NDA & NA Examination Paper-1- Mathematics The National Defence Academy (NDA) and Naval Academy (NA) Examination is a premier entrance test for those aspiring to join the officer cadre of the Indian Armed Forces (Army, Navy, and Air Force) right after completing their higher secondary education. This highly competitive examination is conduc...(Read More)
The National Defence Academy (NDA) and Naval Academy (NA) Examination is a premier entrance test for those aspiring to join the officer cadre of the Indian Armed Forces (Army, Navy, and Air Force) right after completing their higher secondary education.
This highly competitive examination is conducted twice a year by the Union Public Service Commission (UPSC).The eligibility criteria are strict, focusing on age, marital status, and educational background. Candidates must typically be between 16.5 to 19.5 years of age at the time the course commences. The exact dates are specified in the official notification. Only unmarried male and female candidates are eligible to apply.
Must be a citizen of India, a subject of Nepal, or a person of Indian origin who has migrated from certain specified countries with the intention of permanently settling in India.
| Subject | Qns. | Marks |
|---|---|---|
| Mathematics | 120 | 300 |
| Total | 120 | 300 |
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 not earlier than 01st Jul 2007 and not later than 01st July 2010 are eligible.
Age Relaxation Extra as per NDA I Exam 2025 Rules.
• 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.
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.
The following are the likely positions that will be filled up through this Exam:
|
Post Name |
Wing Name |
Total Post |
|||
|
National Defence Academy NDA (Male / Female) |
Army |
208 |
|||
|
Navy |
42 |
||||
|
Airforce |
120 |
||||
|
Naval Academy NA Only for Male |
10+2 Cadet Entry |
36 |
|||
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. |
||
Fee Payable by Candidates for NDA and NA Exam:
Candidates, except SC/ST candidates, female candidates, and wards of JCOs/NCOs/ORs mentioned in Note 2, must pay an examination fee of ₹100 (Rupees one hundred only).
The fee should be paid using Visa, MasterCard, RuPay Credit/Debit Card, UPI, or internet banking from any bank.
1: Only the specified payment methods are valid. Fee payments made through any other means will not be accepted.
Applications without the prescribed fee or valid exemption will be rejected outright.
2: The examination fee, once paid, is non-refundable under any circumstances and cannot be reserved for future exams or selections.
NOTE-1 : Candidates belonging to Scheduled Castes/Scheduled Tribes and those specified in Note 2 below are not required to pay any fee. No fee exemption is, however, available to OBC candidates and they are required to pay the full prescribed fee.
NOTE-2 : The Wards of serving/ex-Junior Commissioned Officers/Non-Commissioned Officers/Other Ranks of Army and equivalent ranks in the Indian Navy/Indian Air Force are also not required to pay the prescribed fee if they are studying in Military School (formerly known as King George's School)/Sainik School run by Sainik Schools.
For further information on how to fill out the online application form, see the instructions below.
1. Online Registration (OTR)
Register on UPSC Portal: Go to the UPSC online application website.
Complete OTR: Fill in your basic details (as per Class 10 certificate) once to get a Universal Registration Number (URN). This is a one-time process for all UPSC exams.
2. Examination Application
Log In: Use your URN to log in and find the link for the NDA & NA Examination notification (e.g., NDA I 2026).
Fill Form Part I: Enter your detailed personal and educational qualifications. Select your service preferences (Army, Navy, Air Force, Naval Academy).
3. Fee and Uploads
Pay Fee: Pay the application fee online (₹100 for General/OBC male candidates; SC/ST/Female candidates are exempted).
Upload Documents: Upload your scanned photograph, signature, and Photo ID proof.
4. Final Submission
Select Centre: Choose your preferred examination city.
Review and Submit: Carefully review all details on the final form. Once satisfied, agree to the declaration and submit.
Print Confirmation: Download and print a copy of the final submitted application form for your records.
Take the daily Quiz available subject wise and topic wise and revise for the upcoming exam
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)
