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Recent questions tagged gatecse-2003
89
votes
12
answers
31
GATE CSE 2003 | Question: 64
Let S be a stack of size $n \geq1$. Starting with the empty stack, suppose we push the first n natural numbers in sequence, and then perform $n$ pop operations. Assume that Push and Pop operations take $X$ seconds each, and $Y$ seconds elapse between the end of one such ... S. The average stack-life of an element of this stack is $n(X+Y)$ $3Y+2X$ $n(X+Y)-X$ $Y+2X$
Kathleen
asked
in
DS
Sep 17, 2014
by
Kathleen
30.8k
views
gatecse-2003
data-structures
stack
normal
65
votes
4
answers
32
GATE CSE 2003 | Question: 63, ISRO2009-25
A data structure is required for storing a set of integers such that each of the following operations can be done in $O(\log n)$ time, where $n$ is the number of elements in the set. Deletion of the smallest element Insertion of an ... used but not a heap Both balanced binary search tree and heap can be used Neither balanced search tree nor heap can be used
Kathleen
asked
in
DS
Sep 17, 2014
by
Kathleen
20.2k
views
gatecse-2003
data-structures
easy
isro2009
binary-search-tree
66
votes
12
answers
33
GATE CSE 2003 | Question: 61
In a permutation \(a_1 ... a_n\), of n distinct integers, an inversion is a pair \((a_i, a_j)\) such that \(i < j\) and \(a_i > a_j\). If all permutations are equally likely, what is the expected number of inversions in a randomly chosen permutation of \(1. . . n\)? \(\frac{n(n-1)}{2}\) \(\frac{n(n-1)}{4}\) \(\frac{n(n+1)}{4}\) \(2n[\log_2n]\)
Kathleen
asked
in
Algorithms
Sep 17, 2014
by
Kathleen
20.3k
views
gatecse-2003
algorithms
sorting
inversion
normal
42
votes
5
answers
34
GATE CSE 2003 | Question: 60, ISRO2007-45
A program consists of two modules executed sequentially. Let $f_1(t)$ and $f_2(t)$ ... $\int_0^t f_1(x)f_2(t-x)dx$ $\max\{f_1(t),f_2(t)\}$
Kathleen
asked
in
Probability
Sep 17, 2014
by
Kathleen
9.1k
views
gatecse-2003
probability
normal
isro2007
probability-density-function
32
votes
4
answers
35
GATE CSE 2003 | Question: 59
Consider the syntax directed definition shown below. ... $t_1 = Y+Z; X=t_1$ $t_1 =Y; t_2=t_1 +Z; X=t_2$ $t_1 =Y; t_2=Z; t_3=t_1+t_2; X=t_3$
Kathleen
asked
in
Compiler Design
Sep 17, 2014
by
Kathleen
8.5k
views
gatecse-2003
compiler-design
target-code-generation
normal
39
votes
4
answers
36
GATE CSE 2003 | Question: 58
Consider the translation scheme shown below. $S \rightarrow T\;R$ $R \rightarrow + T \{\text{print}( +');\} R\mid \varepsilon$ $T \rightarrow$ num $\{\text{print}$(num.val)$;\}$ Here num is a token that represents an integer and num.val represents the corresponding integer value. For an ... scheme will print $9 + 5 + 2$ $9 \ 5 + 2 +$ $9 \ 5 \ 2 + +$ $+ + 9 \ 5 \ 2$
Kathleen
asked
in
Compiler Design
Sep 17, 2014
by
Kathleen
12.6k
views
gatecse-2003
compiler-design
grammar
normal
40
votes
3
answers
37
GATE CSE 2003 | Question: 57
Consider the grammar shown below. $S \rightarrow C \ C$ $C \rightarrow c \ C \mid d$ This grammar is LL(1) SLR(1) but not LL(1) LALR(1) but not SLR(1) LR(I) but not LALR(1)
Kathleen
asked
in
Compiler Design
Sep 17, 2014
by
Kathleen
20.0k
views
gatecse-2003
compiler-design
grammar
parsing
normal
34
votes
3
answers
38
GATE CSE 2003 | Question: 56
Consider the grammar shown below $S \rightarrow i E t S S' \mid a$ $S' \rightarrow e S \mid \epsilon$ $E \rightarrow b$ In the predictive parse table, $M,$ of this grammar, the entries $M[S' , e]$ and $M[S' , \$]$ respectively are $\{S' \ ... $\{S' \rightarrow \epsilon\}$ $\{S' \rightarrow e S, S' \rightarrow \varepsilon$} and $\{S' \rightarrow \epsilon\}$
Kathleen
asked
in
Compiler Design
Sep 17, 2014
by
Kathleen
13.2k
views
gatecse-2003
compiler-design
grammar
normal
parsing
45
votes
5
answers
39
GATE CSE 2003 | Question: 55
Consider the NFA $M$ shown below. Let the language accepted by $M$ be $L$. Let $L_1$ be the language accepted by the NFA $M_1$ obtained by changing the accepting state of $M$ to a non-accepting state and by changing the non-accepting states of $M$ to accepting states. Which ... statements is true? $L_1 = \{0,1\}^*-L$ $L_1 = \{0,1\}^*$ $L_1 \subseteq L$ $L_1 = L$
Kathleen
asked
in
Theory of Computation
Sep 17, 2014
by
Kathleen
14.3k
views
gatecse-2003
theory-of-computation
finite-automata
normal
41
votes
5
answers
40
GATE CSE 2003 | Question: 53
A single tape Turing Machine $M$ has two states $q0$ and $q1$, of which $q0$ is the starting state. The tape alphabet of $M$ is $\{0, 1, B\}$ and its input alphabet is $\{0, 1\}$. The symbol $B$ is the blank symbol used to indicate end of an input ... halt on any string in $(00+1)^*$ $M$ halts on all strings ending in a $0$ $M$ halts on all strings ending in a $1$
Kathleen
asked
in
Theory of Computation
Sep 17, 2014
by
Kathleen
11.8k
views
gatecse-2003
theory-of-computation
turing-machine
normal
64
votes
4
answers
41
GATE CSE 2003 | Question: 51
Let $G=\left(\left\{S\right\}, \left\{a,b\right\},R,S\right)$ be a context free grammar where the rule set R is $S \to a S b \mid S S \mid \epsilon$ Which of the following statements is true? $G$ is not ambiguous There ... $L(G)$ We can find a deterministic finite state automaton that accepts $L(G)$
Kathleen
asked
in
Theory of Computation
Sep 17, 2014
by
Kathleen
17.5k
views
gatecse-2003
theory-of-computation
context-free-language
normal
61
votes
7
answers
42
GATE CSE 2003 | Question: 50
Consider the following deterministic finite state automaton $M$. Let $S$ denote the set of seven bit binary strings in which the first, the fourth, and the last bits are $1$. The number of strings in $S$ that are accepted by $M$ is $1$ $5$ $7$ $8$
Kathleen
asked
in
Theory of Computation
Sep 17, 2014
by
Kathleen
14.9k
views
gatecse-2003
theory-of-computation
finite-automata
normal
35
votes
3
answers
43
GATE CSE 2003 | Question: 48
Consider the following assembly language program for a hypothetical processor $A, B,$ and $C$ are $8-$ ... the program execution will be the number of $0$ bits in $A_0$ the number of $1$ bits in $A_0$ $A_0$ $8$
Kathleen
asked
in
CO and Architecture
Sep 17, 2014
by
Kathleen
15.0k
views
gatecse-2003
co-and-architecture
machine-instruction
normal
53
votes
5
answers
44
GATE CSE 2003 | Question: 46
Consider the ALU shown below. If the operands are in $2's$ complement representation, which of the following operations can be performed by suitably setting the control lines $K$ and $C_0$ only (+ and - denote addition and subtraction respectively)? $A + B$, and $A - B$, but not $A + 1$ ... $A + B$, but not $A - B$ or $A + 1$ $A + B$, and $A - B$, and $A + 1$
Kathleen
asked
in
Digital Logic
Sep 17, 2014
by
Kathleen
16.7k
views
gatecse-2003
digital-logic
normal
adder
54
votes
6
answers
45
GATE CSE 2003 | Question: 45
The literal count of a Boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal count of $\left(xy+xz'\right)$ is $4.$ What are the minimum possible literal counts of the product-of-sum and sum-of-product ... ? Here, $X$ denotes "don't care" $(11, 9)$ $(9, 13)$ $(9, 10)$ $(11,11)$
Kathleen
asked
in
Digital Logic
Sep 17, 2014
by
Kathleen
15.9k
views
gatecse-2003
digital-logic
k-map
normal
54
votes
5
answers
46
GATE CSE 2003 | Question: 44
A $\text{1-input}$, $\text{2-output}$ synchronous sequential circuit behaves as follows: Let $z_k, n_k$ denote the number of $0's$ and $1's$ respectively in initial $k$ bits of the input $(z_k+n_k=k)$. The circuit outputs $00$ until one of the ... is $01$. What is the minimum number of states required in the state transition graph of the above circuit? $5$ $6$ $7$ $8$
Kathleen
asked
in
Digital Logic
Sep 17, 2014
by
Kathleen
11.8k
views
gatecse-2003
digital-logic
synchronous-asynchronous-circuits
normal
65
votes
9
answers
47
GATE CSE 2003 | Question: 43
The following is a scheme for floating point number representation using $16$ bits. Let $s, e,$ and $m$ ... between two successive real numbers representable in this system? $2^{-40}$ $2^{-9}$ $2^{22}$ $2^{31}$
Kathleen
asked
in
Digital Logic
Sep 17, 2014
by
Kathleen
18.0k
views
gatecse-2003
digital-logic
number-representation
floating-point-representation
normal
0
votes
0
answers
48
GATE CSE 2003 | Question: 42
A piecewise linear function $f(x)$ is plotted using thick solid lines in the figure below (the plot is drawn to scale). If we use the Newton-Raphson method to find the roots of \(f(x)=0\) using \(x_0, x_1,\) and \(x_2\) respectively as initial guesses, the ... .6 respectively 0.6, 0.6, and 1.3 respectively 1.3, 1.3, and 0.6 respectively 1.3, 0.6, and 1.3 respectively
Kathleen
asked
in
Numerical Methods
Sep 17, 2014
by
Kathleen
1.4k
views
gatecse-2003
numerical-methods
newton-raphson
normal
out-of-syllabus-now
33
votes
4
answers
49
GATE CSE 2003 | Question: 41
Consider the following system of linear equations ... linearly dependent. For how many values of $\alpha$, does this system of equations have infinitely many solutions? \(0\) \(1\) \(2\) \(3\)
Kathleen
asked
in
Linear Algebra
Sep 17, 2014
by
Kathleen
12.1k
views
gatecse-2003
linear-algebra
system-of-equations
normal
65
votes
9
answers
50
GATE CSE 2003 | Question: 40
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-degree of $G$ cannot be $3$ $4$ $5$ $6$
Kathleen
asked
in
Graph Theory
Sep 17, 2014
by
Kathleen
15.6k
views
gatecse-2003
graph-theory
normal
degree-of-graph
44
votes
6
answers
51
GATE CSE 2003 | Question: 39
Let $\Sigma = \left\{a, b, c, d, e\right\}$ be an alphabet. We define an encoding scheme as follows: $g(a) = 3, g(b) = 5, g(c) = 7, g(d) = 9, g(e) = 11$. Let $p_i$ denote the i-th prime number $\left(p_1 = 2\right)$ ... numbers is the encoding, $h$, of a non-empty sequence of strings? $2^73^75^7$ $2^83^85^8$ $2^93^95^9$ $2^{10}3^{10}5^{10}$
Kathleen
asked
in
Set Theory & Algebra
Sep 17, 2014
by
Kathleen
7.5k
views
gatecse-2003
set-theory&algebra
functions
normal
40
votes
10
answers
52
GATE CSE 2003 | Question: 38
Consider the set \(\{a, b, c\}\) with binary operators \(+\) and \(*\) defined as follows: ... $(x, y)$ that satisfy the equations) is $0$ $1$ $2$ $3$
Kathleen
asked
in
Set Theory & Algebra
Sep 17, 2014
by
Kathleen
7.0k
views
gatecse-2003
set-theory&algebra
normal
binary-operation
59
votes
6
answers
53
GATE CSE 2003 | Question: 37
Let \(f : A \to B\) be an injective (one-to-one) function. Define \(g : 2^A \to 2^B\) as: \(g(C) = \left \{f(x) \mid x \in C\right\} \), for all subsets $C$ of $A$. Define \(h : 2^B \to 2^A\) as: \(h(D) = \{x \mid x \in A, f(x) \in D\}\), for all ... always true? \(g(h(D)) \subseteq D\) \(g(h(D)) \supseteq D\) \(g(h(D)) \cap D = \phi\) \(g(h(D)) \cap (B - D) \ne \phi\)
Kathleen
asked
in
Set Theory & Algebra
Sep 16, 2014
by
Kathleen
8.1k
views
gatecse-2003
set-theory&algebra
functions
difficult
60
votes
9
answers
54
GATE CSE 2003 | Question: 36
How many perfect matching are there in a complete graph of $6$ vertices? $15$ $24$ $30$ $60$
Kathleen
asked
in
Graph Theory
Sep 16, 2014
by
Kathleen
43.8k
views
gatecse-2003
graph-theory
graph-matching
normal
52
votes
7
answers
55
GATE CSE 2003 | Question: 35
Consider the following recurrence relation $T(1)=1$ $T(n+1) = T(n)+\lfloor \sqrt{n+1} \rfloor$ for all $n \geq 1$ The value of $T(m^2)$ for $m \geq 1$ is $\frac{m}{6}\left(21m-39\right)+4$ $\frac{m}{6}\left(4m^2-3m+5\right)$ $\frac{m}{2}\left(3m^{2.5}-11m+20\right)-5$ $\frac{m}{6}\left(5m^3-34m^2+137m-104\right)+\frac{5}{6}$
Kathleen
asked
in
Algorithms
Sep 16, 2014
by
Kathleen
13.8k
views
gatecse-2003
algorithms
time-complexity
recurrence-relation
difficult
23
votes
9
answers
56
GATE CSE 2003 | Question: 34
$m$ identical balls are to be placed in $n$ distinct bags. You are given that $m \geq kn$, where $k$ is a natural number $\geq 1$. In how many ways can the balls be placed in the bags if each bag must contain at least $k$ ... $\left( \begin{array}{c} m - kn + n + k - 2 \\ n - k \end{array} \right)$
Kathleen
asked
in
Combinatory
Sep 16, 2014
by
Kathleen
11.3k
views
gatecse-2003
combinatory
balls-in-bins
normal
113
votes
6
answers
57
GATE CSE 2003 | Question: 33
Consider the following formula and its two interpretations \(I_1\) and \(I_2\). \(\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]\) \(I_1\) : Domain: ... I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
Kathleen
asked
in
Mathematical Logic
Sep 16, 2014
by
Kathleen
15.8k
views
gatecse-2003
mathematical-logic
difficult
first-order-logic
59
votes
7
answers
58
GATE CSE 2003 | Question: 32
Which of the following is a valid first order formula? (Here \(\alpha\) and \(\beta\) are first order formulae with $x$ as their only free variable) $((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α ⇒ β]$ $(∀x)[α] ⇒ (∃x)[α ∧ β]$ $((∀x)[α ∨ β] ⇒ (∃x)[α]) ⇒ (∀x)[α]$ $(∀x)[α ⇒ β] ⇒ (((∀x)[α]) ⇒ (∀x)[β])$
Kathleen
asked
in
Mathematical Logic
Sep 16, 2014
by
Kathleen
16.8k
views
gatecse-2003
mathematical-logic
first-order-logic
normal
57
votes
6
answers
59
GATE CSE 2003 | Question: 31
Let $(S, \leq)$ be a partial order with two minimal elements a and b, and a maximum element c. Let P: S \(\to\) {True, False} be a predicate defined on S. Suppose that P(a) = True, P(b) = False and P(x) \(\implies\) P(y) for all $x, y \in S$ satisfying $x \leq y$ ... for all x \(\in\) S such that b ≤ x and x ≠ c P(x) = False for all x \(\in\) S such that a ≤ x and b ≤ x
Kathleen
asked
in
Set Theory & Algebra
Sep 16, 2014
by
Kathleen
11.7k
views
gatecse-2003
set-theory&algebra
partial-order
normal
propositional-logic
42
votes
4
answers
60
GATE CSE 2003 | Question: 30
Consider the following SQL query Select distinct $a_1, a_2, , a_n$ from $r_1, r_2, , r_m$ ... $\Pi_{a_1, a_2, a_n} \sigma_p \left(r_1 \cap r_2 \cap \dots \cap r_m \right)$
Kathleen
asked
in
Databases
Sep 16, 2014
by
Kathleen
8.9k
views
gatecse-2003
databases
relational-algebra
normal
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