ALGEBRA
1. Theory of Equations and Symmetric Functions of the Roots
2. Progressions (A.P., G.P. and H.P.)
3. Exponential and Logarithmic Series
4. Permutations and Combinations
5. Binomial Theorem
6. Matrices and Determinants
7. Sets and Set Theory
8. Relations and Functions
9. Number Theory
10. Group
11. Linear Algebra

Probability
GEOMETRY
Section–I : Analytical Plane Geometry
1. Pair of Straight Lines
2. The Circle
3. The Parabola
4. The Ellipse
5. The Hyperbola
6. Polar Equations
( vi ) Section–II : Analytical Solid Geometry
Fundamental Concept of 3D
8. The Plane
9. The Straight Line
10. The Sphere
11. The Cone
12. The Cylinder
TRIGONOMETRY
1.Trigonometrical Ratios and Identities
2.Trigonometrical Equations
3.Properties of Triangles
4.Height and Distances
5.Inverse Circular Function
6.Hyperbolic Functions
7.Complex Number and DeMoivre’s Theorem
8.Miscellaneous Exercise
CALCULUS
Section–I : Differential Calculus
1. Function
2. Limit, Continuity and Differentiability
3. Rolle’s Theorem, Mean Value Theorem, Taylor’s Theorem
4. Tangents and Normals
5. Maxima and Minima
6. Curvature
7. Asymptotes
8. Curve Tracing
9. Partial Differentiation
10. Miscellaneous Exercise
( vii )Section–II : Integral Calculus
11. Indefinite Integrals
12. Definite Integrals
13. Rectification, Quadrature, Volume and Surfaces
14. Multiple Integration
Differential Equations
Differential Equations
1 Definition
2 Differential Equations of First Order and First Degree
3 Differential Equation of First Order but not of First Degree
4 Equation Solvable for p, x and y
5 Clairaut’s Equation
6 Geometrical Meaning of a Differential Equation of the First Order
7 Singular Solution
8 Determination of a Singular Solution
9 Trajectory
10 Orthogonal Trajectory
11 Linear Differential Equation with Constant Coefficient
12 Solution of the Differential Equation
13 Particular Integral (P.I.)
14 Methods of Finding Particular Integral
Vector Algebra
Vector Analysis
1 Scalar and Vector Quantities
2 Unit Vector
3 Equal Vector
4 Position Vector
5 Addition of Vectors
6 Properties of Addition
6 Subtraction of Vectors
8 Multiplication of a Vector by a Scalar
9 Properties of Scalar Multiplication
( viii )
10 Position Vector of a Point Dividing a Line in a given Ratio
11 Collinear Vectors
12 Linearly Independent and Dependent System of Vectors
13 Coplanar Vectors
14 Vectorial Equation of a Line
15 Bisectors of the Angles between Two Straight Lines
16 Condition for Three Points to be Collinear
17 Vectorial Equation of a Plane
18 Condition for Four Points to be Coplanar
19 Scalar or Dot Product with their Properties
20 Vector or Cross Product of Two Vectors
21 Properties of Vector Product
22 Scalar Triple Product with Properties
23 Vector Triple Product with their Properties
24 Scalar and Vector Product of Four Vectors
25 Perpendicular Distance of a given Point from a Line
26 Reciprocal System of Vectors
DYNAMICS
1. Velocity, Acceleration and Rectilinear Motion
2. Motion under Gravity
3. Projectiles
4. Impulse, Work, Power and Energy
5. Collision of Elastic Bodies
6. D’ Alemberts Principle (Equation of Motion of a Rigid Body)
7. Moment of Inertia
STATICS
Equilibrium of Three Forces Acting on a Particle
2. Equilibrium of More than Three Forces Acting on a Particle
3. Equilibrium of Three Forces Acting on by a Rigid Body
4. General Conditions of Equilibrium
5. Centre of Gravity
