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Recent questions tagged tifr2012

7 votes

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1

TIFR CSE 2012 | Part B | Question: 20
This question concerns the classes $P$ and $NP.$ If you are familiar with them, you may skip the definitions and go directly to the question. Let $L$ be a set. We say that $L$ is in $P$ if there is some algorithm which given input $x$ decides if ... $\text{MATCH} \notin P\text{ and } \overline{\text{MATCH}} \notin P$ none of the above

Arjun asked in Graph Theory Nov 15, 2015

by Arjun

709 views

23 votes

2 answers

2

TIFR CSE 2012 | Part B | Question: 19
Which of the following statements is TRUE? Every turning machine recognizable language is recursive. The complement of every recursively enumerable language is recursively enumerable. The complement of a recursive language is recursively enumerable. The ... . The set of turning machines which do not halt on empty input forms a recursively enumerable set.

makhdoom ghaya asked in Theory of Computation Nov 2, 2015

by makhdoom ghaya

2.4k views

13 votes

3 answers

3

TIFR CSE 2012 | Part B | Question: 18
Let $a^{i}$ denote a sequence $a . a ... a$ with $i$ letters and let $\aleph$ be the set of natural numbers ${ 1, 2,...}$. Let $L_{1}=\left\{a^{i}b^{2i}\mid i \in \aleph\right\}$ ... $L_{2}$ are recursive but not context-free. $L_{1}$ is regular and $L_{2}$ is context-free. Complement of $L_{2}$ is context-free.

makhdoom ghaya asked in Theory of Computation Nov 2, 2015

by makhdoom ghaya

1.3k views

16 votes

2 answers

4

TIFR CSE 2012 | Part B | Question: 17
Which of the following correctly describes $\text{LR}(k)$ parsing? The input string is alternately scanned left to right and right to left with $k$ reversals. Input string is scanned once left to right with rightmost derivation and $k$ symbol ... string is scanned from left to right once with $k$ symbol to the right as look-ahead to give left-most derivation.

makhdoom ghaya asked in Compiler Design Nov 2, 2015

by makhdoom ghaya

2.1k views

9 votes

1 answer

5

TIFR CSE 2012 | Part B | Question: 16
Consider a complete binary tree of height $n$, where each edge is one Ohm resistor. Suppose all the leaves of the tree are tied together. Approximately how much is the effective resistance from the root to this bunch of leaves for very large $n$? Exponential in $n$. Cubic in $n$. Linear in $n$. Logarithmic in $n$. Of the order square root of $n$.

makhdoom ghaya asked in DS Nov 2, 2015

by makhdoom ghaya

1.6k views

28 votes

8 answers

6

TIFR CSE 2012 | Part B | Question: 15
Let $T$ be a tree of $n$ nodes. Consider the following algorithm, that constructs a sequence of leaves $u_{1}, u_{2}...$. Let $u_{1}$ be some leaf of tree. Let $u_{2}$be a leaf that is farthest from $u_{1}$ ... . For the same tree, the distance between the last two vertices visited can be different, based on the choice of the first leaf $u_{1}$.

makhdoom ghaya asked in DS Nov 2, 2015

by makhdoom ghaya

3.0k views

16 votes

3 answers

7

TIFR CSE 2012 | Part B | Question: 14
Consider the quick sort algorithm on a set of $n$ ... $\Theta (n^{2})$. None of the above.

makhdoom ghaya asked in Algorithms Nov 2, 2015

by makhdoom ghaya

2.9k views

28 votes

4 answers

8

TIFR CSE 2012 | Part B | Question: 13
An array $A$ contains $n$ integers. We wish to sort $A$ in ascending order. We are told that initially no element of $A$ is more than a distance $k$ away from its final position in the sorted list. Assume that $n$ and $k$ are large ... $A$ can be sorted with constant $\cdot k^{2}n$ comparisons but not fewer.

makhdoom ghaya asked in Algorithms Nov 2, 2015

by makhdoom ghaya

2.6k views

21 votes

2 answers

9

TIFR CSE 2012 | Part B | Question: 12
Let $A$ be a matrix such that $A^{k}=0$. What is the inverse of $I - A$? $0$ $I$ $A$ $1 + A + A^{2} + ...+ A^{k - 1}$ Inverse is not guaranteed to exist.

makhdoom ghaya asked in Linear Algebra Nov 1, 2015

by makhdoom ghaya

2.5k views

21 votes

3 answers

10

TIFR CSE 2012 | Part B | Question: 11
Consider the following three version of the binary search program. Assume that the elements of type $T$ can be compared with each other; also assume that the array is sorted. i, j, k : integer; a : array [1....N] of T; x : T; Program 1 : ... $1$ and $2$ are correct. Both Program $2$ and $3$ are correct All the three programs are wrong

makhdoom ghaya asked in Algorithms Nov 1, 2015

by makhdoom ghaya

1.9k views

26 votes

3 answers

11

TIFR CSE 2012 | Part B | Question: 10
Consider the blocked-set semaphore where the signaling process awakens any one of the suspended process; i.e., Wait (S): If $S>0$ then $S\leftarrow S - 1$, else suspend the execution of this process. Signal (S): If there are ... exclusion, but allows starvation for any $N\geq 2$ The program achieves mutual exclusion and starvation freedom for any $N\geq 1$

makhdoom ghaya asked in Operating System Oct 31, 2015

by makhdoom ghaya

2.8k views

20 votes

1 answer

12

TIFR CSE 2012 | Part B | Question: 9
Consider the concurrent program x := 1; cobegin x := x + x + 1 || x := x + 2 coend; Reading and writing of a variable is atomic, but evaluation of an expression is not atomic. The set of possible values of variable $x$ ... $\left\{7\right\}$ $\left\{3, 5, 7\right\}$ $\left\{3, 7\right\}$ $\left\{3, 5\right\}$

makhdoom ghaya asked in Operating System Oct 31, 2015

by makhdoom ghaya

1.8k views

19 votes

2 answers

13

TIFR CSE 2012 | Part B | Question: 8
Consider the parse tree Assume that $*$ has higher precedence than $+$, $-$ and operators associate right to left (i.e $(a + b + c= (a + (b + c)))$. Consider $2 + a - b$ $2 + a - b * a + b$ ... The parse tree corresponds to Expression (i) Expression (ii) Expression (iv) only Expression (ii), (iii), and (iv) Expression (iii) and (iv) only

makhdoom ghaya asked in Compiler Design Oct 31, 2015

by makhdoom ghaya

2.1k views

15 votes

1 answer

14

TIFR CSE 2012 | Part B | Question: 7
A bag contains $16$ balls of the following colors: 8 red, 4 blue, 2 green, 1 black, and 1 white. Anisha picks a ball randomly from the bag, and messages Babu its color using a string of zeros and ones. She replaces the ball in the bag, and repeats this experiment, many ... per experiment? $\dfrac{3}{2}\\$ ${\log 5}\\$ $\dfrac{15}{8}\\$ $\dfrac{31}{16}\\$ $2$

makhdoom ghaya asked in Probability Oct 31, 2015

by makhdoom ghaya

1.7k views

23 votes

4 answers

15

TIFR CSE 2012 | Part B | Question: 6
Let $n$ be a large integer. Which of the following statements is TRUE? $2^{\sqrt{2\log n}}< \frac{n}{\log n}< n^{1/3}$ $\frac{n}{\log n}< n^{1/3}< 2^{\sqrt{2\log n}}$ $2^\sqrt{{2\log n}}< n^{1/3}< \frac{n}{\log n}$ $n^{1/3}< 2^\sqrt{{2\log n}}<\frac{n}{\log n}$ $\frac{n}{\log n}< 2^\sqrt{{2\log n}}<n^{1/3}$

makhdoom ghaya asked in Algorithms Oct 31, 2015

by makhdoom ghaya

3.5k views

12 votes

3 answers

16

TIFR CSE 2012 | Part B | Question: 5
Let $R$ be a binary relation over a set $S$. The binary relation $R$ is called an equivalence relation if it is reflexive transitive and symmetric. The relation is called partial order if it is reflexive, transitive and anti symmetric. ... $\sqsubseteq $ is neither a partial order nor an equivalence relation.

makhdoom ghaya asked in Set Theory & Algebra Oct 31, 2015

by makhdoom ghaya

1.4k views

15 votes

4 answers

17

TIFR CSE 2012 | Part B | Question: 4
Let $\wedge $, $\vee $ denote the meet and join operations of lattice. A lattice is called distributive if for all $x, y, z,$ ... , but not distributive lattice. Distributive lattice. Lattice but not a complete lattice. Under the give ordering positive integers do not form a lattice.

makhdoom ghaya asked in Set Theory & Algebra Oct 31, 2015

by makhdoom ghaya

3.4k views

25 votes

5 answers

18

TIFR CSE 2012 | Part B | Question: 3
For a person $p$, let $w(p)$, $A(p, y)$, $L(p)$ and $J(p)$ denote that $p$ is a woman, $p$ admires $y$, $p$ is a lawyer and $p$ is a judge respectively. Which of the following is the correct translation in first order logic of ...

makhdoom ghaya asked in Mathematical Logic Oct 30, 2015

by makhdoom ghaya

1.6k views

17 votes

3 answers

19

TIFR CSE 2012 | Part B | Question: 2
In a graph, the degree of a vertex is the number of edges incident (connected) on it. Which of the following is true for every graph $G$? There are even number of vertices of even degree. There are odd number of vertices of even degree ... even number of vertices of odd degree. There are odd number of vertices of odd degree. All the vertices are of even degree.

makhdoom ghaya asked in Graph Theory Oct 30, 2015

by makhdoom ghaya

2.3k views

17 votes

3 answers

20

TIFR CSE 2012 | Part B | Question: 1
For $x, y\in \left\{0, 1\right\}^{n}$, let $x ⊕ y$ be the element of $\left\{0, 1\right\}^{n}$ obtained by the component-wise exclusive-or of $x$ and $y$. A Boolean function $F:\left\{0, 1\right\}^{n}\rightarrow\left\{0, 1\right\}$ ... $\left\{0, 1\right\}$ is. $2^{2n}$ $2^{n+1}$ $2^{n-1}+1$ $n!$ $2^{n}$

makhdoom ghaya asked in Set Theory & Algebra Oct 30, 2015

by makhdoom ghaya

1.9k views

22 votes

4 answers

21

TIFR CSE 2012 | Part A | Question: 20
There are $1000$ balls in a bag, of which $900$ are black and $100$ are white. I randomly draw $100$ balls from the bag. What is the probability that the $101$st ball will be black? $9/10$ More than $9/10$ but less than $1$. Less than $9/10$ but more than $0$. $0$ $1$

makhdoom ghaya asked in Probability Oct 30, 2015

by makhdoom ghaya

2.1k views

22 votes

2 answers

22

TIFR CSE 2012 | Part A | Question: 19
An electric circuit between two terminals $A$ and $B$ is shown in the figure below, where the numbers indicate the probabilities of failure for the various links, which are all independent. What is the probability that $A$ and $B$ ... $\left(\dfrac{1}{1200}\right)$ $\left(\dfrac{1199}{1200}\right)$ $\left(\dfrac{59}{60}\right)$

makhdoom ghaya asked in Probability Oct 30, 2015

by makhdoom ghaya

2.0k views

4 votes

1 answer

23

TIFR CSE 2012 | Part A | Question: 18
A large community practices birth control in the following peculiar fashion. Each set of parents continues having children until a son is born; then they stop. What is the ratio of boys to girls in the community if, in the absence of birth control, 51% of the babies are born male? $51:49$ $1:1$ $49:51$ $51:98$ $98:51$

makhdoom ghaya asked in Quantitative Aptitude Oct 30, 2015

by makhdoom ghaya

839 views

9 votes

6 answers

24

TIFR CSE 2012 | Part A | Question: 17
A spider is at the bottom of a cliff, and is $n$ inches from the top. Every step it takes brings it one inch closer to the top with probability $1/3$, and one inch away from the top with probability $2/3$, unless it is at the bottom in which ... $n$? It will never reach the top. Linear in $n$. Polynomial in $n$. Exponential in $n$. Double exponential in $n$.

makhdoom ghaya asked in Probability Oct 30, 2015

by makhdoom ghaya

1.8k views

3 votes

2 answers

25

TIFR CSE 2012 | Part A | Question: 16
Walking at $4/5$ is normal speed a man is $10$ minute too late. Find his usual time in minutes. $81$ $64$ $52$ $40$ It is not possible to determine the usual time from given data.

makhdoom ghaya asked in Quantitative Aptitude Oct 30, 2015

by makhdoom ghaya

685 views

8 votes

2 answers

26

TIFR CSE 2012 | Part A | Question: 15
Consider the differential equation $dx/dt= \left(1 - x\right)\left(2 - x\right)\left(3 - x\right)$. Which of its equilibria is unstable? $x=0$ $x=1$ $x=2$ $x=3$ None of the above

makhdoom ghaya asked in Calculus Oct 30, 2015

by makhdoom ghaya

1.3k views

7 votes

3 answers

27

TIFR CSE 2012 | Part A | Question: 14
The limit $\displaystyle \lim_{n \rightarrow \infty} \left(\sqrt{n^{2}+n}-n\right)$ equals. $\infty$ $1$ $1 / 2$ $0$ None of the above

makhdoom ghaya asked in Calculus Oct 30, 2015

by makhdoom ghaya

1.4k views

3 votes

2 answers

28

TIFR CSE 2012 | Part A | Question: 13
The maximum value of the function $f\left(x, y, z\right)= \left(x - 1 / 3\right)^{2}+ \left(y - 1 / 3\right)^{2}+ \left(z - 1 / 3\right)^{2}$ subject to the constraints $x + y + z=1,\quad x \geq 0, y \geq 0, z \geq 0$ is $1 / 3$ $2 / 3$ $1$ $4 / 3$ $4 / 9$

makhdoom ghaya asked in Calculus Oct 30, 2015

by makhdoom ghaya

1.1k views

14 votes

2 answers

29

TIFR CSE 2012 | Part A | Question: 12
For the polynomial $p(x)= 8x^{10}-7x^{3}+x-1$ consider the following statements (which may be true or false) It has a root between $[0, 1].$ It has a root between $[0, -1].$ It has no roots outside $(-1, 1).$ Which of the above statements are true? Only (i). Only (i) and (ii). Only (i) and (iii). Only (ii) and (iii). All of (i), (ii) and (iii).

makhdoom ghaya asked in Calculus Oct 30, 2015

by makhdoom ghaya

1.1k views

11 votes

3 answers

30

TIFR CSE 2012 | Part A | Question: 11
Let $N$ be the sum of all numbers from $1$ to $1023$ except the five primes numbers: $2, 3, 11, 17, 31.$ Suppose all numbers are represented using two bytes (sixteen bits). What is the value of the least significant byte (the least significant eight bits) of $N$? $00000000$ $10101110$ $01000000$ $10000000$ $11000000$

makhdoom ghaya asked in Digital Logic Oct 30, 2015

by makhdoom ghaya

1.3k views

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