## EXAMINATION NOTICE NO.11/2022-NDA-1 DATED 22.12.2021 (Last Date for Submission of Applications: 11.01.2022)

### NATIONAL DEFENCE ACADEMY & UPSC NDA 1 2022

LAST DATE FOR SUBMISSION AND WITHDRAWAL OF APPLICATIONS for UPSC NDA 1 2022:

(i) The Online Applications can be filled upto 22th Dec, 2021 till 6:00 PM.

(ii) The online Applications can be withdrawn from 22.12.2021 to 11.01.2022 till 6:00 PM. Detailed instructions regarding withdrawal of Applications is available

An Examination will be conducted by the **Union Public Service Commission** on 10th April , 2021 for admission to the Army, Navy and Air Force wings of the NDA for the 149th Course, and for the 110th Indian Naval Academy Course (INAC) commencing from 2nd Jan, 2023.

### CENTRES OF UPSC NDA 1 2022 EXAMINATION:

The Examination will be held at the following Centres :

Agartala, Ahmedabad, Aizawl, Prayagraj (Allahabad), Bengaluru, Bareilly, Bhopal, Chandigarh, Chennai, Cuttack, Dehradun, Delhi, Dharwad, Dispur, Gangtok, Hyderabad, Imphal, Itanagar, Jaipur, Jammu, Jorhat, Kochi, Kohima, Kolkata, Lucknow, Madurai, Mumbai, Nagpur, Panaji (Goa), Patna, Port Blair, Raipur, Ranchi, Sambalpur, Shillong, Shimla, Srinagar, Thiruvananthapuram, Tirupati, Udaipur and Vishakhapatnam.

Applicants should note that there will be a ceiling on the number of candidates allotted to each of the centres except Chennai, Dispur, Kolkata and Nagpur. Allotment of Centres will be on the first-apply-first-allot basis and once the capacity of a particular centre is attained, the same will be frozen. Applicants, who cannot get a centre of their choice due to ceiling, will be required to choose a Centre from the remaining ones. Applicants are, thus, advised that they may apply early so that they could get a Centre of their choice.

### CONDITIONS OF ELIGIBILITY:

(a) Nationality : A candidate must be unmarried male and must be :

(i) (ii)

a citizen of India, or a subject of Nepal, or

a person of Indian origin who has migrated from Pakistan,

(iii)

Burma, Sri Lanka and East African Countries of Kenya, Uganda, the United Republic of Tanzania, Zambia, Malawi, Zaire and Ethiopia or Vietnam with the intention of permanently settling in India.

Provided that a candidate belonging to categories (ii) and (iii), above shall be a person in whose favour a certificate of eligibility has been issued by the Government of India.

### Age Limits, Sex and Marital Status :

Only unmarried male and female candidates born not earlier than 02nd July , 2003 and not later than 2nd July 2006 are eligible.

**Educational Qualifications for UPSC NDA 1 2022**:

- For Army Wing of National Defence Academy :—12th Class pass of the 10+2 pattern of School Education or equivalent examination conducted by a State Education Board or a University.
- For Air Force and Naval Wings of National Defence Academy and for the 10+2 Cadet Entry Scheme at the Indian Naval Academy :—12th Class pass with Physics, Chemistry and Mathematics of the 10+2 pattern of School Education or equivalent conducted by a State Education Board or a University.
- 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.

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 (**i.e. 24th Jan 2023)** 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.

### SCHEME OF EXAMINATION

- The subjects of the written examination, the time allowed and the maximum marks allotted to each subject will be as follows:—

### SYLLABUS OF THE EXAMINATION

**PAPER-I MATHEMATICS (Code No. 01) (Maximum Marks-300)**

** 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 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.

**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.

**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 function–domain, range and graph of a function. Composite functions, one to one, onto and inverse functions. 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.

**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 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 a differential equations, solution of first order and first degree differential equations of various types—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. Applications—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 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.

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 Binominal distribution.

**PAPER-II**

**GENERAL ABILITY TEST (Code No. 02) (Maximum Marks—600)**

**Part ‘A’—ENGLISH (Maximum Marks—200)**

The question paper in English will be designed to test the candidate’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 candidate’s proficiency in English.

**Part ‘B’—GENERAL KNOWLEDGE (Maximum Marks—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. Candidate’s answers are expected to show their knowledge and intelligent understanding of the subject.

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