MATHS

• Concept of set, operations on sets, Venn diagrams.
• De Morgan laws, Cartesian product, relation, equivalence relation.
• Representation of real numbers on a line.
• Complex numbers—basic properties, modulus, argument, cube roots of unity.
• Binary system of numbers.
• Conversion of a number in a decimal system to a binary system and vice-versa.
• Arithmetic, geometric and harmonic progressions.
• Quadratic equations with real coefficients.
• The solution of linear inequations of two variables by graphs.
• Permutation and combination.
• Binomial theorem and its applications.
• Logarithms and their applications.

MATRICES & DETERMINANTS

• Types of matrices
• Operations on matrices
• Determinant of a matrix
• Basic properties of determinants
• Adjoint and inverse of a square matrix
• Applications of matrices

1. Solution of a system of linear equations in two or three unknowns using Cramer’s rule
2. Solution of a system of linear equations in two or three unknowns using Matrix Method

TRIGONOMETRY

• Angles and their measures in degrees and radians
• Trigonometric ratios
• Trigonometric identities including sum and difference formulae
• Multiple and sub-multiple angles
• Inverse trigonometric functions
• Applications such as height and distance and properties of triangles.

ANALYTICAL GEOMETRY OF 2 & 3 DIMENSIONS

• Rectangular Cartesian Coordinate system
• Distance formula
• Equation of a line in various forms
• The angle between two lines
• The distance of a point from a line
• Equation of a circle in standard and general form
• Standard forms of parabola, ellipse, and hyperbola
• Eccentricity and axis of a conic
• A point in three-dimensional space and the distance between two points
• Direction cosines and direction ratios
• Equation of a plane and a line in various forms
• The angle between two lines and the angle between two planes
• Equation of a sphere

DIFFERENTIAL CALCULUS

• Concept of a real-valued function including domain, range, and graph of a function.
• Composite functions and their properties including one-to-one, onto, and inverse functions.
• Understanding of the notion of limit and examples of standard limits.
• Continuity of functions and examples, including algebraic operations on continuous functions.
• Derivative of a function at a point, with geometrical and physical interpretation, and applications.
• Derivatives of sum, product, and quotient of functions, a derivative of a function with respect to another function, a derivative of a composite function, and second-order derivatives.
• Understanding increasing and decreasing functions.
• Application of derivatives in problems of maxima and minima.

INTEGRAL CALCULUS & DIFFERENTIAL EQUATIONS

• Integration as the inverse of differentiation.
• Methods of integration: substitution and by parts.
• Standard integrals involving algebraic expressions, trigonometric, exponential, and hyperbolic functions.
• Evaluation of definite integrals.
• Determination of areas of plane regions bounded by curves.
• Applications of integrals.
• Definition of order and degree of a differential equation.
• Formation of a differential equation by examples.
• General and particular solutions of differential equations.
• Solutions of the first-order and first-degree differential equations of various types.
• Applications in problems of growth and decay.

VECTOR ALGEBRA

• Vectors in two and three dimensions
• Magnitude and direction of a vector
• Unit and null vectors
• Addition of vectors
• Scalar multiplication of a vector
• Scalar product or dot product of two vectors
• Vector product or cross product of two vectors
• Applications in work done by a force and moment of a force and in geometrical problems

STATISTICS & PROBABILITY

• Statistics
• Classification of data
• Frequency distribution
• Cumulative frequency distribution—examples
• Graphical representation—Histogram, Pie Chart, frequency polygon— examples
• Measures of Central tendency—Mean, median and mode
• Variance and standard deviation—determination and comparison
• Correlation and regression
• Probability
• Random experiment, outcomes and associated sample space, events
• Mutually exclusive and exhaustive events, impossible and certain events
• Union and Intersection of events
• Complementary, elementary and composite events
• Definition of probability—classical and statistical—examples
• Elementary theorems on probability—simple problems
• Conditional probability, Bayes’ theorem—simple problems
• Random variable as function on a sample space
• Binomial distribution, examples of random experiments giving rise to Binomial distribution.

ENGLISH

• Grammar & usage
• Comprehension & cohesion
• Spotting errors
• Para Jumbling
• Fill in the blanks
• Synonyms & Antonyms
• Vocabulary
• Cloze Test
• Idioms & Proverbs
• Completion of Sentence & Para
• Sentence Correction & Improvement