UPSC CDS Mathematics - Exam pattern, Eligibility, Vacancy Details and Syllabus

Educational Criteria for UPSC CDS - Combined Defence Service:

(A) For IMA -Indian Military Academy

• Bachelor's Degree of a recognized University or equivalent.

(B) For INA - Indian Naval Academy

• Degree in Engineering from a recognized University/Institution

(C) For Air Force Academy

• Degree of a recognized University (with Physics and Mathematics at 10+2 level) or Bachelor of Engineering.

(D) For Officers’ Training Academy (Male/Female)

• Bachelor Degree of a recognized University or equivalent.

Age Limit for UPSC CDS - Combined Defence Service:

(A) For IMA, INA, AFA

(B) For OTA

Important Note:

NOTE : Male divorcee/widower candidates cannot be treated as unmarried male for the purpose of their admission in IMA/INA/AFA/OTA, Chennai courses and accordingly they are not eligible for these courses.

The date of birth accepted by the Commission is that entered in the Matriculation/Secondary School Examination Certificate or in a certificate recognised by an Indian University as equivalent to Matriculation.

Physical Standard forIMA, INA, AFA and OTA

• 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 link on our website or whether they can check directly from the official link of UPSC.

Schemes of theUPSC CDS - Combined Defence Service Selection Procedure:

The recruitment process will be held in the following phases.

• Written Exam

• Interview for Intelligence and Personality Test

• Medical Examination/ Physical Standard

For IMA, INA, and AFA

Written Examination for OTA

Important Note:

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

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

• The Mode of Examination will be Offline.

Interview for Intelligence and Personality Test forUPSC CDS - IMA, INA, AFA, and OTA

Interview Pattern for IMA, INA, and AFA

The total mark is given in this test is 300.

The interview is divided into two stages:

• Officers Intelligence Rating (OIR).

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

*The Officers Intelligence Rating is Picture Perception and Description Tests (PP & DT). To proceed to the second stage of the SSB interview, a candidate must pass these tests.*

Interview Pattern for OTA

The total mark is given in this test is 200.

The interview is divided into two stages:

• Officers Intelligence Rating (OIR).

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

*The Officers Intelligence Rating is Picture Perception and Description Tests (PP & DT). To proceed to the second stage of the SSB interview, a candidate must pass these tests.*

Important Note:

The above-mentioned number of vacancies is provisional and subject to change at any time by Services H. Q.

Syllabus forUPSC CDS - Combined Defence Service: Written Examinations

For IMA, INA, IFA

(A) English

• Sentence arrangement

• Spotting Error

• Selecting words

• Synonyms and Antonyms

• Comprehension

• Ordering of Sentence

• Ordering of words

• Idioms and Phrases

• Fill up the blanks

(B) General Knowledge

• Current Affairs

• Physics

• Chemistry

• Biology

• Geography

• History

• Politics

• Sociology

• Economics

• Defense Related Awards

• Sports and culture

• Environmental Science

(C) Elementary Mathematics

(C-I) Arithmetic

• Number System—Natural numbers, Integers, Rational and Real numbers.

• Fundamental operations, addition, subtraction, multiplication, division, Square roots, Decimal fractions. Unitary method, time and distance, time and work,

• Percentages, applications to simple and compound interest, profit and loss, ratio and proportion, variation.

• Elementary Number Theory—Division algorithm. Prime and composite numbers.

• Tests of divisibility by 2, 3, 4, 5, 9, and 11. Multiples and factors. Factorisation Theorem. H.C.F. and L.C.M. Euclidean algorithm. Logarithms to base 10, laws of logarithms, use of logarithmic tables.

(C-II) Algebra

• Basic Operations, simple factors, Remainder Theorem, H.C.F., L.C.M., Theory of polynomials, solutions of quadratic equations, the relation between its roots and coefficients (Only real roots to be considered). Simultaneous linear equations in two unknowns—analytical and graphical solutions. Simultaneous linear inequations in two variables and their solutions. Practical problems leading to two simultaneous linear equations or inequations in two variables or quadratic equations in one variable & their solutions. Set language and set notation, Rational expressions, and conditional identities, Laws of indices.

(C-III) Trigonometry

• Sine ×, cosine ×, Tangent × when 0° < × < 90° Values of sin ×, cos ×, and tan ×, for ×= 0°, 30°, 45°, 60° and 90°, Simple trigonometric identities, Use of trigonometric tables, Simple cases of heights and distances.

(C-IV) Geometry

•Lines and angles, Plane and plane figures, Theorems on

(i) Properties of angles at a point,

(ii) Parallel lines,

(iii) Sides and angles of a triangle,

(iv) Congruency of triangles,

(v) Similar triangles,

(vi) Concurrence of medians and altitudes,

(vii) Properties of angles, sides, and diagonals of a parallelogram, rectangle, and square,

(viii) Circles and their properties including tangents and normals,

(ix) Loci.

(C-V) Mensuration

• Areas of squares

• Rectangles

• Parallelograms

• Triangle and circle

• Areas of figures that can be subdivided into these figures (Field Book)

• Surface area and volume of cuboids

• Lateral surface and volume of right circular cones and cylinders

• Surface area and volume of spheres

(C-VI) Statistics

• Collection and tabulation of statistical data

• Graphical representation frequency

• Polygons

• Histograms

• Bar charts

• Pie charts etc.

• Measures of central tendency.

Syllabus forUPSC CDS - Combined Defence Service: Written Examinations

For OTA

(A) English

• Sentence arrangement

• Spotting Error

• Selecting words

• Synonyms and Antonyms

• Comprehension

• Ordering of Sentence

• Ordering of words

• Idioms and Phrases

• Fill up the blanks

(B) General Knowledge

• Current Affairs

• Physics

• Chemistry

• Biology

• Geography

• History

• Politics

• Sociology

• Economics

• Defense Related Awards

• Sports and culture

• Environmental Science

Fee Payable by Candidates forUPSC CDS - Combined Defence Service Exam:

For Other Candidates: Rs. 200/-

For Female/SC/ST candidates: Exempted

Mode of Payment:

• The payment can be made by using Visa/Master/Rupay Credit/Debit Card/UPI Payment or by using internet banking facility of any Bank.

• The payment of the examination fee can be made only through the modes prescribed above.

• Any other method of payment is neither valid nor acceptable.

• The UPSC has no mechanism for refunding any fees paid by candidates, therefore in the event that an application is successfully withdrawn, the fees would not be reimbursed.

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

Stage 1: One-Time Registration (OTR):

Before filling out the exam form, every candidate must register on the UPSC OTR portal. This is a permanent profile.

Visit the Website: Go to the official UPSC portal at upsconline.nic.in.

New Registration: Click on the "One-Time Registration (OTR)" link and select "New Registration."

Enter Details: Fill in your basic information (Name, DOB, Father’s/Mother’s Name, Mobile, Email, and Class 10th Roll No).

Verification: Verify your details using the OTP sent to your mobile and email.

Login: Once registered, log in using your OTR ID/Email and the password you created.

Stage 2: Filling the CDS Application Form:

Once your OTR profile is ready, follow these steps during the active application window:

Select Exam: Under the "Latest Notification" tab, find the link for Combined Defence Services Examination (I), 2026.

Part-I Registration:

Fill in educational qualifications and address.

Academy Preference: Rank your preferences for IMA, INA, AFA, and OTA.

Part-II Registration:

Payment: Pay the application fee of ₹200 (Female/SC/ST candidates are exempted).

Upload Documents: Upload your scanned photograph, signature, and a PDF of your Photo ID (Aadhar, PAN, etc.).

Center Selection: Choose your preferred exam city from the available list.

Final Submission: Review all details, agree to the declaration, and submit. Download a copy of the generated application form for your records.

Important Checklist for Applicants:

Document Size: Photo and Signature must be in JPG format (20 KB – 300 KB). Photo ID must be in PDF format.

First-Apply-First-Allot: Exam centers are allotted on a first-come, first-served basis. If a center's capacity is reached, it will be frozen.

Correction Window: UPSC typically opens a 7-day correction window after the application deadline for minor edits to the OTR profile or form.