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Recent questions tagged tifr2015
+15
votes
3
answers
1
TIFR2015B15
Consider the following grammar (the start symbol is $E$) for generating expressions. $E \rightarrow T  E  T + E  T$ $T \rightarrow T * F  F$ $F \rightarrow 0 123456789$ With respect to this grammar, which of the following trees is the valid evaluation tree for the expression $2*3*4  5*6+7$? (a) (b) (c) (d) (e)
asked
Dec 8, 2015
in
Compiler Design
by
makhdoom ghaya
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47.9k
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tifr2015
parsing
+7
votes
1
answer
2
TIFR2015B14
Consider the following concurrent program (where statements separated by   within cobegincoend are executed concurrently). x:=1 cobegin x:= x + 1  x:= x + 1  x:= x + 1 coend Reading and writing of variables is atomic but evaluation of expressions is not atomic. ... right \}$ $\left \{2, 4 \right \}$ $\left \{ 2, 3 \right \}$ $\left \{2 \right \}$
asked
Dec 8, 2015
in
Operating System
by
makhdoom ghaya
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47.9k
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359
views
tifr2015
processsynchronization
operatingsystem
normal
+4
votes
1
answer
3
TIFR2015B13
Two undirected graphs $G_{1}=(V_{1}, E_{1})$ and $G_{2}= (V_{2}, E_{2})$ are said to be isomorphic if there exist a bijection $\pi: V_{1} \rightarrow V_{2}$ such that for all $u, v \in V_{1}, (u, v) \in E_{1}$ if and only $( \pi (u), \pi ... $L$ is $NP$ hard. (iii) $L$ is undecidable. Only $(i)$ Only $(ii)$ Only $(iii)$ $(i)$ and $(ii)$ $(ii)$ and $(iii)$
asked
Dec 8, 2015
in
Algorithms
by
makhdoom ghaya
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47.9k
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169
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tifr2015
pnpnpcnph
nongate
+7
votes
2
answers
4
TIFR2015B12
Let $t_{n}$ be the sum of the first $n$ natural numbers, for $n > 0$. A number is called triangular if it is equal to $t_{n}$ for some $n$. Which of the following statements are true: (i) There exists three successive triangular numbers whose product is a ... }{t_{n}}<2$ $(i)$ only. $(ii)$ only. $(iii)$ only. All of the above. None of the above.
asked
Dec 8, 2015
in
Numerical Ability
by
makhdoom ghaya
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(
47.9k
points)

359
views
tifr2015
numericalability
normal
numericalcomputation
+12
votes
2
answers
5
TIFR2015B11
Let $K_{n}$ be the complete graph on $n$ vertices labelled $\left\{1, 2,\dots ,n\right\}$ with $m=\frac{n (n  1)}{2}$ edges. What is the number of spanning trees of $K_{n}$? $\frac{m}{n  1}$ $m^{n  1}$ $n^{n  2}$ $n^{n  1}$ None of the above.
asked
Dec 8, 2015
in
Graph Theory
by
makhdoom ghaya
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47.9k
points)

373
views
tifr2015
graphtheory
spanningtree
+14
votes
2
answers
6
TIFR2015B10
Consider the languages $L_{1}= \left\{a^{m}b^{n}c^{p} \mid (m = n \vee n = p) \wedge m + n + p \geq 10\right\}$ $L_{2}= \left\{a^{m}b^{n}c^{p} \mid (m = n \vee n = p) \wedge m + n + p \leq 10\right\}$ State which ... regular. $L_{1}$ is regular and $L_{2}$ is not regular. $L_{1}$ is not regular and $L_{2}$ is regular. Both $L_{1}$ and $L_{2}$ are infinite.
asked
Dec 8, 2015
in
Theory of Computation
by
makhdoom ghaya
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(
47.9k
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403
views
tifr2015
regularlanguages
+11
votes
2
answers
7
TIFR2015B9
A Boolean expression is an expression made out of propositional letters (such as $p, q, r$) and operators $\wedge$, $\vee$ and $\neg$; e.g. $p\wedge \neg (q \vee \neg r)$. An expression is said to be ... expression is equivalent to an expression without $\wedge$ operator. Every Boolean expression is equivalent to an expression without $\neg$ operator.
asked
Dec 8, 2015
in
Digital Logic
by
makhdoom ghaya
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47.9k
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351
views
tifr2015
canonicalnormalform
+11
votes
4
answers
8
TIFR2015B8
Let $\sum_{1}= \left\{a\right\}$ be a one letter alphabet and $\sum_{2}= \left\{a, b\right\}$ be a two letter alphabet. A language over an alphabet is a set of finite length words comprising letters of the alphabet. Let $L_{1}$ and $L_{2}$ ... . $L_{1}$ is countable but $L_{2}$ is not. $L_{2}$ is countable but $L_{1}$ is not. Neither of them is countable.
asked
Dec 7, 2015
in
Theory of Computation
by
makhdoom ghaya
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(
47.9k
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581
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tifr2015
identifyclasslanguage
+13
votes
4
answers
9
TIFR2015B7
Let $a, b, c$ be regular expressions. Which of the following identities is correct? $(a + b)^{*} = a^{*}b^{*}$ $a(b + c) = ab + c$ $(a + b)^{*} = a^{*} + b^{*}$ $(ab + a)^{*}a = a(ba + a)^{*}$ None of the above.
asked
Dec 7, 2015
in
Theory of Computation
by
makhdoom ghaya
Veteran
(
47.9k
points)

386
views
tifr2015
theoryofcomputation
regularexpressions
+8
votes
3
answers
10
TIFR2015B6
Let $B$ consist of all binary strings beginning with a $1$ whose value when converted to decimal is divisible by $7$. $B$ can be recognized by a deterministic finite state automaton. $B$ can be recognized by a nondeterministic ... a deterministic pushdown automaton. $B$ cannot be recognized by any push down automaton, deterministic or nondeterministic.
asked
Dec 7, 2015
in
Theory of Computation
by
makhdoom ghaya
Veteran
(
47.9k
points)

271
views
tifr2015
theoryofcomputation
regularlanguages
+14
votes
5
answers
11
TIFR2015B5
Suppose $\begin{pmatrix} 0&1 &0&0&0&1 \\ 1&0&1&0&0&0 \\ 0&1&0&1&0&1 \\ 0&0&1&0&1&0 \\ 0&0&0&1&0&1 \\ 1&0&1&0&1&0 \end{pmatrix}$ is the ... the above adjacency matrix? Only $(i)$ Only $(ii)$ Only $(iii)$ Only $(iv)$ $(i)$ and $(ii)$
asked
Dec 7, 2015
in
Graph Theory
by
makhdoom ghaya
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47.9k
points)

562
views
tifr2015
graphconnectivity
graphtheory
+23
votes
4
answers
12
TIFR2015B4
First, consider the tree on the left. On the right, the nine nodes of the tree have been assigned numbers from the set $\left\{1, 2,....9\right\}$ so that for every node, the numbers in its left subtree and right subtree lie in disjoint intervals (that is, all numbers in ... ^{9}=512$ $2^{4}.3^{2}.5.9=6480$ $2^{3}.3.5.9=1080$ $2^{4}=16$ $2^{3}.3^{3}=216$
asked
Dec 7, 2015
in
DS
by
makhdoom ghaya
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(
47.9k
points)

628
views
tifr2015
binarytree
permutationsandcombinations
+9
votes
1
answer
13
TIFR2015B3
Consider the following code fragment in the $C$ programming language when run on a nonnegative integer $n$. int f (int n) { if (n==0  n==1) return 1; else return f (n  1) + f(n  2); } Assuming a ... polynomial in $n$. This algorithm runs in polynomial time in $n$ and the optimal running time is polynomial in $n$. The algorithm does not terminate.
asked
Dec 7, 2015
in
Algorithms
by
makhdoom ghaya
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(
47.9k
points)

218
views
tifr2015
timecomplexity
+14
votes
2
answers
14
TIFR2015B2
Consider the following undirected connected graph $G$ with weights on its edges as given in the figure below. A minimum spanning tree is a spanning tree of least weight and a maximum spanning tree is one with largest weight. A second ... tree here. There is unique minimum spanning tree, however there is more than one secondbest minimum spanning tree here.
asked
Dec 7, 2015
in
Algorithms
by
makhdoom ghaya
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(
47.9k
points)

399
views
tifr2015
spanningtree
algorithms
graphalgorithms
+14
votes
2
answers
15
TIFR2015B1
Consider the following recurrence relation: $T(n) = \begin{cases} 2T (\lfloor\sqrt{n}\rfloor)+ \log n & \text{if }n \geq 2 \\ 1& \text{if }n = 1 \end{cases}$ Which of the following statements is TRUE? $T(n)$ is $O(\log n)$. $T(n)$ is $O(\log n. \log \log ... $ but not $O(\log^{3/2} n)$. $T(n)$ is $O(\log^{2} n. \log \log n)$ but not $O(\log^{2} n)$.
asked
Dec 5, 2015
in
Algorithms
by
makhdoom ghaya
Veteran
(
47.9k
points)

451
views
tifr2015
algorithms
recurrence
timecomplexity
+3
votes
0
answers
16
TIFR2015A15
Let $A$ and $B$ be nonempty disjoint sets of real numbers. Suppose that the average of the numbers in the first set is $\mu_{A}$ and the average of the numbers in the second set is $\mu_{B}$; let the corresponding variances be $v_{A}$ and $v_{B}$ respectively. If the average of ... + (\mu_{B}\mu)^{2}]$ $p.v_{A}+ (1  p). v_{B} + (\mu_{A} \mu_{B})^{2}$
asked
Dec 5, 2015
in
Probability
by
makhdoom ghaya
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47.9k
points)

161
views
tifr2015
statistics
+6
votes
2
answers
17
TIFR2015A14
Consider the following $3 \times 3$ matrices. $M_{1}=\begin{pmatrix} 0&1&1 \\ 1&0&1 \\ 1&1&0 \end{pmatrix} $ $M_{2}=\begin{pmatrix} 1&0&1 \\ 0&0&0 \\ 1&0&1 \end{pmatrix} $ How may $01$ column ... all operations are done modulo $2$, i.e, $3 = 1$ (modulo $2$), $4 = 0$ (modulo $2$)). None Two Three Four Eight
asked
Dec 5, 2015
in
Linear Algebra
by
makhdoom ghaya
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(
47.9k
points)

294
views
tifr2015
matrices
+7
votes
2
answers
18
TIFR2015A13
Imagine the first quadrant of the real plane as consisting of unit squares. A typical square has $4$ corners: $(i, j), (i+1, j), (i+1, j+1),$and $(i, j+1)$, where $(i, j)$ is a pair of nonnegative integers. Suppose a ... through a point in the interior of the square. How many unit squares does $l$ pass through? $98,990$ $9,900$ $1,190$ $1,180$ $1,010$
asked
Dec 5, 2015
in
Numerical Ability
by
makhdoom ghaya
Veteran
(
47.9k
points)

327
views
tifr2015
numericalability
cartesiancoordinates
+4
votes
0
answers
19
TIFR2015A12
Consider two independent and identically distributed random variables $X$ and $Y$ uniformly distributed in $[0, 1]$. For $\alpha \in \left[0, 1\right]$, the probability that $\alpha$ max $(X, Y) < XY$ is $1/ (2\alpha)$ exp $(1  \alpha)$ $1  \alpha$ $(1  \alpha)^{2}$ $1  \alpha^{2}$
asked
Dec 5, 2015
in
Probability
by
makhdoom ghaya
Veteran
(
47.9k
points)

153
views
tifr2015
probability
randomvariable
+6
votes
2
answers
20
TIFR2015A11
Suppose that $f(x)$ is a continuous function such that $0.4 \leq f(x) \leq 0.6$ for $0 \leq x \leq 1$. Which of the following is always true? $f(0.5) = 0.5$. There exists $x$ between $0$ and $1$ such that $f(x) = 0.8x$. There exists $x$ between $0$ and $0.5$ such that $f(x) = x$. $f(0.5) > 0.5$. None of the above statements are always true.
asked
Dec 5, 2015
in
Calculus
by
makhdoom ghaya
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(
47.9k
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278
views
tifr2015
maximaminima
calculus
+4
votes
0
answers
21
TIFR2015A10
Let $f(x), x\in \left[0, 1\right]$, be any positive real valued continuous function. Then $\lim_{n \rightarrow \infty} (n + 1) \int_{0}^{1} x^{n} f(x) \text{d}x$ equals. $max_{x \in \left[0, 1\right]} f(x)$ $min_{x \in \left[0, 1\right]} f(x)$ $f(0)$ $f(1)$ $\infty$
asked
Dec 5, 2015
in
Calculus
by
makhdoom ghaya
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(
47.9k
points)

133
views
tifr2015
maximaminima
+3
votes
1
answer
22
TIFR2015A9
Consider a square of side length $2$. We throw five points into the square. Consider the following statements: (i) There will always be three points that lie on a straight line. (ii) There will always be a line connecting a pair of points such that two points lie on one ... true: $(i)$ only. $(ii)$ only. $(iii)$ only. $(ii)$ and $(iii)$. None of the above.
asked
Dec 5, 2015
in
Numerical Ability
by
makhdoom ghaya
Veteran
(
47.9k
points)

174
views
tifr2015
geometry
+14
votes
4
answers
23
TIFR2015A8
There is a set of $2n$ people: $n$ male and $n$ female. A good party is one with equal number of males and females (including the one where none are invited). The total number of good parties is. $2^{n}$ $n^{2}$ $\left(\frac{n}{n/2}\right)^{2}$ $\left(\frac{2n}{n}\right)$ None of the above.
asked
Dec 5, 2015
in
Combinatory
by
makhdoom ghaya
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(
47.9k
points)

523
views
tifr2015
permutationsandcombinations
discretemathematics
normal
+10
votes
5
answers
24
TIFR2015A7
A $1 \times 1$ chessboard has one square, a $2 \times 2$ chessboard has five squares. Continuing along this fashion, what is the number of squares on the regular $8 \times 8$ chessboard? $64$ $65$ $204$ $144$ $256$
asked
Dec 5, 2015
in
Combinatory
by
makhdoom ghaya
Veteran
(
47.9k
points)

412
views
tifr2015
permutationsandcombinations
+8
votes
3
answers
25
TIFR2015A6
Ram has a fair coin, i.e., a toss of the coin results in either head or tail and each event happens with probability exactly half $(1/2)$. He repeatedly tosses the coin until he gets heads in two consecutive tosses. The expected number of coin tosses that Ram does is. $2$ $4$ $6$ $8$ None of the above.
asked
Dec 5, 2015
in
Probability
by
makhdoom ghaya
Veteran
(
47.9k
points)

571
views
tifr2015
expectation
+11
votes
2
answers
26
TIFR2015A5
What is logically equivalent to "If Kareena and Parineeti go to the shopping mall then it is raining": If Kareena and Parineeti do not go to the shopping mall then it is not raining. If Kareena and Parineeti do not go to the ... shopping mall. If it is not raining then Kareena and Parineeti do not go to the shopping mall. None of the above.
asked
Dec 4, 2015
in
Mathematical Logic
by
makhdoom ghaya
Veteran
(
47.9k
points)

313
views
tifr2015
mathematicallogic
propositionallogic
+9
votes
1
answer
27
TIFR2015A4
The Boolean function obtained by adding an inverter to each and every input of an $AND$ gate is: $OR$ $XOR$ $NAND$ $NOR$ None of the above
asked
Dec 2, 2015
in
Digital Logic
by
makhdoom ghaya
Veteran
(
47.9k
points)

312
views
tifr2015
digitallogic
logicgates
+4
votes
1
answer
28
TIFR2015A3
Let $z < 1$. Define $M_{n}(z)= \sum_{i=1}^{10} z^{10^{n}(i  1)}?$ what is $\prod_{i=0}^{\infty} M_{i}(z)= M_{0}(z)\times M_{1}(z) \times M_{2}(z) \times ...?$ Can't be determined. $1/ (1  z)$ $1/ (1 + z)$ $1  z^{9}$ None of the above.
asked
Dec 2, 2015
in
Numerical Ability
by
makhdoom ghaya
Veteran
(
47.9k
points)

132
views
tifr2015
numericalability
numericalcomputation
numberseries
+6
votes
1
answer
29
TIFR2015A2
Consider a circle with a circumference of one unit length. Let $d< \dfrac{1}{6}$. Suppose that we independently throw two arcs, each of length $d$, randomly on this circumference so that each arc is uniformly distributed along the circle circumference. The arc attaches itself ...  3d)$ It equals $(1  2d)$ It equals $1$ It equals $(1  d)$ $(1  d)$
asked
Dec 2, 2015
in
Numerical Ability
by
makhdoom ghaya
Veteran
(
47.9k
points)

176
views
tifr2015
geometry
+7
votes
5
answers
30
TIFR2015A1
Consider a $6$sided die with all sides not necessarily equally likely such that probability of an even number is $P (\left \{2, 4, 6 \right \}) =\dfrac{1}{2}$, probability of a multiple of $3$ is $P (\left \{3, 6 \right \}) = 1/3$ and probability of $1$ is ... \}) \leq \dfrac{1}{6}$ $P(\left \{ 5 \right \}) \leq \dfrac{1}{3}$ $\text{None of the above.}$
asked
Dec 2, 2015
in
Probability
by
makhdoom ghaya
Veteran
(
47.9k
points)

382
views
tifr2015
probability
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