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Recent questions tagged tifr2018
28
votes
6
answers
1
TIFR CSE 2018 | Part A | Question: 9
How many ways are there to assign colours from range $\left\{1,2,\ldots,r\right\}$ to vertices of the following graph so that adjacent vertices receive distinct colours? $r^{4}$ $r^{4} - 4r^{3}$ $r^{4}-5r^{3}+8r^{2}-4r$ $r^{4}-4r^{3}+9r^{2}-3r$ $r^{4}-5r^{3}+10r^{2}-15r$
Rohit Gupta 8
asked
in
Graph Theory
Dec 10, 2017
by
Rohit Gupta 8
3.8k
views
tifr2018
graph-theory
graph-coloring
8
votes
5
answers
2
TIFR CSE 2018 | Part A | Question: 14
Let $A$ be an $n\times n$ invertible matrix with real entries whose row sums are all equal to $c$. Consider the following statements: Every row in the matrix $2A$ sums to $2c$. Every row in the matrix $A^{2}$ sums to $c^{2}$. Every row in ... and $(2)$ are correct but not necessarily statement $(3)$ all the three statements $(1), (2),$ and $(3)$ are correct
Rohit Gupta 8
asked
in
Linear Algebra
Dec 10, 2017
by
Rohit Gupta 8
2.5k
views
tifr2018
matrix
linear-algebra
17
votes
2
answers
3
TIFR CSE 2018 | Part A | Question: 13
A hacker knows that the password to the TIFR server is $10$-letter string consisting of lower-case letters from the English alphabet. He guesses a set of $5$ distinct $10$-letter strings (with lower-case letters) uniformly at random. What is the probability that one of the ... $ \frac{1}{(26)^{10}}$ None of the above
Rohit Gupta 8
asked
in
Probability
Dec 10, 2017
by
Rohit Gupta 8
1.6k
views
tifr2018
probability
conditional-probability
17
votes
3
answers
4
TIFR CSE 2018 | Part A | Question: 15
Suppose a box contains $20$ balls: each ball has a distinct number in $\left\{1,\ldots,20\right\}$ written on it. We pick $10$ balls (without replacement) uniformly at random and throw them out of the box. Then we check if the ball with number $\text{ 1"}$ ... $\text{ 2"}$ on it is present in the box? $9/20$ $9/19$ $1/2$ $10/19$ None of the above
Rohit Gupta 8
asked
in
Probability
Dec 10, 2017
by
Rohit Gupta 8
2.0k
views
tifr2018
probability
conditional-probability
4
votes
1
answer
5
TIFR CSE 2018 | Part B | Question: 15
$G$ respresents an undirected graph and a cycle refers to a simple cycle (no repeated edges or vertices). Define the following two languages. $\text{SCYCLE}=\{(G,k)\mid G \text{ contains a cycle of length at most k}\}$ ... $\text{SCYCLE}$ to $\text{LCYCLE}$).
Arjun
asked
in
Theory of Computation
Dec 10, 2017
by
Arjun
779
views
tifr2018
theory-of-computation
reduction
p-np-npc-nph
non-gate
12
votes
3
answers
6
TIFR CSE 2018 | Part B | Question: 14
Define the language $\text{INFINITE}_{DFA}\equiv \{(A)\mid A \text{ is a DFA and } L(A) \text{ is an infinite language}\},$ where $(A)$ denotes the description of the deterministic finite automata (DFA).Then which ... It is Turing decidable (recursive). It is Turing recognizable but not decidable. Its complement is Turing recognizable but it is not decidable.
Arjun
asked
in
Theory of Computation
Dec 10, 2017
by
Arjun
2.9k
views
tifr2018
theory-of-computation
identify-class-language
9
votes
1
answer
7
TIFR CSE 2018 | Part B | Question: 12
Consider the following statements: For every positive integer $n,$ let $\#{n}$ be the product of all primes less than or equal to $n.$ Then, $\# {p}+1$ is a prime, for every prime $p.$ $\large\pi$ is a universal constant ... . Only statement (ii) is correct. Only statement (iii) is correct. Only statement (iv) is correct. None of the statements are correct.
Arjun
asked
in
Theory of Computation
Dec 10, 2017
by
Arjun
1.6k
views
tifr2018
theory-of-computation
regular-language
11
votes
3
answers
8
TIFR CSE 2018 | Part B | Question: 13
Let $n\geq 3,$ and let $G$ be a simple, connected, undirected graph with the same number $n$ of vertices and edges. Each edge of $G$ has a distinct real weight associated with it. Let $T$ be the minimum weight spanning tree of $G.$ Which of the ... edge of $C$ is not in $T.$ $T$ can be found in $O(n)$ time from the adjacency list representation of $G.$
Arjun
asked
in
Algorithms
Dec 10, 2017
by
Arjun
2.3k
views
tifr2018
graph-algorithms
minimum-spanning-tree
12
votes
2
answers
9
TIFR CSE 2018 | Part B | Question: 11
Consider the language $L\subseteq \left \{ a,b,c \right \}^{*}$ defined as $L = \left \{ a^{p}b^{q}c^{r} : p=q\quad or\quad q=r \quad or\quad r=p \right \}.$ Which of the following answer is TRUE about the complexity of this language ... defined as $\overline{L} = \left \{ a,b,c \right \}^{*}\backslash L,$ is regular. $L$ is regular, context-free and decidable
Arjun
asked
in
Theory of Computation
Dec 10, 2017
by
Arjun
1.9k
views
tifr2018
identify-class-language
theory-of-computation
11
votes
1
answer
10
TIFR CSE 2018 | Part B | Question: 10
For two $n$ bit strings $x,y \in\{0,1\}^{n},$ define $z=x\oplus y$ to be the bitwise XOR of the two strings (that is, if $x_{i},y_{i},z_{i}$ denote the $i^{th}$ bits of $x,y,z$ respectively, then $z_{i}=x_{i}+y_{i} \bmod 2$ ... such linear functions for $n \geq 2$ is: $2^{n}$ $2^{n^{2}}$ $\large2^{\frac{n}{2}}$ $2^{4n}$ $2^{n^{2}+n}$
Arjun
asked
in
Set Theory & Algebra
Dec 10, 2017
by
Arjun
1.2k
views
tifr2018
set-theory&algebra
functions
12
votes
1
answer
11
TIFR CSE 2018 | Part B | Question: 9
Let $G=(V,E)$ be a DIRECTED graph, where each edge $\large e$ has a positive weight $\large\omega(e),$ and all vertices can be reached from vertex $\large s.$ For each vertex $\large v,$ let $\large \phi(v)$ be the length of the shortest ... $G,$ then $\omega'(P)<2\times \omega(P).$ All of the above options are necessarily TRUE.
Arjun
asked
in
Algorithms
Dec 10, 2017
by
Arjun
2.0k
views
tifr2018
graph-algorithms
shortest-path
30
votes
3
answers
12
TIFR CSE 2018 | Part B | Question: 8
In an undirected graph $G$ with $n$ vertices, vertex $1$ has degree $1$, while each vertex $2,\ldots,n-1$ has degree $10$ and the degree of vertex $n$ is unknown, Which of the following statement must be TRUE on the graph $G$? There is a path ... Vertex $n$ has degree $1$. The diameter of the graph is at most $\frac{n}{10}$ All of the above choices must be TRUE
Arjun
asked
in
Graph Theory
Dec 10, 2017
by
Arjun
4.3k
views
tifr2018
graph-theory
degree-of-graph
13
votes
1
answer
13
TIFR CSE 2018 | Part B | Question: 7
Consider the recursive quicksort algorithm with "random pivoting". That is, in each recursive call, a pivot is chosen uniformly at random from the sub-array being sorted.When this randomized algorithm is applied to an array of size $n$ all whose elements are distinct, ... $\Theta\left(\dfrac{1}{n \log^{2} n}\right)$
Arjun
asked
in
Algorithms
Dec 10, 2017
by
Arjun
7.5k
views
tifr2018
algorithms
sorting
quick-sort
4
votes
2
answers
14
TIFR CSE 2018 | Part B | Question: 6
Consider the following implementation of a binary tree data strucrure. The operator $+$ denotes list-concatenation. That is, $[a,b,c]+[d,e]=[a,b,c,d,e].$ struct TreeNode: int value TreeNode leftChild TreeNode rightChild function preOrder(T): if T == null: ... $\text{Cannot be uniquely determined from given information.}$
Arjun
asked
in
DS
Dec 10, 2017
by
Arjun
1.1k
views
tifr2018
data-structures
binary-tree
14
votes
1
answer
15
TIFR CSE 2018 | Part B | Question: 5
Which of the following functions, given by there recurrence, grows the fastest asymptotically? $T(n) = 4T\left ( \frac{n}{2} \right ) + 10n$ $T(n) = 8T\left ( \frac{n}{3} \right ) + 24n^{2}$ $T(n) = 16T\left ( \frac{n}{4} \right ) + 10n^{2}$ $T(n) = 25T\left ( \frac{n}{5} \right ) + 20\left ( n \log n \right )^{1.99}$ They all are asymptotically the same
Arjun
asked
in
Algorithms
Dec 10, 2017
by
Arjun
2.7k
views
tifr2018
asymptotic-notations
recurrence-relation
8
votes
2
answers
16
TIFR CSE 2018 | Part B | Question: 3
How many distinct minimum weight spanning trees does the following undirected, weighted graph have ? $1$ $2$ $4$ $6$ $8$
Arjun
asked
in
Algorithms
Dec 10, 2017
by
Arjun
2.1k
views
tifr2018
algorithms
minimum-spanning-tree
15
votes
12
answers
17
TIFR CSE 2018 | Part B | Question: 1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$
Arjun
asked
in
Quantitative Aptitude
Dec 10, 2017
by
Arjun
2.7k
views
tifr2018
quantitative-aptitude
modular-arithmetic
4
votes
3
answers
18
TIFR CSE 2018 | Part B | Question: 4
The notation "$\Rightarrow$" denotes "implies" and "$\wedge$" denotes "and" in the following formulae. Let $X$ denote the formula: $(b \Rightarrow a ) \Rightarrow ( a \Rightarrow b)$ Let $Y$ denote the formula: ... is not satisfiable. $X$ is not tautology and $Y$ is satisfiable. $X$ is a tautology and $Y$ is satisfiable,
Arjun
asked
in
Mathematical Logic
Dec 10, 2017
by
Arjun
1.5k
views
tifr2018
mathematical-logic
propositional-logic
7
votes
1
answer
19
TIFR CSE 2018 | Part B | Question: 2
Consider the following non-deterministic automation, where $\large s_{1}$ is the start state and $\large s_{4}$ is the final (accepting) state. The alphabet is $\{a,b\}.$ A transition with label $\large\epsilon$ can be taken without consuming any symbol from the input. Which of the ... $aba(a+b)^{*}aba$ $(a+b)aba(b+a)^{*}$ $aba(a+b)^{*}$ $(ab)^{*}aba$
Arjun
asked
in
Theory of Computation
Dec 10, 2017
by
Arjun
1.2k
views
tifr2018
regular-expression
finite-automata
7
votes
2
answers
20
TIFR CSE 2018 | Part A | Question: 10
Let $C$ be a biased coin such that the probability of a head turning up is $p.$ Let $p_n$ denote the probability that an odd number of heads occurs after $n$ tosses for $n \in \{0,1,2,\ldots \},$ ... $p_{n}=1 \text{ if } n \text{ is odd and } 0 \text{ otherwise}.$
Arjun
asked
in
Probability
Dec 10, 2017
by
Arjun
1.5k
views
tifr2018
probability
binomial-distribution
8
votes
1
answer
21
TIFR CSE 2018 | Part A | Question: 12
An $n \times n$ matrix $M$ with real entries is said to be positive definite if for every non-zero $n$-dimensional vector $x$ with real entries, we have $x^{T}Mx>0.$ Let $A$ and $B$ be symmetric, positive definite matrices of size ... $(3)$ Only $(1)$ and $(3)$ None of the above matrices are positive definite All of the above matrices are positive definite
Arjun
asked
in
Linear Algebra
Dec 10, 2017
by
Arjun
1.3k
views
tifr2018
matrix
linear-algebra
3
votes
3
answers
22
TIFR CSE 2018 | Part A | Question: 11
We are given a (possibly empty) set of objects. Each object in the set is colored either black or white, is shaped either circular or rectangular, and has a profile that is either fat or thin, Those properties obey the following principles: Each white ... $(i) \text{ and } (iii)$ only None of the statements must be TRUE All of the statements must be TRUE
Arjun
asked
in
Analytical Aptitude
Dec 10, 2017
by
Arjun
1.0k
views
tifr2018
analytical-aptitude
logical-reasoning
10
votes
2
answers
23
TIFR CSE 2018 | Part A | Question: 8
A crime has been committed with four people at the scene of the crime. You are responsible for finding out who did it. You have recorded the following statements from the four witnesses, and you know one of them has committed the crime. ... $\text{Desmond}$ $\text{Either Anuj or Binky; the information is insufficient to pinpoint the criminal}$
Arjun
asked
in
Analytical Aptitude
Dec 10, 2017
by
Arjun
1.1k
views
tifr2018
analytical-aptitude
logical-reasoning
15
votes
5
answers
24
TIFR CSE 2018 | Part A | Question: 7
Consider the following function definition. void greet(int n) { if(n>0) { printf("hello"); greet(n-1); } printf("world"); } If you run $\textsf{greet(n)}$ ... "helloworld" $\textsf{n+1}$ times "helloworld" $\textsf{n}$ times "helloworld", followed by "world"
Arjun
asked
in
Programming
Dec 10, 2017
by
Arjun
2.3k
views
tifr2018
programming
programming-in-c
recursion
15
votes
6
answers
25
TIFR CSE 2018 | Part A | Question: 6
What is the minimum number of students needed in a class to guarantee that there are at least $6$ students whose birthdays fall in the same month ? $6$ $23$ $61$ $72$ $91$
Arjun
asked
in
Combinatory
Dec 10, 2017
by
Arjun
2.8k
views
tifr2018
pigeonhole-principle
combinatory
3
votes
1
answer
26
TIFR CSE 2018 | Part A | Question: 5
Which of the following is the derivative of $f(x)=x^{x}$ when $x>0$ ? $x^{x}$ $x^{x} \ln \;x$ $x^{x}+x^{x}\ln\;x$ $(x^{x}) (x^{x}\ln\;x)$ $\text{None of the above; function is not differentiable for }x>0$
Arjun
asked
in
Calculus
Dec 10, 2017
by
Arjun
1.1k
views
tifr2018
calculus
differentiation
4
votes
1
answer
27
TIFR CSE 2018 | Part A | Question: 1
Consider a point $A$ inside a circle $C$ that is at distance $9$ from the centre of a circle. Suppose you told that there is a chord of length $24$ passing through $A$ with $A$ as its midpoint. How many distinct chords of $C$ have integer length and pass through $A?$ $2$ $6$ $7$ $12$ $14$
Arjun
asked
in
Quantitative Aptitude
Dec 10, 2017
by
Arjun
1.2k
views
tifr2018
quantitative-aptitude
geometry
circle
2
votes
2
answers
28
TIFR CSE 2018 | Part A | Question: 4
The distance from your home to your office is $4$ kilometers and your normal walking speed is $4$ Km/hr. On the first day, you walk at your normal walking speed and take time $T_1$ to reach office. On the second day, you walk at a speed of $3$ Km/hr from $2$ Kilometers, and at ... $T_{1}=T_{2}$ and $T_{1}<T_{3}$ $T_{1}<T_{2}$ and $T_{1}=T_{3}$
Arjun
asked
in
Quantitative Aptitude
Dec 10, 2017
by
Arjun
477
views
tifr2018
quantitative-aptitude
work-time
21
votes
3
answers
29
TIFR CSE 2018 | Part A | Question: 3
Which of the following statements is TRUE for all sufficiently large integers n ? $2^{2^{\sqrt{\log \log n}}} <2^{\sqrt{\log n}} < n$ $2^{\sqrt{\log n}}<n<2^{2^{\sqrt{\log \log n}}}$ $n<2^{\sqrt{\log n}}<2^{2^{\sqrt{\log \log n}}}$ $n<2^{2^{\sqrt{\log \log n}}} <2^{\sqrt{\log n}}$ $2^{\sqrt{\log n}}<2^{2^{\sqrt{\log \log n}}} < n$
Arjun
asked
in
Algorithms
Dec 10, 2017
by
Arjun
2.4k
views
tifr2018
algorithms
asymptotic-notations
2
votes
1
answer
30
TIFR CSE 2018 | Part A | Question: 2
Consider the following subset of $\mathbb{R} ^{3}$ (the first two are cylinder, the third is a plane): $C_{1}=\left \{ \left ( x,y,z \right ): y^{2}+z^{2}\leq 1 \right \};$ ... $A?$ Circle Ellipse Triangle Square An octagonal convex figure with curved sides
Arjun
asked
in
Quantitative Aptitude
Dec 10, 2017
by
Arjun
625
views
tifr2018
quantitative-aptitude
geometry
three-dimensional-geometry
non-gate
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Recent questions tagged tifr2018
Recent Blog Comments
Please upload updated previous year question...
The last hardcopy that was made was for GATE 2022...
overall only 3 post .no post for gen male
for gen GS in the range of 720-750 approx.
can we get 2023 hark copy from amazon?