Recent questions tagged gate2007

20 votes

2 answers

1

GATE2007-29
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 $5$, respectively $\}$ has $15$ states $11$ states $10$ states $9$ states

asked Sep 22, 2014 in Theory of Computation Kathleen 3.1k views

1 vote

0 answers

2

GATE2007-28
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 to 1.5 $\sqrt{2}$ 1.6 1.4

asked Sep 22, 2014 in IS&Software Engineering Kathleen 360 views

20 votes

4 answers

3

GATE2007-27
Consider the set of (column) vectors defined by$X = \left \{x \in R^3 \mid x_1 + x_2 + x_3 = 0, \text{ where } x^T = \left[x_1,x_2,x_3\right]^T\right \}$ ... a linearly independent set, but it does not span $X$ and therefore is not a basis of $X$. $X$ is not a subspace of $R^3$. None of the above

Consider the set of (column) vectors defined by$X = \left \{x \in R^3 \mid x_1 + x_2 + x_3 = 0, \text{ where } x^T = \left[x_1,x_2,x_3\right]^T\right \}$.Which of the following is TRUE? $\left\{\left[1,-1,0\right]^T,\left[1,0,-1\right]^T\right\}$ is a ... is a linearly independent set, but it does not span $X$ and therefore is not a basis of $X$. $X$ is not a subspace of $R^3$. None of the above

asked Sep 22, 2014 in Linear Algebra Kathleen 4.6k views

30 votes

1 answer

4

GATE2007-26
Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on $S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overline{cd}\},$ ... $π_i \prec π_j$ if and only if $π_i$ refines $π_j$. The poset diagram for $(S',\prec)$ is:

Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on $S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overline{cd}\},$ ... $S' = \{π_1,π_2,π_3,π_4\}$ defined as follows: $π_i \prec π_j$ if and only if $π_i$ refines $π_j$. The poset diagram for $(S',\prec)$ is:

asked Sep 22, 2014 in Set Theory & Algebra Kathleen 4.7k views

26 votes

8 answers

5

GATE2007-24
Suppose we uniformly and randomly select a permutation from the $20 !$ permutations of $1, 2, 3\ldots ,20.$ What is the probability that $2$ appears at an earlier position than any other even number in the selected permutation? $\left(\dfrac{1}{2} \right)$ $\left(\dfrac{1}{10}\right)$ $\left(\dfrac{9!}{20!}\right)$ None of these

Suppose we uniformly and randomly select a permutation from the $20 !$ permutations of $1, 2, 3\ldots ,20.$ What is the probability that $2$ appears at an earlier position than any other even number in the selected permutation? $\left(\dfrac{1}{2} \right)$ $\left(\dfrac{1}{10}\right)$ $\left(\dfrac{9!}{20!}\right)$ None of these

asked Sep 22, 2014 in Probability Kathleen 5.7k views

44 votes

5 answers

6

GATE2007-23
Which of the following graphs has an Eulerian circuit? Any $k$-regular graph where $k$ is an even number. A complete graph on $90$ vertices. The complement of a cycle on $25$ vertices. None of the above

Which of the following graphs has an Eulerian circuit? Any $k$-regular graph where $k$ is an even number. A complete graph on $90$ vertices. The complement of a cycle on $25$ vertices. None of the above

asked Sep 22, 2014 in Graph Theory Kathleen 7.2k views

25 votes

6 answers

7

GATE2007-22
$\def\graph{\text{ Graph}} \def\connected{\text{ Connected}}$ Let $\graph(x)$ be a predicate which denotes that $x$ is a graph. Let $\connected(x)$ be a predicate which denotes that $x$ is connected. Which of the following first order logic sentences DOES NOT represent the ... $\forall x \, \Bigl ( \graph(x) \implies \lnot \connected(x) \Bigr )$

$\def\graph{\text{ Graph}} \def\connected{\text{ Connected}}$ Let $\graph(x)$ be a predicate which denotes that $x$ is a graph. Let $\connected(x)$ be a predicate which denotes that $x$ is connected. Which of the following first order logic sentences DOES NOT represent the statement: ... $\forall x \, \Bigl ( \graph(x) \implies \lnot \connected(x) \Bigr )$

asked Sep 22, 2014 in Mathematical Logic Kathleen 3.5k views

28 votes

4 answers

8

GATE2007-21
How many different non-isomorphic Abelian groups of order $4$ are there? $2$ $3$ $4$ $5$

How many different non-isomorphic Abelian groups of order $4$ are there? $2$ $3$ $4$ $5$

asked Sep 22, 2014 in Set Theory & Algebra Kathleen 7.2k views

25 votes

6 answers

9

GATE2007-20
Which one of the following uses UDP as the transport protocol? HTTP Telnet DNS SMTP

Which one of the following uses UDP as the transport protocol? HTTP Telnet DNS SMTP

asked Sep 22, 2014 in Computer Networks Kathleen 2.8k views

11 votes

3 answers

10

GATE2007-19
In Ethernet when Manchester encoding is used, the bit rate is: Half the baud rate Twice the baud rate Same as the baud rate None of the above

In Ethernet when Manchester encoding is used, the bit rate is: Half the baud rate Twice the baud rate Same as the baud rate None of the above

asked Sep 22, 2014 in Computer Networks Kathleen 4.4k views

12 votes

4 answers

11

GATE2007-18
Which one of the following is a top-down parser? Recursive descent parser. Operator precedence parser. An LR(k) parser. An LALR(k) parser.

Which one of the following is a top-down parser? Recursive descent parser. Operator precedence parser. An LR(k) parser. An LALR(k) parser.

asked Sep 22, 2014 in Compiler Design Kathleen 2.5k views

24 votes

2 answers

12

GATE2007-17
Consider the following statements about user level threads and kernel level threads. Which one of the following statements is FALSE? Context switch time is longer for kernel level threads than for user level threads. User level threads do not need any ... can be scheduled on different processors in a multi-processor system. Blocking one kernel level thread blocks all related threads.

Consider the following statements about user level threads and kernel level threads. Which one of the following statements is FALSE? Context switch time is longer for kernel level threads than for user level threads. User level threads do not need any ... threads can be scheduled on different processors in a multi-processor system. Blocking one kernel level thread blocks all related threads.

asked Sep 22, 2014 in Operating System Kathleen 4.6k views

24 votes

2 answers

13

GATE2007-16
Group 1 contains some CPU scheduling algorithms and Group 2 contains some applications. Match entries in Group 1 to entries in Group 2. ... $P-3; Q-2; R-1$ $P-1; Q-2; R-3$ $P-2; Q-3; R-1$ $P-1; Q-3; R-2$

Group 1 contains some CPU scheduling algorithms and Group 2 contains some applications. Match entries in Group 1 to entries in Group 2. ... $P-3; Q-2; R-1$ $P-1; Q-2; R-3$ $P-2; Q-3; R-1$ $P-1; Q-3; R-2$

asked Sep 22, 2014 in Operating System Kathleen 4k views

15 votes

4 answers

14

GATE2007-14
Which of the following sorting algorithms has the lowest worse-case complexity? Merge sort Bubble sort Quick sort Selection sort

Which of the following sorting algorithms has the lowest worse-case complexity? Merge sort Bubble sort Quick sort Selection sort

asked Sep 22, 2014 in Algorithms Kathleen 2.4k views

21 votes

2 answers

15

GATE2007-13
The maximum number of binary trees that can be formed with three unlabeled nodes is: $1$ $5$ $4$ $3$

The maximum number of binary trees that can be formed with three unlabeled nodes is: $1$ $5$ $4$ $3$

asked Sep 22, 2014 in DS Kathleen 6.5k views

16 votes

4 answers

16

GATE2007-12
The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height $h$ is: $2^h -1$ $2^{h-1} -1$ $2^{h+1} -1$ $2^{h+1}$

The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height $h$ is: $2^h -1$ $2^{h-1} -1$ $2^{h+1} -1$ $2^{h+1}$

asked Sep 22, 2014 in DS Kathleen 6.5k views

19 votes

4 answers

17

GATE2007-11, ISRO2009-36, ISRO2016-21
Consider a disk pack with $16$ surfaces, $128$ tracks per surface and $256$ sectors per track. $512$ bytes of data are stored in a bit serial manner in a sector. The capacity of the disk pack and the number of bits required to specify a particular sector in ... : $256$ Mbyte, $19$ bits $256$ Mbyte, $28$ bits $512$ Mbyte, $20$ bits $64$ Gbyte, $28$ bits

Consider a disk pack with $16$ surfaces, $128$ tracks per surface and $256$ sectors per track. $512$ bytes of data are stored in a bit serial manner in a sector. The capacity of the disk pack and the number of bits required to specify a particular sector in the disk are respectively: $256$ Mbyte, $19$ bits $256$ Mbyte, $28$ bits $512$ Mbyte, $20$ bits $64$ Gbyte, $28$ bits

asked Sep 22, 2014 in Operating System Kathleen 9k views

16 votes

1 answer

18

GATE2007-10
Consider a $4$-way set associative cache consisting of $128$ lines with a line size of $64$ words. The CPU generates a $20-bit$ address of a word in main memory. The number of bits in the TAG, LINE and WORD fields are respectively: $9, 6, 5$ $7, 7, 6$ $7, 5, 8$ $9, 5, 6$

Consider a $4$-way set associative cache consisting of $128$ lines with a line size of $64$ words. The CPU generates a $20-bit$ address of a word in main memory. The number of bits in the TAG, LINE and WORD fields are respectively: $9, 6, 5$ $7, 7, 6$ $7, 5, 8$ $9, 5, 6$

asked Sep 22, 2014 in CO and Architecture Kathleen 4.3k views

14 votes

1 answer

19

GATE2007-9
Consider the following Boolean function of four variables: $f(w, x, y, z) = \Sigma(1, 3, 4, 6, 9, 11, 12, 14)$ The function is independent of one variables. independent of two variables. independent of three variables. dependent on all variables

Consider the following Boolean function of four variables: $f(w, x, y, z) = \Sigma(1, 3, 4, 6, 9, 11, 12, 14)$ The function is independent of one variables. independent of two variables. independent of three variables. dependent on all variables

asked Sep 22, 2014 in Digital Logic Kathleen 1.2k views

20 votes

5 answers

20

GATE2007-8, ISRO2011-31
How many $3$-to-$8$ line decoders with an enable input are needed to construct a $6$-to-$64$ line decoder without using any other logic gates? $7$ $8$ $9$ $10$

How many $3$-to-$8$ line decoders with an enable input are needed to construct a $6$-to-$64$ line decoder without using any other logic gates? $7$ $8$ $9$ $10$

asked Sep 22, 2014 in Digital Logic Kathleen 8.6k views

27 votes

2 answers

21

GATE2007-7
Which of the following is TRUE? Every subset of a regular set is regular Every finite subset of a non-regular set is regular The union of two non-regular sets is not regular Infinite union of finite sets is regular

Which of the following is TRUE? Every subset of a regular set is regular Every finite subset of a non-regular set is regular The union of two non-regular sets is not regular Infinite union of finite sets is regular

asked Sep 22, 2014 in Theory of Computation Kathleen 4.6k views

19 votes

2 answers

22

GATE2007-6
Which of the following problems is undecidable? Membership problem for CFGs Ambiguity problem for CFGs Finiteness problem for FSAs Equivalence problem for FSAs

Which of the following problems is undecidable? Membership problem for CFGs Ambiguity problem for CFGs Finiteness problem for FSAs Equivalence problem for FSAs

asked Sep 22, 2014 in Theory of Computation Kathleen 2.1k views

16 votes

3 answers

23

GATE2007-4
Let $G$ be the non-planar graph with the minimum possible number of edges. Then $G$ has 9 edges and 5 vertices 9 edges and 6 vertices 10 edges and 5 vertices 10 edges and 6 vertices

Let $G$ be the non-planar graph with the minimum possible number of edges. Then $G$ has 9 edges and 5 vertices 9 edges and 6 vertices 10 edges and 5 vertices 10 edges and 6 vertices

asked Sep 22, 2014 in Graph Theory Kathleen 3.6k views

25 votes

4 answers

24

GATE2007-3
What is the maximum number of different Boolean functions involving $n$ Boolean variables? $n^2$ $2^n$ $2^{2^n}$ $2^{n^2}$

What is the maximum number of different Boolean functions involving $n$ Boolean variables? $n^2$ $2^n$ $2^{2^n}$ $2^{n^2}$

asked Sep 22, 2014 in Set Theory & Algebra Kathleen 2.7k views

19 votes

2 answers

25

GATE2007-2
Let $S$ be a set of $n$ elements. The number of ordered pairs in the largest and the smallest equivalence relations on $S$ are: $n$ and $n$ $n^2$ and $n$ $n^2$ and $0$ $n$ and $1$

Let $S$ be a set of $n$ elements. The number of ordered pairs in the largest and the smallest equivalence relations on $S$ are: $n$ and $n$ $n^2$ and $n$ $n^2$ and $0$ $n$ and $1$

asked Sep 22, 2014 in Set Theory & Algebra Kathleen 3k views

9 votes

2 answers

26

GATE2007-1
Consider the following two statements about the function $f(x)=\left\vert x\right\vert$: P. $f(x)$ is continuous for all real values of $x$. Q. $f(x)$ is differentiable for all real values of $x$ . Which of the following is TRUE? $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are true. Both $P$ and $Q$ are false.

Consider the following two statements about the function $f(x)=\left\vert x\right\vert$: P. $f(x)$ is continuous for all real values of $x$. Q. $f(x)$ is differentiable for all real values of $x$ . Which of the following is TRUE? $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are true. Both $P$ and $Q$ are false.

asked Sep 22, 2014 in Calculus Kathleen 2k views

44 votes

3 answers

27

GATE2007-25
Let A be a $4 \times 4$ matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $I$ is the $4 \times 4$ identity matrix? $-5$ $-7$ $2$ $1$

Let A be a $4 \times 4$ matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $I$ is the $4 \times 4$ identity matrix? $-5$ $-7$ $2$ $1$

asked Sep 2, 2014 in Linear Algebra priya 4.6k views

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