Recent questions tagged gatecse-2007 / GATE Overflow for GATE CSE

25 votes

2 answers

31

GATE CSE 2007 | Question: 57
A single processor system has three resource types $X, Y$ and $Z$, which are shared by three processes. There are $5$ units of each resource type. Consider the following scenario, where the column alloc denotes the number of units of each resource type allocated to each ... $P0$ $P1$ $P2$ None of the above, since the system is in a deadlock

A single processor system has three resource types $X, Y$ and $Z$, which are shared by three processes. There are $5$ units of each resource type. Consider the following ...

Kathleen

11.1k views

Kathleen asked Sep 21, 2014

35 votes

3 answers

32

GATE CSE 2007 | Question: 56
A virtual memory system uses First In First Out (FIFO) page replacement policy and allocates a fixed number of frames to a process. Consider the following statements: P: Increasing the number of page frames allocated to a process sometimes increases the page fault rate. Q: ... are true, but Q is not the reason for P. P is false but Q is true Both P and Q are false.

A virtual memory system uses First In First Out (FIFO) page replacement policy and allocates a fixed number of frames to a process. Consider the following statements:P: I...

Kathleen

17.2k views

Kathleen asked Sep 21, 2014

24 votes

4 answers

33

GATE CSE 2007 | Question: 55
An operating system used Shortest Remaining System Time first (SRT) process scheduling algorithm. Consider the arrival times and execution times for the following processes: ... $P2$ ? $5$ $15$ $40$ $55$

An operating system used Shortest Remaining System Time first (SRT) process scheduling algorithm. Consider the arrival times and execution times for the following process...

Kathleen

8.2k views

Kathleen asked Sep 21, 2014

54 votes

7 answers

34

GATE CSE 2007 | Question: 54
In a simplified computer the instructions are: ... computation should be in memory. What is the minimum number of MOV instructions in the code generated for this basic block? $2$ $3$ $5$ $6$

In a simplified computer the instructions are:$$\begin{array}{|l|l|} \hline \text {OP }R _j , R _i & \text{Perform }R _j \text{ OP } R _i \text{ and store the result in r...

Kathleen

13.6k views

Kathleen asked Sep 21, 2014

75 votes

8 answers

35

GATE CSE 2007 | Question: 53
Consider the following two statements: P: Every regular grammar is LL(1) Q: Every regular set has a LR(1) grammar Which of the following is TRUE? Both P and Q are true P is true and Q is false P is false and Q is true Both P and Q are false

Consider the following two statements:P: Every regular grammar is LL(1)Q: Every regular set has a LR(1) grammarWhich of the following is TRUE?Both P and Q are trueP is tr...

Kathleen

35.8k views

Kathleen asked Sep 21, 2014

34 votes

6 answers

36

GATE CSE 2007 | Question: 52
Consider the grammar with non-terminals $N=\left\{S,C,S_1\right\}$, terminals $T=\left\{a, b, i, t, e\right\}$, with $S$ as the start symbol, and the following set of rules: $S \rightarrow iCtSS_1 \mid a$ ... $C \rightarrow b$ The grammar is NOT LL(1) because: it is left recursive it is right recursive it is ambiguous it is not context-free

Consider the grammar with non-terminals $N=\left\{S,C,S_1\right\}$, terminals $T=\left\{a, b, i, t, e\right\}$, with $S$ as the start symbol, and the following set of rul...

Kathleen

12.9k views

Kathleen asked Sep 21, 2014

38 votes

5 answers

37

GATE CSE 2007 | Question: 51
Consider the following C program segment: int IsPrime (n) { int i, n; for (i=2; i<=sqrt(n);i++) if(n%i == 0) {printf("Not Prime \n"); return 0;} return 1; } Let $T(n)$ denote number of times the $for$ loop is executed by the program on input $n$. Which of ... $T(n) = O(n) \: \text{ and } T(n) = \Omega(\sqrt{n})$ None of the above

Consider the following C program segment:int IsPrime (n) { int i, n; for (i=2; i<=sqrt(n);i++) if(n%i == 0) {printf("Not Prime \n"); return 0;} return 1; }Let $T(n)$ deno...

Kathleen

14.7k views

Kathleen asked Sep 21, 2014

64 votes

9 answers

38

GATE CSE 2007 | Question: 50
An array of $n$ numbers is given, where $n$ is an even number. The maximum as well as the minimum of these $n$ numbers needs to be determined. Which of the following is TRUE about the number of comparisons needed? At least $2n-c$ comparisons, for ... $c$ are needed. At most $1.5n-2$ comparisons are needed. At least $n\log_2 n$ comparisons are needed None of the above

An array of $n$ numbers is given, where $n$ is an even number. The maximum as well as the minimum of these $n$ numbers needs to be determined. Which of the following is T...

Kathleen

29.6k views

Kathleen asked Sep 21, 2014

37 votes

3 answers

39

GATE CSE 2007 | Question: 49
Let $w$ be the minimum weight among all edge weights in an undirected connected graph. Let $e$ be a specific edge of weight $w$. Which of the following is FALSE? There is a minimum spanning tree containing $e$ If $e$ is not in a minimum ... edges have the same weight. Every minimum spanning tree has an edge of weight $w$ $e$ is present in every minimum spanning tree

Let $w$ be the minimum weight among all edge weights in an undirected connected graph. Let $e$ be a specific edge of weight $w$. Which of the following is FALSE?There is ...

Kathleen

12.0k views

Kathleen asked Sep 21, 2014

54 votes

5 answers

40

GATE CSE 2007 | Question: 48
Which of the following is TRUE about formulae in Conjunctive Normal Form? For any formula, there is a truth assignment for which at least half the clauses evaluate to true. For any formula, there is a truth assignment for which all the clauses ... formula such that for each truth assignment, at most one-fourth of the clauses evaluate to true. None of the above.

Which of the following is TRUE about formulae in Conjunctive Normal Form?For any formula, there is a truth assignment for which at least half the clauses evaluate to true...

Kathleen

15.0k views

Kathleen asked Sep 21, 2014

76 votes

5 answers

41

GATE CSE 2007 | Question: 47
Consider the process of inserting an element into a $Max \: Heap$, where the $Max \: Heap$ is represented by an $array$. Suppose we perform a binary search on the path from the new leaf to the root to find the position for the newly inserted element, the number of $comparisons$ performed is: $\Theta(\log_2n)$ $\Theta(\log_2\log_2n)$ $\Theta(n)$ $\Theta(n\log_2n)$

Consider the process of inserting an element into a $Max \: Heap$, where the $Max \: Heap$ is represented by an $array$. Suppose we perform a binary search on the path fr...

Kathleen

19.5k views

Kathleen asked Sep 21, 2014

29 votes

4 answers

42

GATE CSE 2007 | Question: 46
Consider the following C program segment where $CellNode$ represents a node in a binary tree: struct CellNode { struct CellNode *leftChild; int element; struct CellNode *rightChild; }; int Getvalue (struct CellNode *ptr) { int value = 0; if (ptr != NULL) ... in the tree the number of internal nodes in the tree the number of leaf nodes in the tree the height of the tree

Consider the following C program segment where $CellNode$ represents a node in a binary tree:struct CellNode { struct CellNode *leftChild; int element; struct CellNode *r...

Kathleen

8.6k views

Kathleen asked Sep 21, 2014

50 votes

8 answers

43

GATE CSE 2007 | Question: 45
What is the $\text{time complexity}$ of the following recursive function? int DoSomething (int n) { if (n <= 2) return 1; else return (DoSomething (floor (sqrt(n))) + n); } $\Theta(n^2)$ $\Theta(n \log_2n)$ $\Theta(\log_2n)$ $\Theta(\log_2\log_2n)$

What is the $\text{time complexity}$ of the following recursive function?int DoSomething (int n) { if (n <= 2) return 1; else return (DoSomething (floor (sqrt(n))) + n); ...

Kathleen

32.1k views

Kathleen asked Sep 21, 2014

64 votes

8 answers

44

GATE CSE 2007 | Question: 44
In the following C function, let $n \geq m$. int gcd(n,m) { if (n%m == 0) return m; n = n%m; return gcd(m,n); } How many recursive calls are made by this function? $\Theta(\log_2n)$ $\Omega(n)$ $\Theta(\log_2\log_2n)$ $\Theta(\sqrt{n})$

In the following C function, let $n \geq m$.int gcd(n,m) { if (n%m == 0) return m; n = n%m; return gcd(m,n); }How many recursive calls are made by this function?$\Theta(\...

Kathleen

26.7k views

Kathleen asked Sep 21, 2014

31 votes

8 answers

45

GATE CSE 2007 | Question: 43
A complete $n-ary$ tree is a tree in which each node has $n$ children or no children. Let $I$ be the number of internal nodes and $L$ be the number of leaves in a complete $n-ary$ tree. If $L = 41$ and $I = 10$, what is the value of $n$? $3$ $4$ $5$ $6$

A complete $n-ary$ tree is a tree in which each node has $n$ children or no children. Let $I$ be the number of internal nodes and $L$ be the number of leaves in a complet...

Kathleen

26.0k views

Kathleen asked Sep 21, 2014

26 votes

1 answer

46

GATE CSE 2007 | Question: 42
Consider the following C function: int f(int n) { static int r = 0; if (n <= 0) return 1; if (n > 3) { r = n; return f(n-2) + 2; } return f(n-1) + r; } What is the value of $f(5)$? $5$ $7$ $9$ $18$

Consider the following C function:int f(int n) { static int r = 0; if (n <= 0) return 1; if (n 3) { r = n; return f(n-2) + 2; } return f(n-1) + r; }What is the value of ...

Kathleen

10.4k views

Kathleen asked Sep 21, 2014

36 votes

5 answers

47

GATE CSE 2007 | Question: 41
In an unweighted, undirected connected graph, the shortest path from a node $S$ to every other node is computed most efficiently, in terms of time complexity, by Dijkstra’s algorithm starting from $S$. Warshall’s algorithm. Performing a DFS starting from $S$. Performing a BFS starting from $S$.

In an unweighted, undirected connected graph, the shortest path from a node $S$ to every other node is computed most efficiently, in terms of time complexity, byDijkstra�...

Kathleen

18.6k views

Kathleen asked Sep 21, 2014

26 votes

3 answers

48

GATE CSE 2007 | Question: 40
Consider a hash table of size seven, with starting index zero, and a hash function $(3x + 4)\mod 7$. Assuming the hash table is initially empty, which of the following is the contents of the table when the sequence $1, 3, 8, 10$ is inserted into the table using closed hashing? Note that − denotes an ... $3$ $1$, −, −, −, −, −, $3$ $1, 10, 8$, −, −, −,$ 3$

Consider a hash table of size seven, with starting index zero, and a hash function $(3x + 4)\mod 7$. Assuming the hash table is initially empty, which of the following is...

Kathleen

16.0k views

Kathleen asked Sep 21, 2014

17 votes

3 answers

49

GATE CSE 2007 | Question: 39, UGCNET-June2015-II: 22
The inorder and preorder traversal of a binary tree are $\text{d b e a f c g}$ and $\text{a b d e c f g}$, respectively The postorder traversal of the binary tree is: $\text{d e b f g c a}$ $\text{e d b g f c a}$ $\text{e d b f g c a}$ $\text{d e f g b c a}$

The inorder and preorder traversal of a binary tree are$\text{d b e a f c g}$ and $\text{a b d e c f g}$, respectivelyThe postorder traversal of the binary tree is:$\text...

Kathleen

7.8k views

Kathleen asked Sep 21, 2014

33 votes

4 answers

50

GATE CSE 2007 | Question: 38, ISRO2016-27
The following postfix expression with single digit operands is evaluated using a stack: $8 \ 2 \ 3 \ {}^\hat{} ∕ \ 2 \ 3 * + 5 \ 1 * -$ Note that $^\hat{}$ is the exponentiation operator. The top two elements of the stack after the first $*$ is evaluated are $6, 1$ $5, 7$ $3, 2$ $1, 5$

The following postfix expression with single digit operands is evaluated using a stack:$$8 \ 2 \ 3 \ {}^\hat{} ∕ \ 2 \ 3 * + 5 \ 1 * -$$Note that $^\hat{}$ is the ex...

Kathleen

16.6k views

Kathleen asked Sep 21, 2014

32 votes

4 answers

51

GATE CSE 2007 | Question: 37, ISRO2009-37
Consider a pipelined processor with the following four stages: IF: Instruction Fetch ID: Instruction Decode and Operand Fetch EX: Execute WB: Write Back The IF, ID and WB stages take one clock cycle each to complete the operation. The number of clock cycles for the EX ... $ R5$-$R4} \\ \end{array}$ $7$ $8$ $10$ $14$

Consider a pipelined processor with the following four stages:IF: Instruction FetchID: Instruction Decode and Operand FetchEX: ExecuteWB: Write BackThe IF, ID and WB stag...

Kathleen

16.1k views

Kathleen asked Sep 21, 2014

66 votes

6 answers

52

GATE CSE 2007 | Question: 36
The control signal functions of a $4$-$bit$ binary counter are given below (where $X$ ... through the following sequence: $0, 3, 4$ $0, 3, 4, 5$ $0, 1, 2, 3, 4$ $0, 1, 2, 3, 4, 5$

The control signal functions of a $4$-$bit$ binary counter are given below (where $X$ is “don’t care”):$$\small {\begin{array}{|c|c|c|c|l|}\hline\textbf{Clear}& ...

Kathleen

19.5k views

Kathleen asked Sep 21, 2014

57 votes

3 answers

53

GATE CSE 2007 | Question: 35
In a look-ahead carry generator, the carry generate function $G_i$ and the carry propagate function $P_i$ for inputs $A_i$ and $B_i$ are given by: $P_i = A_i \oplus B_i \text{ and }G_i = A_iB_i$ The expressions for the sum bit $S_i$ and the carry bit $C_{i+1}$ of ... with $S_3, S_2, S_1, S_0$ and $C_4$ as its outputs are respectively: $6, 3$ $10, 4$ $6, 4$ $10, 5$

In a look-ahead carry generator, the carry generate function $G_i$ and the carry propagate function $P_i$ for inputs $A_i$ and $B_i$ are given by:$$P_i = A_i \oplus B_i \...

Kathleen

12.9k views

Kathleen asked Sep 21, 2014

68 votes

9 answers

54

GATE CSE 2007 | Question: 34
Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of $n$ variables. What is the minimum size of the multiplexer needed? $2^n$ line to $1$ line $2^{n+1}$ line to $1$line $2^{n-1}$ line to $1$line $2^{n-2}$ line to $1$line

Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of $n$ variables. What is the minimum size of the multiplexer neede...

Kathleen

31.6k views

Kathleen asked Sep 21, 2014

42 votes

5 answers

55

GATE CSE 2007 | Question: 33
Define the connective $*$ for the Boolean variables $X$ and $Y$ as: $X * Y = XY + X'Y'.$ Let $Z = X * Y$. Consider the following expressions $P$, $Q$ and $R$. $P : X = Y * Z, \\ Q :Y = X * Z, \\ R : X *Y * Z = 1$ Which of the following is TRUE? Only $P$ and $Q$ are valid. Only $Q$ and $R$ are valid. Only $P$ and $R$ are valid. All $P$, $Q$, $R$ are valid.

Define the connective $*$ for the Boolean variables $X$ and $Y$ as: $$X * Y = XY + X'Y'.$$ Let $Z = X * Y$. Consider the following expressions $P$, $Q$ and $R$.$$P : X = ...

Kathleen

9.0k views

Kathleen asked Sep 21, 2014

43 votes

6 answers

56

GATE CSE 2007 | Question: 32
Let $f(w, x, y, z) = \sum {\left(0,4,5,7,8,9,13,15\right)}$. Which of the following expressions are NOT equivalent to $f$? P: $x'y'z' + w'xy' + wy'z + xz$ Q: $w'y'z' + wx'y' + xz$ ... $x'y'z' + wx'y'+ w'y$ P only Q and S R and S S only

Let $f(w, x, y, z) = \sum {\left(0,4,5,7,8,9,13,15\right)}$. Which of the following expressions are NOT equivalent to $f$?P: $x'y'z' + w'xy' + wy'z + xz$Q: $w'y'z' + wx'y...

Kathleen

10.5k views

Kathleen asked Sep 21, 2014

39 votes

2 answers

57

GATE CSE 2007 | Question: 31
Which of the following languages is regular? $\left\{ww^R \mid w \in \{0, 1\}^+\right\}$ $\left\{ww^Rx \mid x,w \in \{0, 1\}^+\right\}$ $\left\{wxw^R \mid x, w \in \{0, 1\}^+\right\}$ $\left\{xww^R \mid x, w \in \{0, 1\}^+\right\}$

Which of the following languages is regular?$\left\{ww^R \mid w \in \{0, 1\}^+\right\}$$\left\{ww^Rx \mid x,w \in \{0, 1\}^+\right\}$$\left\{wxw^R \mid x, w \in \{0, 1\}...

Kathleen

14.2k views

Kathleen asked Sep 21, 2014

26 votes

4 answers

58

GATE CSE 2007 | Question: 30
The language $L=\left\{0^i21^i \mid i \geq 0\right\}$ over the alphabet $\left\{0, 1, 2\right\}$ is: not recursive is recursive and is a deterministic CFL is a regular language is not a deterministic CFL but a CFL

The language $L=\left\{0^i21^i \mid i \geq 0\right\}$ over the alphabet $\left\{0, 1, 2\right\}$ is:not recursiveis recursive and is a deterministic CFLis a regular langu...

Kathleen

8.4k views

Kathleen asked Sep 21, 2014

32 votes

4 answers

59

GATE CSE 2007 | Question: 29
A minimum state deterministic finite automaton accepting the language $L=\{w\mid w \in \{0, 1\}^*,$ number of $0$s and $1$s in $w$ are divisible by $3$ and $5$, respectively $\}$ has $15$ states $11$ states $10$ states $9$ states

A minimum state deterministic finite automaton accepting the language$L=\{w\mid w \in \{0, 1\}^*,$ number of $0$s and $1$s in $w$ are divisible by $3$ and $5$, respective...

Kathleen

11.6k views

Kathleen asked Sep 21, 2014

1 votes

0 answers

60

GATE CSE 2007 | Question: 28
Consider the series $x_{n+1} = \frac{x_n}{2}+\frac{9}{8x_n},x_0 = 0.5$ obtained from the Newton-Raphson method. The series converges to 1.5 $\sqrt{2}$ 1.6 1.4

Consider the series $x_{n+1} = \frac{x_n}{2}+\frac{9}{8x_n},x_0 = 0.5$ obtained from the Newton-Raphson method. The series converges to1.5$\sqrt{2}$1.61.4

Kathleen

1.0k views

Kathleen asked Sep 21, 2014

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