1.

2.

A fallen wire will shut offIt could still be live, even if it does not produce spark so stay away.

3.

Wood is not a conductorWood is not just a poor conductor, but wet wood is much better conductor of electric current.

4.

Rubber gloves and rubber shoes insulate Only if 100% pure rubber. If not, do not expect them to protect you from a potential electrocution.

5.

8

Don’t worry!!!Check the sorted table

on next page.

Do you find it confusing to learn the compositions

of various alloys?

Compositions of Various Alloys

9

Element Alloy Composition

Brass

Bronze

Bell metal

German silver

Cu

Cu

Cu

Cu

Sn

Sn

Zn

Zn Ni

Copper (Cu) Gun Metal Cu Sn Zn

Different types of alloys are prepared by changing the component elements and also by varying the proportion

of the component elements.

10

Element Alloy Composition

Steel

Stainless steel

Duralumin/Duralium

Magnalium

Fe

Fe

Al

Al

Mg

Mg

Cr

Mn Cu

CIron (Fe)

Aluminium (Al)

Alnico Fe Co Ni Al

Ni

Different types of alloys are prepared by changing the component elements and also by varying the proportion

of the component elements.

11

Different types of alloys are prepared by changing the component elements and also by varying the proportion

of the component elements.

Chromium

Element Alloy Composition

Type metal

SolderChrome-vanadium

Nichrome

Pb

Pb

Cr

Ni

Sn

Sn

V

Cr

Sb

Fe + C

Lead(Pb)

Chromium(Cr)

Nickel(Ni)

12

Auxins as weedicides

Scientific Contribution

Control and Coordination

Some synthetic auxins are used as weedicides (chemicals used to kill unwanted plants growing along with the crops). Example, 2, 4-dichlorophenoxyacetic acid (2, 4-D) is used to remove broad leaved weeds or dicotyledonous weeds in cereal crops or monocotyledonous plants.

Skoog and Miller et al. discovered the first cytokinin from degraded product of autoclaved herring sperm DNA which had a powerful cytokinesis (division of cytoplasm) promoting effect. It is called kinetin. It is a synthetic product and does not occur naturally in plants.

13

Abscisic Acid as Antitranspirant

Scientific Contribution

Control and Coordination

Application of minute quantity of abscisic acid to leaves reduces transpiration to a great extent through partial closure of stomata. Thus, it conserves water and reduces the requirement of irrigation.

Herbert Henry Cousins discovered and confirmed that ripe oranges emitted a volatile substance that brought about early ripening of unripe bananas kept nearby. Later on, this volatile substance was identified as ethylene.

14

AC Gives A cooling Effect

Auxin1 Cytokinin2 Gibberellin3

Abscisic acid4 Ethylene5

Ans. Auxin

HINT: Its concentration is highest at the top of the plant and decreases as you get closer to the roots, this controls the overall shape of the plant and helps keep the primary stem of a plant the leader.

Can you say which is the only plant hormone that istransported in one direction in a plant – downward, that is from the top to the bottom, like a one-wayroad from the stem tip to the roots?

5 PhytohormonesMNEMONIC

15

Fact

You know how a farmer and a businessman makes profit out of stem of a plant?Longer stems would mean more profit, but how? Gibberellins sprayed on sugarcane elongate the stem between the nodes. Longer stems mean more stored sugar. More sugar to sell means more coin.

Fact Tomato farmers noticed something weird happening with their crops. Earlier many farmers used kerosene heaters in their greenhouses to warm the air so that they could grow tomatoes during the winter. With the advent of electricity, some farmers switched to new, fancy electric heaters but they soon found that their tomatoes were not ready to be picked at the same time as it used to be earlier; when the greenhouses were warmed with kerosene heaters.The burning of the kerosene in the heaters produce a molecule similar to ethylene that synchronized the ripening of thetomatoes.

Auxin = Cytokinin Normal cell division occurs Auxin > Cytokinin Root formation

Auxin < Cytokinin Shoot formation

Remember how some hormones work together to affect plants?

Brainstormer

16

Finally, at the break of the dawn, from the cells that remained

open, the jailor must have locked 8 cells as per the rule. How many

prisoners do you think got a chance to escape?

One day, in Citadel prison, an astute jailor played a game with the 80 locked-up inmates in the cells numbered 1 to 80. He announced that he is going to give an opportunity to all the prisoners to escape from the prison if they play a game. In the game, he will give them directions to lock/ unlock a few cells. During the process of locking, the inmate of the cell must be present inside. At the end of the game, some cells may remain open from which he is going to lock only 8 cells of the prison. Once he has locked 8 cells, then whoever isn’t locked is free to escape. This excited all the prisoners and they all participated in his game. He first went to the inmate locked up in Cell No. 1, handed over all 80 keys to him and directed him to open the cells that carry the number of which his cell number is a multiple, including his own cell. The inmate number 1 went ahead and did that. Next, the jailer went to inmate of Cell No. 2, handed over all the keys to him and told him to lock all the cells that carry the number of which his cell number is a multiple, including his own cell (with the cell inmate present inside). The inmate number 2 followed his command. Then, the jailer went to inmate of Cell No. 3, handed over the keys and asked him to go and switch the statuses of all the cells that carry the number of which his cell number is a multiple, including his own cell, i.e., if it was open earlier, he needs to lock it and if it was locked before, he needs to open it. Thus, the third inmate followed same. This process continued in the same manner for the entire night with all the prisoners.

The solution of the puzzle lies in one simple fact - how many times a door was touched.

Brainstormer

Solution

For example:

17

Let’s consider cell number 12 – It was touched by prisoners whose cell numbers were multiples of 12 i.e. by

- Prisoner number 1 (to open), prisoner number 2 (to close), prisoner number 3 (to open), prisoner number 4 (to close), prisoner number 6 (to open), prisoner number 12 (to close)

No other prisoner will touch the door number 12 as there is no other divisor of 12. Therefore, at the end of the game the cell door remains CLOSED. So what’s the conclusion?

With every touch the door is opened, then closed, then again opened and so on. This means that at the end of

the entire game it will remain CLOSED if it is touched even number of times and it will remain OPEN if it is touched odd number of times as the sequence with every touch is – open, close, open, close, open, …

Therefore, the cells numbers with odd number of divisors shall remain open at the end.

As a matter of fact, only perfect squares have odd number of divisors. Therefore, out of first 80 natural numbers, perfect squares are 1, 4, 9, 16, 25, 36, 49, 64. So, total 8 cells shall remain open at the end. Now as per the rule of the intelligent jailor, he will close these 8 doors and no one would get a chance to run away.

If there would have been 800 cells, then the jailor must have announced to close 28 cells at the end to avoid any escape. (SQUARE OF 28 = 784 THE LARGEST PERFECT SQUARE UP TO 800)