Mathematics Optional 2024 Paper Analysis

The following is a question-by-question analysis of the Paper. Irrespective of what coaching institutes are saying, I found it extremely tough in the exam hall conditions.

Paper 1

Q1a Easy. A standard question but maybe people would have fumbled in the extension of basis part.

Q1b Easy. A standard question but still such questions were asked in the non compulsory section for 15 marks. You have to deduce the transformation and then get to the range and null space. So a bit lengthy for 2 pages.

Q1c Easy but you had to completely address the full question. The question was not only about testing continuity at x=0. It was about testing continuity for all values of x.

Q1d Questions on Taylor series are extremely easy if you know the formula. But such type of questions were never asked in Paper 1. Even for Paper 2, Taylor series questions were never asked for estimation of values. This question talks about changing the centre and calculating the value for ln(x). Again, chances of mistakes are there.

Q1e Easy question but lengthy for 10M. If you don't know the standard method, you won't get it. Plus questions on cylinders have been rare. So the basic takeaway is: You can't afford to ignore topics.

Q2a Asked in 3b IFoS 2023, 2a 2009. This question hinged on only one concept that you have to prove kerT = (0,0,0). If you know that, 15M are for you.

Q2b A very easy and straightforward question. But again it is from a topic from which only 10 questions have been asked from CSE 1992 and IFoS 2000 onwards. It is an indirect repeat from CSE 4c(ii) 2019.

2c The most controversial question for now. People have been filing representation on it but I believe the answer given in PN Chatterjee and the solution given by IMS will prevail. I will rate this question as difficult in the exam hall as many people misunderstood the demand of the question and this was a new type which was never asked in CSE or IFoS before (as far as I know)

3a Difficult as you need to know the concept precisely to get this question right. There's a chance of error in every step.

3b A standard question.

3c A standard question if you knew the concept.

4a Standard question and easy if you know the concept. Again, it was not asked in this manner before. Getting all the Eigen vectors correct is a tricky part. So I would say easy but lengthy.

4b CSE doesn't venture into this domain of polar coordinates. So if you did not know the graph of a cardioid or made silly mistakes in calculating the area, 15M down the drain.

4c Question from 4b IFoS 2008. Again a fringe area but still it was easy if you know the concept. Without knowing the concept, deriving it in the exam hall was difficult.

Overall Section A was doable to a certain extent but certain standard questions were missing this time around. The usual question of RREF, inverses and Cayley Hamilton Theorem were ignored this year. I would rate this section as Easy to Moderate.

But then came Section B:

5a CSE doesn't ask orthogonal trajectories in polar coordinates generally. They used to stick to cartesian coordinates. So a major takeaway here is to practice IFoS questions as well. A similar question had appeared in Abhyaas. I would rate it easy.

5b Not for 10 M, solution was long. Laplace has been a fringe area and it was not a popular topic until last year. But it was a proper 15 or a 20M question. I would rate this extremely tough under exam circumstances.

5c Fully formula based. I don't think I have seen such a question before. But again rate of change was asked and the question for the part involves cross product of alpha and gamma. So people may mistakenly calculate the cross product of alpha and beta too (under exam pressure). Second part involved rate of change of vector triple product. Both the parts were lengthy and mistake prone. Extremely tough.

5d Easy but you need to remember the formula.

5e (i) Formula based. If you know the formula then easy if you don't then difficult. Also it was quite lengthy for 5M

5e(ii) Asked in 8c(i) IFoS 2021: Relatively tough and not suitable for 5M

Q6a Virtual work in 3D? A very new type of question.

Q6b Similar type of questions were asked in IFoS. If you don't know the type, this question was difficult.

Q6c(i) A non standard question. Lengthy and mistake prone (due to the minus sign). I would rate it tough.

(ii) Repeat from CSE 7a 2019

Q7a Never heard the concept in context of ODE. I had read this topic in the context of Complex Analysis.

Q7b Easy question.

Q7c Looks easy but it is lengthy because of the state and verify part

Q8a I think Electrical Engineers knew this function as it is part of their course but for Maths optional people, we have not studied it as part of our standard syllabus.

Q8b Easy question

Q8c A similar concept was asked in 5d IFoS 2023. Still I would rate it tough.

Overall view: Extremely tough because of Section B as compared to previous years.

Paper 2:

1a Concept based. If you knew the concept then it was straightforward.

1b Similar concept asked in IFoS 2005 and 2006 but lengthy for 10M

1c Easy concept but again you had to divide the integral into 2 parts and then examine the convergence.

1d Easy but you have to be careful

1e 2 phase is a bit tricky if one doesn't remember the standard algorithm

Q2a Fringe area and it was a bit tricky. But for those who knew e^x expansion, it was easier to get a direction for this question.

2b Basic question but for those who ignore Modern Algebra, it is 15M down the drain.

2c Concept from CSE 1997.

Q3a On the surface, this question seemed easy but when you dig deeper, it will reveal its complexity. It was partially doable still. Only 8 questions of such type have been asked till now.

3b Difficult portion of Real Analysis. Generally, UPSC has stuck to the basic questions for Paper 2 but this question is not that basic.

3c Easy.

4a Tough question imo even if you have studied Ring Theory.

4b Asked in 1b IFoS 2014 and CSE 1992. I would still rate it as difficult if someone doesn't know the concept of Dirichlet functions

4c A tricky question. Looked easy on the surface.

Section B

5a Very easy question if you know how the concept works

5b Mistake prone because of the small difference between Gauss Jordan vs Gauss elimination

5c(i) Those who missed the sign magnitude part, it is 5M gone.

5c(ii) Easy

5d Easy only if you know the concept. If someone ignored Mechanics then there's no chance of getting this right.

5e A basic question. If someone ignored Fluid dynamics then 10 marks gone straightaway. There's a chance for plus minus error.

6a Extremely difficult. It can be done partially. It is a non standard question as they used to ask from Wave and Heat equations generally.

6b I would call it easy.

6c A new type of question and mistake prone as quadrant of an ellipse is being asked. So you have to first calculate the MoI about x axis then the y axis and then use the perpendicular axis theorem to get to the answer. But since the density varies, it was difficult.

7a Moderate because of z and φ confusion else it was relatively easy.

7b(i) A simple question but they do not generally ask about Simpson's 3/8th. People can make mistakes in taking multipliers as Simpson's 1/3rd and 3/8th are closely related.

7b(ii) A simple question. But both these questions have been rarely asked before.

So recall was less. Error prone.

7c Asked in 7a IFoS 2012 and IFoS 2002

8a Standard but tricky question because of the z and φ change.

8b Easy question

8c Easy question but if you miss the last line, you will make mistakes.

Overall, Paper 2 was also difficult. But for those who ignored the basic parts of tough topics, it was extremely difficult.

Finally, both the papers were extremely difficult given the standard pattern of questions asked in PYQs and given the exam environment with the fatigue of GS papers (which were somewhat tough too).

Overall, still there will be people who will get good marks in Maths opt despite the extremely tough paper. Marking scheme and the way UPSC evaluates these papers is a black box, you do not know exactly what would fetch you marks. There's no official say on the scaling factor (we assume it to be 0.7 and 0.8) but given the present circumstances, I find myself not competent enough to comment on it.

For prep, I would say Mathocrat (Shivraj sir) is extremely good for Maths Opt. But balancing his level of content and GS is extremely difficult.