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Recent questions tagged tifr2015
25
votes
5
answers
1
TIFR CSE 2015 | Part B | Question: 15
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 $2*3*4 - 5*6+7$?
makhdoom ghaya
asked
in
Compiler Design
Dec 8, 2015
by
makhdoom ghaya
2.1k
views
tifr2015
parsing
14
votes
3
answers
2
TIFR CSE 2015 | Part B | Question: 14
Consider the following concurrent program (where statements separated by | | with-in cobegin-coend 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 ... $\left \{2, 4 \right \}$ $\left \{ 2, 3 \right \}$ $\left \{2 \right \}$
makhdoom ghaya
asked
in
Operating System
Dec 8, 2015
by
makhdoom ghaya
1.6k
views
tifr2015
process-synchronization
operating-system
normal
4
votes
2
answers
3
TIFR CSE 2015 | Part B | Question: 13
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 $u, v \in V_{1}, (u, v) \in E_{1}$ ... $NP$- hard. (iii) $L$ is undecidable. Only $(i)$ Only $(ii)$ Only $(iii)$ $(i)$ and $(ii)$ $(ii)$ and $(iii)$
makhdoom ghaya
asked
in
Algorithms
Dec 8, 2015
by
makhdoom ghaya
522
views
tifr2015
p-np-npc-nph
non-gate
9
votes
2
answers
4
TIFR CSE 2015 | Part B | Question: 12
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: There exists three successive triangular numbers whose product is a ... $\text{(i)}$ only $\text{(ii)}$ only $\text{(iii)}$ only All of the above None of the above
makhdoom ghaya
asked
in
Quantitative Aptitude
Dec 8, 2015
by
makhdoom ghaya
870
views
tifr2015
quantitative-aptitude
normal
numerical-computation
19
votes
2
answers
5
TIFR CSE 2015 | Part B | Question: 11
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
makhdoom ghaya
asked
in
Graph Theory
Dec 8, 2015
by
makhdoom ghaya
1.7k
views
tifr2015
graph-theory
spanning-tree
20
votes
2
answers
6
TIFR CSE 2015 | Part B | Question: 10
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 ... $L_{1}$ 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.
makhdoom ghaya
asked
in
Theory of Computation
Dec 8, 2015
by
makhdoom ghaya
2.0k
views
tifr2015
regular-language
26
votes
2
answers
7
TIFR CSE 2015 | Part B | Question: 9
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 ... Boolean expression is equivalent to an expression without $\wedge$ operator. Every Boolean expression is equivalent to an expression without $\neg$ operator.
makhdoom ghaya
asked
in
Digital Logic
Dec 8, 2015
by
makhdoom ghaya
1.7k
views
tifr2015
canonical-normal-form
23
votes
6
answers
8
TIFR CSE 2015 | Part B | Question: 8
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 ... $L_{1}$ is countable but $L_{2}$ is not. $L_{2}$ is countable but $L_{1}$ is not. Neither of them is countable.
makhdoom ghaya
asked
in
Theory of Computation
Dec 7, 2015
by
makhdoom ghaya
3.3k
views
tifr2015
identify-class-language
18
votes
4
answers
9
TIFR CSE 2015 | Part B | Question: 7
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.
makhdoom ghaya
asked
in
Theory of Computation
Dec 7, 2015
by
makhdoom ghaya
1.8k
views
tifr2015
theory-of-computation
regular-expression
14
votes
3
answers
10
TIFR CSE 2015 | Part B | Question: 6
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 non-deterministic ... not by a deterministic push-down automaton. $B$ cannot be recognized by any push down automaton, deterministic or non-deterministic.
makhdoom ghaya
asked
in
Theory of Computation
Dec 7, 2015
by
makhdoom ghaya
1.5k
views
tifr2015
theory-of-computation
regular-language
27
votes
7
answers
11
TIFR CSE 2015 | Part B | Question: 5
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 ... the above adjacency matrix? Only $(i)$ Only $(ii)$ Only $(iii)$ Only $(iv)$ $(i)$ and $(ii)$
makhdoom ghaya
asked
in
Graph Theory
Dec 7, 2015
by
makhdoom ghaya
3.0k
views
tifr2015
graph-connectivity
graph-theory
41
votes
4
answers
12
TIFR CSE 2015 | Part B | Question: 4
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 ... $2^{4}.3^{2}.5.9=6480$ $2^{3}.3.5.9=1080$ $2^{4}=16$ $2^{3}.3^{3}=216$
makhdoom ghaya
asked
in
DS
Dec 7, 2015
by
makhdoom ghaya
3.1k
views
tifr2015
binary-tree
combinatory
16
votes
2
answers
13
TIFR CSE 2015 | Part B | Question: 3
Consider the following code fragment in the $C$ programming language when run on a non-negative 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 ... $n$. This algorithm runs in polynomial time in $n$ and the optimal running time is polynomial in $n$. The algorithm does not terminate.
makhdoom ghaya
asked
in
Algorithms
Dec 7, 2015
by
makhdoom ghaya
1.3k
views
tifr2015
time-complexity
27
votes
2
answers
14
TIFR CSE 2015 | Part B | Question: 2
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 ... tree here. There is unique minimum spanning tree, however there is more than one second-best minimum spanning tree here.
makhdoom ghaya
asked
in
Algorithms
Dec 7, 2015
by
makhdoom ghaya
2.6k
views
tifr2015
spanning-tree
algorithms
graph-algorithms
22
votes
3
answers
15
TIFR CSE 2015 | Part B | Question: 1
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 $O(\log n)$. $T(n)$ ... but not $O(\log^{3/2} n)$. $T(n)$ is $O(\log^{2} n \cdot \log \log n)$ but not $O(\log^{2} n)$.
makhdoom ghaya
asked
in
Algorithms
Dec 5, 2015
by
makhdoom ghaya
2.1k
views
tifr2015
algorithms
recurrence-relation
time-complexity
6
votes
2
answers
16
TIFR CSE 2015 | Part A | Question: 15
Let $A$ and $B$ be non-empty 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 the ... $p.v_{A}+ (1 - p). v_{B} + (\mu_{A}- \mu_{B})^{2}$
makhdoom ghaya
asked
in
Quantitative Aptitude
Dec 5, 2015
by
makhdoom ghaya
666
views
tifr2015
statistics
13
votes
1
answer
17
TIFR CSE 2015 | Part A | Question: 14
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 $0-1$ column vectors of the ... are done modulo $2$, i.e, $3 = 1$ (modulo $2$), $4 = 0$ (modulo $2$)). None Two Three Four Eight
makhdoom ghaya
asked
in
Linear Algebra
Dec 5, 2015
by
makhdoom ghaya
1.1k
views
tifr2015
matrix
11
votes
2
answers
18
TIFR CSE 2015 | Part A | Question: 13
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 non-negative integers. Suppose a line segment $l$ ... point in the interior of the square. How many unit squares does $l$ pass through? $98,990$ $9,900$ $1,190$ $1,180$ $1,010$
makhdoom ghaya
asked
in
Quantitative Aptitude
Dec 5, 2015
by
makhdoom ghaya
1.3k
views
tifr2015
quantitative-aptitude
cartesian-coordinates
7
votes
2
answers
19
TIFR CSE 2015 | Part A | Question: 12
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 $(1 - \alpha)$ $1 - \alpha$ $(1 - \alpha)^{2}$ $1 - \alpha^{2}$
makhdoom ghaya
asked
in
Probability
Dec 5, 2015
by
makhdoom ghaya
1.3k
views
tifr2015
probability
random-variable
uniform-distribution
13
votes
5
answers
20
TIFR CSE 2015 | Part A | Question: 11
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.
makhdoom ghaya
asked
in
Calculus
Dec 5, 2015
by
makhdoom ghaya
1.7k
views
tifr2015
maxima-minima
calculus
4
votes
0
answers
21
TIFR CSE 2015 | Part A | Question: 10
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. $\max_{x \in \left[0, 1\right]} f(x)$ $\min_{x \in \left[0, 1\right]} f(x)$ $f(0)$ $f(1)$ $\infty$
makhdoom ghaya
asked
in
Calculus
Dec 5, 2015
by
makhdoom ghaya
423
views
tifr2015
maxima-minima
calculus
non-gate
integration
3
votes
2
answers
22
TIFR CSE 2015 | Part A | Question: 9
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 ... $\text{(ii)}$ only $\text{(iii)}$ only $\text{(ii)}$ and $\text{(iii)}$ None of the above
makhdoom ghaya
asked
in
Quantitative Aptitude
Dec 5, 2015
by
makhdoom ghaya
682
views
tifr2015
geometry
quantitative-aptitude
easy
29
votes
4
answers
23
TIFR CSE 2015 | Part A | Question: 8
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
makhdoom ghaya
asked
in
Combinatory
Dec 5, 2015
by
makhdoom ghaya
2.9k
views
tifr2015
combinatory
discrete-mathematics
normal
balls-in-bins
19
votes
8
answers
24
TIFR CSE 2015 | Part A | Question: 7
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? $64$ $65$ $204$ $144$ $256$
makhdoom ghaya
asked
in
Combinatory
Dec 5, 2015
by
makhdoom ghaya
2.2k
views
tifr2015
combinatory
16
votes
5
answers
25
TIFR CSE 2015 | Part A | Question: 6
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
makhdoom ghaya
asked
in
Probability
Dec 5, 2015
by
makhdoom ghaya
3.5k
views
tifr2015
expectation
17
votes
4
answers
26
TIFR CSE 2015 | Part A | Question: 5
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 ... shopping mall. If it is not raining then Kareena and Parineeti do not go to the shopping mall. None of the above.
makhdoom ghaya
asked
in
Mathematical Logic
Dec 4, 2015
by
makhdoom ghaya
1.5k
views
tifr2015
mathematical-logic
propositional-logic
13
votes
1
answer
27
TIFR CSE 2015 | Part A | Question: 4
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
makhdoom ghaya
asked
in
Digital Logic
Dec 2, 2015
by
makhdoom ghaya
1.6k
views
tifr2015
digital-logic
digital-circuits
5
votes
2
answers
28
TIFR CSE 2015 | Part A | Question: 3
Let $|z| < 1$. Define $M_{n}(z)= \sum_{i=1}^{10} z^{10^{n}(i - 1)}?$ what is $\prod\limits_{i=0}^{\infty} M_{i}(z)= M_{0}(z)\times M_{1}(z) \times M_{2}(z) \times ...?$ Can't be determined $1/ (1 - z)$ $1/ (1 + z)$ $1 - z^{9}$ None of the above
makhdoom ghaya
asked
in
Quantitative Aptitude
Dec 2, 2015
by
makhdoom ghaya
633
views
tifr2015
quantitative-aptitude
numerical-computation
number-series
9
votes
1
answer
29
TIFR CSE 2015 | Part A | Question: 2
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 ... $(1 - 2d)$ It equals $1$ It equals $(1 - d)$ $(1 - d)$
makhdoom ghaya
asked
in
Quantitative Aptitude
Dec 2, 2015
by
makhdoom ghaya
681
views
tifr2015
geometry
12
votes
5
answers
30
TIFR CSE 2015 | Part A | Question: 1
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 ... $P(\left \{ 5 \right \}) \leq \dfrac{1}{3}$ None of the above
makhdoom ghaya
asked
in
Probability
Dec 2, 2015
by
makhdoom ghaya
1.5k
views
tifr2015
probability
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Sure will provide it as soon as possible.
sir in the excel sheet of shedule of test link of...
The spreadsheet is up to date.
Can somebody give the details of how many topic...
@kabir5454 Anyway you should not be looking for...