# UPSC NDA Previous Year Question Papers with Answer Keys

#### About Exam

The **NDA **exam is conducted by **UPSC **for admission to the Army, Navy and Air Force wings of the **NDA**. This exam is a gateway for candidates looking forward to joining Defense Forces including Army, Navy and Air Force.

This is a national level exam conducted twice a year: **NDA I** and **NDA II** to help candidates make a career in Defense services. **NDA **Exam 2019 schedules for **NDA I** and **NDA II** exam has already been released by **UPSC**.

National Defense Academy & Naval Academy Examination will be a two-step process where candidates first need to take the exam and then qualify the **SSB **interview conducted by the Service Selection Board.

#### Exam Pattern

#### NDA & NA (I) and (II) Examination Pattern

Subject | Code | Duration | Maximum Marks |

## Part I - NDA and NA Examination (I) |
|||

Mathematics | 01 | 2 1/2 Hrs | 300 |

General Ability Test | 02 | 2 1/2 Hrs | 600 |

Total | 900 | ||

Part II - SSB Test/Interview | 900 | ||

## Part I - NDA and NA Examination (II) |
|||

Mathematics | 01 | 2 1/2 Hrs | 300 |

General Ability Test | 02 | 2 1/2 Hrs | 600 |

Total | 900 | ||

Part II - SSB Test/Interview | 900 |

#### Note:

- The papers in all the subjects will consist of objective type questions only. The question papers (test booklets) of Mathematics and Part 'B' of General Ability Test will be set bilingually in Hindi as well as English
- In the question papers, wherever necessary, questions involving the metric system of Weights and Measures only will be set
- Candidates must write the papers in their own hand. In no circumstances will they be allowed the help of a scribe to write answers for them
- The Commission has the discretion to fix qualifying marks in any or all the subjects at the examination The candidates are not permitted to use the calculator or Mathematical or logarithmic table for answering objective type papers (test booklets). They should not, therefore, bring the same inside the examination hall

#### Intelligence and Personality Test

The SSB procedure consists of two stage Selection process - stage I and stage II. Only those candidates who clear the stage I are permitted to appear for stage II. The details are :

(a) Stage I comprises of Officer Intelligence Rating (OIR) tests are Picture Perception * Description Test (PP&DT). The candidates will be shortlisted based on combination of performance in OIR Test and PP&DT.

(b) Stage II Comprises of Interview, Group Testing Officer Tasks, Psychology Tests and the Conference. These tests are conducted over 4 days. The details of these tests are given on the website joinindianarmy.nic.in.

The personality of a candidate is assessed by three different assessors

viz. The Interviewing Officer (IO), Group Testing Officer (GTO) and the Psychologist. There are no separate weightage for each test. The mks are allotted by assessors only after taking into consideration the performance of the candidate holistically in all the test. In addition, marks for Conference are also allotted based on the initial performance of the Candidate in the three techniques and decision of the Board. All these have equal weightage.

The various tests of IO, GTO and Psych are designed to bring out the presence/absence of Officer Like Qualities and their trainability in a candidate. Accordingly candidates are Recommended or Not Recommended at the SSB

#### Eligibility

#### Eligibility Criteria

#### Physical Criteria

**NDA**) and Naval Academy (NA) Examination (I) & (II). Every year, many candidates fail to qualify in the medical test. Hence, candidates are advised to get themselves medically examined before applying for the examination.

#### Height And Weight Standard

#### Vision Standard

#### Naval Candidates

- Uncorrected without glass 6/6, 6/9
- Corrected with glass 6/6, 6/6
- Limits of Myopia â€“0.75
- Limits of Hypermetropia +1.5
- Binocular vision III
- Limits of colour perception I

#### Air Force Candidates

#### Physical Conditioning

#### Nationality

- a Citizen of India, or
- a subject of Nepal, or
- a subject of Bhutan, or
- a Tibetan refugee who came over to India before January 1, 1962, with the intention of permanently settling in India, or
- a person of Indian origin who has migrated from Pakistan, Burma, Sri Lanka or East African Countries of Kenya, Uganda, the United Republic of Tanzania, Zambia, Malawi, Zaire, and Ethiopia or from Vietnam with the intention of permanently settling in India

#### Note

#### Educational Qualification:

- Candidates who are appearing in the 12th Class under the 10+2 pattern of School Education or equivalent examination can also apply for this examination. Such candidates who qualify the SSB interview but could not produce Matriculation/10+2 or equivalent certificate in original at the time of SSB interview should forward duly self-attested Photocopies
- Candidates appearing in the 11th class exam are not eligible for this examination
- Those candidates who have yet to qualify in the 12th class or equivalent examination and are allowed to appear in the UPSC Examination should note that this is only a special concession given to them. They are required to submit proof of passing the 12th class or equivalent examination by the prescribed date of UPSC (i.e. for NDA (I) is December 24, 2019, and for NDA (II) is June 24, 2019) and no request for extending this date will be entertained on the grounds of late conduct of Board/University Examination, delay in declaration of results or any other ground whatsoever
- Candidates who are debarred by the Ministry of Defence from holding any type of Commission in the Defence Services shall not be eligible for admission to the examination and if admitted, their candidature will be cancelled
- Those candidates who have failed INSB/PABT earlier are not eligible for Air Force

#### Age Limit

**Age Limits, Sex and Marital Status:**

#### For NDA & NA (I):

#### For NDA & NA (II):

#### Note

- The date of birth accepted by the Commission is that entered in the Matriculation or Secondary School Leaving Certificate or in a certificate recognised by an Indian University as equivalent to Matriculation or in an extract from a Register of Matriculates maintained by a University which must be certified by the proper authority of the University or in the Higher Secondary or an equivalent examination certificates.
- Candidates should note that only the date of birth as recorded in the Matriculation/Higher Secondary Examination Certificate available or an equivalent certificate on the date of submission of applications will be accepted by the Commission and no subsequent request for its change will be considered or granted
- Candidates should also note that once a date of birth has been claimed by them and entered in the records of the Commission for the purpose of admission to an examination, no change will be allowed subsequently or at any subsequent examination on any ground whatsoever
- The candidates should exercise due care while entering their date of birth in the respective column of the Online Application Form for the examination. If on verification at any subsequent stage any variation is found in their date of birth from the one entered in their matriculation or equivalent examination certificate, disciplinary action will be taken against them by the Commission under the Rules
- Candidates must undertake not to marry until they complete their full training. A candidate who marries subsequent to the date of his application though successful at this or any subsequent Examination will not be selected for training. A candidate who marries during training shall be discharged and will be liable to refund all expenditure incurred on him by the Government

#### PAPER-I

#### Mathematics Syllabus

#### 1. ALGEBRA

Concept of set, operations on sets, Venn diagrams. De Morgan laws, Cartesian product, relation, equivalence relation. Representation of real numbers on a line. Complex numbersâ€”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 in equations of two variables by graphs. Permutation and Combination. Binomial theorem and its applications. Logarithms and their applications.

#### 2. 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 Cramerâ€™s rule and by Matrix Method

#### 3. TRIGONOMETRY

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.

#### 4. ANALYTICAL GEOMETRY OF TWO AND THREE DIMENSIONS

Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equation of a circle in standard and in general form. Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic. Point in a three dimensional space, 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.

#### 5. DIFFERENTIAL CALCULUS

Concept of a real valued functionâ€“domain, range and graph of a function. Composite functions, one to one, onto and inverse functions. Notion of limit, Standard limitsâ€”examples. Continuity of functionsâ€”examples, algebraic operations on continuous functions. Derivative of function at a point, geometrical and physical interpretation of a derivativeâ€”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.

#### 6. 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 integralsâ€”determination of areas of plane regions bounded by curvesâ€”applications. Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equations, solution of first order and first degree differential equations of various typesâ€”examples. Application in problems of growth and decay.

#### 7. 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. Applicationsâ€”work done by a force and moment of a force and in geometrical problems.

#### 8. STATISTICS AND PROBABILITY

Statistics : Classification of data, Frequency distribution, cumulative frequency distributionâ€”examples. Graphical representationâ€”Histogram, Pie Chart, frequency polygonâ€”examples. Measures of Central tendencyâ€”Mean, median and mode. Variance and standard deviationâ€”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 probabilityâ€”classical and statisticalâ€”examples. Elementary theorems on probabilityâ€”simple problems. Conditional probability, Bayesâ€™ theoremâ€”simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binomial distribution.

PAPER-II

#### GENERAL ABILITY TEST

(Code No. 02)

(Maximum Marksâ€”600)

#### Part â€˜Aâ€™â€”ENGLISH (Maximum Marksâ€”200)

The question paper in English will be designed to test the candidateâ€™s understanding of English and workman like use of words. The syllabus covers various aspects like : Grammar and usage, vocabulary, comprehension and cohesion in extended text to test the candidateâ€™s proficiency in English.

#### Part â€˜Bâ€™â€”GENERAL KNOWLEDGE (Maximum Marksâ€”400)

The question paper on General Knowledge will broadly cover the subjects : Physics, Chemistry, General Science, Social Studies, Geography and Current Events.

The syllabus given below is designed to indicate the scope of these subjects included in this paper. The topics mentioned are not to be regarded as exhaustive and questions on topics of similar nature not specifically mentioned in the syllabus may also be asked. Candidateâ€™s answers are expected to show their knowledge and intelligent understanding of the subject.

#### Section â€˜Aâ€™ (Physics)

Physical Properties and States of Matter, Mass, Weight, Volume, Density and Specific Gravity, Principle of Archimedes, Pressure Barometer.

Motion of objects, Velocity and Acceleration, Newtonâ€™s Laws of Motion, Force and Momentum, Parallelogram of Forces, Stability and Equilibrium of bodies, Gravitation, elementary ideas of work, Power and Energy. Effects of Heat, Measurement of Temperature and Heat, change of State and Latent Heat, Modes of transference of Heat. Sound waves and their properties, Simple musical instruments. Rectilinear propagation of Light, Reflection and refraction. Spherical mirrors and Lenses, Human Eye. Natural and Artificial Magnets, Properties of a Magnet, Earth as a Magnet.

Static and Current Electricity, conductors and Non-conductors, Ohmâ€™s Law, Simple Electrical Circuits, Heating, Lighting and Magnetic effects of Current, Measurement of Electrical Power, Primary and Secondary Cells, Use of X-Rays. General Principles in the working of the following:

Simple Pendulum, Simple Pulleys, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure Cooker, Thermos Flask, Gramophone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Marinerâ€™s Compass; Lightening Conductors, Safety Fuses.

#### Section â€˜Bâ€™ (Chemistry)

Physical and Chemical changes. Elements, Mixtures and Compounds, Symbols, Formulae and simple Chemical Equations, Law of Chemical Combination (excluding problems). Properties of Air and Water.

Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbondioxide, Oxidation and Reduction. Acids, bases and salts. Carbonâ€”different forms. Fertilizersâ€”Natural and Artificial. Material used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches and Gun-Powder. Elementary ideas about the structure of Atom, Atomic Equivalent and Molecular Weights, Valency.

#### Section â€˜Câ€™ (General Science)

Difference between the living and non-living. Basis of Lifeâ€”Cells, Protoplasms and Tissues.

Growth and Reproduction in Plants and Animals.

Elementary knowledge of Human Body and its important organs. Common Epidemics, their causes and prevention.

Foodâ€”Source of Energy for man. Constituents of food, Balanced Diet. The Solar Systemâ€”Meteors and Comets, Eclipses. Achievements of Eminent Scientists.

#### Section â€˜Dâ€™ (History, Freedom Movement etc.)

A broad survey of Indian History, with emphasis on Culture and Civilisation.

Freedom Movement in India. Elementary study of Indian Constitution and Administration.

Elementary knowledge of Five Year Plans of India. Panchayati Raj, Co-operatives and Community Development. Bhoodan, Sarvodaya, National Integration and Welfare State, Basic Teachings of Mahatma Gandhi.

Forces shaping the modern world; Renaissance, Exploration and Discovery; War of American Independence. French Revolution, Industrial Revolution and Russian Revolution. Impact of Science and Technology on Society. Concept of one World, United Nations, Panchsheel, Democracy, Socialism and Communism. Role of India in the present world.

#### Section â€˜Eâ€™ (Geography)

The Earth, its shape and size. Latitudes and Longitudes, Concept of time. International Date Line. Movements of Earth and their effects. Origin of Earth. Rocks and their classification; Weatheringâ€”Mechanical and Chemical, Earthquakes and Volcanoes. Ocean Currents and Tides Atmosphere and its composition; Temperature and Atmospheric Pressure, Planetary Winds, Cyclones and Anti-cyclones; Humidity; Condensation and Precipitation; Types of Climate, Major Natural regions of the World. Regional Geography of Indiaâ€”Climate, Natural vegetation. Mineral and Power resources; location and distribution of agricultural and Industrial activities. Important Sea ports and main sea, land and air routes of India. Main items of Imports and Exports of India.

#### Section â€˜Fâ€™ (Current Events)

Knowledge of Important events that have happened in India in the recent years. Current important world events. Prominent personalitiesâ€”both Indian and International including those connected with cultural activities and sports.

**NOTE :** Out of maximum marks assigned to part â€˜Bâ€™ of this paper, questions on Sections â€˜Aâ€™, â€˜Bâ€™,â€˜Câ€™, â€˜Dâ€™, â€˜Eâ€™ and â€˜Fâ€™ will carry approximately 25%, 15%, 10%, 20%, 20% and 10% weightages respectively.