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Unacademy GATE, ESE & IRMS

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Number of 0's at the end

Unit Digit Value

Last Two Digits

Concept of Remainders

Factorisation

Divisibility Rules

Important Note

Addition, Multiplication & Filling -1

Addition, Multiplication & Filling (Part 2)

Addition, Multiplication & Filling (Part 3)

Basics of PnC

Letters-Word Arrangement

Team Formation

Question Paperwala Question

Number Sum

Linear and Circular Arrangements

Straight Lines, Triangles, Chess Board, Handshake

Dictionary Word & Important Concepts PnC

Concept Builder 1 (Probability)

Concept Builder 2 (Probability)

Challenge Question (Probability )

Average Speed

Time Difference

Relative Speed

Challenge Questions

Boats

Linear Races

Circular Races & HCF-LCM

Work & Time

Understanding Workdone

Distribution of Wages

Pipes & Cisterns

W=DMTE

Percentage DI (Graphs) (Part 1)

Percentage DI (Graphs) (Part 2)

Percentage DI (Graphs) (Part 3)

Percentage Basic (Part 1)

Percentage Basic (Part 2)

Profit & Loss (Part 1)

Profit & Loss (Part 2)

Mixture Alligation

SICI & Some more Graphs

Logarithms

Odd One Out, Coding, Decoding, Missing Letter & Blood Relations

Simplification, More Graphs & Reasoning (Part-1)

Simplification, Some More Graphs & Reasoning (Part 2)

Logical Connective

Syllogism

Verbal Reasoning (Critical Reasoning) (Part 1)

Verbal Reasoning (Critical Reasoning) (Part 2)

Verbal Reasoning (Critical Reasoning) (Part 3)

Verbal Reasoning (Critical Reasoning) (Part 4)

Verbal Reasoning (Critical Reasoning) (Part 5)

Verbal Ability and Verbal Grammar (VA VG) (Part 1)

Verbal Ability and Verbal Grammar (VA VG) (Part 2)

Verbal Ability and Verbal Grammar (VA VG) (Part 3)

Verbal Ability and Verbal Grammar (VA VG) (Part 4)

Verbal Ability & Verbal Grammar (VA VG) - Part 5

Spatial Aptitude

Introduction & Definition of System

Types of System

Macroscopic, Microscopic & Continuum Approach

Properties of a System & TD Equilibrium

State, Thermal Equilibrium & Temperature

Zeroth Law of TD & Thermometry

Method before 1954

Method After 1954

Gibbs' Phase Rule & Functions

Ideal Gas Behavior

Process Path & Cycle

Types of Processes

Workbook Problems of Basic Concepts

Introduction to Work Interactions

Closed System Work for Various Processes

Open System Work for Various Processes

Heat Interaction & its Types

Specific Heat Analyses

Analysis of Flow Work

Problems Based on WT (Part 1)

Problems Based on WT (Part 2)

PK Nag Problems

Workbook Problems (Part 1)

Workbook Problems (Part 2)

Introduction to the First Law of Thermodynamics

First Law Applied to Processes

Heat Transfer for Various Processes

Heat Transfer for Polytropic Process

Problems Based on 1st Law

Common PV Diagram for all Processes

Derivation of SFEE

SFEE Applied to Steady Flow Devices

Throttling Process & Problem

Introduction to Unsteady Flow

Problems Based on 1st Law

Isolated System & Free Expansion

Paddle Wheel Work Analysis

PK Nag Problems 01

PK Nag Problems 02

PK Nag Problems 03

PK Nag Problems 04

PK Nag Problems 05

Workbook Problems (Part 1)

Workbook Problems (Part 2)

Workbook Problems (Part 3)

Workbook Problems (Part 4)

Introduction to 2nd Law

Different Statements for 2nd Law

Heat Engines, Heat Pumps & Refrigerators

Reversed Engines

Clausius Inequality

Problems Based on Clausius Inequality

Engines in Series (Part 1)

Engines in Series (Part 2)

Workbook Problems (Part 1)

Workbook Problems (Part 2)

PK Nag Problems 01

PK Nag Problems 02

PK Nag Problems 03

PK Nag Problems 04

PK Nag Problems 05

PK Nag Problems 06

Introduction to Entropy

Entropy Change for an Irreversible Process

Entropy Change for a System

Principle of Increase of Entropy of the Universe

TS Diagram & Miscellaneous

Tds Equations & Steady Flow Work

Numericals Based on Entropy

Problems based on Entropy Theory

Problems of Mixing

Problems based on Entropy (Part 1)

Problems based on Entropy (Part 2)

Entropy Change for an Open System

Graph Conversion & Formation of every TD Cycle

Carnot Cycle Complete Analysis

Workbook Problems (Part 1)

Workbook Problems (Part 2)

Workbook Problems (Part 3)

Available Energy Introduction

Changes in AE when Heat Supplied at Different Temperatures

Availability & Unavailability

Gibbs & Gibbs Helmholtz Function

PMMs & Third Law of TD

Problems based on AE

Workbook Problems

Introduction to PV Diagrams

Observations of PV Diagrams

TS Diagrams

H-s & PT Diagrams

Properties Calculations

Workbook Problems (Part 1)

Workbook Problems (Part 2)

Mixture of Ideal Gases

Workbook Problems of Mixture of Ideal Gases

Maxwell Equations & Tds Relations

Difference of Specific Heats

JouleKelvin Effect

Clausius Clapeyron Equation

Workbook Problems

Practice Makes Maths Perfect

Introduction to Linear Algebra

Types of Matrix according to its dimension (R,C)

Formation of Matrix with Elements Position (i,j)

Elementary Transformation of Matrix

Basic Operation of Matrix (Transpose)

Basic Operation of Matrix (Determinants)

Properties of Determinant

Matrix Multiplication

MATH-EN-C01L09 Adjoint

Workbook Questions 01-05

Workbook Questions 06-09

Workbook Questions 10-15

Types of Square Matrix Part 01

Types of Square Matrix Part 02

Types of Square Matrix Part 03

Concept of Characteristics Equation and Eigen Values

Important Examples of Eigen Values

Properties of Eigen Values

Concept of Cayley Hamilton's Theorem

Concept of Eigen Vectors

Concept of Diagonalization of Matrix

Workbook Questions 16-20

Workbook Questions 21-30

Workbook Questions 31-34

Concept of Rank of Matrix

Properties of Rank of Matrix

Workbook Questions 35-38

Solution of Linear Simultaneous Equations (Nonhomogeneous)

Solution of Linear Simultaneous Equations (Homogeneous Form)

Workbook Questions 39-42

Basis of Vector Space

Introduction to Differential Equations

Representation of Ordinary Differential Equations

Examples to Understand Order

Linear

Workbook Questions 1-4

Formation of Differential Equation

Solution of Differential Equation

Solution Higher Order Homogeneous Differential Equation

Solution Higher Order Nonhomogeneous Differential Equation

Workbook Questions 5-15

Workbook Questions 16-21

Cauchy's Higher Order Linear Differential Equation

Workbook Questions 22-24

First Order First Degree Differential Equation

Workbook Questions 25-31

Basics of Partial Derivatives

Homogeneous Function

Concept of Jacobians

Classification of Partial Differential Equation

Workbook Questions 33-35

Solution of Partial Differential Equation

Introduction to Integral Calculus

Definite Integral

Workbook Questions 1-8

Special Function for Single Integral (Gamma

Q Workbook Questions 9-14

Multiple Integrals (Double and Triple)

Workbook Questions 15-19

Change of Order of Double Integral

Workbook Questions 20-22

Application of Multiple Integrals (Area , Length, Volume)

Workbook Questions 23-26

Workbook Questions 27-28

Workbook Questions 29-30

Introduction to Vector Calculus

Basics of Vectors

Basic Applications and Types of Vectors

Workbook Questions 1-7

Vector Differential Calculus

Example of VDC with 3D Position Vector

Concept of Gradient

Concept of Divergence

Workbook Questions 8-9

Workbook Questions 10-16

Vector Integral Calculus

Stoke & Gauss Theorem

Workbook Questions 17-19

Workbook que 20 21

Green's Theorem with Workbook Questions 22-25

Concept of Maxima

Analysis of Maxima

Workbook Questions 1-5

Workbook Questions 6-10

Concept of Maxima

Workbook Questions 11-13

Basic of Calculus

Rolle's Mean Value Theorem

Workbook Questions 1-5

Workbook Questions 6-13

Introduction to Complex Variables

Basic of Complex Variables

Workbook Questions 1-6

Separation of Complex Function with Basic Examples

Concept of Analytic Function (CR Equations)

Examples of Analytic Function

Workbook Questions 7-10

Complex Integration

Cauchy's Theorem, Cauchy Integral Formula

Workbook Questions 11-12

Workbook Questions 13-14

Workbook Questions 15-20

Complex Series Expansion

Laurent Series Expansion with Concept of Singularities

Basics of Limits (L Hospital Method)

Workbook Questions 1-8

Taylor and Maclaurin Series

Workbook Questions 9-18

Introduction to Probability

Sample Space 1 (Coins)

Sample Space 2 (Dice)

Sample Space 3 (52 Playing Cards)

Concept of Events

Types of Events

Basics of Probability

Workbook Questions 1-5

Workbook Questions 6-10

Workbook Questions 11-16

Probability of Distribution (Binomial Distribution)

Workbook Questions 17-20

Probability of Distribution (Poisson Distribution)

Probability of Distribution (Normal Distribution)

Workbook Questions 21-28

Concept of Random Variables

Properties of Expected Value and Variance

Workbook Questions 29-38

Workbook Questions 39-40

Important Point related with Statistics

Introduction to Numerical Methods

Numerical Methods to solve Non-Linear Algebraic Equation (Bisection Method)

Numerical Methods to solve Non-Linear Algebraic Equation (Regula Falsi Method)

Numerical Methods to solve Non-Linear Algebraic Equation (Newton Raphson's Method)

Workbook Questions 1-5

Numerical Methods to Solve Differential Equation

Workbook Questions 16-18

Numerical Methods to Solve Integrals

Workbook Questions 8-15

Introduction to Strength of Materials

Importance for SOM in ME & CE

Equilibrium of Solid Bodies

External Forces (Part 1)

External Forces (Part 2)

External Forces (Part 3)

External Forces (Part 4)

Equation of Static Equilibrium

Types of Supports

Internal Resisting Force (Part 1)

Internal Resisting Force (Part 2)

Stress (Part 1)

Stress (Part 2)

Effect of Forces

Types of Stresses

Representation of Stresses

General State of Stress

Stress Tensor

Strain

Shear Strain & Strain Tensor

Workbook Questions 1-4

Axial Loading

Shear Stress and Strain

Bearing Stress and Bulk Stress

Hooke's Law

Elastic Modulus

Physical Significance of Elastic Modulus

Change in Length of Bar

Workbook Questions 1-4

Workbook Questions 5-8

Poisson's Ratio

Relationship between Elastic Constant

Generalized Hooke's Law

Members in Series

Axial Load Distribution Diagram (Superposition Theorem)

Members in Parallel

Statically Indeterminate Members

Workbook Questions 9-17

Problem With Axially Distributed Load

Stress Strain Diagram

Mechanical Properties (Part 1)

Mechanical Properties (Part 2)

Workbook Quetions 18-22

Deformation due to Self Weight

Workbook Questions 23-25

Workbook Questions 26-28

Workbook Questions 29-31

Thermal Stress And Strain

Member In Series And Parallel

Workbook Questions 1-12

Workbook Questions 13-16

Plane Stress Stress And Strain

Stress Transformation

Principal Stresses

Important Concept For Design Problem

Maximum Shear Stress

Mohr's Circle (Part 1)

Mohr's Circle (Part 2)

Important Concepts From Mohr's Circle (Part 1)

Important Concepts From Mohr's Circle (Part 2)

Workbook Questions 1-3

Workbook Questions 4-10

Workbook Question 11

Workbook Questions 12-14

Workbook Questions 15-16

Plane Strain Transformation

Workbook Questions 17-19

Workbook Question 20

Thin Cylindrical Pressure Vessel

Spherical Pressure Vessel & Design Of Thin Pressure Vessel

Strain in Pressure Vessel

Workbook Questions

Beams and Types of Beams

Types of Loads on a Beam

Basics of Centroid

Shear Force & Bending Moment in Beam

SFD BMD (Part 1)

SFD BMD (Part 2)

SFD BMD (Part 3)

SFD BMD (Part 4)

SFD BMD (Part 5)

SFD BMD (Part 6)

SFD BMD (Part 7)

SFD BMD (Part 8)

Workbook Questions 1-2

Workbook Questions 3-7

Workbook Questions 8-16

Workbook Questions 17-21 & Some Concepts

Introduction

Flexure Formula

Design of Beams

Beam of Uniform Strength

Workbook Questions 1-7

Workbook Questions 8-10

Transverse Shear Stress (Part 1)

Transverse Shear Stress (Part 2)

Transverse Shear Stress (Part 3)

Transverse Shear Distribution in Composite Section

Workbook Questions

Torsion Equation

Important Concepts

Shaft in Series And Parallel

Statically inDeterminate Shaft

Workbook Questions

Combined Bending And Torsion

Equivalent Bending Moment And Torque

Workbook Questions

Governing Equation Of Elastic Curve

Methods of Calculating Deflection And Slope

Deflection Of Beam

Macaulay's Method

Moment Area Method

Conjugate Beam Method

Example of Conjugate Beam Method

Strain Energy Of Beam In Bending

Castigliano Theorem

Workbook Question 1-7

Workbook Question 8-9

Workbook Question 10-11

Workbook Question 12-15

Workbook Question 16-19

Recoprocal Theorem

Workbook Question 20-22

Theory of Column (Part 1)

Theory of Column (Part 2)

Theory of Column (Part 3)

Strut Subjected to Eccentric Load

Workbook Questions

Shear Centre

Workbook Questions