UPSC Maths Optional Coaching for IAS/IFoS

Live Online Classes by : K. Venkanna

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Indian Administrative Service (IAS) – Mathematics

Director Message

After spending many years in the field of teaching to IAS aspirants, I have analyzed very minutely the pros and cons of the entire system and the strategy prerequisite for this coveted examination. The civil services examination, the crème de la crème of all exams, is known as the toughest and the longest examination of the world. Therefore it becomes very important to share my own viewpoints for the bright future of the aspiring candidates. I have observed that the kind of phobia in the mindset of students for mathematics optional.

I can broadly categorize all science students specially mathematics background students who are preparing for this exam into two main categories. First category is of those students who opt mathematics as their one of the optional in this prestigious examination and the second category is of those students who do not opt this subject. I don’t have to say much about the first category of students as they are self motivate aspirants and moreover they have penchant for this subject. In fact, they are passionate and devoted for this and they can’t give ever the second thought as it seems that mathematics is in their bones…. Read More>>

Venkanna Sir 675x

K. Venkanna

Director - IMS (Institute of Mathematical Sciences)


Regular Batches
12th dec.2023

Fast Track Batch 7th Dec. 2023

Admission Open, Limited Seats, available on first come first serve basis.


Schedule for IAS/IFoS Classroom Programme & Test Series Programme – 2023
Best Mathematics Optional Online Class for UPSC 1
Best Mathematics Optional Online Class for UPSC 2
Best Mathematics Optional Online Class for UPSC 3

Regular Classes

(Monday to Friday)

Weekend Classes

(Saturday & Sunday)

Note: Different Batches with different chapters (topics).

  • It is expected that the regular students (non-working) have to attend 7 days classes.
  • Student may attend multiple classes with prior permission. (If Online/Offline Classroom Space is available)
  • Can study multiple chapters simultaneously (if interested).
  • Complete your syllabus at your own pace.
  • Convenience of choosing flexible timings to balance your GS preparation.
  • You will have enough time in hand for self-study after syllabus completion.

Note: Class Test will be conducted after completion of every chapter followed by feedback & detailed explanation/discussion.

Best Mathematics Optional Online Class for UPSC 4

Only IMS Provides Scientific, Innovative Teaching Methodologies, Fully Revised Study Materials & Test Series.

IMS is now Online Class with face to face!!!


  • Feeling of offline classes in the online mode.
  • Classes via live interactive session.
  • IMS has a full studio setup for video live interactive / conferencing with HD cameras and
    state of art technology.
  • So that your studies don’t get affected by any future lock-downs or else.
  • The course will contain :
    1. Classroom Program
    2. Study Materials
    3. Test Series



  1. Laptop*/ Desktop/ MacBook/ Tabs/ Smart Phones (Android/iPhone)
  2.  Headphone/Earphone is mandatory.
  3. Chrome/Mozilla/Firefox/Microso Edge browser is enough for
    laptop*/desktop (Link will be provided via email to every student)
  4. Collaborate space app is required for tabs/smart phones
    (Link will be provided via email to every student)
  5. Internet connecon with minimum speed of 512kbps (To fully enjoy
    class we recommend 4 MBPS connecon/ 4G connecon)
  6. An isolated space / four wall side room without outside interferences
    to hear the classes properly and ask doubts without interference.


  1. Students will be provided with email before every class. Email will contain a unique link that will
    allow students to join the classes.
  2. Choose an isolated space/four wall side room before joining the class.
  3. Then click on the link, It will open in the browser or in the collaborate space app (if downloaded
    previously Tabs/ smart phones).
  4. By default your mic and video will be off. It will ensure your privacy and it will make you classroom
  5. Student can use raise hand feature (opon available on screen) to ask any queson. By raising
    hand, admin will open a 2 way communication with mic and video of student on display. So raise
    hand can work only if you allow your video and mic (to be shown).


  1. Student must provide email ID along with mobile number to the IMS. This will ensure free
    communication between the instiute and student. Daily email will be sent with class link.
  2. Student must have decent internet connection and all the assisting devices
    (laptop/desktop/smart phone etc. with earphones/headphones)
  3. Attend the class in safe and isolated place/ four wall side room.
  4. Do not attend the classes among the family persons/ among the friends/ public places/ in
    dangerous places like walking on the road side. (IMS does not hold any responsibility for
    accident caused in this manner).
  5. Attend the class on me according to the class schedule.
  6. Read study material before attending the class. It will increase/ensure you understanding of
    the topic.
  7. If class(es) will be missed out by any student(s), no extra class(es) will be entertained.


  1. Maintain decency in the class. Any obscene Language/Gesture and activity will attract severe
  2. If student raise hand, he/she has given permission to IMS to open audio-video link. So after raising hand either you cancel the raised hand or wait for you’re turn to come on the screen
    and ask your doubt.
  3. You can use chat option also which will be replied after the classes/accordingly.
  4. Make notes of the lecture and solving problems are compulsory accordingly and attend the class sincerely.


  1. Complete the notes by referring study materials.
  2. Complete the exercise which will be provided in the classroom etc.
  3. Again students be ready/ prepare for next class in advance.
  4. So, class will run smoothly with good understanding and interactive mode.


  1. IMS (INSTITUTE OF MATHEMATICAL SCIENCES) is only presenting solution to online classes in
    it’s best possible way. If any student is having any technical problem / subject understanding
    problem on online then students have right to give a suggeson to make this experience
  2. If any student wants to turn into offline from online, prior information is required at the me
    of admission and vice versa.
  3. Once course will be over class link will not be provided (by email conformation).
  4. Particularly online students are allowed with one me payment only before the admission.
  5. After deposing the fees, if a student disinterested or fails to join the classes in the instiute
    due to any reason whatsoever and wants to take his/her fees (money) back, the institute will
    not refund the fees under any circumstances.


  • Sharing of the unique id and video recording / screen capturing is strictly prohibited under any circumstances. IP addresses will be recorded and any violation will be severely punished as per law, apart from necessary penalties.
  • During the classes the students are expected to behave in a orderly and decent manner. Any obscene/ malafide behaviour or gesture will be punished as per IT Act and matter will be taken up with relevant authorities.
  • Further, If IP address masking tools are used, the online access given to the student will be permanently terminated immediately without any discussion.

Previous Years IAS Mathematics Question Papers



Download Link

IAS – Mathematics Optional

2022 Question Paper

IAS – Mathematics Optional

2021 Question Paper

IAS – Mathematics Optional

2020 Question Paper

IAS – Mathematics Optional

2019 Question Paper

Best Mathematics Optional Online Class for UPSC 5

Download IMS Online Class Information Brochure

Admission Open, Limited Seats, available on first come first serve basis.

Eligibility Criteria for IAS

The candidate must hold a degree of any of the Universities incorporated by an Act of the Central or State Legislature in India or other educational institutions established by an Act of Parliament or declared to be deemed as a University Under Section-3 of the University Grants Commission Act, 1956, or possess an equivalent qualification.

NOTE I : Candidates who have appeared at an examination the passing of which would render them educationally qualified for the Commission’s examination but have not been informed of the results as also the candidates who intend to appear at such a qualifying examination will also be eligible for admission to the Preliminary Examination. All candidates who are declared qualified by the Commission for taking the Civil Services (Main) Examination will be required to produce proof of passing the requisite examination with their application for the Main Examination failing which such candidates will not be admitted to the Main Examination. The applications for the Main Examination will be called sometime in the month of August/September.

IAS Mains Mathematics Syllabus


Linear Algebra: Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; Linear transformations, rank and nullity, matrix of a linear transformation.
Algebra of Matrices; Row and column reduction, Echelon form, congruence’s and similarity; Rank of a matrix; Inverse of a matrix; Solution of system of linear equations; Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices and their eigenvalues.

Calculus: Real numbers, functions of a real variable, limits, continuity, differentiability, mean-value theorem, Taylor’s theorem with remainders, indeterminate forms, maxima and minima, asymptotes; Curve tracing; Functions of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange’s method of multipliers, Jacobian.

Riemann’s definition of definite integrals; Indefinite integrals; Infinite and improper integrals; Double and triple integrals (evaluation techniques only); Areas, surface and volumes.


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