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Use the google search bar on side panel. It searches through all previous GATE/other questions. For hardcopy of previous year questions please see
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+2
votes
1
Gateforum mock 2
answered
Aug 12
in
Theory of Computation

78
views
decidability
+1
vote
2
TM Decidablity
Why this statement Turing Machine accepts the null string epsilon ? is not Decidable ? explain with an example.
answered
Aug 7
in
Theory of Computation

587
views
theoryofcomputation
turingmachine
0
votes
3
GATE199773
A concurrent system consists of $3$ processes using a shared resource $R$ in a nonpreemptible and mutually exclusive manner. The processes have unique priorities in the range $1 \dots 3$, $3$ being the highest priority. It is required to synchronize the processes ... ]:=true; else begin V(proceed [priority]); busy:=true; end V(mutex) Give the pseudo code for the procedure release_R.
answered
Jul 15
in
Operating System

414
views
gate1997
operatingsystem
processsynchronization
+1
vote
4
GATE19889iii
In the program scheme given below indicate the instructions containing any operand needing relocation for position independent behaviour. Justify your answer. ...
answered
Jul 15
in
CO and Architecture

127
views
gate1988
normal
descriptive
coandarchitecture
addressingmodes
+1
vote
5
GATE19936.2
If the state machine described in figure should have a stable state, the restriction on the inputs is given by $a.b=1$ $a+b=1$ $\bar{a} + \bar{b} =0$ $\overline{a.b}=1$ $\overline{a+b} =1$
answered
Jul 14
in
Digital Logic

1.5k
views
gate1993
digitallogic
normal
circuitoutput
0
votes
6
GATE2014133
Assume that there are $3$ page frames which are initially empty. If the page reference string is $\text{1, 2, 3, 4, 2, 1, 5, 3, 2, 4, 6}$ the number of page faults using the optimal replacement policy is__________.
answered
Jul 14
in
Operating System

1.4k
views
gate20141
operatingsystem
pagereplacement
numericalanswers
+2
votes
7
GATE198811
A number of processes could be in a deadlock state if none of them can execute due to nonavailability of sufficient resources. Let $P_i, 0 \leq i \leq 4$ represent five processes and let there be four resources types $r_j, 0 \leq j \leq 3$. Suppose the following data ... Is the system currently in a safe state? If yes, explain why.
answered
Jul 14
in
Operating System

558
views
gate1988
normal
descriptive
operatingsystem
resourceallocation
0
votes
8
GATE199772
Following floating point number format is given $f$ is a fraction represented by a $6bit$ mantissa (includes sign bit) in sign magnitude form, $e$ is a $4bit$ exponent (includes sign hit) in sign magnitude form and $n=(f, e) = f. 2^e$ is a ... point addition of $A$ and $B.$ What is the percentage error (up to one position beyond decimal point) in the addition operation in (b)?
answered
Jul 13
in
Digital Logic

387
views
gate1997
digitallogic
floatingpointrepresentation
normal
+2
votes
9
GATE2014245
The value of a $\text{float}$ type variable is represented using the singleprecision $\text{32bit}$ floating point format of $IEEE754$ standard that uses $1$ $\text{bit}$ for sign, $\text{8 bits}$ ... is assigned the decimal value of $−14.25$. The representation of $X$ in hexadecimal notation is $C1640000H$ $416C0000H$ $41640000H$ $C16C0000H$
answered
Jul 13
in
Digital Logic

2.6k
views
gate20142
digitallogic
numberrepresentation
normal
ieeerepresentation
+1
vote
10
GATE19883ab
The Karnaugh map of a function of (A, B, C) is shown on the left hand side of the above figure. The reduced form of the same map is shown on the right hand side, in which the variable C is entered in the map itself. Discuss, The methodology by ... the reduced map has been derived and the rules (or steps) by which the boolean function can be derived from the entries in the reduced map.
answered
Jul 13
in
Digital Logic

201
views
gate1988
descriptive
digitallogic
kmap
+8
votes
11
GATE200361
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 \(1. . . n\)? \(\frac{n(n1)}{2}\) \(\frac{n(n1)}{4}\) \(\frac{n(n+1)}{4}\) \(2n[\log_2n]\)
answered
Jul 6
in
Algorithms

4.6k
views
gate2003
algorithms
sorting
normal
+1
vote
12
GATE199325
A simple Pascal like language has only three statements. assignment statement e.g. x:=expression loop construct e.g. for i:=expression to expression do statement sequencing e.g. begin statement ;…; statement end Write a contextfree grammar (CFG) for statements in the ... in CFG. Show the parse tree for the following statements: for j:=2 to 10 do begin x:=expr1; y:=expr2; end
answered
Jul 6
in
Compiler Design

327
views
gate1993
compilerdesign
parsing
normal
0
votes
13
GATE199011a
What does the following program output? program module (input, output); var a:array [1...5] of integer; i, j: integer; procedure unknown (var b: integer, var c: integer); var i:integer; begin for i := 1 to 5 do a[i] := i; b:= 0; c := 0 for i := 1 to 5 do write (a[i]); writeln(); a[3 ... b); b := 5; c := 6; end; begin i:=1; j:=3; unknown (a[i], a[j]); for i:=1 to 5 do write (a[i]); end;
answered
Jul 6
in
Compiler Design

258
views
gate1990
descriptive
compilerdesign
runtimeenvironments
parameterpassing
0
votes
14
TIFR2012B20
This question concerns the classes $P$ and $NP.$ If you are familiar with them, you may skip the definitions and go directly to the question. Let $L$ be a set. We say that $L$ is in $P$ if there is some algorithm which given input $x$ decides if $x$ is in $L$ ... $\text{MATCH} \notin P\text{ and } \overline{\text{MATCH}} \notin P$ none of the above
answered
Jul 6
in
Algorithms

218
views
tifr2012
algorithms
pnpnpcnph
+2
votes
15
TIFR2019B8
Consider the following program fragment: var a,b : integer; procedure G(c,d: integer); begin c:=cd; d:=c+d; c:=dc end; a:=2; b:=3; G(a,b); If both parameters to $G$ are passed by reference, what are the values of $a$ and $b$ at the end of the above program fragment ? $a=0$ and $b=2$ $a=3$ and $b=2$ $a=2$ and $b=3$ $a=1$ and $b=5$ None of the above
answered
Jul 6
in
Programming

171
views
tifr2019
programming
parameterpassing
0
votes
16
GATE19882viii
State the halting problem of the Turing machine.
answered
Jul 4
in
Theory of Computation

137
views
gate1988
theoryofcomputation
descriptive
decidability
0
votes
17
GATE19877a
List the invariant assertions at points $A, B, C, D$ and $E$ in program given below: Program division (input, output) Const dividend = 81; divisor = 9; Var remainder, quotient:interger begin (*(dividend >= 0) AND (divisor > 0)*) remainder := dividend; quotient := ... := remainder  divisor; (*C*) end; (*D*) quotient := quotient  1; remainder := remainder + divisor; (*E*) end
answered
Jul 4
in
Programming

266
views
gate1987
programming
loopinvariants
0
votes
18
GATE19886i
Given below is the sketch of a program that represents the path in a twoperson game tree by the sequence of active procedure calls at any time. The program assumes that the payoffs are real number in a limited range; that the constant INF is larger ... end; (search) Comment on the working principle of the above program. Suggest a possible mechanism for reducing the amount of search.
answered
Jul 3
in
Algorithms

153
views
gate1988
normal
descriptive
algorithms
timecomplexity
+4
votes
19
GATE2015245
Suppose you are provided with the following function declaration in the C programming language. int partition(int a[], int n); The function treats the first element of $a[\:]$ as a pivot and rearranges the array so that all elements less than or equal to the pivot is in the left part of the ... $(a, $ left_end$, k)$ $(a, n$left_end$1, k$left_end$1)$ and $(a, $left_end$, k)$
answered
Jul 2
in
Algorithms

3.6k
views
gate20152
algorithms
normal
sorting
+1
vote
20
GATE19888i
Consider the procedure declaration: Procedure P (k: integer) where the parameter passing mechanism is callbyvalueresult. Is it correct if the call, P (A[i]), where A is an array and i an integer, is implemented as below. create a new local variable, say z; ... body of P using z for k; set A [i] to z; Explain your answer. If this is incorrect implementation, suggest a correct one.
answered
Jun 30
in
Compiler Design

316
views
gate1988
descriptive
compilerdesign
runtimeenvironments
parameterpassing
0
votes
21
GATE19923,i
Write short answers to the following: (i). Which of the following macros can put a macro assembler into an infinite loop? .MACRO MI,X .IF EQ,X M1 X+1 .ENDC .IF NE,X .WORD X .ENDC .ENDM .MACRO M2,X .IF EQ,X M2 X .ENDC .IF NE,X .WORD X+1 .ENDC .ENDM Give an example call that does so.
answered
Jun 30
in
Compiler Design

353
views
gate1992
compilerdesign
assembler
normal
+2
votes
22
GATE19903v
Choose the correct alternatives (More than one may be correct). The complexity of comparision based sorting algorithms is: $\Theta (n \log n)$ $\Theta (n)$ $\Theta \left(n^2\right)$ $\Theta (n\sqrt n)$
answered
Jun 27
in
Algorithms

336
views
gate1990
normal
algorithms
sorting
0
votes
23
TIFR2015A9
Consider a square of side length $2$. We throw five points into the square. Consider the following statements: There will always be three points that lie on a straight line. There will always be a line connecting a pair of points such that two points lie on one side of the line and one ... above is true: $(i)$ only. $(ii)$ only. $(iii)$ only. $(ii)$ and $(iii)$. None of the above.
answered
Jun 20
in
Numerical Ability

262
views
tifr2015
geometry
numericalability
easy
0
votes
24
TIFR2018A11
We are given a (possibly empty) set of objects. Each object in the set is colored either black or white, is shaped either circular or rectangular, and has a profile that is either fat or thin, Those properties obey the following principles: Each white object is also circular ... $(i) \text{ and } (iii)$ only None of the statements must be TRUE All of the statements must be TRUE
answered
Jun 19
in
Numerical Ability

277
views
tifr2018
numericalability
logicalreasoning
+1
vote
25
TIFR2014A18
We are given a collection of real numbers where a real number $a_{i}\neq 0$ occurs $n_{i}$ times. Let the collection be enumerated as $\left\{x_{1}, x_{2},...x_{n}\right\}$ so that $x_{1}=x_{2}=...=x_{n_{1}}=a_{1}$ and so on, and $n=\sum _{i}n_{i}$ is finite. What is ... $\min_{i} a_{i}$ $\min_{i} \left(n_{i}a_{i}\right)$ $\max_{i} a_{i}$ None of the above.
answered
Jun 17
in
Calculus

172
views
tifr2014
limits
+4
votes
26
GATE198913b
Find a solution to the following recurrence equation: $T(n)=\sqrt{n}+T(\frac{n}{2})$ $T(1)=1$
answered
Jun 16
in
Algorithms

607
views
gate1989
descriptive
algorithms
recurrence
+1
vote
27
TIFR2011B23
Suppose $(S_{1}, S_{2},\ldots,S_{m})$ is a finite collection of nonempty subsets of a universe $U.$ Note that the sets in this collection need not be distinct. Consider the following basic step to be performed on this sequence. While there exist sets $S_{i}$ and ... of a finite universe $U$ and a choice of $S_{i}$ and $S_{j}$ in each step such that the process does not terminate.
answered
Jun 16
in
Set Theory & Algebra

377
views
tifr2011
settheory&algebra
sets
0
votes
28
TIFR2015A15
Let $A$ and $B$ be nonempty disjoint sets of real numbers. Suppose that the average of the numbers in the first set is $\mu_{A}$ and the average of the numbers in the second set is $\mu_{B}$; let the corresponding variances be $v_{A}$ and $v_{B}$ ... $p.v_{A}+ (1  p). v_{B} + (\mu_{A} \mu_{B})^{2}$
answered
Jun 16
in
Numerical Ability

262
views
tifr2015
statistics
+1
vote
29
TIFR2018A10
Let $C$ be a biased coin such that the probability of a head turning up is $p.$ Let $p_n$ denote the probability that an odd number of heads occurs after $n$ tosses for $n \in \{0,1,2,\ldots \},$ ... $p_{n}=1 \text{ if } n \text{ is odd and } 0 \text{ otherwise}.$
answered
Jun 16
in
Probability

279
views
tifr2018
probability
+2
votes
30
TIFR2019A10
Avni and Badal alternately choose numbers from the set $\{1,2,3,4,5,6,7,8,9\}$ without replacement (starting with Avni). The first person to choose numbers of which any $3$ sum to $15$ wins the game (for example, Avni wins if she chooses ... a winning strategy Both of them have a winning strategy Neither of them has a winning strategy The Player that picks $9$ has a winning strategy
answered
Jun 16
in
Numerical Ability

238
views
tifr2019
generalaptitude
numericalability
logicalreasoning
0
votes
31
TIFR2013A18
Consider three independent uniformly distributed (taking values between $0$ and $1$) random variables. What is the probability that the middle of the three values (between the lowest and the highest value) lies between $a$ and $b$ where $0 ≤ a < b ≤ 1$? $3 (1  b) a (b  a)$ ... $(1  b) a (b  a)$ $6 ((b^{2} a^{2})/ 2  (b^{3}  a^{3})/3)$.
answered
Jun 16
in
Probability

229
views
tifr2013
probability
randomvariable
uniformdistribution
+1
vote
32
GATE19894viii
Provide short answers to the following questions: $P_{n} (t)$ is the probability of $n$ events occurring during a time interval $t$. How will you express $P_{0} (t + h)$ in terms of $P_{0} (h)$, if $P_{0} (t)$ has stationary independent increments? (Note: $P_{t} (t)$is the probability density function).
answered
Jun 15
in
Probability

116
views
gate1989
descriptive
probability
poissondistribution
0
votes
33
TIFR2015A12
Consider two independent and identically distributed random variables $X$ and $Y$ uniformly distributed in $[0, 1]$. For $\alpha \in \left[0, 1\right]$, the probability that $\alpha$ max $(X, Y) < XY$ is $1/ (2\alpha)$ exp $(1  \alpha)$ $1  \alpha$ $(1  \alpha)^{2}$ $1  \alpha^{2}$
answered
Jun 15
in
Probability

230
views
tifr2015
probability
randomvariable
uniformdistribution
+3
votes
34
TIFR2013A5
The late painter Maqbool Fida Husain once coloured the surface of a huge hollow steel sphere, of radius $1$ metre, using just two colours, Red and Blue. As was his style however, both the red and blue areas were a bunch of highly irregular disconnected regions. The late ... $11 sq. metres$; None of the above.
answered
Jun 15
in
Numerical Ability

741
views
tifr2013
geometry
numericalability
+1
vote
35
GATE199012b
Consider the following problem. Given $n$ positive integers $a_{1}, a_{2}\dots a_n,$ it is required to partition them in to two parts $A$ and $B$ such that $\sum_{i \in A} a_{i}  \sum_{i \in B} a_{i}$ is minimised Consider a greedy ... in that part whose sum in smaller at that step. Give an example with $n=5$ for which the solution produced by the greedy algorithm is not optimal.
answered
Jun 14
in
Algorithms

157
views
gate1990
descriptive
algorithms
algorithmdesigntechniques
0
votes
36
TIFR2018B10
For two $n$ bit strings $x,y \in\{0,1\}^{n},$ define $z=x\oplus y$ to be the bitwise XOR of the two strings (that is, if $x_{i},y_{i},z_{i}$ denote the $i^{th}$ bits of $x,y,z$ respectively, then $z_{i}=x_{i}+y_{i} \bmod 2$ ... The number of such linear functions for $n \geq 2$ is: $2^{n}$ $2^{n^{2}}$ $\large2^{\frac{n}{2}}$ $2^{4n}$ $2^{n^{2}+n}$
answered
Jun 14
in
Set Theory & Algebra

231
views
tifr2018
functions
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