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 ... x_n ∈ Σⁿ, n ≥ 0. Let π(x) = x₁ º x₂ º ... º x_n.

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

/* 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.

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

begin
  if (a== b) {S1; exit;}
  else if (c== d) {S2;]
       else {S3; exit;}
  S4;
end

• (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

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”)

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

 IF ((A > B) AND (C > D)) THEN
       A = A + 1
       B = B + 1
ENDIF

 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

1. E - N + P
2. E - N + 2
3. P +  2
4. P + 1

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?

<!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>

void swap(float* A1, float* A2)
{
    float temp;
    if (*A1 = = *A2) return;
    temp = *A1;
    *A1 = *A2;
    *A2 = temp;
    return;
}

void swap(float* A1, float* A2)
{
    float temp;
    if (*A1 = = *A2) return;
    temp = *A1;
    *A1 = *A2;
    *A2 = temp;
    return;
}

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