Mathematics syllabus

General knowledge (detailed breakdown not specified in notification — indicative)

• Indian history and freedom movement
• Geography of India and Uttar Pradesh
• Indian constitution and polity
• Basic Indian economy
• General science and everyday science
• Environment and ecology
• Uttar Pradesh special — geography history culture and administration
• Current national and international events
• Current affairs of the education sector
• Sports awards and books-authors

Algebra

• Relations and functions
• Equivalence relations and classes
• One-one and onto functions
• Inverse of function and binary operations
• Matrices types and operations
• Symmetric and skew-symmetric matrices
• Invertible matrices
• Determinants and properties
• Adjoint and inverse of square matrix
• System of linear equations
• Theory of equations
• Arithmetic geometric harmonic progressions
• Permutations and combinations
• Binomial theorem
• Exponential and logarithmic series
• Probability multiplication theorem
• Conditional probability
• Independent events and total probability

Calculus

• Limits of a function
• Continuity and differentiability
• Derivative of composite function
• Rolle theorem
• Lagrange and Cauchy mean value theorems
• Taylor and Maclaurin series
• L Hospital rule
• Successive differentiation and Leibnitz theorem
• Tangent and normal
• Increasing and decreasing functions
• Maxima and minima
• Methods of integration
• Definite integral as limit of sum
• Area under curves
• Riemann integration

Ordinary differential equations

• Order and degree of differential equations
• Formation of differential equations
• First order first degree solutions
• Singular solutions
• Linear DE with constant coefficients
• Homogeneous differential equations

Coordinate geometry of two dimensions

• General equation of second degree
• Pair of straight lines
• Circle
• Parabola
• Ellipse
• Hyperbola
• Equations of tangents and normals
• Common tangents to two conics
• Pair of tangents and chord of contact

Vectors and three-dimensional geometry

• Vectors and scalars
• Unit vectors direction cosines and ratios
• Scalar and vector products
• Cartesian and vector equations of lines
• Coplanar and skew lines
• Shortest distance between two lines
• Cartesian and vector equations of planes
• Angles between lines and planes
• Distance of a point from a plane
• Equations of sphere cone and cylinder

Abstract algebra

• Groups and examples
• Subgroups
• Homomorphism and isomorphism
• Order of an element
• Cyclic groups
• Symmetric group Sn
• Lagrange theorem
• Fermat theorem
• Normal subgroups
• Fundamental theorem of homomorphism
• Rings and fields with examples

Linear algebra

• Vector spaces
• Subspaces
• Linear dependence and independence
• Basis and dimension
• Quotient space
• Linear sum and direct sum
• Linear transformations
• Kernel and image
• Rank and nullity
• Rank-nullity theorem
• Singular and non-singular transformations
• Matrix of a linear transformation

Vector calculus

• Scalar and vector fields
• Gradient divergence and curl
• Vector identities
• Directional derivatives
• Line surface and volume integrals
• Green theorem
• Gauss divergence theorem
• Stokes theorem

Mechanics

• Equilibrium under three forces
• Coplanar forces
• Centre of gravity
• Common catenary
• Moment of inertia
• Projectile motion
• Work power and energy
• Radial and transverse velocity and acceleration
• Tangential and normal velocity and acceleration
• Central orbits

Trigonometry

• Trigonometric equations
• Properties of triangles
• Inverse circular functions
• Height and distance
• Complex numbers
• De Moivre theorem and applications