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Recent questions tagged tifr2015
+19
votes
4
answers
1
TIFR2015B15
Consider the following grammar (the start symbol is $E$) for generating expressions. $E \rightarrow T  E \mid T + E \mid T$ $T \rightarrow T * F \mid F$ $F \rightarrow 0 \mid1\mid 2\mid 3\mid 4\mid 5\mid 6\mid 7\mid 8\mid 9$ With respect to this grammar, which of the following trees is the valid evaluation tree for the expression $2*3*4  5*6+7$?
asked
Dec 8, 2015
in
Compiler Design
by
makhdoom ghaya
Boss
(
30.8k
points)

767
views
tifr2015
parsing
+10
votes
3
answers
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. The set of possible values ... $\left \{2, 4 \right \}$ $\left \{ 2, 3 \right \}$ $\left \{2 \right \}$
asked
Dec 8, 2015
in
Operating System
by
makhdoom ghaya
Boss
(
30.8k
points)

647
views
tifr2015
processsynchronization
operatingsystem
normal
+4
votes
2
answers
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 $( \pi (u), \pi (v)) \in E_{2}$. ... ii) $L$ 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
Boss
(
30.8k
points)

237
views
tifr2015
pnpnpcnph
nongate
+8
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 perfect square. (ii) If ... $(i)$ only. $(ii)$ only. $(iii)$ only. All of the above. None of the above.
asked
Dec 8, 2015
in
Numerical Ability
by
makhdoom ghaya
Boss
(
30.8k
points)

486
views
tifr2015
numericalability
normal
numericalcomputation
+15
votes
2
answers
5
TIFR2015B11
Let $K_{n}$ be the complete graph on $n$ vertices labeled $\left\{1, 2,\dots ,n\right\}$ 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
Boss
(
30.8k
points)

680
views
tifr2015
graphtheory
spanningtree
+17
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 of the following is true? ... 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
Boss
(
30.8k
points)

695
views
tifr2015
regularlanguages
+20
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 in sum of product ... . Every Boolean 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
Boss
(
30.8k
points)

694
views
tifr2015
canonicalnormalform
+22
votes
5
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 $L_{2}$ be the set of ... infinite. $L_{1}$ 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
Boss
(
30.8k
points)

1.2k
views
tifr2015
identifyclasslanguage
+17
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
Boss
(
30.8k
points)

619
views
tifr2015
theoryofcomputation
regularexpressions
+10
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 finite state ... but not by 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
Boss
(
30.8k
points)

600
views
tifr2015
theoryofcomputation
regularlanguages
+22
votes
7
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 adjacency matrix of an ... below has 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
Boss
(
30.8k
points)

962
views
tifr2015
graphconnectivity
graphtheory
+31
votes
3
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 $\left\{1, 2,\ldots,9\right\}$ so that for every node, the numbers in its left subtree and right subtree lie in disjoint intervals (that is, all numbers in one subtree are less than all ... $2^{4}.3^{2}.5.9=6480$ $2^{3}.3.5.9=1080$ $2^{4}=16$ $2^{3}.3^{3}=216$
asked
Dec 7, 2015
in
DS
by
makhdoom ghaya
Boss
(
30.8k
points)

1.2k
views
tifr2015
binarytree
permutationandcombination
+14
votes
2
answers
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 typical implementation of the ... 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
Boss
(
30.8k
points)

450
views
tifr2015
timecomplexity
+18
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 best minimum ... spanning 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
Boss
(
30.8k
points)

888
views
tifr2015
spanningtree
algorithms
graphalgorithms
+20
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 $O(\log n. \log \log n)$ ... $O(\log^{3/2} n)$. $T(n)$ is $O(\log^{2} n. \log \log n)$ but not $O(\log^{2} n)$.
asked
Dec 5, 2015
in
Algorithms
by
makhdoom ghaya
Boss
(
30.8k
points)

747
views
tifr2015
algorithms
recurrence
timecomplexity
+5
votes
2
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 $v_{B}$ ... $p.v_{A}+ (1  p). v_{B} + (\mu_{A} \mu_{B})^{2}$
asked
Dec 5, 2015
in
Numerical Ability
by
makhdoom ghaya
Boss
(
30.8k
points)

297
views
tifr2015
statistics
+9
votes
1
answer
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 vectors of the form $X$= ... 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
Boss
(
30.8k
points)

486
views
tifr2015
matrices
+8
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 line segment $l$ ... 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
Boss
(
30.8k
points)

706
views
tifr2015
numericalability
cartesiancoordinates
+4
votes
2
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
Boss
(
30.8k
points)

287
views
tifr2015
probability
randomvariable
uniformdistribution
+9
votes
5
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
Boss
(
30.8k
points)

663
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 $\displaystyle \lim_{n \rightarrow \infty} (n + 1) \int_{0}^{1} x^{n} f(x) \text{d}x$ 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
Boss
(
30.8k
points)

215
views
tifr2015
maximaminima
calculus
nongate
integration
+3
votes
2
answers
22
TIFR2015A9
Consider a square of side length $2$. We throw five points into the square. Consider the following statements: There will always be three points that lie on a straight line. There will always be a line connecting a pair of points such that two points lie on one side of the line and one ... above is true: $(i)$ only. $(ii)$ only. $(iii)$ only. $(ii)$ and $(iii)$. None of the above.
asked
Dec 5, 2015
in
Numerical Ability
by
makhdoom ghaya
Boss
(
30.8k
points)

290
views
tifr2015
geometry
numericalability
easy
+23
votes
3
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. $2^{n}$ $n^{2}$ $\binom{n}{⌊n/2⌋}^{2}$ $\binom{2n}{n}$ None of the above.
asked
Dec 5, 2015
in
Combinatory
by
makhdoom ghaya
Boss
(
30.8k
points)

1.1k
views
tifr2015
permutationandcombination
discretemathematics
normal
ballsinbins
+14
votes
6
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
Boss
(
30.8k
points)

825
views
tifr2015
permutationandcombination
+10
votes
4
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
Boss
(
30.8k
points)

1.3k
views
tifr2015
expectation
+14
votes
3
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 then it is ... 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
Boss
(
30.8k
points)

518
views
tifr2015
mathematicallogic
propositionallogic
+11
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
Boss
(
30.8k
points)

508
views
tifr2015
digitallogic
digitalcircuits
+5
votes
2
answers
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
Boss
(
30.8k
points)

256
views
tifr2015
numericalability
numericalcomputation
numberseries
+7
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 exactly to the circumference ... $(1  3d)$ It equals $(1  2d)$ It equals $1$ It equals $(1  d)$ $(1  d)$
asked
Dec 2, 2015
in
Numerical Ability
by
makhdoom ghaya
Boss
(
30.8k
points)

342
views
tifr2015
geometry
+9
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 $1$ ... $P(\left \{ 5 \right \}) \leq \dfrac{1}{3}$ $\text{None of the above.}$
asked
Dec 2, 2015
in
Probability
by
makhdoom ghaya
Boss
(
30.8k
points)

672
views
tifr2015
probability
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