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Search results for tifr2015
43
votes
4
answers
1
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 ... $2^{4}.3^{2}.5.9=6480$ $2^{3}.3.5.9=1080$ $2^{4}=16$ $2^{3}.3^{3}=216$
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 ...
makhdoom ghaya
4.1k
views
makhdoom ghaya
asked
Dec 7, 2015
DS
tifr2015
binary-tree
combinatory
+
–
32
votes
4
answers
2
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
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 n...
makhdoom ghaya
4.0k
views
makhdoom ghaya
asked
Dec 5, 2015
Combinatory
tifr2015
combinatory
discrete-mathematics
normal
balls-in-bins
+
–
20
votes
8
answers
3
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? $64$ $65$ $204$ $144$ $256$
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 \time...
makhdoom ghaya
3.0k
views
makhdoom ghaya
asked
Dec 5, 2015
Combinatory
tifr2015
combinatory
counting
+
–
20
votes
5
answers
4
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
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 u...
makhdoom ghaya
5.0k
views
makhdoom ghaya
asked
Dec 5, 2015
Probability
tifr2015
expectation
+
–
22
votes
3
answers
5
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 $O(\log^{2} n)$.
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...
makhdoom ghaya
3.0k
views
makhdoom ghaya
asked
Dec 5, 2015
Algorithms
tifr2015
algorithms
recurrence-relation
time-complexity
+
–
18
votes
4
answers
6
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.
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 n...
makhdoom ghaya
2.2k
views
makhdoom ghaya
asked
Dec 4, 2015
Mathematical Logic
tifr2015
mathematical-logic
propositional-logic
+
–
25
votes
5
answers
7
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 $2*3*4 - 5*6+7$?
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 \m...
makhdoom ghaya
3.0k
views
makhdoom ghaya
asked
Dec 8, 2015
Compiler Design
tifr2015
parsing
expression-evaluation
+
–
17
votes
2
answers
8
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.
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 -...
makhdoom ghaya
1.8k
views
makhdoom ghaya
asked
Dec 7, 2015
Algorithms
tifr2015
algorithms
identify-function
time-complexity
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–
25
votes
6
answers
9
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.
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 len...
makhdoom ghaya
4.4k
views
makhdoom ghaya
asked
Dec 7, 2015
Theory of Computation
tifr2015
identify-class-language
+
–
28
votes
7
answers
10
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 $(ii)$
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 undirected graph...
makhdoom ghaya
4.2k
views
makhdoom ghaya
asked
Dec 7, 2015
Graph Theory
tifr2015
graph-connectivity
graph-theory
+
–
7
votes
2
answers
11
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 $(1 - \alpha)$ $1 - \alpha$ $(1 - \alpha)^{2}$ $1 - \alpha^{2}$
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 t...
makhdoom ghaya
1.9k
views
makhdoom ghaya
asked
Dec 5, 2015
Probability
tifr2015
probability
random-variable
uniform-distribution
+
–
7
votes
2
answers
12
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 ... $p.v_{A}+ (1 - p). v_{B} + (\mu_{A}- \mu_{B})^{2}$
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 se...
makhdoom ghaya
1.0k
views
makhdoom ghaya
asked
Dec 5, 2015
Quantitative Aptitude
tifr2015
statistics
+
–
15
votes
5
answers
13
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.
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 $...
makhdoom ghaya
2.7k
views
makhdoom ghaya
asked
Dec 5, 2015
Calculus
tifr2015
maxima-minima
calculus
+
–
3
votes
2
answers
14
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
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 lin...
makhdoom ghaya
979
views
makhdoom ghaya
asked
Dec 5, 2015
Quantitative Aptitude
tifr2015
geometry
quantitative-aptitude
easy
+
–
15
votes
3
answers
15
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 ... $\left \{2, 4 \right \}$ $\left \{ 2, 3 \right \}$ $\left \{2 \right \}$
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:=...
makhdoom ghaya
2.2k
views
makhdoom ghaya
asked
Dec 8, 2015
Operating System
tifr2015
process-synchronization
operating-system
normal
+
–
15
votes
3
answers
16
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.
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...
makhdoom ghaya
1.9k
views
makhdoom ghaya
asked
Dec 7, 2015
Theory of Computation
tifr2015
theory-of-computation
regular-language
+
–
14
votes
5
answers
17
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
Consider a $6$-sided die with all sides not necessarily equally likely such that probability of an even number is $P (\left \{2, 4, 6 \right \}) =\dfrac{1}{2}$, probabil...
makhdoom ghaya
2.1k
views
makhdoom ghaya
asked
Dec 2, 2015
Probability
tifr2015
probability
conditional-probability
+
–
5
votes
2
answers
18
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 $u, v \in V_{1}, (u, v) \in E_{1}$ ... $L$ is $NP$- hard. $L$ is undecidable. Only $(i)$ Only $(ii)$ Only $(iii)$ $(i)$ and $(ii)$ $(ii)$ and $(iii)$
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...
makhdoom ghaya
972
views
makhdoom ghaya
asked
Dec 8, 2015
Algorithms
tifr2015
graph-theory
graph-isomorphism
p-np-npc-nph
non-gate
+
–
14
votes
1
answer
19
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
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} ...
makhdoom ghaya
1.5k
views
makhdoom ghaya
asked
Dec 5, 2015
Linear Algebra
tifr2015
matrix
+
–
29
votes
2
answers
20
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.
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 a...
makhdoom ghaya
3.6k
views
makhdoom ghaya
asked
Dec 7, 2015
Algorithms
tifr2015
algorithms
graph-algorithms
minimum-spanning-tree
+
–
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