NDA & NA Examination Paper-1- Mathematics

UPSC NDA 2024: Syllabus, Exam Pattern, Eligibility Criteria, Vacancy

UPSC (Union Public Service Commission) conducts the National Defence Academy & National Naval Academy Examination (NDA & NA Examination) twice a year. It is a national-level exam for recruiting the candidates in Army, Navy, and Air force. In a year it is conducted as NDA & NA (I), and N...(Read More)

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Summary

UPSC (Union Public Service Commission) conducts the National Defence Academy & National Naval Academy Examination (NDA & NA Examination) twice a year. It is a national-level exam for recruiting the candidates in Army, Navy, and Air force.

In a year it is conducted as NDA & NA (I), and NDA & NA (II) Examinations. The exam consists of 2 Papers- (1) Mathematics and (2) General Ability Test (GAT). The syllabus of both papers is based on CBSE 10+2 standards. After qualifying for the written test the candidates are called for an NDA SSB Interview. And hence the final selection of Students depends on their performance in the written exam and SSB Interview.

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  • Exam Pattern

    Total Marks : 300
    Total Time : 150 Min
    -ve marking : 0.83 (For each wrong answer)
    Subject Qns. Marks
    Mathematics 120 300
    Total 120 300

    Eligibility Criteria

    Educational Qualifications for NDA and NA:

    (A) For Army Wing of National Defence Academy:

    • 12th Class pass in the 10+2 school education pattern, or equivalent examination administered by a State Education Board or a University.

     

    (B)  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 from the 10+2 school education pattern or equivalent from a State Education Board or a University

     

    Age Limit for NDA and NA:

    *Only unmarried male/female candidates born between the dates of July 2nd, 2005 and July 1st, 2008 are eligible.*

    Age Relaxation Extra as per NDA I Exam 2024 Rules.

    Important Note: 

    • Candidates enrolled in the 12th grade under the 10+2 school education pattern or an equivalent examination are also eligible to take this exam. They are required to submit proof of passing the 12th class or equivalent examination by the prescribed date (i.e. 24th December, 2024) 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 have been prohibited from holding any form of commission in the Defence Services by the Ministry of Defence will be ineligible to take the exam.

    Physical Standard for NDA and NA:

    • Aspirants for admission to the National Defence Academy and Naval Academy Examination must be physically fit according to physical standards.

    • Aspirants are also advised to correct a few minor flaws/ailments such as Wax (ears), Deviated Nasal Septum, Hydrocele/Phimosis, Overweight/Underweight, Undersized Chest, Piles, Tonsillitis, and Varicocele.

    • UPSC has set the different physical, visual, and medical standards for males and females for different posts of CDS, so candidates can check the information of physical standards through the official Website link on our website or whether they can check directly from the official Website of UPSC.

    Exam Pattern

    Schemes of the NDA and NA Selection Procedure:

    The recruitment process will be held in the following phases.

    • Written Exam

    • SSB Test/ Interview

    • Medical Examination/ Physical Standard

     

    NDA and NA: Written Exam  

    Subject 

    Code

    Duration

    Maximum Marks

    Total number of Questions

    Total Marks

    Mathematics

    01

    2½ Hours

    300

    120

    300

    Important Note:

    • The examination will take place offline.

    • All the questions in the written examination will be of Multiple Choice (MCQs) type.

    • In the mathematics section each question carries 2.5 marks.

    • Each incorrect answer will be 1/3rd marks deduction.

    • The Examination test will be conducted in both English and Hindi (`Bilingual).

     

    NDA and NA: Intelligence and Personality Test

    The total marks given for the SSB Test/ Interview is 900.

    The SSB procedure is divided into two stages:

    • Stage-I and Stage-II.

    *Only those candidates who pass stage-I are eligible to take stage-II.*

    • Stage-I: Officers Intelligence Rating (OIR) Test are Picture Perception * Description Test (PP & DT) 

    • Stage-II: The second stage consists of an interview, Group Testings Officers Task (GTO), psychological tests, and the conference.

    Vacancy Details

    The following are the likely positions that will be filled up through this Exam:

     

    Organization Name

    TOTAL

    NDA – National Defence Academy

    Army

    208 (including 10 for female candidates)

    Navy

    42 (including 12 for female candidates)

    Air Force

    Flying

    92 (including 02 for female candidates)

    Ground Duties (Tech)

    18 (including 02 for female candidates)

    Ground Duties (Non-Tech)

    10 (including 02 for female candidates)

    Naval Academy (10+2 Cadet Entry Scheme)

    30 (Including 09 for Femaler candidates)

    TOTAL

     

    400

    Syllabus

    Syllabus for NDA and NA: Written Examinations

    Mathematics (Paper-1 or Code-1)

    S.No

    Chapter

    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 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.

    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 Cramer’s rule and by Matrix Method.

    3

    Trigonometry

    Angles and their measures in degrees and 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-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

    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.

     

    Application Fee

    Fee Payable by Candidates for NDA and NA Exam:

    For All Other Candidates: Rs. 100/-

    SC/ST candidates/female candidates/Wards of JCOs/NCOs/ORs: Exempted

     

    Mode of Payment:

    • The payment can be made by using either depositing the money in any Branch of SBI by cash, or by using the net banking facility of State Bank of India, or by using Visa/Master/Rupay Credit/Debit Card.

    • Applicants who choose the "Pay by Cash" option should print the Pay-in-slip issued by the system during Part-II registration and deposit the fee at the SBI Branch counter the next working day only.

    • The sons of serving/ex-Junior Commissioned Officers/Non-Commissioned Officers/Other Ranks of the Army, as well as equivalent ranks in the Indian Navy/Indian Air Force, are exempt from paying the prescribed fee if they attend a Military School/Sainik School run by the Sainik Schools Society.

    How to Apply

    For further information on how to fill out the online application form, see the instructions below.

    .Visit the official website of UPSC

    .Candidate has to register himself/ herself on OTR (One Time Registration) portal by Clicking the New Registration button.

    .After registration, he/she has to login (by Email ID/ Mobile Number/ OTR ID) to verify the already registered OTR application.

    .Go to the Latest Notification tab in the OTR application.

    .Apply for desirable Examination.

    .Candidate can check active examination Notification (in English and Hindi) on URL: https://www.upsc.gov.in

    .Submit the application.

    .Make a hard copy for future reference.

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    This exam is part of a combo package. You will get access of below exams in single purchase.

    NDA & NA Examination Paper-1 (Mathematics)

    NDA & NA Examination Paper-2 (General Ability Test)

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