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UPSC NDA Mathematics 6

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About UPSC NDA  Mock Test

The UPSC NDA (National Defence Academy) Mock Test is an essential preparation tool for candidates who aspire to join the Indian Armed Forces. It is a practice test that simulates the actual UPSC NDA exam and is designed to help candidates assess their level of preparation and identify areas of weakness.

The UPSC NDA exam is conducted twice a year, and the mock test is typically held a few weeks before the actual exam date. It is conducted by various coaching institutes and online portals, and candidates can choose to take it in online or offline mode.The UPSC NDA mock test usually consists of two papers - Mathematics and General Ability Test (GAT). The Mathematics paper tests the candidate's knowledge of mathematics, including topics such as algebra, trigonometry, geometry, and calculus. The GAT paper, on the other hand, tests the candidate's proficiency in English, general knowledge, and reasoning.

UPSC NDA Mock Test: Overview

Authority Name Union Public Service Commission, UPSC.
Exam National Defence Academy (NDA)
Level of Exam National Level
Category Mock Tests, Syllabus, and Exam Pattern
Posts Name NDA
Selection Process Written Test consisting of Objective Type Questions
Intelligence & Personality Test (SSB)
Official Website upsc.gov.in

Elements which Are Required for UPSC NDA  Mock Test:

Taking the UPSC NDA Mock Test is an excellent way to prepare for the actual exam. It helps candidates assess their knowledge and performance in a simulated environment, giving them a clear understanding of their strengths and weaknesses. However, it's important to note that taking the mock test without plagiarism can provide even greater benefits.

One of the primary advantages of taking the UPSC NDA Mock Test without plagiarism is that it allows candidates to develop their critical thinking skills. When a candidate prepares for the exam by simply memorizing answers or copying them from others, they do not gain a deep understanding of the concepts.

  • The UPSC NDA Mock Test consists of a total of 10 Full-Length Mock Tests.
  • The Mock Tests are available in both Hindi and English language for the candidate's convenience.
  • The performance summary of the mock tests along with the solutions & explanations is also provided at the end of each UPSC NDA mock test.

Why should you take the UPSC NDA Mock Test?

Taking the UPSC NDA mock test helps candidates to get familiar with the exam pattern and the types of questions that may appear in the actual exam. It also helps them to manage their time effectively and improve their speed and accuracy.

Candidates who take the mock test can also get their answers evaluated and receive feedback from experts. This feedback can be extremely valuable in identifying areas of weakness and developing a strategy to improve performance.However, when a candidate takes the mock test without plagiarism, they are forced to think critically and apply their knowledge in unique ways. This not only helps them prepare for the exam but also develops their ability to analyze complex problems.

What are the advantages of taking the UPSC NDA Mock Test?

Updated Syllabus: Before taking the mock test, candidates must ensure that they have an updated syllabus. The syllabus provides an outline of the topics and concepts that are covered in the exam. Candidates should ensure that they have the latest syllabus to ensure that they are studying the right material.

Question Bank: A question bank is an essential element for any mock test. It provides candidates with a variety of questions that are similar to those in the actual exam. A question bank can help candidates prepare for different types of questions that they may encounter in the exam.

Timer: A timer is required for a mock test to simulate the actual exam environment. Candidates must ensure that they keep track of time while taking the mock test. This will help them manage their time effectively during the actual exam.

Exam-like Environment: It is essential to create an exam-like environment while taking the mock test. Candidates should ensure that they are in a quiet place with no distractions. This will help them concentrate better and simulate the actual exam environment.

Answer Key: After taking the mock test, candidates must check their answers using an answer key. The answer key provides candidates with the correct answers to the questions. This will help candidates identify their mistakes and learn from them.

UPSC NDA Mock Test: Exam Pattern

Code Exam Name Duration No. of Questions Maximum Marks



2 ½ hours




General Ability Test

2 ½ hours






SSB Interview






UPSC NDA  Mock Test: Syllabus

NDA Mathematics Syllabus

Topic Topic-wise Syllabus
Algebra Sets, Venn diagrams, De Morgan laws, Cartesian product, relation, equivalence relation. Real numbers, Complex numbers, Modulus, Cube roots, Conversion of a number in a 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. The notion of limit, Standard limits, Continuity of functions, and 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, a derivative of a function concerning another function, the 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 solutions of differential equations, solutions of the 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 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 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 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. The angle between two lines and the 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.

NDA Syllabus- Physics

NDA Syllabus For Physics  
  1. Physical Properties and States of Matter
  2. Modes of transference of Heat
  3. Mass, Weight, Volume, Sound waves and their properties
  4. Simple musical instruments
  5. Rectilinear propagation of Light
  6. Density and Specific Gravity
  7. Reflection and refraction
  8. Principle of Archimedes
  9. Spherical mirrors and Lenses
  10. Pressure Barometer
  11. Human Eye
  12. Motion of objects
  13. Natural and Artificial Magnets
  14. Velocity and Acceleration
  15. Properties of a Magnet
  16. Newton’s Laws of Motion
  17. Earth as a Magnet
  18. Force and Momentum
  19. Static and Current Electricity
  20. Parallelogram of Forces
  21. Conductors and Non-conductors
  22. Stability and Equilibrium of bodies
  23. Ohm’s Law
  24. Gravitation
  25. Simple Electrical Circuits
  26. Elementary ideas of work
  27. Heating, Lighting, and Magnetic effects of Current
  28. Power and Energy
  29. Measurement of Electrical Power
  30. Effects of Heat
  31. Primary and Secondary Cells
  32. Measurement of Temperature and Heat
  33. Use of X-Rays
  34. General Principles in the working of Simple Pendulum, Simple Pulleys, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure Cooker, Thermos Flask, Gramophone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Mariner’s Compass; Lightning Conductors, Safety Fuses.

NDA Syllabus- Chemistry

NDA Syllabus For Chemistry  
  1. Preparation and Properties of Hydrogen, Oxygen, Nitrogen, and Carbon Dioxide, Oxidation, and Reduction.
  2. Acids, bases, and salts.
  3. Carbon— different forms
  4. Physical and Chemical Changes
  5. Fertilizers—Natural and Artificial
  6. Elements
  7. The material used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, and Gunpowder
  8. Mixtures and Compounds
  9. Elementary ideas about the structure of Atom
  10. Symbols, Formulae, and simple Chemical Equation
  11. Atomic Equivalent and Molecular Weights
  12. Law of Chemical Combination (excluding problems)
  13. Valency
  14. Properties of Air and Water

NDA Syllabus- General Science

NDA Syllabus For General Science  
  1. Common Epidemics, their causes, and prevention
  2. Difference between the living and non-living
  3. Food—Source of Energy for man
  4. Basis of Life—Cells, Protoplasms, and Tissues
  5. Constituents of food
  6. Growth and Reproduction in Plants and Animals
  7. Balanced Diet
  8. Elementary knowledge of the Human Body and its important organs
  9. The Solar System—Meteors and Comets, Eclipses. Achievements of Eminent Scientists

NDA Syllabus- History, Freedom Movement

NDA Syllabus For History  
  1. Forces shaping the modern world;
  2. Renaissance
  3. Exploration and Discovery;
  4. A broad survey of Indian History, with emphasis on Culture and Civilisation
  5. Freedom Movement in India
  6. French Revolution, Industrial Revolution, and Russian Revolution
  7. War of American Independence,
  8. Impact of Science and Technology on Society
  9. Elementary study of Indian Constitution and Administration
  10. Concept of one World
  11. Elementary knowledge of Five Year Plans of India
  12. United Nations,
  13. Panchsheel,
  14. Panchayati Raj, Democracy, Socialism and Communism
  15. Role of India in the present world
  16. Co-operatives and Community Development
  17. Bhoodan, Sarvodaya,
  18. National Integration and Welfare State
  19. Basic Teachings of Mahatma Gandhi

NDA Syllabus- Geography

NDA Syllabus For Geography  
  1. The Earth, its shape and size
  2. Ocean Currents and Tides Atmosphere and its composition
  3. Latitudes and Longitudes
  4. Temperature and Atmospheric Pressure, Planetary Winds, Cyclones, and Anticyclones; Humidity; Condensation and Precipitation
  5. Concept of time
  6. Types of Climate
  7. International Date Line
  8. Major Natural Regions of the World
  9. Movements of Earth and their effects
  10. Regional Geography of India
  11. Climate, Natural vegetation. Mineral and Power resources;
  12. Location and distribution of agricultural and Industrial activities
  13. Origin of Earth. Rocks and their classification
  14. Important Sea ports and main sea, land, and air routes of India
  15. Weathering—Mechanical and Chemical, Earthquakes and Volcanoes
  16. Main items of Imports and Exports of India

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1) What is a UPSC NDA Mock Test?

Ans: A mock test is a practice test that simulates the actual NDA exam. It includes questions based on the NDA syllabus, and is designed to help candidates assess their preparation and identify their strengths and weaknesses.

2) Why is it important to take UPSC NDA mock tests?

Ans: Mock tests help candidates get a feel for the actual exam and improve their time management skills. They also help candidates identify their weak areas and focus their preparation accordingly.

3) How many mock tests should I take?

Ans: It's recommended that you take at least 5-6 mock tests before the actual exam. This will help you practice and improve your performance.

4) What is the duration of the mock test?

Ans: The duration of the mock test is usually the same as the actual NDA exam, which is 5 hours for both the Mathematics and General Ability Test.

5) What types of questions are included in the mock test?

Ans: The mock test includes multiple choice questions (MCQs) based on the NDA syllabus for Mathematics and General Ability Test.

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