Question 1

Let Σ be the set of all bijections from {1, ..., 5} to {1, ..., 5}, where id denotes the identity function i.e. id(j) = j,∀j. Let º denote composition on functions. For a string x = x1 x2 ... xn ∈ Σn, n ≥ 0. Let π(x) = x1 º x2 º ... º xn.

Consider the language L = {x ∈ Σ* | π(x) = id}. The minimum number of  states in any DFA accepting L is ______.

 A 120 B 136 C 125 D 132
GATE 2019
 Question 2
Which one of the following is NOT logically equivalent to ¬∃x(∀y(α) ∧ ∀z(β))?
 A ∀x(∃z(¬β)→∀y(α)) B ∀x(∀z(β)→∃y(¬α)) C ∀x(∀y(α)→∃z(¬β)) D ∀x(∃y(¬α)→∃z(¬β))
Gate 2013
Question 2 Explanation:
Option A:
∀x(∃z(¬β) → ∀y(α))
⇒ ∀x(¬∃z(¬β) ∨ ∀y(α))
⇒ ∀x(∀z(β)∨y(α))
⇒ ¬∃x¬(∀z(β)∨∀y(α))
⇒ ¬∃x(¬∀z(β)∧¬∀y(α))
A is Not equivalent to the given.
Option B:
∀x(∀z(β)→∃y(¬α))
⇒ ∀x(¬∀z(β)∨∃y(¬α))
⇒ ¬∃x¬(¬∀z(β)∨∃y(¬α))
⇒ ¬∃x(∀z(β)∨∀y(α))
B is Matching and equivalent to given.
Option C:
∀x(∀y(α)→∃z(¬β))
⇒ ∀x(¬∀y(α)∨∃z(¬β))
⇒ ¬∃x¬(¬∀y(α)∨∃z(¬β))
⇒ ¬∃x(∀y(α)∧z(β))
C is equivalent to the given.
Option D:
∀x(∃y(¬α)→∃z(¬β))
⇒ ∀x(¬∃y(¬α)∨∃z(β))
⇒ ∀x(∀y(α)∨∃z(β))
⇒ ¬∃x¬(∀y(α)∨∃z(β))
⇒ ¬∃x(¬∀y(α)∧¬∃z(β))
⇒ ¬∃x(¬∀y(α)∧∀z(¬β))
So D is Not equivalent to the given.
 Question 3
A company needs to develop digital signal processing software for one of its newest inventions. The software is expected to have 40000 lines of code. The company needs to determine the effort in person-months needed to develop this software using the basic COCOMO model. The multiplicative factor for this model is given as 2.8 for the software development on embedded systems, while the exponentiation factor is given as 1.20. What is the estimated effort in person-months?
 A 234.25 B 932.5 C 287.8 D 122.4
Gate 2011
Question 3 Explanation:
Note: Out of syllabus.
 Question 4
HTML (Hyper Text Markup Language) has language elements which permit certain actions other than describing the structure of the web document. Which one of the following actions is NOT supported by pure HTML (without any server or client side scripting) pages?
 A Embed web objects from different sites into the same page B Refresh the page automatically after a specified interval C Automatically redirect to another page upon download D Display the client time as part of the page
Gate 2011
Question 4 Explanation:
Note: Out of syllabus.
 Question 5
Which of the following is NOT desired in a good Software Requirement Specifications (SRS) document?
 A Functional Requirements B Non-Functional Requirements C Goals of Implementation D Algorithms for Software Implementation
Gate 2011
Question 5 Explanation:
Note: Out of syllabus.
 Question 6
The following is the comment written for a C function
```/* This function computes the roots of a quadratic equation
a.x^2 + b.x + c = . The function stores two real roots
in *root1 and *root2 and returns the status of validity
of roots. It handles four different kinds of cases.
(i) When coefficient a is zero irrespective of discriminant
(ii) When discreminant is positive
(iii) When discriminant is zero
(iv) When discriminant is negative.
Only in case (ii) and (iii) the stored roots are valid.
Otherwise 0 is stored in roots. The function returns
0 when the roots are valid and -1 otherwise.
The function also ensures root1 >= root2
int get_QuadRoots( float a, float b, float c,
float *root1, float *root2);
*/

```

A software test engineer is assigned the job of doing black box testing. He comes up with the following test cases, many of which are redundant.

Which one of the following option provide the set of non-redundant tests using equivalence class partitioning approach from input perspective for black box testing?
 A T1, T2, T3, T6 B T1, T3, T4, T5 C T2, T4, T5, T6 D T2, T3, T4, T5
Gate 2011
Question 6 Explanation:
Note: Out of syllabus.
T1 and T2 checking same condition a = 0 hence, any one of T1 and T2 is redundant.
T3, T4: in both case discriminant (D) = b2 – 4ac = 0. Hence any one of it is
T5 : D > 0
T6 : D < 0
 Question 7
The cyclomatic complexity of each of the modules A and B shown below is 10. What is the cyclomatic complexity of the sequential integration shown on the right hand side?
 A 19 B 21 C 20 D 10
2010
Question 7 Explanation:
Note: Out of syllabus.
 Question 8
What is the appropriate pairing of items in the two columns listing various activities encountered in a software life cycle?
```P. Requirements Capture	 1.Module Development and Integration
Q. Design	         2.Domain Analysis
R. Implementation	 3.Structural and Behavioral Modeling
S. Maintenance	         4.Performance Tuning```
 A P-3, Q-2, R-4, S-1 B P-2, Q-3, R-1, S-4 C P-3, Q-2, R-1, S-4 D P-2, Q-3, R-4, S-1
2010
Question 8 Explanation:
Note: Out of syllabus.
 Question 9
The following program is to be tested for statement coverage:
```begin
if (a== b) {S1; exit;}
else if (c== d) {S2;]
else {S3; exit;}
S4;
end```
The test cases T1, T2, T3 and T4 given below are expressed in terms of the properties satisfied by the values of variables a, b, c and d. The exact values are not given. T1 : a, b, c and d are all equal T2 : a, b, c and d are all distinct T3 : a = b and c != d T4 : a != b and c = d Which of the test suites given below ensures coverage of statements S1, S2, S3 and S4?
 A T1, T2, T3 B T2, T4 C T3, T4 D T1, T2, T4
2010
Question 9 Explanation:
T1 covers S1
T2 covers S3
T4 covers S2, S4.
 Question 10
The coupling between different modules of a software is categorized as follows: I.  Content coupling           II. Common coupling III. Control coupling                IV .Stamp coupling V. Data coupling Coupling between modules can be ranked in the order of strongest (least desirable) to weakest (most desirable) as follows
 A I-II-III-IV-V B V-IV-III-II-I C I-III-V-II-IV D IV-II-V-III-I
2009
Question 10 Explanation:
Note: Out of syllabus. [Software Engineering]
 Question 11
Consider the HTML table definition given below: < table border=1> <tr> <td rowspan=2> ab </td> <td colspan=2> cd </td> </tr> <tr> <td> ef </td> <td rowspan=2> gh </td> </tr> <tr> <td colspan=2> ik </td> </tr> </table> The number of rows in each column and the number of columns in each row are:
 A 〈2, 2, 3〉 and 〈2, 3, 2〉 B 〈2, 2, 3〉 and 〈2, 2, 3〉 C 〈2, 3, 2〉 and 〈2, 3, 2〉 D 〈2, 3, 2〉 and 〈2, 2, 3〉
2009
Question 11 Explanation:
Note: Out of syllabus. [Web Technologies]
 Question 12
Which of the following statements are TRUE? I.The context diagram should depict the system as a single bubble. II.External entities should be identified clearly at all levels of DFDs. III. Control information should not be represented in a DFD. IV. A data store can be connected either to another data store or to an external entity.
 A II and III B II and III C I and III D I, II and III
2009
Question 12 Explanation:
Note: Out of Syllabus. [Software Engineering]
 Question 13
Consider the following statements about the cyclomatic complexity of the control flow graph of a program module. Which of these are TRUE? I.The cyclomatic complexity of a module is equal to the maximum number of linearly independent circuits in the graph II.The cyclomatic complexity of a module is the number of decisions in the module plus one, where a decision is effectively any conditional statement in the module III.The cyclomatic complexity can also be used as a number of linearly independent paths that should be tested during path coverage testing.
 A I and II B II and III C I and III D I, II and III
2009
Question 13 Explanation:
Note: Out of syllabus. [Software Engineering]
 Question 14
Find if the following statements in the context of software testing are TRUE or FALSE. (S1) Statement coverage cannot guarantee execution of loops in a program under test. (S2) Use of independent path testing criterion guarantees execution of each loop in a program under test more than once.
 A True, True B True, False C False, True D False, False
Gate 2008-IT
Question 14 Explanation:
Note: Out of syllabus.
 Question 15
Which of the following is TRUE only of XML but NOT HTML?
 A It is derived from SGML B It describes content and layout C It allows user defined tags D It is restricted only to be used with web browsers
Gate 2008-IT
Question 15 Explanation:
Note: Out of syllabus.
 Question 16
Which of the following are NOT considered when computing function points for a software project?
• (O1) External inputs and outputs
• (O2) Programming language to be used for the implementation
• (O3) User interactions
• (O4) External interfaces
• (O5) Number of programmers in the software project
• (O6) Files used by the system

 A 02, 03 B 01, 05 C 04, 06 D 02, 05
Gate 2008-IT
Question 16 Explanation:
Note: Out of syllabus.
 Question 17
A software project plan has identified ten tasks with each having dependencies as given in the following table: Task        Depends On T1                 - T2                T1 T3                T1 T4                T1 T5                T2 T6                T3 T7                T3, T4 T8               T4 T9               T5, T7, T8 T10             T6, T9 Answer the following questions: (Q1) What is the maximum number of tasks that can be done concurrently? (Q2) What is the minimum time required to complete the project, assuming that each task requires one time unit and there is no restriction on the number of tasks that can be done in parallel ?
 A 5, 5 B 4, 5 C 5, 4 D 4, 4
Gate 2008-IT
Question 17 Explanation:
Note: Out of syllabus.
 Question 18
A software engineer is required to implement two sets of algorithms for a single set of matrix operations in an object oriented programming language; the two sets of algo­rithms are to provide precisions of 10-3and 10-6, respectively. She decides to implement two classes, Low Precision Matrix and High Precision Matrix, providing precisions 10-3and 10-6 respectively. Which one of the following is the best alternative for the imple­mentation?
• (S1)  The two classes should be kept independent.
• (S2)  Low Precision Matrix should be derived from High Precision Matrix.
• (S3)  High Precision Matrix should be derived from Low Precision Matrix.
• (S4)  One class should be derived from the other; the hierarchy is immaterial.
 A S1 B S2 C S3 D S4
Gate 2008-IT
Question 18 Explanation:
Note: Out of syllabus.
 Question 19
Which of the following requirement specifications can be validated? (S1) If the system fails during any operation, there should not be any loss of data (S2) The system must provide reasonable performance even under maximum load conditions (S3) The software executable must be deployable under MS Windows 95, 2000 and XP (S4) User interface windows must fit on a standard monitor's screen
 A S4 and S3 B S4 and S2 C S3 and S1 D S2 and S1
Gate 2008-IT
Question 19 Explanation:
Note: Out of syllabus.
 Question 20
Consider the table employee(empId, name, department, salary) and the two queries Q1 ,Q2 below. Assuming that department 5 has more than one employee, and we want to find the employees who get higher salary than anyone in the department 5, which one of the statements is TRUE for any arbitrary employee table?
```Q1 : Select e.empId
From employee e
Where not exists
(Select * From employee s where s.department = “5” and
s.salary >=e.salary)
Q2 : Select e.empId
From employee e
Where e.salary > Any
(Select distinct salary From employee s Where s.department = “5”)```
 A Q1 is the correct query B Q2 is the correct query C Both Q1 and Q2 produce the same answer D Neither Q1 nor Q2 is the correct query
Gate-2007
Question 20 Explanation:
The required output is find the employees who get higher salary than anyone in the department “5”.
Query 1: Results the empId's which have higher salary than anyone in the department 5.
Query 2: Results the empId's which have higher salary than atleast one employee of department 5.
 Question 21
In the Spiral model of software development, the primary determinant in selecting activities in each iteration is
 A Iteration size B Cost C Adopted process such as Rational Unified Process or Extreme Programming D Risk
Gate 2007-IT
Question 21 Explanation:
Note: Out of syllabus.
 Question 22
Which of the following systems is a most likely candidate example of a pipe and filter architecture ?
 A Expert system B DB repository C Aircraft flight controller D Signal processing
Gate 2007-IT
Question 22 Explanation:
Note: Out of syllabus.
 Question 23
Given below are HTML lines, With reference to the HTML lines given above, consider the following statements. 1. Clicking on the point <80, 75> does not have any effect. 2. The web browser can identify the area applicable to the mouse-click within the image and the subsequent action to be taken without additional responses from the web server. 3. The dots in the cgi-bin URL will be resolved by the web browser before it is sent to the web server 4. The "fd.html" request when sent to the web server will result in a GET request. Exactly how many of the statements given above are correct?
 A 0 B 1 C 2 D 3
Gate 2007-IT
Question 23 Explanation:
Note: Out of syllabus.
 Question 24
Consider the XML document fragment given below: Consider the XPath expression: *[not (self ) : : TOC] What would be the result of the given XPath expression when the current node is Book?
 A The Title and Content elements B The Content and TOC elements C The Title and TOC elements D The Title, Content and TOC elements
Gate 2007-IT
Question 24 Explanation:
Note: Out of syllabus.
 Question 25
The following table shoes the time between failures for a software system The reliability of the system for one hour of operation assuming an exponential model is
 A 0.45 B 0.63 C 0.84 D 0.95
Gate 2007-IT
Question 25 Explanation:

The probability or reliability that the product will work for a defined period of time without failure is given by
 Question 26

 A 20 B 50 C 80 D 110
Gate 2007-IT
 Question 27
In the simplified flowchart given below, the shaded boxes represent code that is executed during a test case. The Branch coverage is
 A 3/4 B 2/3 C 1/2 D 3/8
Gate 2007-IT
Question 27 Explanation:
Note: Out of syllabus.
 Question 28

Consider the CPM activity chart where an arc connecting two milestones is labeled with a task identifier and the time taken in days. For example in order to go from A to B, task T1 takes 180 days. A dashed line depicts an additional dependency that is equivalent to a zero time task.

The set of activities that lie on the critical path are

 A T1, T2, T8, T10 B T1, T3, T8, T10 C T1, T2, T3, T4, T5, T6, T7, T8, T9, T10 D T1, T4, T5, T7, T8, T10
Gate 2007-IT
Question 28 Explanation:
Note: Out of syllabus.
 Question 29
Consider the following pseudo-code:
``` IF ((A > B) AND (C > D)) THEN
A = A + 1
B = B + 1
ENDIF
```
The cyclomatic complexity of the pseudo-code is
 A 2 B 3 C 4 D 5
Gate 2007-IT
Question 29 Explanation:
Note: Out of syllabus.
 Question 30
The contents of the text file t1 txt containing four lines are as follows : a1 b1 a2 b2 a3 b2 a4 b1 The contents of the text file t2 txt containing five lines are as follows : a1 c1 a2 c2 a3 c3 a4 c3 a5 c4 Consider the following Bourne shell script :
``` awk - F '  '  ' {Print \$1, \$2} ' t1.txt |
while read a b ; do
awk -v aV = \$ a - v by = \$b  - F ' '
aV = = \$1 (print aV, bV, \$2 ) ' t2.txt
done
```
Which one of the following strings will NOT be present in the output generated when the above script in run? (Note that the given strings may be substrings of a printed line.)
 A "b1 c1" B "b2 c3" C "b1 c2" D "b1 c3"
Gate 2007-IT
Question 30 Explanation:
Note: Out of syllabus.
 Question 31
The cyclomatic complexity of the flow graph of a program provides
 A an upper bound for the number of tests that must be conducted to ensure that all statements have been executed at most once B a lower bound for the number of tests that must be conducted to ensure that all statements have been executed at most once C an upper bound for the number of tests that must be conducted to ensure that all statements have been executed at least once D a lower bound for the number of tests that must be conducted to ensure that all statements have been executed at least once
Gate 2006-IT
Question 31 Explanation:
Note: Out of syllabus.
 Question 32
With respect to software testing, consider a flow graph G with one connected component. Let E be the number of edges, N be the number of nodes, and P be the number of predicate nodes of G. Consider the following four expressions:
1. E - N + P
2. E - N + 2
3. P +  2
4. P + 1
The cyclomatic complexity of G is given by
 A 1 or 3 B 2 or 3 C 2 or 4 D 1 or 4
Gate 2006-IT
Question 32 Explanation:
Note: Out of syllabus.
 Question 33

A software program consists of two modules M1 and M2 that can fail independently, but never simultaneously. The program is considered to have failed if any of these modules fails. Both the modules are ‘repairable’ and so the program starts working again as soon as the repair is done. Assume that the mean time to failure (MTTF) of M1is T1 with a mean time to repair (MTTR) of R1. The MTTF of M2 is T2 with an MTTR of R2. What is the availability of the overall program given that the failure and repair times are all exponentially distributed random variables?

 A B C D
Gate 2006-IT
Question 33 Explanation:
Note: Out of syllabus.
 Question 34
Consider the following structure chart diagram. The boxes have function names embedded in them, while the variables are indicated along the arcs. Given below are a set of statements relevant to the above diagram. I. F3 and F6 can be in the same module. II. F4 and F6 can be in the same module. III. A4 is both an output and a control variable. IV. It is incorrect to pass A1 as data and use it as a control variable. Which combination of these statements is TRUE?
 A III and IV B I and IV C II and IV D I, II and IV
Gate 2006-IT
Question 34 Explanation:
Note: Out of syllabus.
 Question 35
Consider the following XML DTD describing course information in a university:
```<!ELEMENT Univ (Course+, Prof+)>
<!ELEMENT Course (Title, Eval*)>
<!ATTLIST Course Number ID #REQUIRED Instructor IDREF #IMPLIED>
<!ELEMENT Title (#PCDATA)>
<!ELEMENT Eval (#PCDATA)>
<!ATTLIST Eval Score CDATA #REQUIRED>
<!ELEMENT Prof EMPTY>
<!ATTLIST Prof Name ID #REQUIRED Teaches IDREF #IMPLIED>
```
What is returned by the following XQuery? let \$as := / /@Score for \$c in /Univ/Course[Eval] let \$cs := \$c/Eval?@Score where min(\$cs) > avg(\$as) return \$c
 A The professor with the lowest course evaluation B Professors who have all their course evaluations above the university average C The course with the lowest evaluation D Courses with all evaluations above the university average
Gate 2006-IT
Question 35 Explanation:
Note: Out of syllabus.
 Question 36
Consider the following program module:
```void swap(float* A1, float* A2)
{
float temp;
if (*A1 = = *A2) return;
temp = *A1;
*A1 = *A2;
*A2 = temp;
return;
}
```
The program volume for the above module using Halstead's method is
 A 60 B 63 C 66 D 69
Gate 2006-IT
Question 36 Explanation:
Note: Out of syllabus.
 Question 37
```void swap(float* A1, float* A2)
{
float temp;
if (*A1 = = *A2) return;
temp = *A1;
*A1 = *A2;
*A2 = temp;
return;
}
```
The program effort for the above module using Halstead's method is
 A 315 B 330 C 393 D 403
Gate 2006-IT
Question 37 Explanation:
Note: Out of syllabus.
 Question 38
A software project has four phases P1, P2, P3 and P4. Of these phases, P1 Is the first one and needs to be completed before any other phase can commence. Phases P2 and P3 can be executed in parallel. Phase P4 cannot commence until both P2 and P3 are completed. The optimistic, most likely, and pessimistic estimates of the phase completion times in days, for Pl, P2, P3 and P4 are, respectively, (11, 15, 25), (7, 8, 15), (8, 9, 22), and (3, 8, 19). The critical path for the above project and the slack of P2 are, respectively,
 A P1-P2-P4, 1 day B P1-P3-P4, 1 day C P1-P3-P4, 2 days D P1-P2-P4, 2 days
Gate 2006-IT
Question 38 Explanation:
Note: Out of syllabus.
 Question 39
A software project has four phases P1, P2, P3 and P4. Of these phases, P1 Is the first one and needs to be completed before any other phase can commence. Phases P2 and P3 can be executed in parallel. Phase P4 cannot commence until both P2 and P3 are completed. The optimistic, most likely, and pessimistic estimates of the phase completion times in days, for Pl, P2, P3 and P4 are, respectively, (11, 15, 25), (7, 8, 15), (8, 9, 22), and (3, 8, 19). The costs (in Rupees per day) of crashing the expected phase completion times for the four phases, respectively, are 100, 2000, 50, and 1000. Assume that the expected phase completion times of the phases cannot be crashed below their respective most likely completion times. The minimum and the maximum amounts (in Rupees) that can be spent on crashing so that ALL paths are critical are, respectively.
 A 100 and 1000 B 100 and 1200 C 150 and 1200 D 200 and 2000
Gate 2006-IT
Question 39 Explanation:
Note: Out of syllabus.
 Question 40
A function f defined on stacks of integers satisfies the following properties. f(∅) = 0 and f (push (S, i)) = max (f(S), 0) + i for all stacks S and integers i.
If a stack S contains the integers 2, -3, 2, -1, 2 in order from bottom to top, what is f(S)?
 A 6 B 4 C 3 D 2
Gate 2005-IT
Question 40 Explanation:
2, -3, 2, -1, 2
f(Ø)=0 and f(push(S,i) = max(f(S),0) + i;
Initially stack is empty and for empty stack 0 is given.
f(push(0,2)) = max(f(Ø),0) + 2 = max(Ø,0) + 2 = 2
f(push(2,-3)) = max(2,0) + (-3) = 2 - 3 = -1
f(push(-1,2)) = max(-1,0) + 2 = 0 + 2 = 2
f(push(2,-1)) = max(2,0)+ (-1) = 2 - 1 = 1
f(push(1,2)) = max(1,0) + 2 = 1 + 2 = 3
So, 3 will be the answer.
∴ Option C is correct.
 Question 41
Amongst the ACID properties of a transaction, the 'Durability' property requires that the changes made to the database by a successful transaction persist
 A Except in case of an Operating System crash B Except in case of a Disk crash C Except in case of a power failure D Always, even if there is a failure of any kind
Gate 2005-IT
Question 41 Explanation:
Durability gurantees that once a transition has been committed, it will remain committed even in the case of a system failure.
 Question 42

In a data link protocol, the frame delimiter flag is given by 0111. Assuming that bit stuffing is employed, the transmitter sends the data sequence 01110110 as

 A 01101011 B 011010110 C 011101100 D 0110101100
Gate 2004-IT
Question 42 Explanation:
In the data link layer, bits stuffing is employed then bit stuffing is done using the flag delimiter. If there is a flag of n bits then we will compare the data sequence with the flag and for every n-1 bits matched found, a bit 0 is stuffed in the data sequence.
Thus using the above logic,
Delimiter flag: 0111
Data sequence: 01110110
So, for a flag of 4 bits we will compare data sequence with a pattern of 3 bits, i.e., 011.
0 1 1 0 1 0 1 1 0 0
In the above pattern the underlined bits are found matched. Hence, 0 in italics is stuffed. Thus resulting in the data sequence as 0110101100 which is option (D).
There are 42 questions to complete.
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