Mathematics
Concepts
- Set operations, 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
- 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
- Solution of a system of linear equations using Cramer’s rule
- Solution of a system of linear equations 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, 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 two planes
- Equation of a sphere
Differential Calculus
- Concept of a real-valued function, domain, range, and graph
- Composite functions, one-to-one, onto, inverse functions
- Notion of limit, standard limits
- Continuity of functions, algebraic operations on continuous functions
- Derivative of a function at a point, geometrical and physical interpretation
- Derivatives of sum, product, quotient, and composite functions
- Second-order derivatives
- Increasing and decreasing functions
- Application of derivatives in maxima and minima
Integral Calculus & Differential Equations
- Integration as the inverse of differentiation
- Methods of integration: substitution and by parts
- Standard integrals involving algebraic, trigonometric, exponential, and hyperbolic functions
- Evaluation of definite integrals
- Determination of areas of plane regions bounded by curves
- Applications of integrals
- Differential equations: order, degree, formation, and solutions
- 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
- Vector operations: addition, scalar multiplication
- Dot product, cross product
- Applications in work, force, and geometrical problems
Statistics & Probability
- Classification of data, frequency distribution
- Graphical representation: Histogram, Pie Chart, frequency polygon
- Measures of Central tendency: Mean, median, mode
- Variance and standard deviation
- Probability concepts, random experiments
- Probability theorems, Bayes’ theorem
- 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