PHYSICS

Introduction to Vectors and Forces
Sub Topics
1. Basics of Vectors
2. Triangle Law of vector Addition
3. Parallelogram Law of Vector Addition
4. Components of a Vector
5. Addition of Vectors using Component Method
6. Polygon Law of Vector Addition
7. Some Common Forces Normal Force, Weight, Tension
8. Equilibrium of a Particle
9. Dot Product between two Vectors
10. Cross Product between two vectors
11.Subtraction of Vectors

Kinematics of a Particle
Sub Topics
1. Kinematical Quantities
2. Displacement, Distance, Average Velocity, Average Acceleration
3. Uniformly Accelerated Motion Three Equations of Motion
4. Instantaneous Velocity and Acceleration (Differentiation)
5. Graphs of One-Dimensional Motion
6. Non-Uniform Acceleration (Integration)
7. Relative Velocity in one dimension
8. Velocity of Approach
9. Using Three Equations for Relative Motion
10. Infinite Collisions of Particle on Ground (Geometric Progression, Graphs)

Motion in Two Dimensions
Sub Topics
1. Projectile Motion
2. Equation of Trajectory of projectile
3. Projectile from a height
4. Projectile on Inclined Plane
5. Relative Motion between Two Projectiles
6. Circular Motion
7. Angular Variables
8. Uniform Circular Motion Centripetal Acceleration
9. Non Uniform Circular Motion Tangential Acceleration
10. Radius of Curvature of a Curve
11. Relative Motion between two Circular Motion
12. Relative Velocity in two dimensions
13. Swimmer River Problem
14. Rain Wind Problem
15. Rain Man Problem
16. Aircraft Wind Problem
17. Minimum Separation Between two Moving Bodies

Dynamics of a Particle
Sub Topics
1. Newton’s 2nd Law (Rate of Change of Momentum)
2. Force on Liquid in a bent pipe (Momentum flowing per second)
3. Steps to Apply Newton 2nd Law
4. Force of Friction
5. Tension in a string with mass
6. Dynamics of circular motion
7. Maximum velocity of car on rough horizontal ground
8. Banking of roads smooth and rough
9. Conical pendulum
10. Non Uniform Circular Motion
11. Moving Pulley Problems, String Constraint Problems
12. Wedge Constraint (Relative Motion of one body over another)

Work, Energy, Power
Sub Topics
1. Work done by constant and variable force
2. Applying Conservation of Energy
3. Motion in Vertical Circle
4. Projectile Motion in Vertical Circle
5. Conservation of Linear Momentum
6. Impulse due to a force
7. Head on Collisions
8. Oblique Collision
9. Derivation pf Center of Mass of Bodies
10. Center of Mass Cavity Problems
11. Acceleration of Center of
12. Stable, Unstable, Neutral Equilibrium

Rotational Motion
Sub Topics
1. Cross Product
2. Torque About a Point
3. Derivation of Moment of Inertia
4. Parallel and Perpendicular Axis Theorem
5. Moment of Inertia Cavity Problems
6. Fixed Axis of Rotation Hinged Body Problems
7. Calculating Hinge Force
8. General Rigid Body Motion
9. Rolling without Slipping on Ground
10. Angular Momentum of a Particle about a point
11. Angular Momentum in FAOR, GRBM
12. Conservation of Angular Momentum
13. Collision Problems in Rotational Motion
14. Toppling Problems
15. Instantaneous Center of Rotation

Gravitation
Sub Topics
1. Variation of Acceleration due to Gravity
2. Gravitational Potential Energy
3. Escape Velocity
4. Satellite in Circular orbit around earth
5. Satellite in elliptical orbit around earth
6. Binary star system

Liquids
Sub Topics
1. Hydrostatics, Pressure in liquid column
2. Pascal’s Law
3. Archimedes Principle Buoyant Force
4. Center in Buoyancy
5. Pressure in Accelerating Liquids
6. Buoyant Force in accelerating liquids
7. Equation of Continuity
8. Bernoulli’s equation
9. Pitot tube, Venturi meter, Velocity of efflux
10. Surface tension
11. Excess pressure inside drop, bubble, double bubble
12. Surface potential energy, conservation of energy
13. Capillarity rise of liquid in cylindrical tube
14. Rise of liquid between two parallel plates
15. Viscosity, Velocity Profile
16. Poiseuille equation
17. Stokes’s law, Terminal velocity, Graph of velocity with time

Properties of Matter
Sub Topics
1. Calorimetry
2. Water Equivalent, Specific Heat, Thermal Capacity, Latent Heat
3. Thermal Expansion
4. Water overflow Problems
5. Bimetallic Strip
6. Conduction
7. Thermal Resistance of hollow cylinder, hollow spherical shell
8. Growth of ice on lake surface
9. Radiation
10. Black Body Radiation
11. Stefan Law of cooling
12. Newton law of cooling
13. Wien Law
14. Elasticity
15. Stress, Strain, Longitudinal, Shearing
16. Hooke Law
17. Young Modulus, Bulk Modulus, Shear Modulus
18. Elongation under its own weight
19. Torsion
20. Energy Density in elongated bodies

Kinetic Theory of Gases and Thermodynamics
Sub Topics
1. Kinetic theory of gases
2. Degrees of Freedom
3. Root mean square velocity derivation
4. Internal energy of gas
5. Barometer Problems
6. Thermodynamics
7. First Law to Thermodynamics
8. Work done in Isothermal process
9. Work done in Adiabatic process
10. Work done in Polytropic process
11. Molar specific heat
12. Cp and Cv, Meyer Formula
13. PV, VT, PT Graphs
14. Efficiency of Cyclic Processes
15. Carnot Cycle efficiency

Simple Harmonic Motion
Sub Topics
1. Kinematics of linear SHM
2. Finding Phase using Circle of Reference
3. Energy Considerations in SHM
4. Dynamics of linear SHM
5. SHM of Floating Cylinder
6. SHM of liquid in U Tube
7. SHM of Particle in Tunnel inside Earth
8. Series and Parallel combination of springs
9. Moving pulley questions
10. Phase difference and time lag between two SHMs
11. Angular SHM Kinematics, Dynamics
12. Physical Pendulum
13. Part of SHM
14. Damped SHM, Forced SHM
15. Superposition of SHM
16. Shifting of mean position in SHM

Wave Motion
Sub Topics
1. Wave speed in tight string
2. Speed of sound in solids
3. Speed of sound in liquids
4. Speed of sound in gases
5. General form of wave equation
6. Equation of sinusoidal wave
7. Principle of superposition
8. Standing waves in wire fixed at both ends
9. Standing wave in wire free at one end and fixed at other end
10. Phase Difference in Standing Wave
11. Energy between two nodes
12. Beats
13. Filing and waxing of tuning fork
14. Doppler effect in 1 dimension
15. Doppler effect in 2 dimensions
16. Apparent wavelength due to motion of source
17. Variation of intensity is function of distance

 

MATHS

Trigonometry
Sub Topics
1. Problems based on trig. Identities
2. Measurement of angle and trigonometry function for more than right angle
3. Graphs of trigo. functions and their range
4. Trigonometric ratios for allied angles
5. Compound angle formulas for sine and cosine_Part I
6. Compound angle formulas for sine and cosine_Part II
7. Expression acos x + bsin x
8. Compound angle formulas for tangent
9. Transformation formula_Product to addition and difference
10. Transformation formulas_Addition and subtrction to product
11. Multiple angle formulas_Part I
12. Multiple angle formula_Part II
13. Multiple angle formula_Part III
14. Multiple angle formula_Part IV
15. Conditional identities in triangle
16. Value of sin18 and cos 36
17. Important results of multiple angle formula
18. Range of expression using trig. Substitution
19. Trigonometric inequalities in triangle

Trigonometric Equations
Sub topics
1. Trigonometric Equations – Part 1
2. Trigonometric Equations – Part 2
3. Important points for solving Trigonometric Equations
4. Trigonometric Equations based on extreme values

Set Theory
Sub Topics
1. Introduction to set
2. Subset and power set
3. Intersection of sets
4. Union of sets
5. Difference of sets
6. Complement of sets
7. Properties of Operations on Sets
8. Intervals
9. Cardinal number of set

Basic Maths
Sub Topics
1. Linear inequalities in one variable
2. Linear inequalities in two variables
3. Values of square
4. Values of reciprocal
5. Sign Scheme Method
6. Modulus Introduction
7. General definition of modulus and equations
8. Inequalities involving Modulus
9. Exponential Function
10. Logarithm and logarithmic function
11. Properties of logarithm
12. Logarithmic equations
13. Logarithmic inequalities

Relation Functions
Sub Topics
1. Cartesian product of set
2. Relation and function
3. Range of elementary functions
4. Graph of quadratic functions

Quadratic Equations
Sub Topics
1. Remainder and factor theorem
2. Nature of roots
3. Sum and product of roots
4. Common roots
5. Use of discriminant
6. Sign of quadratic function
7. Location of roots

Complex Numbers
Sub Topics
1. Introduction to imaginary number
2. structure of complex number and its operations
3. Comparison of complex numbers
4. Polar form of complex number
5. Properties of polar form
6. De-moivres theorem
7. Cube roots of unity
8. Collinearity of origin and two non-zero complex numbers
9. Inequalities
10. Locus based on modulus_Theory
11. Locus based on Modulus of Complex Number Questions
12. Angle between two lines
13. Geometry using Argument of complex numbers
14. Rotation formula in complex numbers
15. nth roots of unity_Theory
16. nth roots of unity_Problems discussion

Sequences and Series
Sub Topics
1. General term of AP
2. Sum of AP
3. GP and its general term
4. Sum of n terms of GP
5. Harmonic Progression
6. Sigma operator and method of difference
7. Finding nth term from the given sum of n terms
8. Multiple sigma with dependent & independent variables
9. AGP
10. Sum of series by method of difference

Binomial Theorem
Sub Topics
1. Binomial expansion – general
2. Finding coefficients
3. Sum of coefficients
4. Greatest term
5. Sum of Binomial Coefficients
6. Finding Remainder and other applications

Permutations and Combinations
Sub Topics
1. Factorial notations and Counting Principles
2. Permutations of distinct objects
3. Permutation of objects in which some objects are identical
4. Circular permutations
5. Combination – formula
6. Problems based on combinations
7. All possible selections
8. Division distribution of distinct objects
9. Distribution of identical objects
10. Dearrangement

Straight lines
Sub Topics
1. Distance formula, Section Formula, Area of a polygon, Slope, Centroid
2. Incentre, orthocentre, Point slope form, Two point form of Straight line
3. Different forms of straight lines, Dist of a point from a line
4. Family of lines, Locus problems
5. Concurrent lines, point w r t line, angle bisector

Circles
Sub Topics
1. Equation of circle_Center-radius form
2. Equation of circle in general form
3. Equation of circle in parametric form
4. Elementary locus problems
5. Equation of chord whose midpoint is given
6. Position of point w.r.t. circle
7. Length of tangent to circle
8. Position of line w.r.t. circle
9. Equation of tangent at a given point on the circle
10. Equation of tangnet having given slope
11. Tangent to circle from external point
12. Chord of contact of circle
13. Director circle
14. Two circles in different positions
15. Angle between circles and orthogonal circles
16. Family of circles

Parabola
Sub Topics
1. Equation of parabola
2. Focal Chord_
3. Tangent having given slope,_Tangent at a given point on the curve
4. Common Tangent
5. Tangent from external point
6. Properties of Tangent of parabola
7. Normal to parabola at a point on it or having given slope
8. Normal to parabola from a point not lying on it
9. Chord of contact to parabola

Ellipse
Sub Topics
1. Equation of ellipse
2. Ellipse and a line
3. Tangent to ellipse at at point on it_Problems discussion
4. Tangent having given slope and tanent from outside point
5. Director Circle of Ellipse
6. Tangent and normal to ellipse

Hyperbola
Sub topics
1. Equation of Hyperbola
2. Equation of tangent, normal to hyperbola
3. Asymptote to hyperbola

Limits and Derivatives
Sub Topics
1. Limits – elementary
2. Limits – algebraic
3. Limits – trigonometric
4. Limits – exp and logarithm
5. One power infinity form
6. Limits – L’Hopital rule
7. Limits – use of expansion
8. Limits – finding unknowns
9. Differentiation by first principal

Statistics
Sub Topics
Range, Mean deviation, Standard Deviation