Essay For Upsc 2013 Math



Nitish K, IAS (Rank – 8, CSE – 2014) 

His Blog


Who can take Mathematics as an optional?

A large number of aspirants called or messaged me saying that they have decided to or wanted to take Maths and asked me to share my strategy. When I asked them why they wanted to choose Maths, most of them told that it was because of good performance of Maths in recent years.

Is Mathematics really performing well in recent years?

On the surface it might look that Maths is doing well. This time around 25-30 candidates have got in the range 290-310. But the problem with Maths optional is scaling. Due to scaling (I don’t know how UPSC does it), a very few number of candidates get high and remaining ones get very low. The ones who get high would have obviously done better than the rest. But due to scaling, difference in marks between the highest and the lowest increases drastically. If the difference in correct attempts is say 60-70, then after scaling the difference becomes 110-120. Thus in Maths, marks are binary. Either you get high or you get low. There are no average marks in Maths, unlike humanities optional. Therefore one should not get attracted to Maths by marks obtained by a few successful candidates. A huge majority would have got very low marks in Maths. Thus Maths is performing well for say around 10% and poor for 90%.

Who are the ones who usually take Maths as an optional?

A large number of those who take Maths as optional come from reputed institutions like IITs, BITS and NITs etc. Due to this the competition is very high.

So back to first question, who can take Maths as an optional?

I feel only those who are very strong in Maths and have genuine interest should take Maths. Unlike humanities optional which can be taken by anybody, Mathematics requires aptitude. As there is huge competition, unless one is at the topmost part of the pyramid, Maths would result in low marks. I have seen many people who take Maths in haste, waste attempts and later change optional.

I was not from any IIT, BITS or NIT. I still went for Maths because I felt I am good in Maths. Mine previous performance in Maths boosted my confidence. I had got 99/100 in 10th (CBSE), 100/100 in both 11th and 12th, 10/10 grade in all four semesters in Engineering Maths. This is not to boast about myself, but to press the point that Maths should be taken only if you have good track record in Maths.

Also given the complexity of topics and huge syllabus, I don’t think any coaching institute will be able to fully cover all the topics. I feel coaching has a limited role and own effort matters more.


Paper I

Booklist and Strategy 

Book List

Paper I

  1. Linear Algebra :
  2. Schaum’s outline on Linear Algebra: this book has explained linear algebra in a far better and simpler manner than Krishna Series. Due to its clarity, it can be read quickly also.
  3. Krishna Series on Matrices
  4. Calculus :
  5. Krishna Series on Differential calculus
  6. Krishna Series on Integral calculus
  7. Mathematical Analysis by Malik and Arora : a must read book for both Paper I and II
  8. Analytical Geometry :
  9. Krishna Series on Analytical Geometry : this book is better than Shantinarayan and has many solved examples
  10. Krishna Series on Analytical Solid Geometry : for Conicoids, Generating Lines
  11. Ordinary Differential Equations:
  12. Ordinary and Partial Differential Equations by MD Raisinghania
  13. Advanced Differential Equations by MD Raisinghania : required for Laplace Transforms (Paper-I) and Boundary value problems (Paper-II)
  14. Dynamics and Statics
  15. Krishna Series on Statics
  16. Krishna Series on Dynamics
  17. Vector Analysis
  18. Krishna Series on Vector Calculus (~ 330 pages)
  19. Schaum’s outline on Vector Analysis


          Strategy for Paper I:

  1. Paper I being easier compared to Paper II, all the topics have to be covered in detail.
  2. For Analytical Geometry, read all the solved examples given in above mentioned books. Regularly revise particularly skew lines, sphere, cone and conicoids. In many problems you would have to remember how to start the problem i.e. you would have to mug the approach to solve specific problems.
  3. For Calculus, focus more on Calculus of many variables. This is well covered in Malik and Arora. Also many topics of Paper I and Paper II overlap, which can be prepared simultaneously from the above mentioned book.
  4. In Statics & Dynamics, try to solve all the problems. You can leave very complex problems which are usually given at the end of every chapter.
  5. Make formula sheet for every chapter and revise it regularly. Otherwise you might forget many formulas in exam.
  6. Practice makes perfect. Try solving problems with pen and paper with book closed, instead of just reading.


Paper II :

Booklist and Strategy


Paper II

  1. Abstract Algebra: This being my favourite topic, I had referred many books. But as many candidates find this topic tough, I would suggest referring to following books.
  2. Abstract Algebra, Group Theory by R Kumar (Vardhaman Publications)
  3. Abstract Algebra, Ring Theory by R Kumar (Vardhaman Publications)
  4. Abstract Algebra by Joseph Gallian (optional)
  5. Real Analysis:
  6. Mathematical Analysis by Malik and Arora
  7. Real Analysis by MD Raisinghania
  8. Complex Analysis:
  9. Krishna Series
  10. Linear Programming:
  11. Operations Research by JK Sharma or Kanti Swarup or Krishna Series
  12. Partial Differential Equations:
  13. ODE and PDE by MD Raisinghania
  14. Engineering Maths by Grewal : for boundary value problems
  15. Advanced Differential Equations by M.D Raisinghania (for boundary value problems)
  16. Numerical Analysis and Computer programming:
  17. Numerical Methods by Jain and Iyengar (but questions are not coming from this book from past few years)
  18. Numerical Analysis chapter from Grewal, Engineering Mathematics
  19. For Algorithms and flowcharts, I am having soft copy of a book which I will share.
  20. Mechanics and Fluid Dynamics:
  21. Fluid Dynamics by MD Raisinghania
  22. Krishna Series, Dynamics for Moment of Inertia and D Alembert’s Principle
  23. Krishna Series, Rigid Dynamics for Lagrangian and Hamiltonian. (Unfortunately this is a poorly written book with lot of mistakes. Will try to upload material for these topics)

Strategy for Paper – 2:

  1. Usually Paper II is tough for many. Hence if you are able to master it, then you will able to score very high compared to others
  2. Abstract Algebra is a unique topic. Either you like the topic or you don’t. In first case it will be easy otherwise very tough. I loved the topic and did not read it from exam point of view. If you are finding it tough, I would suggest you to do it from 10 markers point of view. There is no point in spending a lot of time on Abstract Algebra as you won’t be rewarded proportionately. The same time could be used for studying other topics of Maths or GS, which would fetch much more marks. For 10 markers point of view, read books (a) and (b) mentioned above. Memorize all the theorems. Skip proofs of theorems which are big, particularly in Permutation groups, Cayley’s theorem, PID, Euclidean Domain and UFDs. On the other hand, if you are comfortable with Abstract algebra and want to do it in a detailed manner, I will shortly share various e-books, pdfs etc.
  3. For Real Analysis, Malik and Arora is the best. You can supplement it by MD Raisinghania. I felt it is better to leave the proofs. Focus more on Riemann Integral, Improper Integrals and Series and Sequences of functions.
  4. Linear Programming: I feel books for MBA like JK Sharma are written more clearly that Krishna Series.
  5. PDE: Even though not mentioned in syllabus, Charpit’s method has to be covered as questions are regularly asked. For Boundary Value problems (heat equation etc.) first read from Grewal. For more types of problems you should refer to book (c) mentioned above in the booklist.
  6. Mechanics and Fluid Dynamics: From last year UPSC has started mixing questions from PDE, Numerical Analysis and Fluid & Rigid Dynamics. Therefore to score high it has become imperative to cover this topic. But the problem is the syllabus has been vaguely defined and there is confusion about which topics are there in syllabus. By analyzing past years question papers. I covered only the following topics. In Fluid dynamics cover Kinematics of Fluids in Motion, Equations of Motions of Inviscid Fluids, Sources and Sinks, Vortex Motion. No need to see proof of any theorems. From Navier Stokes equations, just try to see only solved examples. For Rigid Dynamics, cover those topics mentioned in booklist above.


  1. The fixed space for each question in Mathematics causes lot of disadvantage vis-à-vis other optional, particularly humanities. If you made a mistake while solving a problem and have consumed most of the available space, then despite knowing the correct method you would not have space to rectify your mistake. To tackle this, practice solving problems and write many mock tests. By greater practice you will be able to reduce unforced errors. Also if the problem is new or unfamiliar, I used to briefly solve it in the last page with pencil, later transferring it to main page.
  2. A lot of aspirants face the dilemma of how much time to give for Maths compared to GS. There is no hard and fast rule. I used to give 50% of my time (say around 5 hrs per day) for Maths and 50% for GS. Owing to huge syllabus of Maths, candidates generally tend to neglect GS and Essay. This has to be avoided.
  3. It is very important to complete at least 80% of syllabus before prelims. Also between prelims and mains, try to do both Maths and GS everyday. Don’t lose touch of Maths. The last one month before Mains is very important. During this period keep on revising formulas and practicing problems.
  4. Join Test Series programme between Prelims and Mains. This helps you to complete the syllabus in time, gives you practice, improve your speed and accuracy etc. I had joined Venkanna’s (IMS) test series 4 times (2011,12,13,14) and found them very helpful. I did not attend their classroom coaching and went only for test series programme.


My Sample Answer-scripts:

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Scan 11-Nov-2014 9.26 pm

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Scan 31-Oct-2014 10.22 am

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I wrote above tests during last year online test series at IMS.


Related Article:

My Overall Strategy for Essay, GS, Interview

PS: Mathematics Marks in CSE Mains 2014: Paper – 1 – 173; Paper – 2 – 173

Note from Insights: 

Please visit His Blog (CLICK HERE) for any queries. and ask him there your doubts. Thank you.





Gaurav Agrawal from Rajastan topped UPSC Civil Services Exam 2013. Gaurav did his graduation from IIT and post graduation from IIM. He got IPS in his first chance before securing All India Rank 1 this year. We have already shared Gaurav Agrawal’s UPSC interview transcript. In this post, we shall analyze how should one score to become an All India Topper and clear IAS! This post also examines the subjective nature in the present pattern of UPSC exam, especially the interview/personality test.

How well should you score to clear IAS with AIR 1?

As you all might be aware, there cannot be any generalizations. We have already done an analysis on UPSC mains marks cut-offs and have shown that the competition is getting tougher and the mains exam is becoming low scoring. Let’s have a quick look at AIR 1, Gaurav Agrawal’s total marks, which is 975/2025. This comes around 48.15 percentage, around 3 percent less than last year topper Haritha V. Kumar’s total. The decrease in percentage can be attributed to the reduction in number of optional papers and increase in general studies papers, with tight valuation. But the point here is : You just need around 48% marks to become All India Topper! And to clear IAS which has around 180 seats this year including reservation, the percentage needed is again less! However, things are not that easy! Let’s see.

Gaurav Agrawal’s UPSC Civil Services Preliminary Exam Marks

  • General Studies Paper 1 (GS): 121.34 / 200
  • General Studies Paper 2 (CSAT): 182.50 / 200
  • Total: 304 / 400

PS : Marks of UPSC Preliminary Exam is not counted for final ranking. For 2013, the cut-off mark for general category was 241, OBC – 222, SC -207, ST-201, PH1 -199, PH2 – 184 and PH3 – 163.

It can be seen that Gaurav was way above the cut-off, even for Prelims. A high score in CSAT, can naturally be attributed to his IIT+IIM brain, but the score of 120+ in GS shows his command over the general studies paper too.

A good command over GS paper even at the time of Prelims would naturally give an edge to the candidate for Mains, as he/she already know many of the general studies topics. And a 300+ score for Prelims is just awesome! 🙂

Motivational quote from the topper for those who start late:

If you are confident enough in paper 2 (CSAT) , prelims specific preparation can be done in last 1-2 months itself.

Gaurav Agrawal’s UPSC Civil Services Mains Exam Marks

Thanks to Gaurav for sharing his detailed marks-break up.

  1. Essay: 135 / 250
  2. GS 1: 85 / 250
  3. GS 2: 63 / 250
  4. GS 3: 88 / 250
  5. GS 4: 102 / 250
  6. Economics 1: 134 / 250
  7. Economics 2: 162 / 250
  • Total GS: 338 / 1000 (33.8%)
  • Total Economics Optional : 296 / 500  (59.2%)
  • Mains (written) total = 769 / 1750 (43.94%)

PS : Mains cut-off for general category was 564, and Gaurav had scored 205 marks above that minimum qualifying mark. 🙂

Gaurav Agrawal’s UPSC Civil Services Mains Exam Marks

  • Interview (Dr. Kilemsungla board): 206 / 275
  • Total: 975 / 2025
  • Rank 1.

PS : After interview, Gaurav was 200 marks above the last recommended candidate in general category. (517th candidate)

All India Topper’s Mark for Mains and Interview : An Analysis

As per our analysis, there are three crucial areas which determines a mains qualified candidate his/her final rank, after the changed pattern.

  1. Essay Paper (250 marks).
  2. Optional Paper (500 marks).
  3. Interview (275 marks.)

You might be surprised why we didn’t include General Studies Paper in this list. Of-course, General Studies is also a factor, but in 2013, it was not a very crucial element, as there was no very big difference in the mark range even when the total General Studies weigtage was out of 1000 marks. Reason : GS1, GS2 and G3 papers had 25 questions each while GS4 had 14 questions. So the 1000 marks were divided among 89 main questions and 20+ sub questions. That will reduce the subjective elements and variations to a great extent. Analyze this break-up, in contrast to a single essay question worth 250 marks!

Subjectivity in the Essay Paper

Gaurav Agrawal scored 135 in essay paper, which is a very high score for essay this year. Yes, there are candidates who scored, 145 for essay, but the difference between the 145 and 135 is not that really big. But those who got only 50 or 60 mark in essay, are lagging behind the topper by near 80+ marks soon after the first paper itself! This is not a small difference to neglect. A single essay worth 250 marks can always lead to mark variations like this. Unless the next year essay paper contains 2-3 essays, the volatility of essay marks will remain.

Subjectivity in the Optional Paper

Gaurav Scored 296 marks in economics optional which is exceptional! Here also, there might be other candidates who scored higher for other optionals, but 296/500 is never a mean achievement. Gaurav said that it was his optional marks which secured him the first rank. We would only partly agree. He performed really well across sections 🙂 .

But again, who much is the marks range in optional paper? If Gaurav’s total was 296/500, there are also candidates who made it to the final list with less than 180/500 as optional paper mark. That means a big difference of 120+ marks is possible for optionals.

PS : The wide variation of marks between optional papers is well known. This has nothing to do with number of questions in each paper, but is often associated with the scaling process for equating marks between different optional papers. There are also unfortunate candidates with such low marks 3-11 in certain optional papers, after writing for 3 hour each (who of-course didn’t qualify) probably due to the scaling process for that optional paper!

Subjectivity in the UPSC Interview/Personality Test

Now let’s see how a candidate’s life and years of preparation can be drastically ruined in half an hour. For 2013 interview, there were as high marks as 210+ and low marks as 90 also. This means 120+ marks difference was possible in 30 minutes, which as per our analysis is the most life changing one. Even if you were 120+ marks above mains cut-off (mains = the stage which checks your knowledge and analytical abilities, with a weightage of 1750 marks ), a very low mark like 90 or less in the UPSC interview/personality test can spoil your chances.

PS : There are many instances of candidates securing very low marks like 90 or 100 one year crossing 200+ when he attends the UPSC board next year. It can be the reverse also. There are many who wonder how the personality of a candidate rise or fall so much in one year. This just point outs the subjectivity in a 30 minute interview. There are many who wonder if the personality of candidate can be judged at all in 30 minutes.

Gaurav scored 206 for interview, which is again very high marks. His GS score of 338/1000, though not exceptional, corresponds to around 85 marks per each paper out of 250, which is well above the average.

Conclusion :

To conclude our analysis on UPSC Civil Services mains+interview, it is worrysome to note that the high range of marks existing in a 20-30 minute subjective process like interview. The subjective nature also exists in the valuation of a single essay worth 250 marks. Again, scaling in optional papers has been a matter of debate by lot of unfortunate candidates for many years. UPSC had made some reforms in exam pattern and syllabus in last 2-3 years, but still there is definite scope for improvement in the whole exam process, and we strongly suggest reducing the ‘range of marks’ that can be awarded for interview and essay. The difference between top and bottom marks should be a maximum 50. Except under exceptional circumstances, this rule should not be violated. Either remove the optional paper completely or bring more transparency to the scaling process for optional paper. Many successful and unsuccessful candidates associate the ‘luck element’ with the subjective and impulsive nature of awarding marks. The selection of the top bureaucrats who steer the governance and future of India, can never be left to any luck element, but should always be on the basis of merit.

And for Gaurav Agrawal, a consistent high scoring in all papers of mains and interview fetched him the top slot. He might not be the topper in individual papers, but he remained consistently high across all papers with exceptional performance in Economics optional. We are happy that his hard-work is finally rewarded, in-spite of the uncertainties existing in the system and exam process. A truly deserving candidate who crossed all hurdles, after being a little short the first time. All the very best to him! 🙂


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