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Recent questions tagged tifr2013
+16
votes
3
answers
1
TIFR2013B20
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 processor $\ ... the values? $n \log n$ steps $n^2$ steps $n$ steps $n^{1.5}$ steps The algorithm is not guaranteed to sort
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Nov 8, 2015
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Algorithms
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makhdoom ghaya
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tifr2013
algorithms
sorting
+14
votes
3
answers
2
TIFR2013B19
In a relational database there are three relations: Customers = $C$(CName), Shops = $S$(SName), Buys = $B$(CName, SName). Which of the following relational algebra expressions returns the names of shops that have no customers at all? [Here $\Pi$ is the projection operator.] $\Pi _{S Name}B$ $S  B$ $S  \Pi _{S Name}B$ $S  \Pi _{S Name}((C \times S)  B)$ None of the above
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Nov 8, 2015
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Databases
by
makhdoom ghaya
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48k
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363
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tifr2013
databases
relationalalgebra
+6
votes
3
answers
3
TIFR2013B18
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 Select $(S, r)$ takes a set $S$ of numbers and a rank $r\left(1 \leq r \leq S\right)$ and returns the element in $S$ of ... $S$ constant · $SR$ constant · $R \log S$ constant · $S(1 + \log R)$
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Nov 8, 2015
in
Algorithms
by
makhdoom ghaya
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48k
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190
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tifr2013
algorithms
+8
votes
2
answers
4
TIFR2013B17
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. $n^{n2}$
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Nov 8, 2015
in
Algorithms
by
makhdoom ghaya
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241
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tifr2013
spanningtree
+5
votes
3
answers
5
TIFR2013B16
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 $y \in \left\{0, 1\right\}^{n}$ be such that $y$ ... \right)$ (where $y_{i}$ is omitted) is equivalent to $T_{k1}, n(y)$ $T_{k, n}(y)$ $y_{i}$ $\neg y_{i}$ None of the above.
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Nov 8, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
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48k
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255
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tifr2013
settheory&algebra
functions
+6
votes
1
answer
6
TIFR2013B15
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 that every subset of ... log n)$ $O \left(\sqrt{n}\right)$ but not $O (\log n)$ $O (n)$ but not $O \left(\sqrt{n}\right)$
asked
Nov 7, 2015
in
Algorithms
by
makhdoom ghaya
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48k
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297
views
tifr2013
graphalgorithms
+16
votes
2
answers
7
TIFR2013B14
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 replaced ... times, respectively $1,1,1,2$ times, respectively $1,1,1,1$ times, respectively $2,1,2,2$ times, respectively None of the above
asked
Nov 7, 2015
in
Operating System
by
makhdoom ghaya
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48k
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355
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tifr2013
operatingsystem
pagereplacement
+26
votes
4
answers
8
TIFR2013B13
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.
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Nov 7, 2015
in
DS
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48k
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527
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tifr2013
binarytree
datastructure
+11
votes
1
answer
9
TIFR2013B12
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 given as two lists ... $O \left(\log n\right)$ $O (n)$ but not $O (\sqrt{n})$ $O \left(n \log n\right)$ but not $O (n)$
asked
Nov 7, 2015
in
Algorithms
by
makhdoom ghaya
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48k
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357
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tifr2013
algorithms
timecomplexity
+9
votes
3
answers
10
TIFR2013B11
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 free The ... regular language is context free. The intersection of a regular language and the complement of a regular language is regular.
asked
Nov 7, 2015
in
Theory of Computation
by
makhdoom ghaya
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48k
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348
views
tifr2013
theoryofcomputation
closureproperty
+3
votes
1
answer
11
TIFR2013B10
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 $S_{i}= 10 n \log m$ and $S_{i} \cap S_{j}\leq \log m$ for all $1 \leq i < j ... $x ∉ T$. $1$ if $x \in T$ and at least $0.9$ if $x ∉ T$. At least $0.9$ if $x \in T$ and $1$ if $x ∉ T$.
asked
Nov 7, 2015
in
Probability
by
makhdoom ghaya
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48k
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135
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tifr2013
probability
+5
votes
1
answer
12
TIFR2013B9
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 in $R$, then ... $ regions are produced, but they need not all be convex. All regions are convex but there may be exponentially many of them.
asked
Nov 6, 2015
in
Numerical Ability
by
makhdoom ghaya
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48k
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132
views
tifr2013
numericalability
+9
votes
2
answers
13
TIFR2013B8
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 left. $L= \left \{ ... , where $L$ is the language in $(c)$ above. $\left \{ 0^{m} 1^{n}  1 \leq m \leq n\right \}$
asked
Nov 6, 2015
in
Theory of Computation
by
makhdoom ghaya
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48k
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456
views
tifr2013
theoryofcomputation
regularlanguages
+4
votes
1
answer
14
TIFR2013B7
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.
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Nov 6, 2015
in
Algorithms
by
makhdoom ghaya
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48k
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200
views
tifr2013
algorithms
npcompleteness
+12
votes
3
answers
15
TIFR2013B6
Let $L$ and $L'$ be languages over the alphabet $\Sigma $. The left quotient of $L$ by $L'$ is $L/L'\overset{\underset{\mathrm{}}{def}}{=} \left\{w âˆˆ \Sigma^* : wx âˆˆ L\text{ for some }x âˆˆ L'\right\}$ Which of the following is true? If $L/L'$ is regular then ... . If $L/L'$ is regular then $L$ is regular. $L/L'$ is a subset of $L$. If $L/L'$ and $L'$ are regular, then $L$ is regular.
asked
Nov 6, 2015
in
Theory of Computation
by
makhdoom ghaya
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48k
points)

409
views
tifr2013
theoryofcomputation
regularlanguages
+15
votes
2
answers
16
TIFR2013B5
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 $O(n^{3})$
asked
Nov 6, 2015
in
Algorithms
by
makhdoom ghaya
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48k
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563
views
tifr2013
algorithms
graphalgorithms
+8
votes
3
answers
17
TIFR2013B4
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 $i$. Consider the set ... are only $2^{24}$ words. $W$ is not a partial order. $W$ is a partial order but not a well order. $W$ is a well order.
asked
Nov 6, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
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48k
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360
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tifr2013
settheory&algebra
partialorder
+10
votes
1
answer
18
TIFR2013B3
How many $4 \times 4$ matrices with entries from ${0, 1}$ have odd determinant? Hint: Use modulo $2$ arithmetic. $20160$ $32767$ $49152$ $57343$ $65520$
asked
Nov 6, 2015
in
Linear Algebra
by
makhdoom ghaya
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48k
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505
views
tifr2013
linearalgebra
matrices
+2
votes
0
answers
19
TIFR2013B2
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 coordinates where the ... $C_{p}, C_{q}$ differ is. At most $d$ At most $n  d$ Between $d$ and $n  d$ At least $n  d$ None of the above.
asked
Nov 6, 2015
in
Numerical Ability
by
makhdoom ghaya
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(
48k
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79
views
tifr2013
+9
votes
2
answers
20
TIFR2013B1
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 numbers of colours needed ... \frac{n}{\chi \left(G\right)}$ $a\left(G\right)\leq \frac{n}{\chi \left(G\right)}$ None of the above.
asked
Nov 5, 2015
in
Graph Theory
by
makhdoom ghaya
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48k
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463
views
tifr2013
graphtheory
graphcoloring
+3
votes
3
answers
21
TIFR2013A20
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 ... have moved an integer multiple of $1/60$ th of the circumference. $144$ minutes $66$ minutes $96$ minutes $72$ minutes $132$ minutes
asked
Nov 5, 2015
in
Numerical Ability
by
makhdoom ghaya
Veteran
(
48k
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163
views
tifr2013
numericalability
clocktime
+4
votes
1
answer
22
TIFR2013A19
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: Consider the ... The sequence $\large (\epsilon _{n}: n= 1, 2,...)$ is decreasing and then increasing. Finally it converges to $1.$ None of the above.
asked
Nov 5, 2015
in
Numerical Ability
by
makhdoom ghaya
Veteran
(
48k
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101
views
tifr2013
numericalability
sequence
+2
votes
0
answers
23
TIFR2013A18
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 $0 ≤ a < b ≤ 1$. $3 (1  b) a (b  a)$ $3 (b  a)  (b^{2 ...  a)$ $(1  b) a (b  a)$ $6 ((b^{2} a^{2})/ 2  (b^{3}  a^{3})/3)$.
asked
Nov 5, 2015
in
Probability
by
makhdoom ghaya
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48k
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148
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tifr2013
probability
randomvariable
+3
votes
2
answers
24
TIFR2013A17
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? $1/4$ $1/3$ $5/6$ $1/2$ $\log_{e}(2)/2$
asked
Nov 5, 2015
in
Probability
by
makhdoom ghaya
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287
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tifr2013
probability
+6
votes
2
answers
25
TIFR2013A16
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
asked
Nov 5, 2015
in
Calculus
by
makhdoom ghaya
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48k
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227
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tifr2013
calculus
maximaminima
+3
votes
1
answer
26
TIFR2013A15
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? $$\sum_{i=0}^{50} \S \Bigl ( (2i  1) (2i  3) \dots (2i  99) \Bigr )$$ $0$ $1$ $+1$ $25$ $50$
asked
Nov 4, 2015
in
Numerical Ability
by
makhdoom ghaya
Veteran
(
48k
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97
views
tifr2013
numericalability
numberseries
+8
votes
3
answers
27
TIFR2013A14
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.
asked
Nov 4, 2015
in
Probability
by
makhdoom ghaya
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48k
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284
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tifr2013
probability
+5
votes
3
answers
28
TIFR2013A13
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 have survived ($78$ stage $III$ and ... be more successful There is not enough data since the choice depends on the stage of the disease the patient is suffering from.
asked
Nov 4, 2015
in
Probability
by
makhdoom ghaya
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48k
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430
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tifr2013
probability
+4
votes
1
answer
29
TIFR2013A12
Among numbers $1$ to $1000$ how many are divisible by $3$ or $7$? $333$ $142$ $475$ $428$ None of the above.
asked
Nov 4, 2015
in
Numerical Ability
by
makhdoom ghaya
Veteran
(
48k
points)

117
views
tifr2013
numericalability
factors
normal
+5
votes
1
answer
30
TIFR2013A11
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.
asked
Nov 4, 2015
in
Numerical Ability
by
makhdoom ghaya
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48k
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161
views
tifr2013
logicalreasoning
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