Mathematics (NDA)

• 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 decimal system to 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.

• Angles and their measures in degrees and in radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications-Height and distance, properties of triangles.

• Types of matrices, operations on matrices. Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix, Applications-Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.

• Concept of a real-valued function–domain, range, and graph of a function. Composite functions, one-to-one, onto, and inverse functions. The notion of limit, Standard limits—examples. Continuity of functions—examples, algebraic operations on continuous functions. Derivative of function at a point, geometrical and physical interpretation of a derivative—applications. Derivatives of sum, product, and quotient of functions, derivative of a function with respect to another function, derivative of a composite function. Second-order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima .

• Integration as inverse of differentiation, integration by 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.
• Definition of order and degree of a differential equation, formation of a differential equation by examples. A general and particular solution of differential equations, solution of the first order and first-degree differential equations of various types—examples. Application in problems of growth and decay .

• 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. Application work done by a force and moment of a force and in geometrical problems

• 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. 

• 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 Binominal distribution .

Mathematics Bookslist for Nda -2024

• Quantitative Aptitude for Competitive Examinations by R.S. Aggarwal
• Study Package for NDA/NA Entrance Exam by Tata McGraw-Hill Education India
• Chapter wise-Section wise Solved Papers NDA & NA by Arihant

Here's a strategy to tackle the Maths section of the NDA exam:

Master the Fundamentals:

• Build a strong foundation in Algebra, Trigonometry, Geometry, and Calculus. These are the pillars of the NDA Maths syllabus.
• NCERT books (up to Class 12) are a great resource to grasp the core concepts
• Focus on Important Chapters:

Analyze previous years' question papers to identify high-weightage chapters. These typically include:

• Complex numbers
• Permutations and Combinations
• Coordinate Geometry (considered to be scoring)
• Trigonometry ratios & identities
• Calculus (differentiation, integration)
• Vectors & 3D Geometry

Develop a Study Plan:

• Divide the syllabus into manageable portions and create a daily or weekly schedule.
• Allot more time to challenging topics and revise weaker areas regularly.
• Practice Makes Perfect:

Consistent practice is key. Solve problems from different sources like:

• Previous years' NDA question papers [You can find these online on various coaching websites]
• Mock tests (offered by coaching institutes or online platforms)
• Chapter-wise practice problems from NDA prep books
• Sharpen Your Speed and Accuracy:

Time management is crucial in the NDA exam.

• Practice solving questions within the stipulated time frame to improve speed and accuracy.

Additional Tips:

• Clear your doubts: Don't hesitate to clarify doubts with teachers, mentors, or online forums.
• Learn from mistakes: Analyze your errors from practice tests and mock exams to avoid repetition.
• Stay focused and motivated: Consistency and perseverance are key to success in the NDA Maths exam.
• By following these strategies and devoting focused study time, you can significantly improve your chances of scoring well in the NDA Maths section.