Loading dataset...
Total Questions
Unique Topics
Repeated Questions
Years Covered
Mentor Analysis — ISI MTech CSA (PCA Paper)
Based on 273 questions from 2017–2026. Read this before you open the Practice Arena.
What This Exam Actually Tests
The PCA paper is 30 MCQs in 2 hours, mixing Mathematics and Computer Science. From 10 years of data: 71.4% questions are pure Mathematics, 15.8% are Discrete Mathematics, and 12.8% are core CS (Algorithms, TOC, Digital Logic). This is not a CS exam with math sprinkled in — it is fundamentally a mathematics exam that now has a growing CS component.
The difficulty distribution is brutal: 52% Medium, 32% Hard, 16% Easy. Only 5 of every 30 questions are straightforward. The exam is testing whether you can think under pressure, not whether you memorized formulas. Most questions require applying 2–3 concepts together, not recalling one.
Topic Priority (2021–2026)
Where to spend your preparation time
Together these two guarantee 6–7 questions every paper. Master them completely — limits, continuity, differentiability, integration techniques, sequences for Calculus; eigenvalues, rank, determinants, linear transformations for Linear Algebra.
The 2023 Shift
The most important thing to understand about this exam
From 2017 to 2021, this was almost a pure mathematics paper. Calculus alone had 10 questions in both 2020 and 2021. CS topics barely appeared.
In 2023, everything changed. Graph Theory jumped from 0 to 6 questions. Theory of Computation appeared with 6 questions. This CS push has been sustained through 2024, 2025, and 2026.
Calculus is still the single biggest topic, but its dominance has halved. Do not ignore CS topics thinking this is purely a math exam — in 2023, 12 out of 30 questions were from CS/Discrete Math.
The trend will likely continue. Budget at least 4–5 questions from CS topics in your mental model for the 2027 exam.
Exam Strategy
+4 correct · 0 wrong · +1 unattempt · 120 total
Score targets to be competitive
Most people score 80–100. 96+ is a strong score.
The Skip Rule
Skipping gives +1. A random guess on 4 options gives an expected value of +1 (= +4 × 0.25). So random guessing is exactly as good as skipping — the exam is designed this way. Only attempt if you can eliminate at least 2 wrong options. Then your EV is +4 × 0.5 = +2, which beats skipping.
Time Allocation
2 hours = 120 min for 30 questions = 4 min/question average. But don't spread evenly. Spend the first 60 min on Calculus + Linear Algebra questions — these are solvable and high volume. Then tackle the CS questions which are often binary (you know it or you don't). Spend the last 20 min on harder algebra/probability where careful reading helps.
On Hard Questions
32% of questions are Hard. Don't spend more than 6 minutes on any single question. Mark it, skip, and come back. A question you can't solve in 6 min is unlikely to be solved in 10 min under exam stress.
Question Patterns That Have Repeated — Study These First
20 questions appeared more than once in the 2017–2026 data. These concept-types are clearly favourites of the paper setters.
Where to Focus Your Remaining Preparation
Mathematics (must be rock solid)
- Calculus: Limits using L'Hôpital and squeeze, continuity/differentiability (standard discontinuity types), definite integrals with substitution, improper integrals, sequences/series convergence (ratio test, comparison).
- Linear Algebra: Rank-nullity, system of equations (consistency conditions), eigenvalues of functions of matrices (e.g., $A^2$, $Adj(A)$, $A^{-1}$), diagonalization, linear transformations and their matrices.
- Combinatorics: Binomial identities, inclusion-exclusion, pigeonhole, counting functions/bijections/surjections, recurrences.
- Probability: Conditional probability, Bayes, random variables, expectation/variance from first principles. The dice/coin/card problems are straightforward if you know Bayes well.
- Algebra: Roots of polynomials (Descartes, Vieta), AP/GP/HP mixed, inequalities (AM-GM, Cauchy).
CS / Discrete Math (the new battleground)
- Graph Theory: Planarity (Euler's formula), bipartite graphs, Hamiltonian/Eulerian conditions, graph coloring, spanning trees. 2023 had 6 graph questions — this is now a major topic.
- TOC: DFA/NFA state minimization, regular languages and closure properties, CFLs and pushdown automata, decidability. Questions are usually conceptual, not computation-heavy.
- Logic: Propositional logic (tautology, satisfiability), predicate logic (quantifier manipulation), truth tables. These are typically Easy-Medium and quick to solve.
- Algorithms: Worst-case complexity (sorting, searching), divide-and-conquer recurrences (Master theorem), basic dynamic programming patterns.
- Skip: Digital Logic, Data Structures, Coordinate Geometry — appeared once or twice, not worth deep preparation unless you have time.
Subject Trends Over Years
How the focus on subjects has shifted.
Subject Distribution
Overall proportion of Subjects.