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# List of Important topics for NDA Mathematics from which more questions were asked by UPSC.

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NDA Paper I consists of questions from Mathematics. In comparison to the General Ability Test, this section carries less weight. It does, however, play an important role in the selection of candidates. The NDA Mathematics section is not difficult to master because the questions are mostly from Classes 11 and 12. Candidates can achieve good exam results with revision and practice. NDA toppers have suggested that candidates cover the entire Math syllabus. Students must consult school-level textbooks to understand the fundamental concepts. Here are a few pointers to help you prepare for the NDA Mathematics exam.

### NDA Mathematics weightage:-

The NDA Mathematics section contains 120 objective-type multiple-choice questions. This section is worth 300 marks in total. Candidates have two hours and thirty minutes to complete the question paper. Candidates receive 2.5 marks for correct answers and 0.83 marks for incorrect answers.

#### What is the Math Level in NDA?

The NDA Maths syllabus is at Class 11 and 12 levels. Algebra, Matrices and Determinants, Trigonometry, Calculus, Probability, Complex Numbers, and Quadratic Equation questions are asked. The Math paper is worth a total of 300 marks.

## Important topics for NDA Mathematics

Subjects Number of Question

Algebra

30

Trigonometry

20

Determinants and matrices

10

Analytical Geometry

20

Vector Algebra

10

Statistics and Probability

10

Differential calculus and Integral calculus

20

Total

120

#### Syllabus for NDA Mathematics:-

Algebra, Matrices and Determinants, Trigonometry, Analytical Geometry in two and three dimensions, Differential Calculus, Integral Calculus and Differential Equations, Vector Algebra, Statistics and Probability are all covered in the NDA curriculum. The following is the detailed syllabus for the Maths paper:

Topics Sub-Topics

Algebra

Sets, Venn diagrams, De Morgan laws, Cartesian product, relation, equivalence relation. Real numbers, Complex numbers, Modulus, Cube roots, Conversion of a number in Binary system to Decimals and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations, Linear inequations, Permutation and Combination, Binomial theorem and Logarithms.

Calculus

Concept of a real valued function, domain, range and graph of a function. Composite functions, one to one, onto and inverse functions. Notion of limit, Standard limits, Continuity of functions, algebraic operations on continuous functions. Derivative of function at a point, geometrical and physical interpretation of a derivative-application. 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

Matrices and Determinants

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.

Integral Calculus and Differential Equations

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. General and particular solution of differential equations, solution of first order and first-degree differential equations of various types-examples. Application in problems of growth and decay.

Trigonometry

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

Vector Algebra

Vectors in two and three dimensions, magnitude, and direction of a vector. Unit and null vectors, the 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—work done by a force and moment of a force and in geometrical problems.

Analytical Geometry Of Two and Three Dimension

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

Statistics and Probability

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.

#### How to prepare for NDA Mathematics?

Follow the tips and tricks below for the NDA Mathematics section:

1. Candidates must understand the NDA syllabus and mark the important topics after reviewing the previous year’s question papers.
2. Begin by preparing the important NDA Mathematics topics first, and then delegate time for the difficult topics.
3. Mock tests can be used to determine how much time to devote to each type of question. Candidates should also solve previous year’s question papers to get a sense of the types of questions that will be asked in the exam.
4. Candidates must learn time management tips, tricks, and shortcuts.
5. Memorize basic calculations like squares and cubes.
6. Make a list of shortcuts and formulas to refer to during final revisions.
7. Because there is negative marking in the exam, they should only mark the answer if they are certain of it. During the exam, do not guess the answers.
8. For NDA preparation, candidates should read good mathematics books.
9. During the final stage of preparation, set aside at least three hours to go over the formula.
10. Don’t get confused when converting numbers from decimal to binary.
11. Trigonometry can be difficult. To understand concepts like Triangle Properties and Inverse Trigonometric Functions. As a result, answer such questions at the end.
12. The most important unit in the curriculum is Vector Algebra. Practice problems involving the Vector Product or Cross Product of two vectors.

#### NDA 2022 Cut-off Marks (Expected):-

The probable cut-off for this NDA written exam which is going to be held on 10th April 2022 is as per the cut-off of the last 5 years. Probably the cut-off of this NDA written exam can be between 350 to 360. Below we are giving you information about the last 5 years’ cut-off.

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