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Recent questions tagged tifr2013
33
votes
4
answers
1
TIFR CSE 2013 | Part B | Question: 20
Suppose $n$ processors are connected in a linear array as shown below. Each processor has a number. The processors need to exchange numbers so that the numbers eventually appear in ascending order (the processor $\rm P1$ should have the minimum value and the the ... $n^2$ steps $n$ steps $n^{1.5}$ steps The algorithm is not guaranteed to sort
makhdoom ghaya
asked
in
Algorithms
Nov 8, 2015
by
makhdoom ghaya
2.5k
views
tifr2013
algorithms
sorting
26
votes
3
answers
2
TIFR CSE 2013 | Part B | Question: 19
In a relational database there are three relations: $Customers = C\textsf{(CName)}$, $Shops = S \textsf{(SName)}$, $Buys = B\textsf{(CName, SName)}$ ... $S - \Pi _{\textsf{SName}}((C \times S) - B)$ None of the above
makhdoom ghaya
asked
in
Databases
Nov 8, 2015
by
makhdoom ghaya
2.6k
views
tifr2013
databases
relational-algebra
17
votes
6
answers
3
TIFR CSE 2013 | Part B | Question: 18
Let $S$ be a set of numbers. For $x \in S$, the rank of $x$ is the number of elements in $S$ that are less than or equal to $x$. The procedure $\textsf{Select}(S, r)$ takes a set $S$ of numbers and a rank $r\left(1 \leq r \leq |S|\right)$ and returns the ... $|S|$ constant · $|S||R|$ constant · $|R| \log |S|$ constant · $|S|(1 + \log |R|)$
makhdoom ghaya
asked
in
Algorithms
Nov 8, 2015
by
makhdoom ghaya
2.0k
views
tifr2013
algorithms
quick-sort
time-complexity
15
votes
2
answers
4
TIFR CSE 2013 | Part B | Question: 17
In a connected weighted graph with $n$ vertices, all the edges have distinct positive integer weights. Then, the maximum number of minimum weight spanning trees in the graph is $1$ $n$ equal to number of edges in the graph. equal to maximum weight of an edge of the graph. $n^{n-2}$
makhdoom ghaya
asked
in
Algorithms
Nov 8, 2015
by
makhdoom ghaya
1.5k
views
tifr2013
algorithms
minimum-spanning-tree
12
votes
4
answers
5
TIFR CSE 2013 | Part B | Question: 16
Consider a function $T_{k, n}: \left\{0, 1\right\}^{n}\rightarrow \left\{0, 1\right\}$ which returns $1$ if at least $k$ of its $n$ inputs are $1$. Formally, $T_{k, n}(x)=1$ if $\sum ^{n}_{1} x_{i}\geq k$. Let $y \in \left\{0, 1\right\}^{n}$ ... $y_{i}$ is omitted) is equivalent to $T_{k-1}, n(y)$ $T_{k, n}(y)$ $y_{i}$ $\neg y_{i}$ None of the above
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 8, 2015
by
makhdoom ghaya
1.1k
views
tifr2013
set-theory&algebra
functions
7
votes
2
answers
6
TIFR CSE 2013 | Part B | Question: 15
Let $G$ be an undirected graph with $n$ vertices. For any subset $S$ of vertices, the set of neighbours of $S$ consists of the union of $S$ and the set of vertices $S'$ that are connected to some vertex in $S$ by an edge of $G$. The graph $G$ has the nice property ... $O \left(\sqrt{n}\right)$ but not $O (\log n)$ $O (n)$ but not $O \left(\sqrt{n}\right)$
makhdoom ghaya
asked
in
Algorithms
Nov 7, 2015
by
makhdoom ghaya
1.1k
views
tifr2013
graph-algorithms
time-complexity
23
votes
3
answers
7
TIFR CSE 2013 | Part B | Question: 14
Assume a demand paged memory system where ONLY THREE pages can reside in the memory at a time. The following sequence gives the order in which the program references the pages. $1, 3, 1, 3, 4, 2, 2, 4$ Assume that least frequently used page is ... $1,1,1,2$ times, respectively $1,1,1,1$ times, respectively $2,1,2,2$ times, respectively None of the above
makhdoom ghaya
asked
in
Operating System
Nov 7, 2015
by
makhdoom ghaya
2.2k
views
tifr2013
operating-system
page-replacement
38
votes
2
answers
8
TIFR CSE 2013 | Part B | Question: 13
Given a binary tree of the following form and having $n$ nodes, the height of the tree is $\Theta \left(\log n\right)$ $\Theta \left(n\right)$ $\Theta \left(\sqrt{n}\right)$ $\Theta \left(n / \log n\right)$ None of the above.
makhdoom ghaya
asked
in
DS
Nov 7, 2015
by
makhdoom ghaya
2.9k
views
tifr2013
binary-tree
data-structures
24
votes
2
answers
9
TIFR CSE 2013 | Part B | Question: 12
It takes $O(n)$ time to find the median in a list of $n$ elements, which are not necessarily in sorted order while it takes only $O(1)$ time to find the median in a list of $n$ sorted elements. How much time does it take to find the median of $2n$ elements which are ... $O (n)$ but not $O (\sqrt{n})$ $O \left(n \log n\right)$ but not $O (n)$
makhdoom ghaya
asked
in
Algorithms
Nov 7, 2015
by
makhdoom ghaya
2.6k
views
tifr2013
algorithms
sorting
time-complexity
16
votes
4
answers
10
TIFR CSE 2013 | Part B | Question: 11
Which of the following statements is FALSE? The intersection of a context free language with a regular language is context free. The intersection of two regular languages is regular. The intersection of two context free languages is context ... language is context free. The intersection of a regular language and the complement of a regular language is regular.
makhdoom ghaya
asked
in
Theory of Computation
Nov 7, 2015
by
makhdoom ghaya
2.2k
views
tifr2013
theory-of-computation
closure-property
5
votes
1
answer
11
TIFR CSE 2013 | Part B | Question: 10
Let $m, n$ be positive integers with $m$ a power of $2$. Let $s= 100 n^{2} \log m$. Suppose $S_{1}, S_{2},\dots ,S_{m}$ are subsets of ${1, 2, \dots, s}$ such that $ \mid S_{i} \mid= 10 n \log m$ and $ \mid S_{i} \cap S_{j} \mid \leq \log m$ ... $x ∉ T$. $1$ if $x \in T$ and at least $0.9$ if $x ∉ T$. At least $0.9$ if $x \in T$ and $1$ if $x ∉ T$.
makhdoom ghaya
asked
in
Probability
Nov 7, 2015
by
makhdoom ghaya
622
views
tifr2013
probability
conditional-probability
8
votes
2
answers
12
TIFR CSE 2013 | Part B | Question: 9
Suppose $n$ straight lines are drawn on a plane. When these lines are removed, the plane falls apart into several connected components called regions. $A$ region $R$ is said to be convex if it has the following property: whenever two points ... are produced, but they need not all be convex. All regions are convex but there may be exponentially many of them.
makhdoom ghaya
asked
in
Quantitative Aptitude
Nov 6, 2015
by
makhdoom ghaya
1.1k
views
tifr2013
quantitative-aptitude
geometry
cartesian-coordinates
17
votes
3
answers
13
TIFR CSE 2013 | Part B | Question: 8
Which one of the following languages over the alphabet ${0, 1}$ is regular? The language of balanced parentheses where $0, 1$ are thought of as $(,)$ respectively. The language of palindromes, i.e. bit strings $x$ that read the same from left to right as well as right to ... $(c)$ above. $\left \{ 0^{m} 1^{n} | 1 \leq m \leq n\right \}$
makhdoom ghaya
asked
in
Theory of Computation
Nov 6, 2015
by
makhdoom ghaya
3.1k
views
tifr2013
theory-of-computation
regular-language
4
votes
1
answer
14
TIFR CSE 2013 | Part B | Question: 7
Which of the following is not implied by $P=NP$? $3$SAT can be solved in polynomial time. Halting problem can be solved in polynomial time. Factoring can be solved in polynomial time. Graph isomorphism can be solved in polynomial time. Travelling salesman problem can be solved in polynomial time.
makhdoom ghaya
asked
in
Algorithms
Nov 6, 2015
by
makhdoom ghaya
1.3k
views
tifr2013
algorithms
p-np-npc-nph
25
votes
2
answers
15
TIFR CSE 2013 | Part B | Question: 6
Let $L$ and $L'$ be languages over the alphabet $\Sigma $. The left quotient of $L$ by $L'$ is $L/L'\overset{{def}}{=} \left\{w \in \Sigma^* : wx ∈ L\text{ for some }x \in L'\right\}$ Which of the following is true? If $L/L'$ ... $L$ is regular. $L/L'$ is a subset of $L$. If $L/L'$ and $L'$ are regular, then $L$ is regular.
makhdoom ghaya
asked
in
Theory of Computation
Nov 6, 2015
by
makhdoom ghaya
2.7k
views
tifr2013
theory-of-computation
regular-language
29
votes
3
answers
16
TIFR CSE 2013 | Part B | Question: 5
Given a weighted directed graph with $n$ vertices where edge weights are integers (positive, zero, or negative), determining whether there are paths of arbitrarily large weight can be performed in time $O(n)$ $O(n . \log(n))$ but not $O (n)$ $O(n^{1.5})$ but not $O (n \log n)$ $O(n^{3})$ but not $O(n^{1.5})$ $O(2^{n})$ but not $O(n^{3})$
makhdoom ghaya
asked
in
Algorithms
Nov 6, 2015
by
makhdoom ghaya
3.7k
views
tifr2013
algorithms
graph-algorithms
time-complexity
17
votes
5
answers
17
TIFR CSE 2013 | Part B | Question: 4
A set $S$ together with partial order $\ll$ is called a well order if it has no infinite descending chains, i.e. there is no infinite sequence $x_1, x_2,\ldots$ of elements from $S$ such that $x_{i+1} \ll x_i$ and $x_{i+1} \neq x_i$ for all $i$. ... $2^{24}$ words. $W$ is not a partial order. $W$ is a partial order but not a well order. $W$ is a well order.
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 6, 2015
by
makhdoom ghaya
2.2k
views
tifr2013
set-theory&algebra
partial-order
23
votes
3
answers
18
TIFR CSE 2013 | Part B | Question: 3
How many $4 \times 4$ matrices with entries from ${0, 1}$ have odd determinant? Hint: Use modulo $2$ arithmetic. $20160$ $32767$ $49152$ $57343$ $65520$
makhdoom ghaya
asked
in
Linear Algebra
Nov 6, 2015
by
makhdoom ghaya
3.7k
views
tifr2013
linear-algebra
matrix
2
votes
1
answer
19
TIFR CSE 2013 | Part B | Question: 2
Consider polynomials in a single variable $x$ of degree $d$. Suppose $d < n/2$. For such a polynomial $p(x)$, let $C_{p}$ denote the $n$-tuple $(P\left ( i \right ))_{1 \leq i \leq n}$. For any two such distinct polynomials $p, q,$ the number of ... $d$ At most $n - d$ Between $d$ and $n - d$ At least $n - d$ None of the above.
makhdoom ghaya
asked
in
Quantitative Aptitude
Nov 6, 2015
by
makhdoom ghaya
502
views
tifr2013
polynomials
non-gate
24
votes
4
answers
20
TIFR CSE 2013 | Part B | Question: 1
Let $G= (V, E)$ be a simple undirected graph on $n$ vertices. A colouring of $G$ is an assignment of colours to each vertex such that endpoints of every edge are given different colours. Let $\chi (G)$ denote the chromatic number of $G$, i.e. the minimum ... $a\left(G\right)\leq \frac{n}{\chi \left(G\right)}$ None of the above
makhdoom ghaya
asked
in
Graph Theory
Nov 5, 2015
by
makhdoom ghaya
3.6k
views
tifr2013
graph-theory
graph-coloring
8
votes
5
answers
21
TIFR CSE 2013 | Part A | Question: 20
Consider a well functioning clock where the hour, minute and the seconds needles are exactly at zero. How much time later will the minutes needle be exactly one minute ahead ($1/60$ th of the circumference) of the hours needle and the seconds needle again ... of $1/60$ th of the circumference. $144$ minutes $66$ minutes $96$ minutes $72$ minutes $132$ minutes
makhdoom ghaya
asked
in
Quantitative Aptitude
Nov 5, 2015
by
makhdoom ghaya
1.3k
views
tifr2013
quantitative-aptitude
clock-time
5
votes
2
answers
22
TIFR CSE 2013 | Part A | Question: 19
Consider a sequence of numbers $\large (\epsilon _{n}: n= 1, 2,...)$, such that $\epsilon _{1}=10$ and $\large \epsilon _{n+1}=\dfrac{20\epsilon _{n}}{20+\epsilon _{n}}$ for $n\geq 1$. Which of the following statements is true? Hint ... $\large (\epsilon _{n}: n= 1, 2,...)$ is decreasing and then increasing. Finally it converges to $1.$ None of the above.
makhdoom ghaya
asked
in
Quantitative Aptitude
Nov 5, 2015
by
makhdoom ghaya
946
views
tifr2013
quantitative-aptitude
sequence-series
5
votes
1
answer
23
TIFR CSE 2013 | Part A | Question: 18
Consider three independent uniformly distributed (taking values between $0$ and $1$) random variables. What is the probability that the middle of the three values (between the lowest and the highest value) lies between $a$ and $b$ where $0 ≤ a < b ≤ 1$? $3 (1 - b) a (b - a)$ ... $(1 - b) a (b - a)$ $6 ((b^{2}- a^{2})/ 2 - (b^{3} - a^{3})/3)$.
makhdoom ghaya
asked
in
Probability
Nov 5, 2015
by
makhdoom ghaya
1.1k
views
tifr2013
probability
random-variable
uniform-distribution
8
votes
4
answers
24
TIFR CSE 2013 | Part A | Question: 17
A stick of unit length is broken into two at a point chosen at random. Then, the larger part of the stick is further divided into two parts in the ratio $4:3$. What is the probability that the three sticks that are left CANNOT form a triangle? $1/4$ $1/3$ $5/6$ $1/2$ $\log_{e}(2)/2$
makhdoom ghaya
asked
in
Probability
Nov 5, 2015
by
makhdoom ghaya
1.5k
views
tifr2013
probability
7
votes
2
answers
25
TIFR CSE 2013 | Part A | Question: 16
The minimum of the function $f(x) = x \log_{e}(x)$ over the interval $[\frac{1}{2}, \infty )$ is $0$ $-e$ $\frac{-\log_{e}(2)}{2}$ $\frac{-1}{e}$ None of the above
makhdoom ghaya
asked
in
Calculus
Nov 5, 2015
by
makhdoom ghaya
1.2k
views
tifr2013
calculus
maxima-minima
3
votes
2
answers
26
TIFR CSE 2013 | Part A | Question: 15
Let $\DeclareMathOperator{S}{sgn} \S (x)= \begin{cases} +1 & \text{if } x \geq 0 \\ -1 & \text{if } x < 0 \end{cases}$ What is the value of the following summation? $\sum_{i=0}^{50} \S \left ( (2i - 1) (2i - 3) \dots (2i - 99) \right)$ $0$ $-1$ $+1$ $25$ $50$
makhdoom ghaya
asked
in
Quantitative Aptitude
Nov 4, 2015
by
makhdoom ghaya
683
views
tifr2013
quantitative-aptitude
number-series
17
votes
5
answers
27
TIFR CSE 2013 | Part A | Question: 14
An unbiased die is thrown $n$ times. The probability that the product of numbers would be even is $\dfrac{1}{(2n)}$ $\dfrac{1}{[(6n)!]}$ $1 - 6^{-n}$ $6^{-n}$ None of the above
makhdoom ghaya
asked
in
Probability
Nov 4, 2015
by
makhdoom ghaya
1.3k
views
tifr2013
probability
binomial-distribution
11
votes
3
answers
28
TIFR CSE 2013 | Part A | Question: 13
Doctors $A$ and $B$ perform surgery on patients in stages $III$ and $IV$ of a disease. Doctor $A$ has performed a $100$ surgeries (on $80$ stage $III$ and $20$ stage $IV$ patients) and $80$ out of her $100$ patients ... she appears to be more successful There is not enough data since the choice depends on the stage of the disease the patient is suffering from.
makhdoom ghaya
asked
in
Probability
Nov 4, 2015
by
makhdoom ghaya
1.1k
views
tifr2013
probability
8
votes
1
answer
29
TIFR CSE 2013 | Part A | Question: 12
Among numbers $1$ to $1000$ how many are divisible by $3$ or $7$? $333$ $142$ $475$ $428$ None of the above
makhdoom ghaya
asked
in
Quantitative Aptitude
Nov 4, 2015
by
makhdoom ghaya
741
views
tifr2013
quantitative-aptitude
factors
normal
9
votes
2
answers
30
TIFR CSE 2013 | Part A | Question: 11
Let there be a pack of $100$ cards numbered $1$ to $100$. The $i^{th}$ card states: "There are at most $i - 1$ true cards in this pack". Then how many cards of the pack contain TRUE statements? $0$ $1$ $100$ $50$ None of the above
makhdoom ghaya
asked
in
Analytical Aptitude
Nov 4, 2015
by
makhdoom ghaya
877
views
tifr2013
logical-reasoning
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