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Recent questions tagged tifr2016
2
votes
1
answer
1
doubt
https://gateoverflow.in/30720/tifr2016-b-7 the above question is already discussed but still am not clear enuf can someone help
A_i_$_h
asked
in
Algorithms
Oct 22, 2017
by
A_i_$_h
266
views
asymptotic-notations
tifr2016
3
votes
1
answer
2
TIFR CSE 2016 | Part B | Question: 15
Let $G$ be an undirected graph. For a pair $(x, y)$ of distinct vertices of $G$, let $\mathsf{mincut}(x, y)$ be the least number of edges that should be delted from $G$ so that the resulting graph has no $x-y$ ... and iv are possible but neither ii nor iii ii and iv are possible but neither i not iii iii and iv are possible but neither i nor ii
go_editor
asked
in
Graph Theory
Dec 29, 2016
by
go_editor
575
views
tifr2016
graph-theory
graph-connectivity
6
votes
1
answer
3
TIFR CSE 2016 | Part B | Question: 14
Consider a family $\mathcal{F}$ of subsets of $\{1, 2, \dots , n\}$ such that for any two distinct sets $A$ and $B$ in $\mathcal{F}$ we have: $A \subset B$ or $ B \subset A$ or $A \cap B = \emptyset$. Which of the following statements is TRUE? ... $\mathcal{F}$ such that $\mid \mathcal{F} \mid =2^{n-1}$ None of the above
go_editor
asked
in
Set Theory & Algebra
Dec 29, 2016
by
go_editor
661
views
tifr2016
set-theory&algebra
set-theory
3
votes
4
answers
4
TIFR CSE 2016 | Part B | Question: 13
An undirected graph $G = (V, E)$ is said to be $k$-colourable if there exists a mapping $c: V \rightarrow \{1, 2, \dots k \}$ such that for every edge $\{u, v\} \in E$ we have $c(u) \neq c(v)$. Which of the following ... degree in $G$ There is a polynomial time algorithm to check if $G$ is $2$-colourable If $G$ has no triangle then it is $3$-colourable
go_editor
asked
in
Graph Theory
Dec 29, 2016
by
go_editor
698
views
tifr2016
graph-theory
graph-coloring
6
votes
1
answer
5
TIFR CSE 2016 | Part B | Question: 12
A computer program computes a function $\: f \: \{0, 1\}^* \times \{0, 1\}^* \rightarrow \{0, 1\}^*$. Suppose $f(a, b)$ ahs length $\mid b \mid ^2$, where $\mid a \mid$ and $\mid b \mid$ are the lengths of $a$ and $b$. Suppose, using this program, the following ... $n^2 < t \leq n^{\log_2 n}$ $ n^{\log_2 n} < t \leq 2^{(2n)}$ $2^{(2n)} < t$
go_editor
asked
in
Algorithms
Dec 29, 2016
by
go_editor
474
views
tifr2016
algorithms
identify-function
6
votes
1
answer
6
TIFR CSE 2016 | Part B | Question: 11
Let $n \geq 4$ be an integer. Regard the set $\mathbb{R}^n$ as a vector space over $\mathbb{R}$. Consider the following undirected graph $H$ ... inifinite number of vertices The diameter of $H$ is infinite $H$ is conneceted $H$ contains an infinite clique $H$ contains an infinite independent set
go_editor
asked
in
Graph Theory
Dec 29, 2016
by
go_editor
501
views
tifr2016
graph-theory
graph-connectivity
4
votes
1
answer
7
TIFR CSE 2016 | Part B | Question: 10
A $vertex \: cover$ in an undirected graph $G$ is a subset $ C \subseteq V(G)$ such that every edge of $G$ has an endpoint in $C$. An independent set in $G$ is a subset $I \subseteq V(G)$ such that no edge has both its endpoints in $I$. Which of the ... $\mid C \mid \: \: \geq \: \: \mid V(G)\mid /2$ $C$ intersects every independent set
go_editor
asked
in
Graph Theory
Dec 29, 2016
by
go_editor
546
views
tifr2016
graph-theory
vertex-cover
6
votes
1
answer
8
TIFR CSE 2016 | Part B | Question: 9
Which of the following graphs DOES NOT have an Eulerian circuit? (Recall that an Eulerian circuit in an undirected graph is a walk in the graph that starts at a vertex ans returns to the vertex after tracelling on each edge exactly once.) $K_{9, 9}$ $K_{8, 8}$ $K_{12, 12}$ $K_9$ The ...
go_editor
asked
in
Graph Theory
Dec 29, 2016
by
go_editor
1.6k
views
tifr2016
discrete-mathematics
graph-theory
euler-graph
normal
5
votes
1
answer
9
TIFR CSE 2016 | Part B | Question: 8
Consider the following language $\mathsf{PRIMES} = \Biggl\{ \underbrace{111 \dots 11}_{p \: \text{ times} } : \: p \: \text{ is prime } \Biggl\}$ Then, which of the following is TRUE? $\mathsf{PRIMES}$ ... is decidable in polynomial time $\mathsf{PRIMES}$ is context free but not regular $\mathsf{PRIMES}$ is NP-complete and P $\neq$ NP
go_editor
asked
in
Theory of Computation
Dec 29, 2016
by
go_editor
468
views
tifr2016
theory-of-computation
decidability
p-np-npc-nph
2
votes
0
answers
10
TIFR CSE 2016 | Part B | Question: 6
A subset $X$ of $\mathbb{R}^n$ is convex if for all $x, y \in X$ and all $\lambda \in (0, 1)$, we have $\lambda x + (1- \lambda)y \in X$. If $X$ is a convex set, which of the following statements is necessarily TRUE? For every $ x \in X$ ... $x \in X$, then $\lambda x \in X$ for all scalars $\lambda$ If $x, y \in X$, then $x-y \in X$
go_editor
asked
in
Linear Algebra
Dec 28, 2016
by
go_editor
330
views
tifr2016
linear-algebra
vector-space
non-gate
6
votes
1
answer
11
TIFR CSE 2016 | Part B | Question: 5
Consider the recursive function $\mathsf{mc91}$ ... $\{ n: 0 \leq n \leq 110 \}$ $\{ n: 0 \leq n \leq 111 \}$ $\{ n: 0 \leq n < + \infty \}$
go_editor
asked
in
Programming
Dec 28, 2016
by
go_editor
422
views
tifr2016
programming-in-c
recursion
23
votes
4
answers
12
TIFR CSE 2016 | Part B | Question: 4
In the following, $A$ stands for a set of apples, and $S(x, y)$ stands for "$x$ is sweeter than $y$. Let $\Psi \equiv \exists x : x \in A$ $\Phi \equiv \forall x \in A : \exists y \in A : S(x, y).$ Which of the following statements implies that there are ...
go_editor
asked
in
Mathematical Logic
Dec 28, 2016
by
go_editor
2.3k
views
tifr2016
mathematical-logic
first-order-logic
3
votes
1
answer
13
TIFR CSE 2016 | Part B | Question: 3
Assume $P \neq NP$. Which of the following is not TRUE? $2$-SAT in NP $2$-SAT in coNP $3$-SAT is polynmial-time reducible to $2$-SAT 4-SAT is polynmial-time reducible to $3$-SAT $2$-SAT in P
go_editor
asked
in
Theory of Computation
Dec 28, 2016
by
go_editor
439
views
tifr2016
theory-of-computation
reduction
p-np-npc-nph
3
votes
1
answer
14
TIFR CSE 2016 | Part B | Question: 2
Which language class has the following properties? $\quad$ It is closed under union and intersection but not complement. Regular language Context-free language Recursive language Recursively enumerable language Languages that are not recursively enumerable
go_editor
asked
in
Theory of Computation
Dec 28, 2016
by
go_editor
401
views
tifr2016
theory-of-computation
closure-property
13
votes
5
answers
15
TIFR CSE 2016 | Part B | Question: 1
A Boolean formula is said to be a $tautology$ if it evaluates to TRUE for all assignments to its variables. Which one of the following is NOT a tautology? $(( p \vee q) \wedge (r \vee s)) \Rightarrow (( p \wedge r) \vee q \vee s)$ ... $(( p \vee q ) \wedge ( r \vee s)) \Rightarrow ( p \vee q)$
go_editor
asked
in
Mathematical Logic
Dec 28, 2016
by
go_editor
1.6k
views
tifr2016
mathematical-logic
propositional-logic
32
votes
5
answers
16
TIFR CSE 2016 | Part A | Question: 15
In a tournament with $7$ teams, each team plays one match with every other team. For each match, the team earns two points if it wins, one point if it ties, and no points if it loses. At the end of all matches, the teams are ordered in the descending ... of points a team must earn in order to be guaranteed a place in the next round? $13$ $12$ $11$ $10$ $9$
go_editor
asked
in
Combinatory
Dec 28, 2016
by
go_editor
5.0k
views
tifr2016
combinatory
pigeonhole-principle
normal
3
votes
3
answers
17
TIFR CSE 2016 | Part A | Question: 14
A $diagonal$ in a polygon is a straight line segment that connects two non-adjacent vertices, and is contained in the interior of the polygon (except for its points). Two such diagonals are said to cross if they have a point in common in the interior of the polygon. In one such ... the information given $\frac{n}{2}-2$ $\frac{n}{4}-1$ $n-4$ $n^2 - 9.5 n +22$
go_editor
asked
in
Graph Theory
Dec 28, 2016
by
go_editor
583
views
tifr2016
graph-theory
graph-connectivity
4
votes
3
answers
18
TIFR CSE 2016 | Part A | Question: 13
Let $n \geq 2$ be any integer. Which of the following statements is not necessarily true? $\begin{pmatrix} n \\ i \end{pmatrix} = \begin{pmatrix} n-1 \\ i \end{pmatrix} + \begin{pmatrix} n-1 \\ i-1 \end{pmatrix}, \text{ where } 1 \leq i \leq n-1$ $n!$ divides the ... $ i \in \{1, 2, \dots , n-1\}$ If $n$ is an odd prime, then $n$ divides $2^{n-1} -1$
go_editor
asked
in
Combinatory
Dec 28, 2016
by
go_editor
669
views
tifr2016
combinatory
binomial-theorem
4
votes
1
answer
19
TIFR CSE 2016 | Part A | Question: 11
In one of the islands that his travels took him to, Gulliver noticed that the probability that a (uniformly) randomly chosen inhabitant has height at least $2$ meters is $0.2$. Also, $0.2$ is the probability that a a (uniformly) randomly ... Which of the above statements is necessarily true? ii only iii only i, ii and iii ii and iii only None of the above
go_editor
asked
in
Probability
Dec 28, 2016
by
go_editor
482
views
tifr2016
probability
uniform-distribution
3
votes
2
answers
20
TIFR CSE 2016 | Part A | Question: 10
Consider the sequence $\langle s_n : n \geq 0 \rangle$ defined as follows: $s_0=0, s_1=1, s_2=1$, and $s_n = s_{n-1} +s_{n-2}+s_{n-3}$, for $n \geq 3$. Which of the following statements is FALSE? $s_{4k}$ is even, for any $ k \geq 0$ ... $ k \geq 0$ $s_n$ is a multople of 3, for only finitely many values of $n$ $s_{4k+3}$ is even, for any $ k \geq 0$
go_editor
asked
in
Quantitative Aptitude
Dec 27, 2016
by
go_editor
346
views
tifr2016
quantitative-aptitude
sequence-series
3
votes
3
answers
21
TIFR CSE 2016 | Part A | Question: 9
Suppose a rectangular farm has area $100$ square meters. The lengths of its sides are not known. It is known, however, that all the edges are at least $2$ meters in length. Which of the following statements about the rectangle's perimeter $p$ (in ... values between $55$ and $60$ $p$ can be $70$ for some configuration $p$ can be $39$ for some configuration
go_editor
asked
in
Quantitative Aptitude
Dec 27, 2016
by
go_editor
550
views
tifr2016
quantitative-aptitude
geometry
19
votes
4
answers
22
TIFR CSE 2016 | Part A | Question: 8
Let $A$ and $B$ be finite sets such that $A \subseteq B$. Then, what is the value of the expression: $ \sum \limits_{C:A \subseteq C \subseteq B} (-1)^{\mid C \setminus A \mid,}$ Where $C \setminus A=\{x \in C : x \notin A \}$? Always $0$ Always $1$ $0$ if $A=B$ and $1$ otherwise $1$ if $A=B$ and $0$ otherwise Depends on the size of the universe
go_editor
asked
in
Set Theory & Algebra
Dec 27, 2016
by
go_editor
1.9k
views
tifr2016
set-theory&algebra
set-theory
5
votes
1
answer
23
TIFR CSE 2016 | Part A | Question: 7
Let $S$ be the $4 \times 4$ square grid $\{(x, y): x, y \in \{0, 1, 2, 3\} \}$. A $monotone \: \: path$ in this grid starts at $(0, 0)$ and at each step either moves one unit up or one unit right. For example, from the point $(x, y)$ one ... many distinct monotone paths are there to reach point $(3, 3)$ starting from $(0, 0)$? $2z+6$ $3z+6$ $2z+8$ $3z+8$ $3z+4$
go_editor
asked
in
Combinatory
Dec 27, 2016
by
go_editor
467
views
tifr2016
combinatory
counting
3
votes
1
answer
24
TIFR CSE 2016 | Part A | Question: 6
Which of the following statements about the eigen values of $I_n$, the $n \times n$ identity matrix (over complex numbers), is true? The eigen values are $1, \omega, \omega^2, \dots , \omega^{n-1}$, where $\omega$ is a primitive $n$-th root of unity ... there are no other eigen values The eigen values are $1, 1/2, 1/3, \dots , 1/n$ The only eigen value is $1$
go_editor
asked
in
Linear Algebra
Dec 26, 2016
by
go_editor
417
views
tifr2016
linear-algebra
eigen-value
7
votes
2
answers
25
TIFR CSE 2016 | Part A | Question: 5
For a positive integer $N \geq 2$, let $A_N := \Sigma_{n=2}^N \frac{1}{n};$ $B_N := \int\limits_{x=1}^N \frac{1}{x} dx$ Which of the following statements is true? As $N \rightarrow \infty, \: A_N$ increases to infinity but $B_N$ ... $B_N < A_N < B_N +1$ As $N \rightarrow \infty, \: B_N$ increases to infinity but $A_N$ coverages to a finite number
go_editor
asked
in
Calculus
Dec 26, 2016
by
go_editor
693
views
tifr2016
calculus
convergence
divergence
integration
non-gate
9
votes
3
answers
26
TIFR CSE 2016 | Part A | Question: 4
There are $n$ balls $b_1, \dots ,b_n$ and $n$ boxes. Each ball is placed in box chosen independently and uniformly at random. We say that $(b_i, b_j)$ is a $\textit{colliding pair}$ if $i<j$, and $b_i$ and $b_j$ are placed in the same box. What is the ... $\frac{n-1}{2}$ $0$ $1$ $\frac{n}{4}$ $\begin{pmatrix} n \\ 2 \end{pmatrix}$
go_editor
asked
in
Probability
Dec 26, 2016
by
go_editor
1.3k
views
tifr2016
probability
random-variable
uniform-distribution
3
votes
1
answer
27
TIFR CSE 2016 | Part A | Question: 3
Consider the following set of $3n$ linear equations in $3n$ ... $\mathbb{R}^{3n}$ of dimension n $S$ is a subspace of $\mathbb{R}^{3n}$ of dimension $n-1$ $S$ has exactly $n$ elements
go_editor
asked
in
Linear Algebra
Dec 26, 2016
by
go_editor
375
views
tifr2016
linear-algebra
vector-space
non-gate
7
votes
5
answers
28
TIFR CSE 2016 | Part A | Question: 2
Consider the graph shown below: The following experiment is performed using this graph. First, an edge $e =\{i,j\}$ of the graph is chosen uniformly at random from the set of $9$ possibilities. Next, a common neighbour $k$ of $i$ and $j$ is chosen, again uniformly from the set of ... $\frac{1}{6}$ $\frac{1}{4}$ $\frac{1}{3}$ $\frac{2}{3}$ $\frac{5}{6}$
go_editor
asked
in
Graph Theory
Dec 26, 2016
by
go_editor
697
views
tifr2016
graph-theory
graph-connectivity
probability
4
votes
2
answers
29
TIFR CSE 2016 | Part A | Question: 1
Suppose the following statements about three persons in a room are true. Chandni, Sooraj and Tara are in a room. Nobody else is in the room. Chandni is looking at Sooraj. Sooraj is looking at Tara. Chandni is married. ... The situation described is impossible There is insufficient information to conclude if Sooraj is married or unmarried None of the above
go_editor
asked
in
Analytical Aptitude
Dec 26, 2016
by
go_editor
885
views
tifr2016
logical-reasoning
6
votes
1
answer
30
TIFR CSE 2016 | Part A | Question: 12
There are two rocks $A$ and $B$, located close to each other, in a lily pond. There is a frog that jumps randomly between the two rocks at time $t = 0,1, 2, \ldots$. The location of the frog is determined as follows. Initially, at time $t = 0$ ... its third jump)? $\frac{1}{2}$ $\frac{31}{54}$ $\frac{14}{27}$ $\frac{61}{108}$ $\frac{2}{3}$
Ad Ri Ta
asked
in
Probability
Oct 11, 2016
by
Ad Ri Ta
914
views
tifr2016
probability
conditional-probability
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