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GATE Computer Science 2007 questions and solutions

Recent questions tagged gate2007

20 votes
2 answers
1
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
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
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
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
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
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
$\def\graph{\text{ Graph}} \def\connected{\text{ Connected}}$ 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
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
11 votes
3 answers
10
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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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