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JEST TCS ANSWER KEY OUT. Those who attempted the exam, how much did you score?
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JEST 2026 Theoretical Computer Science Subjective Paper (part-2 : 105 minutes)
I am reaching out to fellow JEST 2026 Theoretical Computer Science (TCS) candidates to compile a comprehensive list of subjective questions from the recent examination. P...
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JEST TCS 2021 | SECTION A | Q1
1. Let f : {0, 1}n → {0, 1} be a Boolean function of arity n. It is said to depend on its ith argument ifthere exist a1, a2, . . . , an ∈ {0, 1} such thatf (a1, . . . , a...
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JEST TCS EXAM
How to approach JEST theoretical computer science exam and where to study from? Is gate pyq enough for objective questions?I am 2025 graduate, currently working. Appeard ...
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JEST TCS 2025 | Section B Part 2 | Question: 04
Let $S$ be a set of $2n$ (not necessarily distinct) integers.Design an efficient algorithm that finds a partition of $S$ into $n$ pairs such that the maximum sum of the t...
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JEST TCS 2025 | Section B Part 2 | Question: 03
An induced subgraph of an undirected graph $G = (V,E)$ is a graph formed from a non-empty subset $S$ of the vertices $V$ and all of the edges in $E$ connecting pairs of v...
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JEST TCS 2025 | Section B Part 2 | Question: 02
Let $\mathscr{A} = (Q,\Sigma,\delta,q_0,F)$ be a finite-state automaton, where$Q$ is a finite set of states,$\Sigma$ is a finite alphabet,$\delta \subseteq Q \times \Sigm...
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JEST TCS 2025 | Section B Part 2 | Question: 01
Suppose you are consulting for a company that manufactures PC equipment and ships it to distributors all over the country. For each of the next $n$ weeks, they have a pro...
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JEST TCS 2025 | Section B Part 1 | Question: 05
A plane passing through the Earth's centre separates the Earth into two equal hemispheres. The intersection of such a plane with the Earth's surface is a circle on the Ea...
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JEST TCS 2025 | Section B Part 1 | Question: 04
Let $G = (V,E)$ be an undirected connected graph with a cost, $c_e \geq 0$ on each edge e. The costs on the edges may not all be different. A minimum-cost spanning tree o...
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JEST TCS 2025 | Section B Part 1 | Question: 03
Let $G = (V,E)$ be an undirected graph with $n$ vertices. Suppose $G$ contains two vertices $s$ and $t$ such that the shortest distance between $s$ and $t$ is strictly gr...
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JEST TCS 2025 | Section B Part 1 | Question: 02
On a $2n \times 2n$ chess-board, $2n^2$ rooks are placed, at most one per square, in a way so that there are $n$ rooks in each row and $n$ rooks in each column of the boa...
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JEST TCS 2025 | Section B Part 1 | Question: 01
Fix a finite alphabet $\Sigma$. For any two languages $L_1, L_2 \subseteq \Sigma^*$, the extension of $L_2$ with respect to $L_1$, denoted ext($L_1,L_2)$ is the language ...
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JEST TCS 2025 | Section A (MCQ) | Question: 25
Let $S = \sum_{n\geq1} \dfrac{1}{n^2}$ and $A = \sum_{n\geq1}(-1)^{n+1}\dfrac{1}{n^2}$. Then which of the following statements is true?$S$ converges but $A$ does not conv...
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JEST TCS 2025 | Section A (MCQ) | Question: 24
Let $a, b$ and $c$ denote regular expressions. Which of the following is an identity$?$None of the choices$a . (b + c) = (b + c) . a$$$c^* . a^* . b^* = c^* . b^* . a^*$$...
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352
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JEST TCS 2025 | Section A (MCQ) | Question: 23
Let $f(n) := 2^n, g(n) := n$ and $h(n) :=$ $n^{log n}$. Which of the following statements is true$?$log $h(n) = O(g(n))$ and log $h(n) = \Omega$(log $f(n)).$$f(n)= O(g(n)...
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JEST TCS 2025 | Section A (MCQ) | Question: 22
Consider $n$ points equi-separated on a circle of radius one.Fix one of the points, and consider the product of the lengths of the chord from this point to all the other ...
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352
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JEST TCS 2025 | Section A (MCQ) | Question: 21
Let $\Sigma =$ {$a,b$}.For a word $w \in \Sigma^*$ and a letter $x \in \Sigma$, let $\#_x(w)$ denote the number of occurrences of $x$ in $w$. For example, for $w = abaab$...
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343
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JEST TCS 2025 | Section A (MCQ) | Question: 20
Consider the following recurrence: $A_n$ is the sum of $A_{n-1}$ and a number chosen uniformly at random from {$1,...,n$}, starting from $A_0 :=1$. What is the expected v...
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JEST TCS 2025 | Section A (MCQ) | Question: 19
If $\lambda_1,...,\lambda_k$, where $k \geq 2$, are $k$ distinct eigenvalues of a singular $n \times n$ matrix $A$, with associated eigenvectors $v_1,...,v_k$, then which...
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JEST TCS 2025 | Section A (MCQ) | Question: 18
Let $X$ be a set of propositional formulas and let $f,g$ be two propositional formulas. An assignment is a function mapping propositional variables to {$true, false$}, an...
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JEST TCS 2025 | Section A(MCQ) | Question: 17
A cut-edge in a graph is an edge whose removal disconnects the graph. Let $T$ be a tree with $n$ vertices. Consider the following statements. $T$ has no cycles and $n-1$...
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JEST TCS 2025 | Section A (MCQ) | Question: 16
In how many different ways can you distribute three identical red balls and two identical blue balls into one white bin and one black bin$?$$9$$12$$32$$5$
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JEST TCS 2025 | Section A (MCQ) | Question: 15
Starting with $x_0 = 0$, suppose you do the following:, at the $n^{th}$ stepyou flip a fair coin: if it is heads then $x_n := x_{n-1} + 1$ and if it is tails then $x_n :=...
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JEST TCS 2025 | Section A (MCQ) | Question: 14
A graph property (of simple graphs) is said to be $monotone$ $increasing$ if whenever a graph $G = (V,E)$ has the property, then every graph $G' = (V,E')$ with $E \subset...
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JEST TCS 2025 | Section A (MCQ) | Question: 13
Let $\Sigma =$ {$a,b$}. For a word $w \in \Sigma^*$ and a letter $x \in \Sigma$, let $\#_x(w)$ denote the number of occurrences of $x$ in $w$. For example, for $w = abaab...
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JEST TCS 2025 | Section A (MCQ) | Question: 12
How many numbers $x \in$ {$1,...,99$} are there such that $x^{\lceil{\sqrt[3]{x}}\rceil}$ is a perfect cube$?$$4$$23$$19$$22$
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JEST TCS 2025 | Section A (MCQ) | Question: 11
Suppose that we roll a fair six-sided die until either a six comes up or we have rolled it ten times. The expected number of times we roll the die isLess than $5$.$8$More...
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JEST TCS 2025 | Section A (MCQ) | Question: 10
If $S$ is a set of size $n$, then how many triplets ($A,B,C$) $\subseteq S \times S \times S$ are there such that $A,B$ are disjoint subsets of $C?$$4^n$$3^n$$n^2$$n^n$
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229
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JEST TCS 2025 | Section A (MCQ) | Question: 09
Suppose we pick two distinct elements uniformly at random from the set {$1,...,n$}. Let $p$ be the probability that one is twice the other. Which of the following stateme...
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