recursal/Fanatic-Fandom huggingface dataset:
Periodic Table

## Atomic Size

The distance between the centre of the nucleus and the outermost shell of an atom is it's atomic radius . The Atomic radius determines the Atomic Size , since an atom is radially symmetric .

## Nuclear Charge

the amount of Electrostatic Force of Attraction exerted by the Nucleus on the outermost shell is called Nuclear Charge .

## Shielding Effect

Due to presence of innermost electrons , the nuclear charge on the outermost shell is suppressed . This is called Shielding Effect .

Effective Nuclear Charge = Z - σ

where σ is the shielding constant .

## Inert Pair Effect

The presence of intervening d & f electrons produce poor shielding effect in heavier atoms . This poor shielding effect gives rise to higher nuclear charge and smaller atomic size .

## Ionisation Enthalpy

The amount of energy absorbed during ionization of an atom is called ionization enthalpy .

## Electron Gain Enthalpy

The amount of energy released while gaining an electron is called Electron Gain Enthalpy .

## Electronegativity

The stability of elements and compounds is decided by its electron charge density .

The electron charge density is calculated by considering the no. of electrons and Atomic Size . Charge density is directly proportional to no. of electrons and it is inversely proportional to the atomic size .

While considering elements of the same period , we consider their electronegativity values and not their atomic sizes to determine their stability . e,g . C , O , N .

Elements having higher electronegativity values are more stable , since they have the ability to carry the negative charge .
Working Grup

## Episodes

**"Working Grup"** is the twenty-third short of *Mighty Magiswords* which was uploaded on the MagiMobile map on November 11, 2016 and uploaded on Cartoon Network Africa's YouTube channel on February 11, 2017. The short, alongside Phil's in the House, was uploaded in the United States on Cartoon Network Video.

## Synopsis

Vambre and Prohyas visit Grup's job to test some traps. They find the Frog Missile Magisword and they try to contain themselves to not steal it.

## Characters

### Major characters

* Prohyas Warrior
* Vambre Warrior
* Grup the Dragon
* Lady Hiss
* Skullivan
* Prug

## Magiswords used

* Hoversword Magiswords (Prohyas; 4) (Vambre; 6)
* Frog Missle Magisword (*debut*) (Vambre; 1)
* Electric Eel Magisword (Vambre; 5)
* Rad Rocket Magisword (Vambre; 7)
* Accordion Magisword (Prohyas; 6)
* Boulder Magisword (Prohyas; 4)
* Sharkblade Magisword (Vambre; 1)
* Lobster Claw Magiswored (Vambre; 10)
* Nail Clipper Magisword (Prohyas; 2)
* Boomerang Magisword (Prohyas; 1)
* Hook Magisword (Prohyas; 2)

## Trivia

* This episode reveals how the Warriors met the Cave Weirdos. It also reveals that Prug is Grup's brother.
* This is the first 5-minute short released for CN Video after a 2-month hiatus. It was first released in CN Africa's YouTube channel where it became an interactive video, similar to the MagiMobile app.

## Episode connections

* Prug reminds Grup on how he met the Warriors in the first short, To Boulderly Go.
	+ The Warriors do not remember, which may be based on the fact that the 3-minute shorts have a different continuity than the 5-minute shorts and the series.
	+ However, in Random Acts of Memory, it was revealed that Nohyas wiped the memories of the Warriors so they'd only remember him and not Prug.
* Jarham, from the episode Cleanliness Is Next to Grupliness, debuts here and is a delicacy for Prohyas and Skullivan.

## Real-world references

* The song the Warriors and Cave Weirdos dance to at the end resembles the Peanuts theme.
* The directions/notes for the Music Locked Gate are similar to the Konami code.
* **Prohyas:** Sister no swiping!
	+ This is a direct reference to the series *Dora the Explorer* where the characters would stop the thieving fox Swiper from stealing by shouting "Swiper no Swiping!".
Electromagnetic Induction

## Faraday's Laws of Electromagnetic Induction

1. Whenever , a coil is associated with a changing magnetic flux , an emf is induced in it .
2. The emf induced in a coil is directly proportional to the rate of change of magnetic flux .

## Lenz's Law

Whenever a coil , is associated with a changing magnetic flux , emf is induced in the coil such that it opposes the cause of it .

## Eddy Currents

Eddy currents are formed in conductors of large surface areas . In such conductors , whenever an emf is induced , the electrons in it start moving in circular orbits like whirlpools or eddies .

## Self Induction

When a circuit is subjected to alternating current , the magnetism due to electric current changes . Thus , the coil is subjected to a changing magnetic flux under it's own influence .

e = -L [di/dt]

## Mutual Induction

When a primary coil is subjected to alternating Current and a Secondary coil is placed adjacent to it , then the secondary coil comes under the influence of the primary coil's changing magnetic flux .

e = -M [di/dt]

## Induction

Energy = 1/2 Li2

Power = Work / TIme

## Displacement Current

According to Ampere's Circuital Law ;

∫ B dl = μI

But for an inductive circuit ;

## Transformer

Transformer Works on the principle of Mutual Induction .

np/ns = ep/es = is/ip

## A.C. Generator

An A.C. generator works on a simple principle , that an emf is induced when there is relative motion between magnetic field and conductor . An AC motor xonsists of an iron core on which copper wire is wound , and this core is made to rotate in a magnetic field . Thus , the coil is subjected to a changing magnetic flux . The arrangement of the core is such that current flows out of the brush B1 in first cycle , and out of the brush B2 in second cycle . In this way , an Alternating Current can be generated .

## Alternating Current

In an alternating Current , the emf and current vary with time as harmonic functions (sine or cosine) .

## Alternating Current with LCR Series

The resonant frequency of a LCR circuits depends upon its L & C values .
JEE : Important Skills

**Elementary Skills**

Calculation Tricks

Mental Calculations

Percentage Calculations

Ratio and Proportions

Indices

Logarithms

**Chemistry Skills**

Mole Calculations

IUPAC Nomenclature

**Simplifications**

Trigonometric Simplifications

Algebraic Simplifications

Logarithmic Simplification (e.g. To convert multiplication to addition)

**Applied Mathematics (**Essential for Physics**)**

Applied Calculus

Vector Algebra

**Applied Physics**

Units and Conevrsions

Complex Electric Circuits

Understanding Vectors

Understanding Graphs

**Aptitude - Based**

Percentage Calculations

Ratio and Proportions

Exploring Permutations and Combinations

Understanding Probability

 **Paper Solving**

Decision Making Skills
Decision Making Skills

For every good decision you make in JEE , your rank raises up and for every bad decision your rank ceases down .

Thus good decision making skill is crucial in JEE .

Here are a few tips for making good decisions in JEE :)

1) Have a close look at the options before solving the queation .

2) If a question takes more than 2 minutes to solve , don't attempt it . Having vision is important to save these 2 minutes as well .
Keito Tentsui

## General Information

**Keito tentsui**, (計都・天墜) is an offensive technique used by Yakou Madara.

## Ability

By creating a hole in the zenith of heaven with hand seals, Yakou causes the sky to be filled with a multi-layered mandala that shakes the elements of Heaven and causes a comet to fall on his foes. This technique instantly kills anyone he targets upon completion without damaging the surrounding area. The technique destroyed Tenma Awaumi in a single blow and also used in the fight with Tenma Morei.

## Trivia

* The word "Keito" originated from Indian deity named Ketu (केतु), which has a role in Indian astrology as he is responsible for Lunar eclipse.
* The incantation has a reference of "Bagua" or "Eight Trigrams".
Measurements

## Units and Measurements

If n is the numerical value and u is the unit then ;

Q = nu

n1u1 = n2u2 ( bigger the unit , smaller is the value )

## Systems of Measurement

SI

MKS - meter , kilogram , seconds

CGS - centimeter , gram , seconds

FPS - foot , pound , seconds

## Fundamental Units

Mass - kilogram - M

Length - meter - L

Time - seconds - T

Temperature - Kelvin - K

Current - Ampere - I/A

Luminous Intensity - Candela - C

Amount of Substance - mole - mol

## Methods of Measurement

For measuring distance of stars , planets , we use the parallax method . For determining mass of planets , we use gravitational methods . For the measurement of masses of atomic species , mass spectrographs are used . For accurate measurement of time , we use atomic clocks based on the vibrations produced in a Cesium - 133 atom .

## Dimensional Analysis

Dimensional Analysis deals with the powers to which the unit of a physical quantity is raised to .

Uses of Dimensional Analysis :

1. To check the correctness of an equation
2. To find the conversion factor
3. To find the dimensions by comparison method

## Significant Figures

In order to understand significant figures , we must try to understand and accept that no measurement can be accurate . For example , when the Least count of a measuring instrument is 0.01 m , it will give us accurate readings up to 0.01 m only , measurements smaller than 0.01 m cannot be measured by it . This means that no matter how small the least count of the measuring instrument is , there will always be an error of order one less up to 10-∞ .

Thus , we need to decide the accuracy , which is enough to give a good idea of the quantity .

For example , a person's height is 1.62 m ; but the measurement is accurate only up to 3 digits or 3 significant figures . The actual height could be 1.61927457634752641 m (even this would have an error beyond least count) .But 3 digits is enough to give a good amount of idea about a person's height . Thus , we measure it with 3 significant figures .

## Order of Magnitude

Order of Magnitude is the power to which 10 is raised to ; to indicate the size of the quantity .

## Errors

### **Random Error**

Error occurring due to random changes in the environment of the experiment .

### **Systematic Error**

Error occurring due to a constant error in the readings of instrument . This is caused due to the faulty calibration of instrument .

### **Instrumental Error**

Error occurring due to faulty construction of instrument .

## Error Analysis

**Mean Value  :** Average of All readings

**Absolute Error  :** Individual Reading - Mean Value

**Mean Absolute Error  :** Average of all Absolute values

**Relative Error  :** Mean Absolute Error / Mean Value

**Percentage Error  :** Relative Error x 100

1) If xn , then Error is multiplied by n

2) The errors in the measurement of two quantities are added when the two quantities are multiplied or divied .

if xy ; then add the errors

3)If the quantities are added or subtracted , then the errors are added .

## Tips and Tricks

1. Use dimensional analysis to eliminate options . Try to match dimensions .
States Of Matter

## Intermolecular Force of Attraction

Dipole - Dipole

Dipole - Induced Dipole

Ion - Dipole

Hydrogen Bonding

Dispersion Forces

**NOTE :-**

**1) All kinds of molecues show dispersion forces .**

**2) Higher the intermolecular force , easier is the liquefaction , difficult is the vaporization .**

**3) More is the mass , more is the intermolecular force of Attraction .**

## The Gaseous State

NOTE : The Gaseous State is a big chapter . Study it here .

## The Solid State

NOTE : The Solid State is a big chapter . Study it here
Maths : Tips & Tricks

Some Critical Tips :

1. If certain conditions are given , look for the options that satisfy the condition .
2. If an equation is asked then substitute the values in the option in the equation .
3. Use Trial and Error Method / Elimination method .
4. For co-ordinate geometry , draw graphs according to equations given and predict the answer .
5. The first step in Mathematics is mostly crucial and may require Simplification . Here are techniques of SImplifications that you should try : **1.** Rationalizing **2.** Plus & Minus **3.** Multiplying and Dividing **4.** Dividing Throughout by **5.**Splitting the Numerator **6.** Squaring on Both Sides .

## Sets, Relations and Functions

1) For functions , try to plot graphs . So learn more different kinds of functions and their graphs , or else derive the graph using x-y method .

2) For Set theory draw venn diagrams for better understanding of the question .

## Theory of Equations

1. For Analyzing an equation , remember :
	1. If ∆ = 0 ; then there will be infinite solutions if ∆x,∆y,∆z = 0 . And there will b no solution otherwise .
	2. If ∆ =/= 0 ; then there will be an unique solution .
	3. If ∆ = 0 ; then equations will have nontrivial solution
2. For an equation to have no solution , the ratios of co-efficients of x , y and constant will be equal to each other .
3. A Monotonic Function (Increasing/Decreasing) has only one root .

## Complex Numbers

1. In order to get rid of i term , you can rationalize the question to convert i into i2 . Prefer to reach i2 .
2. Use Geometrical interpretation of Complex Numbers along with De Moivre's Theorem for solving geometry based questions .

## Sequences and Series

1. For Infinite Series , first find the equation of the series in general terms . Then use the Sum of /infite Series Formulae .
2. For AP , GP and HP ; trying out the 4 options can be helpful .

## Trigonometry

1. For General Solution , bring the equation in one of the sandard forms . This can be done by using factorization formulae (i.e. to convert from addition to multiplication) .
2. For Solutions of Triangle problems , the following techniques should be used :
	1. sin
	2. a2, b2,c2
	3. A + B + C = 180
	4. Half Angle
	5. Factorization formulae

## Circle & Conics

1. Draw a graph with the help of given equations , to predict the answer .

## Limits

1. If the Question is of the form 0/0 , then apply L' Hospitals Rule .

## Differentiation and Application

1. For Implicit , use shortcut .

## Integral Calculus and Area under Curve

1. For Indefinite Integration ; Differentiate the options to reach the Question .
2. For u.v ; use the shortcut

## Matrices

1. Do Adjoint first or transpose/square/other operation first , the answer is same .
2. Try to use the options for finding the answer , rather than solving the entire sum .
3. Use properties of determinants to simplify a given matrix .

## 3 Dimensional Geometry

1. In formulas dealing with ratios (e.g. cartesian equation of line , condition for parallel and perpendicular lines) direction ratios can be replaced with direction cosines .
Work , Energy & Power

The concepts of Work and Energy can be applied to all MCQs , dealing with momentum , force , velocity , acceleration and height .

## Work

### Work Energy Theorem

Work Energy Theorem states that the amount of Work Done is the change in Kinetic Energy .

### Nature of Work

Work is a scalar product which occurs in the direction of Force applied .

## Conservative Forces

The forces that conserve kinetic energy are called as conservative forces .

## Energy

### Kinetic Energy

Kinetic Energy is the energy of a body by virtue of its motion .

### Potential Energy

Potential Energy is the energy of a body by virtue of its shape , size , position . A body always tries to move to the position of lowest potential energy .

## Co-efficient of restitution

e = [u1 - u2] / [v2 - v1]

For an object bouncing back from height h and and stopping after covering d horizontal distance can be given by the series :-

d = h + 2h(e2+e4+e6+.......)

The velocity of an object after collision is e times that of velocity before collision .
Preparation Centre

* Boards
* JEE
* CET

* Physics
* Chemistry
* Maths

* Circular Motion
* Gravitation
* Rotational Motion
* Oscillations
* Elasticity
* Surface Tension
* Wave Motion

Derivations

Formulae

Applications of Circular Motion

Numericals

Solved Examples

Textual Theory Questions

* Physics
* Chemistry
* Maths

* Physics
* Chemistry
* Maths
Percentage Calculations

## Standard Ratios and their Percentages

1)1/2 5) 3/4

2)1/3 6) 5/4

3)2/3 7) 3/2

4)1/4 8) 5/2

Ans. 1) 50% 2) 33% 3) 66% 4) 25% 5) 75% 6) 125% 7) 150% 8) 250%

1) 5 of 60

1) 75% of 45

## Concept of Addition and Multiplication in Percentages

Assume x and y as two variables forming total of (x+y) .

## Comprehensive Questions

Questions :

1) x & y are given as y = 2x . By How much percentage is y greater or lesser than x ?

2) If the value of g is increased by double it's original value , What is it's percentage increase ?

3) The value of a variable p changes and becomes q , such that q = 3p + 2 . Calculate the percentage increase or decrease of p .

4) The value of a variable 'A' changes and becomes 'B' ; such that 2B = 3A - 2 . Calculate the percentage change of 'A' . Does it increase or decrease ?

5) The Ratio of A to B is 3:2 ; What are the percentages of A & B out of total ?

6) If x is 62% of y and z is 38% of y , then what is the percentage of y in (x+y+z)
Organic Compounds containing Nitrogen

### **Physical Properties**

The MP of Tertiary amines is lower due to absence of hydrogen to form intermolecular hydrogen bonding .

## Diazonium Salts

### **Reactions**

1. Halogenation by Sandmeyer Reaction (For Cl , Br , CN)
2. Gattermann Reaction (For Cl , Br)
3. For Halogenation using Iodine and Fluorine
4. Formation of Nitrobenzene , Phenol and Benzene
5. Azo Coupling
Aldehydes & Ketones

## Preparation

1. Oxidation of Alcohols
2. From Calcium Salts of Fatty Acids
3. By Reduction
	* of Acyl Chlorides
	* of Cyanides
4. From Alkenes and Alkynes
5. Preparation of Aromatic Aldehydes
	* From Toluene (Etard Reaction)
		+ with CrO2Cl2
		+ WIth CrO3
		+ Chlorination and Hydrolysis
	* From Benzene
6. Preparation of Aromatic Ketone
	* From Benzene (with Acid Chloride)
7. Ketones from R2Cd

## Reactions

1. Addition
	* HCN
	* NaHSO3
	* NH3
	* Grignard Reagent (Formation of Alcohols)
2. Condensation with Derivatives of Ammonia
	* NH2OH (Oxime)
	* NH2NH2 (Hydrazine)
	* C6H5NHNH2 (Phenyl Hydrazine)
3. Reduction
	* Reduction to Alcohol
	* to Alkane
4. Oxidation
	* to Carboxylic Acid
5. Haloform Reaction

## Uses

1. 40% aqueous Formaldehyde is called as Formalin , which is used in preservation of biological and anatomical species .
Sigma Weishaupt

**Sigma Weishaupt** is the brother of Azlan Weishaupt, acting as his shadow warrior. He was later defeated by Dezard Grave, which caused his body to mutate, forcing him to rely on cybernetic parts. Afer he got banished out of the Isolated City, he starts to form a secret society known as Illuminati. He harbors absolute hatred towards the Isolated City.

## Story

Sigma ordered soldier to attack Nerose Satanael in order to test capability of his angel, Astaroth. He later order Judas Strife to kill his brother and destoy the Ähnlichkeit Viper, which he complid. However, Judas later return to finish Sigma off with Belial.
Sets , Relations and Functions

## Sets

A set is a collection of elements . There are various forms of set declaration e.g. roster method , set builder method or direct method .

**Union**

If A and B are two sets then the collection of all elements of A as well as B , is called as A Union B .

**Intersection**

If A and B are two Sets then the collection of elements common to both , is called as A intersection B .

**Venn Diagram**

**Sets Formulae**

**De Morgan's Theorem**

## Relations

A relation is used to describe certain properties that connect two sets . Basically , a relation is linkage between elements of two sets , based on certain properties .

## Properties

**Reflexive**

A->A

**Transitive**

If A->B , B->C then A->C

**Symmetric**

If A->B , then B->A

**Equivalence Relation**

A relation that is reflexive , symmetric and transitive .

## Function

A function defines the behavior of y co-ordinate w.r.t. x co-ordinate . A function is represented by f(x) . f(x) stands for the value of y co-ordinate , for corresponding values of x co-ordinates .

### **Domain & Range**

The set of x co-ordinates is called as the domain and the set of y co-ordinates is called as the Range of Function .

### **Types of Functions**

1. One-One : If each element of Domain points to exactly one element in Range .
2. Many-One : If many elements of Domain are pointing to a single element in Range .
3. Into  : Some elements of Range remain unpointed by Domain .
4. Onto  : Some elements of Domain do not point to Range .

### **Inverse Function**

If y = f(x)

then f-1(y) = x

### **Composite Function**

A function defined within a function is called as a Composite function .

e.g. g(f(x))

thus , the domain of f is x , while domain of g is f(x) .

### **Intervals**

Functions can also b defined within certain intervals . Many times , periodic functions like sin and cosine are defined using intervals .

## Tips and Tricks

1) For functions , try to plot graphs . So learn more different kinds of functions and their graphs , or else derive the graph using x-y method .

2) For Set theory draw venn diagrams for better understanding of the question .
Semiconductors

## Energy Bands

The highest energy level for an electron at 0 K is called Fermi level . The Fermi level for intrinsic semiconductor lies in centre of valence and conduction band . For n type , it lies close to the valence band . For p type it lies close to conduction band .

## PN Junction Diode

### Forward Biased

The dominant mechanism of Forward biased diode is diffusion .

Forward resistance is very low or zero .

### Reverse Biased

The dominant mechanism of Forward biased diode is drift .

Reverse Resistance is infinitely high .

## Common Base Connections

Here, the base is connected to both input as well as output .
Differentiation

## Concept of Derivatives

Derivatives find the amount of change in y , with an infinitesimally small change in x .

## Composite Functions

g(f(x)) can be differentiated as d f(x)/dx . d (g(x))/dx

## Inverse Functions

Inv (A) : Substitution of the variables to simplify the equation .

Inv (B) : Substitution using pythagorean triplets of a triangle .

## Logarithmic Differentiation

1) This method is used when a variable is raised to a variable .

2) Take log on both sides .

3) Differentiate w.r.t. x

Log(A) : Differentiating logs on both sides . (Used with multiplication and Division)

log (B) : Differentiating logs separately and then addition / subtraction (Used with Addition and Subtraction)

## Explicit & Implicit Functions

Explicit Function : y = 3x2 + 2x + 5

Implicit Function : y2 + x2 + xy = 0

To differentiate implicit functions , differentiate the entire equation w.r.t. x and then bring dy/dx terms together .

## Parametric Functions

Parametric functions , are those functions which can be expressed using a common variable . We first differentiate both functions w.r.t. the common variable . Then we divide their differential values , to find their differential w.r.t. each other .

Para (A) : Differentiating separately with respect to the common variable and then dividing them .

Para (B) : Differentiate separately and then divide dx/dy

## Higher Order Differential

Higher Order differentiation deals with differentiating a function multiple times .

## Differentiability and Continuity

If a function is differentiable at a given point , then it is continuous at that point.

If a function is continuous at a point , it is not necessary that it is differentiable .

## Applications of Derivatives

### **1) Rate Measurer**

When an equation is differentiated with respect to time , we can measure the rat of change .

### **2) Tangents and Normals**

**Slope of tangent** = dy/dx = tanθ

**Slope of Normal** = -dx/dy = -1/tanθ

**Equation of Tangent** : y - y1 = m ( x - x1 ) m = dy/dx

**Equation of Normal** : y - y1 = m ( x - x1) m = - dx/dy

**length of Tangent** = y1 sqrt (1 + (dx/dy)2)

**length of Normal** = y1 sqrt (1 + (dy/dx)2)
Complex Numbers

## Imaginary Numbers

z = a + ib is a complex number. Real part of z is denoted as Re(z) = a & Imaginary part is denoted by Im(z) = b

i = √(-1)

z1± z2 = a1 ± a2 ± ib1 ± ib2

z1z2 = (a1a2 - b1b2)+ i(a1b2 + a2b1)

If z1 = z2

a1 + ib1 = a2 + ib2

a1=a2 & b1=b2 ; thus one complex equation is equivalent to two real equations .

## Complex Numbers

A Complex Number is a number consisting of a real and an imaginary part .

e.g. a + ib is a Complex number .

## Equality of Complex Numbers

Complex Numbers can be equated but operations such as greater than , lesser than cannot be performed with imaginary parts .

## Complex Conjugate

If a + bi is a complex number , then it's complex conjugate is a - bi .

z = a + bi z' = a - bi

## Polar Representation

z = |z| {cos(amp z) + i sin(amp z)}

i.e. z = r[cosθ + i sinθ] where r = |z|  ; θ = amp z

## Modulus of a Complex Numbers

Modulus of a complex number is the same as the modulus of a vector . The modulus of a complex number is its magnitude of it sqrt (a2 + b2)

amp(z) = arg(z) = tan-1(y/x)

amplitude is the angle subtended by line joining the point (a,b) and the positive X-axis .

**Properties**

(z1 ± z2)' = z1' ± z2'

(z1z2)' = z1'z2'

(z1 / z2)' = z1' / z2'

amp(z1z2) = amp z1 + amp z2

amp(z1 / z2) = amp z1 - amp z2

amp z2 = 2 amp z

amp [z/z'] = 2 amp z

## Argand's Diagram

Argand's Diagram is the graphical representation of complex numbers . a & b represent the axes of the graph .

## Tips & Tricks

1) In order to get rid of i term , you can rationalize the question to convert i into i2 . Prefer to reach i2 .
Mathematics

Syllabus

Basic Mathematics

#Sets , Relations and Functions#

#Mathematical Logic#

#Quadratic Equations#

#Complex Numbers#

Sequences and Series

Permutations and Combinations

Mathematical Induction

Binomial Theorem

Limits

#Continuity#
#Differentiation#

Integral Calculus

Differential Equations

Trigonometry

Vector Algebra

Three Dimensional Geometry

Locus

Straight Lines

Circle and Conics

Determinants

Matrices

Statistics

Probability
Motivation

Quoutes from Robin Sharma , Zig Ziglar and Brian Tracy .

Many people cannot see possibilty

because their sight is blinded by cynicism

Where the victim sees a problem ,

a leader sees an opportunity

Once you choose hope ,

anything is possible

When you start practicing difficult things ,

You become masterful at doing difficult things

World - Class performance is less a natural gift

and more a daily decision .

The best just practice more .

* The universe doesn’t care if I succeed or fail.
* The biggest obstacle I have to overcome in pursuing success is myself.
* I’m the sole owner of my thoughts and emotions.
* Other people seldom see me the way I think they do, or the way I want them to.
* I can’t change you.
* Nobody owes me anything.
* I can’t get the time back.
* I won’t be here one day, and I have no idea when that day will come or how I’m going to exit this life.

* No one is watching you; no one is interested in what you’re doing. So get over it.
* Life, money, emotions, and people all lies in ephemeral state. What you have today doesn’t equals you to be its proprietor forever. So start living for today rather than for past or tomorrow.
* Keep yourself occupied, busy, and productive. Maintain your health.
* Trying out diversified things, especially things which frightens you. It will give enormous strength and will boost your confidence.
* You’re alone. You’ll die alone. Hence, do what you love and travel alone frequently.
* Being yourself.
Viktor Frost

Viktor Forst is Franz Faber 2nd in the Gestapo. He went to see Faber at his home when he saw his son who was down syndrome and he got very angry at him.

He was with Faber when the SS capture Alfred Graves they had Alfred beaten and tortured by his henchman and they even used Rene Villiers who they thought he was killed in their first mission. He had to bring Alfred and Rene and other resistance fighters to Berlin because the resistance fighters were attack the Gestapo Headquarters while Viktor was with amoured car and prison van and his car to the train station . They see a truck on the road and the driver who was Neil Mackay pretending he was drunk and they were attacked by team and was shot by Aurora Luft . After the attack he was wounded in stomach Franz Faber came and was very upset with Viktor he beats him with a stone and he shoots him in the head and dies.
Calculation Tricks

## Multiplication of Numbers near 100

e.g. 95 x 97 = x

100 - 95 = 5 & 100 - 97 = 3

First 2 digits = 95-3 or 97-5 .

Last 2 digits = 5x3

... 95 x 97 = 9215

## Multiplication of Numbers close to 10

e.g. 13x15 = x

Add 13 + 5 = 18

Multiply 3x5 = 15

... x = 195

## Square of Numbers close to 100

(112)2

Difference = 12

Add 12 = 124

square 12 for last 2 digits = 144 (1 carry)

1122 = 12544

(96)2

Difference = 4

Subtract 4 = 92

Square 4 = 16

962 = 9216

## Division by 9

2231 / 9 =

247 Remainder = 8

## Multiplication with 11

13 x 11 = 1\_3

1+3 = 4

... 1\_3 = 143

121 x 11 =

1\_ \_1

1 2 1 = 3 3

121 x 11 = 1331
Three Dimensional Geometry

# 3 D Geometry

## Axes

There are three axes in 3-D Geometry , X , Y & Z . There are 8 quadrants in 3d axes .

x-coordinate is the distance of the point from y-z plane .

**Division of a line lying in a plane of axes**

Suppose the XZ plane is dividing a line, it does so in the ratio -y1/y2 .

Similarly for yz and xy planes ,too .

## Direction Cosines

If α β γ are the angles made by a line with positive direction of X, Y and Z axes , then they are called as direction angles of the line .

The cos of α , β & γ are called as direction cosines of the line .

**cos2α + cos2β** **+ cos2γ = 1**

If l , m , n are direction cosines of a given line , and a,b,c are any real numbers such that :-

l/a = m/b = n/c ; then a,b,c are called as direction ratios of a line .

If P(x1,y1,z1) and Q(x2,y2,z2) then the direction Ratios of PQ are :-

x2 - x1 , y2 - y1 , z2 - z1

If AB = ax + by + cz , then direction ratios of line AB are a, b ,c .

Suppose Ray BD bisects angle ABC , then the direction ratios of Bisector BD are equal to sum of the Direction ratios of AB and BC

The vector li + mj + nk is a unit vector always . while ai + bj + ck is not a unit vector .

## Angle between two Lines

If a1 b1 c1 and a2 b2 c2 are the direction ratios of two given lines , then

or cos θ = l1l2 + mm2 + n1n2

# Lines

 Vector Equation of a Line

1) If a line passes through a point and is parallel to another vector , then **r = a + λb**

2) In non-parametric form , rxa = rxb

## Cartesian Equation

x - x1 / a = y - y1 / b = z - z1 / c {Derived from 2 point form }

In 2 point form :- x - x1 / x1 - x2 = y - y1 / y1 - y2 = z - z1 / z1 - z2

a = x1 - x2  ; b = y1 - y2  ; c = z1 - z2

Note :

For a point on the line , the Cartesian equation can be used to find the point coordinates . (equate the cartesian equation with a constant )

x = x1 + ka

y = y2 + kb

z = z2 + kc

Where , k is a constant that decides the distance of a point from the point A , on the line .

## Collinearity of 3 points

three points are collinear if a1/a2 = b1/b2 = c1/c2

## Section and Mid-point Formula

For Section formula you can either consider m : n or λ : 1

## Skew Lines

Shortest Distance between 2 lines in plane is given by :-

For intersecting lines , [a2 - a1  b1 b2] = 0 ... Shortest distance = 0

# Plane

## Equation of a Plane

r.n = a.n

r.n = p

For plane passing through intersection of two planes ;

a + **λ**b = 0 (Where a & b are the equations of the two planes)

## Co-planarity of two lines

If angle between a line and plane is 0 , it lies in the plane . (This can be used to check coplanarity )

## Distance between a Point & Plane

l(AP) = (a.n - p) / n

l(AP) = ( ax + by + cz + d ) / sqrt (a2 + b2 + c2)

where (x,y,z) = coordinates of point in space .

ax + by + cz + d is equation of plane .

## Tips and Tricks

1. In formulas dealing with ratios (e.g. cartesian equation of line , condition for parallel and perpendicular lines) direction ratios can be replaced with direction cosines .
Sequences and Series

## Arithmetic Progression

tn = a + (n-1)d

Sn = n/2 [2a + (n-1)d] =n/2 [a + tn]

tn = Sn - Sn-1

.

.

a2 - a1 = an - an-1 = constant

a1 + an = a2 + an-1 = constant

a1 + k , a2 + k , a3 + k ,......., an + k are also in A.P.

a1k , a2k , a3k ,......., ank are also in A.P.

a1 , a3 , a5  are also in AP

a2 , a4 , a6  are also in AP

{terms falling after equal intervals are in AP}

.

..

AM = (a + b) / 2  ; for two numbers

AM = (a1 + a2 + a3 + ..... + an) / n (for n numbers)

## Geometric Progression

tn = arn-1

Sn = a(rn-1) / (r - 1) if r > 1

S∞ = a / (1 - r) if 1 < r

tn = Sn /Sn-1

.

,

a2/a1 = a3/a2 = an/an-1 = common ratio

a1an = a2an-1 = constant

a1 + k , a2 + k , a3 + k ,......., an + k are also in A.P.

a1k , a2k , a3k ,......., ank are also in G.P.

a1 , a3 , a5  are also in GP

a2 , a4 , a6  are also in GP

{terms falling after equal intervals are in GP}

.

.

.

GM = √(ab) for two numbers

GM = √(a1aca3....an)n (for n numbers)

## Harmonic Progression

tn = 1 / A.P.

.

.

(1 / an) - (1 / an-1) = constant

HM = 2ab / (a+b)

.

## Aritmetico - Geometrico Series

a.b + (a+d)br + (a+2d)br2 ........ (a+(n-1)d)brn-1

is called an Arithmetico Geometrico Series

For such series , we multiply the equation with r and then subtract it from the original equation .

## Sum of Finite Series

Σn0 = n

Σn = n(n-1) / 2

Σn2 = n(n-1)(2n-1) / 6

Σn3 = n(n-1)/ 2]2

Note : For other summations , convert the expression into the above given expressions .

## Special Series

Special Series works on the Principle of Binomial Expansion .

**Algebraic Expansions**

(1-x)-1 = 1 + x + x2 + x3 + ...... ∞

(1+x)-1 = 1 - x + x2 - x3 + ..... ∞

(1 - x)-2 = 1+ 2x + 3x2 + 4x3 + .....∞

(1+ x)-2 = 1 - 2x + 3x2 - 4x3 + ....∞

**Exponential Series**

ex = 1 + x/1! + x2/2! + x3/3!......∞

e-x = 1 - x/1! + x2/2! - x3/3!......∞

**Logarithmic Series**

log(1+x) = x - x2/2+ x3/3 - ....... ∞

log (1-x) = - x - x2/2- x3/3 - ....... ∞
Test Page

## Welcome to the IIT JEE Wiki

Boards Strategy      Mock Test Strategy      Exam Day Strategy      Last Minute Strategy      Exam Strategy Stress Management JEE : Important Skills

## JEE Main

Revise & Practice these chapters : (January)

* Physics
* Chemistry
* Maths

Kinematics

Force

Heat

Ray Optics

Electrostatics

Organic Chemistry (All together)

Solutions & Colligative Properties

Equilibrium

Surface Chemistry

Theory Chapters of inorganic Chemistry

Biomolecules & Chemistry in action
Circle & Conics

1. Solve Higher level MCQs from Marvel and mark those chapters that were difficult to handle . Also solve Easier chapters from HC Verma (January - February)
2. Study important chapters from NCERT thoroughly (January - February - March)
	1. Study these chapters :

* Physics
* Chemistry
* Maths

Force

Current Electricity

Electrostatics & Magnetism
Ionic Equilibrium

Circle & Conics

1. Solve 5 - 10 Numericals from books like HC Verma from all chapters and note the chapters that were difficult to handle . (March 14-March 31)
	1. Study & Practice these chapters intensively . Take chapter wise tests of these chapters on Embibe .

* Physics
* Chemistry
* Maths

1. Solve Practice Papers and Note down your problems : (March 14 - April 9)
	1. Making decision amongst options
	2. Getting Stuck in questions

## JEE Advanced

1. Order these Books : Arihant JEE Advanced Past year's IIT JEE Questions ; Guidebook by Arpit Agarwal
2. Do Complete Revision of JEE Advanced . Read in-depth abbout chapters in Physics & Chemistry on Wikipedia (April 10 - April 15)
3. Solve 10 problems from each book daily ( April 11 - May 20 )
4. Solve JEE Advanced Practice Tests and note down the problems ( May 1 - May 20 )
	1. Above the head questions
Matrices

A Matrix is an array of real numbers .

## Equality of Matrices

If two matrices are equal then their corresponding elements are equal .

For two matrices to b equal their order has to be exactly same .

## Algebra of Matrices

When Matrices are added or subtracted , their corresponding elements are added or subtracted .

## Transpose of a Matrix

Transpose of a matrix is a matrix of inverted rows and columns .

## Determinant of a Matrix

Determinant of Matrix gives the magnitude of the matrix .

## Inverse of a Matrix

Inverse of an identity matrix is an identity matrix again .

## Properties of Matrices

1. .
	1. AA-1 = I
	2. (A-1)-1 = A
	3. (AT)T = A
2. .
	1. (AB)-1 = B-1A-1
	2. (AB)T = BTAT
3. (A + B)T = AT + BT (If addition subtraction possible)
	2. (Ak)-1 = (A-1)k
	3. (AT)-1 = (A-1)T
4. Do Adjoint first or any other operation first , the answer is same .
	1. (Adj A )m = (Adj Am)
	2. (Adj A)T = (Adj AT)
	3. (Adj A)-1 = (Adj A-1)

## Useful Formulae

1. (kA)-1 = 1/k A-1
2. A.(Adj A) = (Adj A)A = |A| = In
4. adj(adj A) = |A|n-2. A
5. adj (kA) = kn-1 (Adj A)

## Other Types of Matrices

1. **Orthogonal Matrix :** If ATA = AAT = I  ; i.e. Transpose is the inverse of the matrix . If A is an orthogonal Matrix , the A-1 is also an orthogonal matrix .

## Tips and Tricks

1) Prefer Adjoint Method over row transformations .
Stoichiometry

## Chemical Equivalence

**Law of Equivalence :** One equivalent of a substance reacts with one equivalent of another substance .

eg. H2O **:** 1 equivalent of H2 reacts with 1 equivalent of O2

i.e. 1 gram of Hydrogen reacts with 8 grams of Oxygen .

For aA + bB --------> mM + nN

(wt. of A / eq wt of A) = (wt. of B / eq wt of B) = (wt. of M / eq wt of M) = 9wt. of N / eq wt of N)

## Volumetric Calculations

1) m.e. = normality x Volume in mililitres = NV

2) At the end of titration of two solutions , N1V1 = N2V2

3) No. of Equivalents = m.e. / 1000

4) No. of Equivalents = weight in grams / equivalent weight

For gases , No. of equivalents = volume at NTP / Equivalent Volume

5) Grams per litre = normality x equivalent weight

6) Normality = molarity x Valency

7) In a reaction , the equivalents of individual reactants and individual products is the same .

8) In a compound MxNy , eq. of MxNy = eq of M = eq of N
Chemistry : Tips & Tricks

## Mole Concept

Principle of Atom Conservation :

No. of moles of an atom in Reactants = No. of moles of the atom in Products .

In reaction , H2 + O2 -------> H2O

No. of moles of O2= No. of moles of H2O

2 x No. of moles of O2 = No. of moles of O in H2O

## Chemical Bonding

1. To detect the type of Hybridization , use the formula : N = GA + 1/2 {VE - V - C}  ; where N is the number of hybrid orbitals , GA is Number of Atoms or groups attached , VE is number of Valence Electrons , V is Valency of Central Atom , C is charge on cation or anion .

## Equilibrium

1. While dealing with Ksp , Ionic Product , ka and kb, Rely on the equations and it's stoichiometry . Raise the concentrations to the power of stoichiometric co-efficient . The PPowers are **not raised onl**y in the chapter Chemical Kinetics .

## Nuclear Chemistry

1. The Radioactive disintegration follows first Order Kinetics . Thus , formulae of Chemical Kinetics for first order kinetics can be used .

## Organic Chemistry

1. For Stability , consider Resnance . If the compound has double/triple bond or lone pair of electrons in conjugation , then it is stabilized by resonance .
2. For Organic Chemistry Reactions , for predicting the product , use the concept of Nucleophiles/Electrophiles . Negative part goes to positive part of carbon chain and vice versa . The positive/negative part of carbon chain may shift according to stability .
P-Block Elements

## Important Compounds

Nitrogen :- 1) Ammonia

2) Nitric Acid

3) Nitrogen Oxides

Phosphorous :- 1) Phosphine

2) Phosphorous trichloride

3) Phosphorous Pentachloride

4) Oxyacids

Oxygen :- 1) Dioxygen

2) Ozone

Sulphur :- 1) Sulphur dioxide

2) Sulphuric Acid

3) Oxoacids

Halogens :- 1) Chlorine

2) Hydrogen Chloride

3) Interhalogen Compounds
Savitr

## Savitr Bhagavan Gita

"To witness this is unbearable. This is the landscape of that Hell known as staying alive."

## Characteristics

### Character Type:

Amrita
Krishna

## Personal Status

### Affiliation:

Saiva
Aditya Fleet
Naraka

### Position:

Colonel
Retainer

### Relationships:

Terminus (Master)
Mitra(Rival)

## Abilities

### Avatara:

Vajra Bhairava

**Savitr Bhagavan Gita** (サヴィトリ・バガヴァンド・ギーター, *Savitori Bagavando Gītā*?) is a soldier from the faction that desire normal life and normal death. Due to complete opposite ideaology with Mitra's faction that desire to be immortal, they clashes. He is Mitra's nemesis that she has to fight over and over again, but unlike her, who fight in the front line, he instead command his army from behind the scene like a strategist.

## Personality

Savitr was described as a a ruthless man who is cold and calculate, willing to do anything for his objective. As a clever, cool headed strategist, he's feared from the inside and the outside of the Empire, however, his loyalty towards Terminus is something that comes from the bottom of his heart. Therefore, he acts in an overprotective way, and doesn't necessarily hold absolute obedience towards his lord.

He's a supremely excellent servant, who is always at his lord's side and puts everything in order. In short, he's kind of Terminus' butler.

## Powers & Abilities

### Avatara

#### **Vajra Bhairava**

A Spatial-type Avatara affecting the surrounding and environment. It allows him to teleport across distances to escape dangerous situations.

## Trivia

* Namsake Savitr is a name of a Vedic God that is part of Aditya who act as a protector of all beings.
JEE : Force

If 3 Forces can be represented by sides of a triangle , then they are said to be in equilibrium ; i.e. their resultant is 0 .

According to Lami's Theorem ; F1 / sin α = F2 / sinβ = F3 / sin γ ( For forces in equilibrium)

1) If lift is moving upward , the weight of object is **added** to the Force exerted by lift . mg + ma

2) If the lift is stationary or in state of uniform motion , then the weight of the object is the only force acting on it

3) If the lift is moving down , the weight of the object is **subtracted**  by the Force exerted by the lift . mg - ma

4) If a > g ; then the body will rise and stick to the ceiling of the lift .

**Inclined Plane :-**

a = g sinθ (vertical)

A = g tanθ (horizontal)

**Blocks over Pulley :-**

T = g [ 2m1m2 / m1 + m2 ]
Nagaraja

The planet that became the original battlefield of the great war in between the Federation and the Empire, which broke out in Year 1198 of the 4th Kalpa.

Originally it was nothing but a colony planet from the border region, sold off by the Federation to the Empire as part of the stipulations of a cease fire, however, due to the discovery of large deposits of Kala Stones, things escalated to the point of war.

The peculiar shape of its four continents' arrangements resembles a dragon, which became the source of the planet's name; **Nagaraja: The Dragon's Ark of the Covenant** (龍の聖櫃ナーガラージャ, *Ryū no SeihitsuNāgarāja*?), The Federation, in contempt, calls this land **Magoraka: The Island of the Snake** (蛇の島マゴーラカ, *Hebi no ShimaMagōraka*?), but taking into account the reality of the heavenly body, the Imperial nomenclature appears to be the more justified one.

Its capital city, Kyoufu, is situated in the heart of the central continent. The Kala Stone deposits are in Touto in the east, Hiroi in the west, and finally Nagamisaki in the western edge.

Furthermore, the aforementioned names imitate 1st Kalpa folklore which remains at this place.
Projectile Motion

## Trajectory

The path traced by a projectile projected from a height above the ground is Parabolic in Nature

y = (tanθ)x - [g / 2u2cos2θ]x2

Features of Projectile Motion

1. The path is Parabolic .
2. The horizontal Velocity is always constant .
3. The vertical velocity decreases and then becomes zero at maximum height and then it's velocity increases .

## Horizontal Range

R = u2sin2θ / g

Maximum Range = u2/g

## Projectile Motion on an Inclined Plane

θ = θ - α

g = gcosα

Time of Flight = 2 u sin(θ - α) / gcosα

Maximum Height = u2sin2(θ - α) / 2gcosα

Horizontal Range = 2u2sin(θ - α)cosθ / gcos2α

## Tips and Tricks

1. Projectile Motion questions can be handled by using Kinematical Equations , keeping x & y components in mind .
Wave Motion

## Elements of a Wave

**Amplitude**

The maximum displacement of a particle from mean position is called as Amplitude of a transverse Wave . The maximum pressure exerted on medium is called as Amplitude of a longitudinal Wave .

**Period**

The time taken for the execution of one complete wave is called as Time Period .

**Frequency**

The number of waves executed per second is called as Frequency of he wave .

**Wavelength**

The distance traversed by one complete wave is called as wavelength .

**Wave Number**

The number of waves passing through 1 metre of medium is called as wave number . It is the reciprocal of wavelength (in metres)

**Velocity**

The velocity of a wave is the displacement of the ave per unit time .

**Phase**

**Periodicity**

**Path Difference and Phase Difference**

Phase Difference = ( 2π / λ ) Path Difference

Where (2π / λ ) is the propagation constant

## Types of waves

### Longitudinal

Velocity = v = sqrt [T/μ] where μ is the linear charge density

## Simple Harmonic Progressive Waves

A Simple Harmonic Motion is periodic in space as well as in time . This property is called double periodicity .

Displacement :

y = a sin2π [t/T - x/λ]

## Reflection of Waves

For transverse waves , the wave is reflected back in the same phase .

For longitudinal Waves , the wave is reflected back in the same phase ; but if at the other end of boundary , there exists a rarer medium , the reverse condition will be valid .

## Superposition of Waves

When two or more waves travelling through a medium arrive at a point of the medium simultaneously , each wave produces its own displacement , independently of others . Hence , the resultant displacement at that point is equal to the vector sum of the displacements due to all the waves .

## Beats

The alternate waxing and waning of sound after definite intervals of time , due to superposition of two waves of nearly equal frequencies , is called production of beats . The number of times the sound waxes or wanes in one second is called as frequency of waves .

y = R sin 2π nt ; where n is the average frequency of superposing waves , t is the time period of beat .

N = n1 - n2

Imax α (a1+a2)2

Imin α (a1-a2)2

## Doppler Effect

na = [v ± vo / v ∓ vs]

If the source and observer are approaching each other , numerator has addition .

If the source and observer are moving apart from each other , numerator has subtraction .

## Stationary Waves

When 2 identical progressive waves both travelling in opposite directions , interfere with each other , by superposition of waves resultant wave obtained in the form of loops is called a Stationary Wave .

## Resonance

If the resonance frequencies of a body are in the ratio xa : xb : xc ,
then x is the frequency of the body .