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Recent questions tagged tifr2010

15 votes

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1

TIFR CSE 2010 | Part B | Question: 40
Which of the following statement is FALSE? All recursive sets are recursively enumerable. The complement of every recursively enumerable sets is recursively enumerable. Every Non-empty recursively enumerable set is the range of some totally recursive function. All finite sets are recursive. The complement of every recursive set is recursive.

makhdoom ghaya asked in Theory of Computation Oct 11, 2015

by makhdoom ghaya

2.5k views

8 votes

3 answers

2

TIFR CSE 2010 | Part B | Question: 39
Suppose a language $L$ is $\mathbf{NP}$ complete. Then which of the following is FALSE? $L \in \mathbf{NP}$ Every problem in $\mathbf{P}$ is polynomial time reducible to $L$. Every problem in $\mathbf{NP}$ is polynomial time reducible to $L$. The Hamilton cycle problem is polynomial time reducible to $L$. $\mathbf{P} \neq \mathbf{NP}$ and $L \in \mathbf{P}$.

makhdoom ghaya asked in Algorithms Oct 11, 2015

by makhdoom ghaya

1.6k views

24 votes

6 answers

3

TIFR CSE 2010 | Part B | Question: 38
Suppose three coins are lying on a table, two of them with heads facing up and one with tails facing up. One coin is chosen at random and flipped. What is the probability that after the flip the majority of the coins(i.e., at least two of them) will have heads facing up ... $\left(\frac{1}{4}+\frac{1}{8}\right)$ $\left(\frac{2}{3}\right)$

makhdoom ghaya asked in Probability Oct 10, 2015

by makhdoom ghaya

3.5k views

23 votes

3 answers

4

TIFR CSE 2010 | Part B | Question: 37
Consider the program where $a, b$ are integers with $b > 0$. x:=a; y:=b; z:=0; while y > 0 do if odd (x) then z:= z + x; y:= y - 1; else y:= y % 2; x:= 2 * x; fi Invariant of the loop is a condition which is ... terminate for some values of $a, b$ but when it does terminate, the condition $z = a * b$ will hold. The program will terminate with $z=a^{b}$

makhdoom ghaya asked in Programming in C Oct 10, 2015

by makhdoom ghaya

3.3k views

37 votes

6 answers

5

TIFR CSE 2010 | Part B | Question: 36
In a directed graph, every vertex has exactly seven edges coming in. What can one always say about the number of edges going out of its vertices? Exactly seven edges leave every vertex. Exactly seven edges leave some vertex. Some vertex has at least seven edges leaving it. The number of edges coming out of vertex is odd. None of the above.

makhdoom ghaya asked in Graph Theory Oct 10, 2015

by makhdoom ghaya

5.8k views

15 votes

2 answers

6

TIFR CSE 2010 | Part B | Question: 35
Consider the following languages over the alphabet $\{0, 1\}$. $L1=\left \{ x.x^{R}\mid x\in \left \{ 0, 1 \right \}^* \right \}$ $L2=\left \{ x.x\mid x\in \left \{ 0, 1 \right \}^* \right \}$ Where $x^{R}$ is the ... and $L2$ are context free and neither is regular. $L1$ is context free but $L2$ is not context free. Both $L1$ and $L2$ are not context free.

makhdoom ghaya asked in Theory of Computation Oct 10, 2015

by makhdoom ghaya

1.8k views

21 votes

3 answers

7

TIFR CSE 2010 | Part B | Question: 34
Let $r, s, t$ be regular expressions. Which of the following identities is correct? $(r + s)^* = r^*s^*$ $r(s + t) = rs + t$ $(r + s)^* = r^* + s^*$ $(rs + r)^* r = r (sr + r)^*$ $(r^*s)^* = (rs)^*$

makhdoom ghaya asked in Theory of Computation Oct 10, 2015

by makhdoom ghaya

2.6k views

39 votes

5 answers

8

TIFR CSE 2010 | Part B | Question: 33
In a relational database there are three relations: $Customers = C \textsf{(CName)}$ $Shops = S \textsf{(SName)}$ $Buys = B \textsf{(CName, SName)}$ Then the Relational Algebra expression ( $\Pi $ ... from at least two shops. Customers who buy from all shops. Customers who do not buy buy anything at all. None of the above.

makhdoom ghaya asked in Databases Oct 10, 2015

by makhdoom ghaya

3.7k views

16 votes

6 answers

9

TIFR CSE 2010 | Part B | Question: 32
Consider the following solution (expressed in Dijkstra's guarded command notation) to the mutual exclusion problem. process P1 is begin loop Non_critical_section; while not (Turn=1) do skip od; Critical_section_1; Turn:=2; end loop end process P2 is begin ... ), but does not satisfies the requirement (2). Satisfies all the requirement (1), (2), and (3).

makhdoom ghaya asked in Operating System Oct 10, 2015

by makhdoom ghaya

4.7k views

16 votes

2 answers

10

TIFR CSE 2010 | Part B | Question: 31
Consider the following computation rules. Parallel-outermost rule: Replace all the outermost occurrences of F (i.e., all occurrences of F which do not occur as arguments of other F's) simultaneously. Parallel - innermost rule: Replace all the innermost ... $0$ and $0$ respectively $w$ and $w$ respectively $w$ and $1$ respectively none of the above

Arjun asked in Programming in C Oct 10, 2015

by Arjun

1.6k views

16 votes

2 answers

11

TIFR CSE 2010 | Part B | Question: 30
Consider the following program for summing the entries of the array $b$: array $[0 .. N-1]$ of integers, where $N$ is a positive integer. (The symbol '$<>$' denotes 'not equal to'). var i, s: integer; Program i:= 0; s:= 0; [*] while i <> N ... $s = \sum\limits^{i-1}_{j=0}b[j] \;\&\; 0 \leq i \leq N$

makhdoom ghaya asked in Programming in C Oct 8, 2015

by makhdoom ghaya

2.7k views

26 votes

1 answer

12

TIFR CSE 2010 | Part B | Question: 29
Suppose you are given an array $A$ with $2n$ numbers. The numbers in odd positions are sorted in ascending order, that is, $A[1] \leq A[3] \leq \ldots \leq A[2n - 1]$. The numbers in even positions are sorted in ... on the entire array. Perform separate binary searches on the odd positions and the even positions. Search sequentially from the end of the array.

makhdoom ghaya asked in Algorithms Oct 6, 2015

by makhdoom ghaya

4.3k views

16 votes

4 answers

13

TIFR CSE 2010 | Part B | Question: 28
Consider the concurrent program: x: 1; cobegin x:= x + 3 || x := x + x + 2 coend Reading and writing of variables is atomic, but the evaluation of an expression is not atomic. The set of possible values of variable $x$ at the end of the execution of the program is: $\{4\}$ $\{8\}$ $\{4, 7, 10\}$ $\{4, 7, 8, 10\}$ $\{4, 7, 8\}$

makhdoom ghaya asked in Operating System Oct 6, 2015

by makhdoom ghaya

3.7k views

22 votes

4 answers

14

TIFR CSE 2010 | Part B | Question: 27
Consider the Insertion Sort procedure given below, which sorts an array $L$ of size $n\left ( \geq 2 \right )$ in ascending order: begin for xindex:= 2 to n do x := L [xindex]; j:= xindex - 1; while j > 0 and L[j] > x do L[j + ... $n (n - 1) / 2$ comparisons whenever all the elements of $L$ are not distinct.

makhdoom ghaya asked in Algorithms Oct 6, 2015

by makhdoom ghaya

3.8k views

49 votes

5 answers

15

TIFR CSE 2010 | Part B | Question: 26
Suppose there is a balanced binary search tree with $n$ nodes, where at each node, in addition to the key, we store the number of elements in the sub tree rooted at that node. Now, given two elements $a$ and $b$, such that $a < b$ ... $O(n)$ comparisons and $O(n)$ additions, using depth-first- search.

makhdoom ghaya asked in DS Oct 6, 2015

by makhdoom ghaya

8.7k views

21 votes

3 answers

16

TIFR CSE 2010 | Part B | Question: 25
Which of the following problems is decidable? (Here, CFG means context free grammar and CFL means context free language.) Given a CFG $G$, find whether $L(G) = R$, where $R$ is regular set. Given a CFG $G$, find whether $L(G) = \{\}$. Find whether ... whether CFG $G_1$ and CFG $G_2$ generate the same language, i.e, $L\left (G_1 \right ) = L\left (G_2 \right)$.

makhdoom ghaya asked in Theory of Computation Oct 6, 2015

by makhdoom ghaya

4.8k views

12 votes

2 answers

17

TIFR CSE 2010 | Part B | Question: 24
Consider the following program operating on four variables $u, v, x, y$, and two constants $X$ and $Y$. x, y, u, v:= X, Y, Y, X; While (x ≠ y) do if (x > y) then x, v := x - y, v + u; else if (y > x) then y, u:= y ... . The program prints $\frac1 2 \times \text{gcd}(X, Y)$ followed by $\frac1 2 \times \text{lcm}(X, Y)$. The program does none of the above.

makhdoom ghaya asked in Algorithms Oct 6, 2015

by makhdoom ghaya

1.8k views

15 votes

3 answers

18

TIFR CSE 2010 | Part B | Question: 23
Suppose you are given $n$ numbers and you sort them in descending order as follows: First find the maximum. Remove this element from the list and find the maximum of the remaining elements, remove this element, and so on, until all elements are exhausted. How many comparisons ... $O\left ( n^{1.5} \right )$ but not better.

makhdoom ghaya asked in Algorithms Oct 5, 2015

by makhdoom ghaya

4.9k views

21 votes

2 answers

19

TIFR CSE 2010 | Part B | Question: 22
Let $L$ consist of all binary strings beginning with a $1$ such that its value when converted to decimal is divisible by $5$. Which of the following is true? $L$ ... deterministic push-down automaton but not by a deterministic push-down automaton. $L$ cannot be recognized by any push-down automaton.

makhdoom ghaya asked in Theory of Computation Oct 5, 2015

by makhdoom ghaya

2.0k views

33 votes

3 answers

20

TIFR CSE 2010 | Part B | Question: 21
For $x \in \{0,1\}$, let $\lnot x$ denote the negation of $x$, that is $\lnot \, x = \begin{cases}1 & \mbox{iff } x = 0\\ 0 & \mbox{iff } x = 1\end{cases}$. If $x \in \{0,1\}^n$, then $\lnot \, x$ denotes the component wise negation of $x$; that ... $g(x) = f(x) \land f(\lnot x)$ $g(x) = f(x) \lor f(\lnot x)$ $g(x) = \lnot f(\lnot x)$ None of the above.

makhdoom ghaya asked in Digital Logic Oct 5, 2015

by makhdoom ghaya

3.4k views

13 votes

2 answers

21

TIFR CSE 2010 | Part A | Question: 20
How many integers from $1$ to $1000$ are divisible by $30$ but not by $16$? $29$ $31$ $32$ $33$ $25$

makhdoom ghaya asked in Quantitative Aptitude Oct 4, 2015

by makhdoom ghaya

1.8k views

32 votes

6 answers

22

TIFR CSE 2010 | Part A | Question: 19, TIFR CSE 2014 | Part A | Question: 6
Karan tells truth with probability $\dfrac{1}{3}$ and lies with probability $\dfrac{2}{3}.$ Independently, Arjun tells truth with probability $\dfrac{3}{4}$ and lies with probability $\dfrac{1}{4}.$ Both watch a cricket match. Arjun tells ... $\left(\dfrac{5}{6}\right)$ $\left(\dfrac{6}{7}\right)$

makhdoom ghaya asked in Probability Oct 4, 2015

by makhdoom ghaya

6.0k views

40 votes

5 answers

23

TIFR CSE 2010 | Part A | Question: 18
Let $X$ be a set of size $n$. How many pairs of sets (A, B) are there that satisfy the condition $A\subseteq B \subseteq X$ ? $2^{n+1}$ $2^{2n}$ $3^{n}$ $2^{n} + 1$ $3^{n + 1}$

makhdoom ghaya asked in Set Theory & Algebra Oct 4, 2015

by makhdoom ghaya

4.6k views

7 votes

1 answer

24

TIFR CSE 2010 | Part A | Question: 17
Suppose there is a sphere with diameter at least $6$ inches. Through this sphere we drill a hole along a diameter. The part of the sphere lost in the process of drilling the hole looks like two caps joined to a cylinder, where the cylindrical part has length $6$ ... $36\pi$ cu. inches $27\pi$ cu. inches $32\pi$ cu. inches $35\pi$ cu. inches

makhdoom ghaya asked in Quantitative Aptitude Oct 4, 2015

by makhdoom ghaya

907 views

19 votes

1 answer

25

TIFR CSE 2010 | Part A | Question: 16
Let the characteristic equation of matrix $M$ be $\lambda ^{2} - \lambda - 1 = 0$. Then. $M^{-1}$ does not exist. $M^{-1}$ exists but cannot be determined from the data. $M^{-1} = M + I$ $M^{-1} = M - I$ $M^{-1}$ exists and can be determined from the data but the choices (c) and (d) are incorrect.

makhdoom ghaya asked in Linear Algebra Oct 4, 2015

by makhdoom ghaya

12.2k views

8 votes

3 answers

26

TIFR CSE 2010 | Part A | Question: 15
Let $A, B$ be sets. Let $\bar{A}$ denote the compliment of set $A$ (with respect to some fixed universe), and $( A - B)$ denote the set of elements in $A$ which are not in $B$. Set $(A - (A - B))$ is equal to: $B$ $A\cap \bar{B}$ $A - B$ $A\cap B$ $\bar{B}$

makhdoom ghaya asked in Set Theory & Algebra Oct 3, 2015

by makhdoom ghaya

1.5k views

13 votes

3 answers

27

TIFR CSE 2010 | Part A | Question: 14
A marine biologist wanted to estimate the number of fish in a large lake. He threw a net and found $30$ fish in the net. He marked all these fish and released them into the lake. The next morning he again threw the net and this time caught $40$ fish, ... two were found to be marked. The (approximate) number of fish in the lake is: $600$ $1200$ $68$ $800$ $120$

makhdoom ghaya asked in Quantitative Aptitude Oct 3, 2015

by makhdoom ghaya

1.3k views

10 votes

3 answers

28

TIFR CSE 2010 | Part A | Question: 13
A cube whose faces are colored is split into $1000$ small cubes of equal size. The cubes thus obtained are mixed thoroughly. The probability that a cube drawn at random will have exactly two colored faces is: $0.096$ $0.12$ $0.104$ $0.24$ None of the above

makhdoom ghaya asked in Probability Oct 3, 2015

by makhdoom ghaya

2.4k views

29 votes

7 answers

29

TIFR CSE 2010 | Part A | Question: 12
The coefficient of $x^{3}$ in the expansion of $(1 + x)^{3} (2 + x^{2})^{10}$ is. $2^{14}$ $31$ $\left ( \frac{3}{3} \right ) + \left ( \frac{10}{1} \right )$ $\left ( \frac{3}{3} \right ) + 2\left ( \frac{10}{1} \right )$ $\left ( \frac{3}{3} \right ) \left ( \frac{10}{1} \right ) 2^{9}$

makhdoom ghaya asked in Combinatory Oct 3, 2015

by makhdoom ghaya

3.2k views

9 votes

1 answer

30

TIFR CSE 2010 | Part A | Question: 11
The length of a vector $X = (x_{1},\ldots,x_{n})$ is defined as $\left \| X\right \| = \sqrt{\sum \limits^{n}_{i=1}x^{2}_{i}}$ Given two vectors $X=(x_{1},\ldots, x_{n})$ and $Y=(y_{1},\ldots, y_{n})$, which of the following measures of ... $\left \| \frac{X}{\left \| X \right \|}-\frac{Y}{\left \| Y \right \|} \right \|$ None of the above

makhdoom ghaya asked in Linear Algebra Oct 3, 2015

by makhdoom ghaya

1.3k views

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