Question 1
The following relation records the age of 500 employees of a company, where empNo (indicating the employee number) is the key: empAge (empNo, age) Consider the following relational algebra expression:

What does the above expression generate?
Employee numbers of all employees whose age is not the maximum.
Employee numbers of only those employees whose age is the maximum.
Employee numbers of all employees whose age is not the minimum.
Employee numbers of only those employees whose age is more than the age of exactly one other employee.
Question 1 Explanation: 
The given relational algebra expression will result in employees whose age is not minimum. The given conditional join, joins the relations if the age is greater than any of the ages mentioned in the database.
Question 2
Let ri(z) and wi(z) denote read and write operations respectively on a data item z by a transaction Ti. Consider the following two schedules.
            S1: r1(x) r1(y) r2(x) r2(y) w2(y) w1(x)
            S2: r1(x) r2(x) r2(y) w2(y) r1(y) w1(x)
Which one of the following options is correct?
S1is not conflict serializable, and S2 is conflict serializable.
Neither S1nor S2is conflict serializable.
Both S1and S2are conflict serializable.
S1is conflict serializable, and S2is not conflict serializable.
Question 2 Explanation: 
Question 3
Consider the relation R(P, Q, S, T, X, Y, Z, W) with the following functional dependencies

Consider the decomposition of the relation R into the consistent relations according to the following two decomposition schemes.               
D1: R=[(P,Q,S,T); (P,T,X); (Q,Y); (Y,Z,W)]               
D2: R=[(P,Q,S);(T,X);(Q,Y);(Y,Z,W)]
Which one of the following options is correct?
D1is a lossy decomposition, but D2is a lossless decomposition.
Both D1and D2are lossy decompositions.
Both D1and D2are lossless decompositions.
D1is a lossless decomposition, but D2is a lossy decomposition.
Question 3 Explanation: 

Given functional dependencies set:





  • While merging the tables there should be some common attribute(s) and it should be a candidate key of one of the tables.

  • R1 should be merged with R2 because PT is a key of R2.
  • R3 should be merged with PQSTX because Q is a key of R3.
  • R4 should be merged with PQSTXY because Y is a key of R4.

  • R1 should be merged with R3 because Q is a key of R3.
  • R4 should be merged with PQSY because Y is a key of R4.
  • Now, there is no common attribute in between R2(TX) and PQSYZW.
  • Hence, D2 is lossy decomposition.
Question 4
Suppose a database system crashes again while recovering from a previous crash. Assume checkpointing is not done by the database either during the transactions or during recovery. Which of the following statements is/are correct?
The same undo and redo list will be used while recovering again.
The database will become inconsistent.
The system cannot recover any further.
All the transactions that are already undone and redone will not be recovered again.
Question 4 Explanation: 
Suppose a database system crashes again while recovering it from the previous crash then also we need to make use of the redo and undo list to recover the system.
Question 5
 A relation r(A, B) in a relational database has 1200 tuples. The attribute A has integer values ranging from 6 to 20, and the attribute B has integer values ranging from 1 to 20. Assume that the attributes A and B are independently distributed.
Question 5 Explanation: 

Explanation :

Probability of 1st condition being satisfied(say P(A)) = 10/15 = 2/3

Probability of 2nd condition being satisfied(say P(B)) = 1/20

Probability of both conditions being satisfied(say P(A intersection B)) = 2/3*1/20 = 1/30

Probability of any one condition being satisfied = P(A union B) = P(A)+P(B)-P(A intersection B) = 2/3 + 1/20 - 1/30 = 41/60

therefore, expected number of tuples = (41/60)*1200 = 820

Question 6

(a) Consider the relation scheme R(A, B, C) with the following functional dependencies:
A, B → C, C → A
Show that the scheme R is the Third Normal Form (3NF) but not in Boyce-Code Normal Form (BCNF).
(b) Determine the minimal keys of relation R.

Theory Explanation.
Question 7

Consider the relation scheme.


Express the following queries using (one or more of )SELECT, PROJECT, JOIN and DIVIDE operations.
(a) Get the names of all publishers.
(b) Get values of all attributes of all authors who have published a book for the publisher with PNAME = ‘TECHNICAL PUBLISHERS’.
(c) Get the names of all authors who have published a book for any publisher located in Madras.

Theory Explanation.
Question 8

Consider a relational database containing the following schemas.

The primary key of each table is indicated by underlying the constituent fields.

SELECT s.sno, s.sname
FROM Suppliers s, Catalogue c
WHERE s.sno = c.sno AND
              Cost > (SELECT AVG (cost)
                      FROM Catalogue
                      WHERE pno = ‘P4’
                      GROUP BY pno);

The number of rows returned by the above SQL query is

Question 8 Explanation: 
The inner query “select avg(cost) from catalogue where pno='P4' group by pno;” returns:
The outer query “select s.sno, s.sname from suppliers s, catalogue c where s.sno=c.sno” returns:
S1 M/s Royal furniture
S1 M/s Royal furniture
S1 M/s Royal furniture
S2 M/s Balaji furniture
S2 M/s Balaji furniture
S3 M/s Premium furniture
S3 M/s Premium furniture
S3 M/s Premium furniture
S3 M/s Premium furniture
So, the final result of the query is:
S2 M/s Balaji furniture
S3 M/s Premium furniture
S3 M/s Premium furniture
S3 M/s Premium furniture
Therefore, 4 rows will be returned by the query.
Question 9

Which one of the following is used to represent the supporting many-one relationships of a weak entity set in an entity-relationship diagram?

Ovals that contain underlined identifiers
Rectangles with double/bold border
Diamonds with double/bold border
Ovals with double/bold border
Question 9 Explanation: 
An entity set that does not have sufficient attributes to form a primary key is termed as a weak entity and an entity set that has a primary key is termed as strong entity set. For a weak entity set to be meaningful, it must be associated with another entity set, called identifying or owner entity set. The relationship associating the weak entity set with the identifying entity set is called the identifying relationship and it is represented by double diamond. The identifying relationship is many-to-one from the weak entity set to the identifying entity set and the participation of weak entity set in the relationship is total.
Question 10

Consider a schedule of transactions T1 and T2:

Here, RX stands for “Read(X)” and WX stands for “Write(X)”. Which one of the following schedules is conflict equivalent to the above schedule?

Question 10 Explanation: 
• Two schedules are said to be conflict equivalent, if conflict operations in both the schedules are executed in the same order.
• First, let’s list the conflict operations of each of the schedule given in the options and compare with the conflict operations of schedule which is given in the question.
Given schedule:

Conflict operations:
R2(B) → W1(B)
W2(B) → W1(B)
R1(C) → W2(C)
R2(D) → W1(D)

Conflict operations:
R1(C) → W2(C)
W1(D) → R2(D)
W1(B) → R2(B)
W1(B) → W2(B)

Conflict operations:
R2(B) → W1(B)
W2(B) → W1(B)
R2(D) → W1(D)
R1(C) → W2(C)

Conflict operations:
R2(B) → W1(B)
W2(B) → W1(B)
R2(D) → W1(D)
W2(C) → R1(C)

Conflict operations:
R1(C) → W2(C)
W1(D) → R2(D)
R2(B) → W1(B)
W2(B) → W1(B)
The conflict operations in the option (2) and given schedule are appearing in the same sequence order, so option (2) is the answer.
Question 11

Consider a relational table R that is in 3NF, but not in BCNF. Which one of the following statements is TRUE?

A cell in R holds a set instead of an atomic value.
R has a nontrivial functional dependency X→A, where X is not a superkey and A is a non-prime attribute and X is not a proper subset of any key.
R has a nontrivial functional dependency X→A, where X is not a superkey and A is a non-prime attribute and X is a proper subset of some key.
R has a nontrivial functional dependency X→A, where X is not a superkey and A is a prime attribute.
Question 11 Explanation: 
AB → C
BC → A
(BD)+ = BD ✖
(ABD)+ = ABDC ✔
(CBD)+ = CBDA ✔
Candidate keys = {ABD, CBD}
• The relation R is in 3NF, as there are no transitive dependencies.
• The relation R is not in BCNF, because the left side of both the FD’s are not Super keys.
• In R, BC → A is a non-trivial FD and in which BC is not a Super key and A is a prime attribute.
Question 12

Consider a database implemented using B+ tree for file indexing and installed on a disk drive with block size of 4 KB. The size of search key is 12 bytes and the size of tree/disk pointer is 8 bytes. Assume that the database has one million records. Also assume that no node of the B+ tree and no records are present initially in main memory. Consider that each record fits into one disk block. The minimum number of disk accesses required to retrieve any record in the database is ______.

Question 12 Explanation: 
Block factor = 4096/20 = 204
(1) Database BF = 1
No. of block = 106 } ➝ 1 block access from database
(2) ⎡106/204⎤ = 491
(3) ⎡491/204⎤ = 3
(4) ⎡3/204⎤ = 1
So, 1+3 = 4 disk accesses are required to retrieve any record in the database.
Question 13

A library relational database system uses the following schema

USERS (User#, UserName, HomeTown)
BOOKS (Book#, BookTitle, AuthorName)
ISSUED (Book#, User#, Date) 

Explain in one English sentence, what each of the following relational algebra queries is designed to determine

(a) σ User #=6 (11 User #, Book Title ((USERS ISSUED) BOOKS))
(b) σ Author Name (BOOKS (σ Home Town) = Delhi (USERS ISSUED))) 
Theory Explanation.
Question 14

For a database relation R(a,b,c,d), where the domains a, b, c, d include only atomic values, only the following functional dependencies and those that can be inferred from them hold:

   a → c 
   b → d  

This relation is

in first normal form but not in second normal form
in second normal form but not in third normal form
in third normal form
None of the above
Question 14 Explanation: 
Candidate key is ab.
Since all a, b, c, d are atomic. So the relation is in 1NF.
Checking the FD's
a → c
b → d
We can see that there is partial dependencies. So it is not 2NF.
So answer is option (A).
Question 15

Let R(a,b,c) and S(d,e,f) be two relations in which d is the foreign key of S that refers to the primary key of R. Consider the following four operations R and S

   (a) Insert into R            (b) Insert into S 
   (c) Delete from R            (d) Delete from S    

Which of the following can cause violation of the referential integrity constraint above?

None of (a), (b), (c) or (d) can cause its violation
All of (a), (b), (c) and (d) can cause its violation
Both (a) and (d) can cause its violation
Both (b) and (c) can cause its violation
Question 15 Explanation: 
Let take example:

Here 'd' is the foreign key of S and let 'a' is the primary key of R.
(A) Insertion into R: will cause no violation.
(B) Insertion into S: may cause violation because there may not be entry of the tuple in relation R. Example entry of 〈S4, __, __〉 is not allowed.
(C) Delete from R: may cause violation. For example, deletion of tuple 〈S2, __, __〉 will cause violation as there is entry of S2 in the foreign key table.
(D) Delete from S: will cause no violation as it does not result inconsistency.
Question 16

Match the pairs in the following questions:

(a) Secondary index                  (p) Function dependency
(b) Non-procedural query language    (q) B-tree
(c) Closure of a set of attributes   (r) Domain calculus
(d) Natural join                     (s) Relational algebraic operations   
(a) - (q), (b) - (r), (c) - (p), (d) - (s)
Question 16 Explanation: 
Secondary index → B-Tree
Non-procedural query language → Domain calculus
Closure of set of attributes → Function dependency
Natural join → Relational algebraic operations
Question 17

Choose the correct alternatives (More than one may be correct).

Indicate which of the following statements are true: A relational database which is in 3NF may still have undesirable data redundancy because there may exist:

Transitive functional dependencies.
Non-trivial functional dependencies involving prime attributes on the right-side.
Non-trivial functional dependencies involving prime attributes only on the left-side.
Non-trivial functional dependencies involving only prime attributes.
Both (B) and (D).
Question 17 Explanation: 
A) Transitive functional dependency, so not in 3NF.
B) 3NF because right side is prime attribute.
C) Not in 3NF, because lets suppose ABC is a candidate key. Now consider
AB → Non-prime attribute
which show it is not in 3NF
D) Involves only prime attribute, so right side should definitely contain only prime attribute. So in 3NF.
Question 18

Given two union compatible relations R1(A,B) and R2(C,D), what is the result of the operation R1A = CAB = DR2?

R1 ∪ R2
R1 × R2
R1 - R2
R1 ∩ R2
Question 18 Explanation: 
The join here will be selecting only those tuples where A=C and B=D, meaning it is the intersection.
Question 19

Which normal form is considered adequate for normal relational database design?

2 NF
5 NF
4 NF
3 NF
Question 19 Explanation: 
3NF, is considered as adequate for normal relational database design, because we can have a 3NF decomposition which is dependency preserving and lossless (not possible for any higher forms).
Question 20

There are 5 records in a database.

There is an index file associated with this and it contain the values 1, 3, 2, 5 and 4. Which one of the fields is the index built form?

Question 20 Explanation: 
Indexing will be on occupation field because occupation field lexigraphically sorted will give the sequence 1, 3, 2, 5, 4.
Question 21

Which of the following query transformations (i.e. replacing the l.h.s. expression by the r.h.s. expression) is incorrect? R1 and R2 are relations, C1, C2 are selection conditions and A1, A2 are attributes of R1?

σC1C1(R1)) → σC2C2(R1))
σC1A1(R1)) → σA1C1(R1))
σC1(R1 ∪ R2) → σC1(R1) ∪ σC1
πA1C1(R1)) → σC1A1(R1))
Question 21 Explanation: 
If the selection condition is on attribute A2, then we cannot replace it by RHS as there will not be any attribute A2 due to projection of A1 only.
Question 22

(a) Suppose we have a database consisting of the following three relations.
FREQUENTS(student, parlor) giving the parlors each student visits.
SERVES(parlor, ice-cream) indicating what kind of ice-creams each parlor serves.
LIKES(student, ice-cream) indicating what ice-creams each parlor serves.
(Assuming that each student likes at least one ice-cream and frequents at least one parlor)
Express the following in SQL:
Print the students that frequent at least one parlor that serves some ice-cream that they like.

(b) In a computer system where the 'best-fit' algorithm is used for allocating 'jobs' to 'memory partitions', the following situation was encountered:

When will the 20K job complete? Note - This question was subjective type.

Theory Explanation.
Question 23

(a) Four jobs are waiting to be run. Their expected run times are 6, 3, 5 and x. In what order should they be run to minimize the average response time?

(b) Write a concurrent program using par begin - par end to represent the precedence graph shown below.

Theory Explanation.
Question 24

Consider the following database relations containing the attributes

with Book_id as the Primary Key. 

(a) What is the highest normal form satisfied by this relation?

(b) Suppose the attributes Book_title and Author_address are added to the relation, and the primary key is changed to (Name_of_Author, Book_Title), what will be the highest normal form satisfied by the relation?

Theory Explanation.
Question 25

Consider the following relational database schemes:

  COURSES(Cno, name)
  PRE-REQ(Cno, pre_Cno)
  COMPLETED(student_no, Cno) 

COURSES give the number and the name of all the available courses.
PRE-REQ gives the information about which course are pre-requisites for a given course.
COMPLETED indicates what courses have been completed by students.

Express the following using relational algebra:
List all the courses for which a student with student_no 2310 has completed all the pre-requisites.

Theory Explanation.
Question 26

Consider the join of a relation R with a relation S. If R has m tuples and S has n tuples then the maximum and minimum sizes of the join respectively are

m + n and 0
mn and 0
m + n and |m – n|
mn and m + n
Question 26 Explanation: 
For maximum:
Suppose there is no common attribute in R and S due to which natural join will act as cross product. So then in cross product total no. of tuples will be mn.
For minimum:
Suppose there is common attribute in R and S, but none of the row of R matches with rows of S then minimum no. of tuples will be 0.
Question 27

The relational algebra expression equivalent to the following tuple calculus expression:

{t| t ∈ r ∧(t[A] = 10 ∧ t[B] = 20)} is
σ(A=10∨B=20) (r)
σ(A=10) (r) ∪ σ(B=20) (r)
σ(A=10) (r) ∩ σ(B=20) (r)
σ(A=10) (r) - σ(B=20) (r)
Question 27 Explanation: 
The given relational algebra expression represents tuples having A=10 and B=20 which is equivalent to
σ(A=10) (r) ∩ σ(B=20) (r)
Question 28

Let R = (A, B, C, D, E, F) be a relation scheme with the following dependencies: C→F, E→A, EC→D, A→B. Which of the following is a key of R?

Question 28 Explanation: 
Let's check closure for each option,
A) (CD)+ = cdf
Not a key.
B) (EC)+ = ecdabf
Yes, it is a key.
C) (AE)+ = aeb
Not a key. D) (AC)+ = abcf
Not a key.
Question 29

Which of the following is correct?

B-trees are for storing data on disk and B+ trees are for main memory.
Range queries are faster on B* trees.
B-trees are for primary indexes and B* trees are for secondary indexes.
The height of a B* tree is independent of the number of records.
Question 29 Explanation: 
Range queries are faster on B+ trees.
Question 30
For the schedule given below, which of the following is Correct?
1 Read A
2 Read B
3 Write A
4 Read A
5 Write A
6 Write B
7 Read B
8 Write B
This schedule is serialized and can occur in a scheme using 2PL protocol
This schedule is serializable but cannot occur in a scheme using 2PL protocol
This schedule is not serialiable but can occur in a scheme using 2PL protocol
This schedule is not seralisable and cannot occur in a scheme using 2PL protocol.
Question 30 Explanation: 
Let's draw precedence graph,

Since cycle exist so not conflict serializable.
And we know that if the schedule is not serializable then it is not 2PL.
Hence correct option is (D).
Question 31

Consider the schema R = (S T U V) and the dependencies S → T, T → U, U → V and V → S. Let R = (R1 and R2) be a decomposition such that R1 ∩ R2 ≠ ∅ . The decomposition is

not in 2NF
in 2NF but not 3NF
in 3NF but not in 2NF
in both 2NF and 3NF
Question 31 Explanation: 
Since R1 ∩ R2 ≠ ∅, so the decomposition is lossless join. Now since all the attributes are keys, so R1 ∩ R2 will be a key of the decomposed relation.
And since every attribute is key so the decomposed relation will be in BCNF and hence in 3NF.
Question 32

Consider the circuit shown below. In a certain steady state, the line Y is at '1'. What are the possible values of A, B and C in this state?

A = 0, B = 0, C = 1
A = 0, B = 1, C = 1
A = 1, B = 0, C = 1
A = 1, B = 1, C = 1
Question 32 Explanation: 

So the above equation is satisfied if either C=0 or A=0 and B=1.
Hence, Option (B) is correct.
Question 33

Which of the following sets of component(s) is/are sufficient to implement any arbitrary Boolean function?

XOR gates, NOT gates
2 to 1 multiplexors
AND gates, XOR gates
Three-input gates that output (A⋅B) + C for the inputs A⋅B and C
Both B and C
Question 33 Explanation: 
(A) Not complete because, XOR can be used to make only NOT gate and NOT gate is already available. Hence not complete.
(B) 2 to 1 multiplexors is functionally complete.
(C) XOR gate can be used to make a NOT gate. So, (AND, NOT) is functionally complete.
(D) With given gates and inputs NOT gate cannot be derived.
Hence, not complete.
Question 34

Which of the following is/are correct?

An SQL query automatically eliminates duplicates
An SQL query will not work if there are no indexes on the relations
SQL permits attribute names to be repeated in the same relation
None of the above
Question 34 Explanation: 
→ SQL won't remove duplicates like relational algebra projection, we have to remove it explicitly by distinct.
→ If there are no indexes on the relation SQL, then also it works.
→ SQL does not permit 2 attributes to have same name in a relation.
Question 35

Consider a B-tree with degree m, that is, the number of children, c, of any internal node (except the root) is such that m ≤ c ≤ 2m-1. Derive the maximum and minimum number of records in the leaf nodes for such a B-tree with height h, h≥1. (Assume that the root of a tree is at height 0.)

Theory Explanation.
Question 36

Consider the set of relations

EMP(Employee-no, Dept-no, Employee-name, Salary)
DEPT(Dept-no, Dept-name, Location) 

Write an SQL query to:
(a) Find all employee names who work in departments located at "Calcutta" and whose salary is greater than Rs. 50,000.
(b) Calculate, for each department number, the number of employees with a salary greater than Rs. 100,000.

Theory Explanation.
Question 37

B+-trees are preferred to binary trees in databases because

Disk capacities are greater than memory capacities
Disk access is much slower than memory access
Disk data transfer rates are much less than memory data transfer rates
Disks are more reliable than memory
Question 37 Explanation: 
In B+ trees it is easy to reduce the number of last level access from the disk when the disk size is too large.
Question 38

Given the relations

   employee (name, salary, deptno) and
   department (deptno, deptname, address)  

Which of the following queries cannot be expressed using the basic relational algebra operations (σ, π, ×, ⋈, ∪, ∩, -)?

Department address of every employee
Employees whose name is the same as their department name
The sum of all employees’ salaries
All employees of a given department
Question 38 Explanation: 
The sum of all employee’s salaries can’t be represented by using the given six basic algebra operation. If we want to represent sum of salaries then we need to use aggregation operator.
Question 39

Given the following relation instance.

          x  y  z
          1  4  2
          1  5  3
          1  6  3
          3  2  2  

Which of the following functional dependencies are satisfied by the instance?

XY → Z and Z → Y
YZ → X and Y → Z
YZ → X and X → Z
XZ → Y and Y → X
Question 39 Explanation: 
A functional dependency A→B is said to hold if for two tuples t1 and t2.
If for t1[A] = t2[A] then t1[Y] = t2[Y].
Question 40

Given relations r(w, x) and s(y, z), the result of

    select distinct w, x
    from r, s  

is guaranteed to be same as r, provided

r has no duplicates and s is non-empty
r and s have no duplicates
s has no duplicates and r is non-empty
r and s have the same number of tuples
Question 40 Explanation: 
r has no duplicate, if r can have duplicates it can be remove in the final state. s in non-empty if s is empty then r*s becomes empty.
Question 41

In SQL, relations can contain null values, and comparisons with null values are treated as unknown. Suppose all comparisons with a null value are treated as false. Which of the following pairs is not equivalent?

x = 5 not AND (not (x = 5)
x = 5 AND x > 4 and x < 6, where x is an integer
x ≠ 5 AND not (x = 5)
None of the above
Question 41 Explanation: 
For all values less than five, x<5 is true and if x=5 then it is false.
Question 42

(a) Suppose you are given an empty B+-tree where each node (leaf and internal) can store up to 5 key values. Suppose values 1,2,….. 10 are inserted, in order, into the tree, Show the tree pictorially
(i) After 6 insertions, and
(ii) After all 10 insertions
Do NOT show intermediate stages.

(b) Suppose instead of splitting a node when it is full, we try to move a value to the left sibling. If there is no left sibling, or the left sibling is full, we split the node. Show the tree after values, 1, 2,….., 9 have been inserted. Assume, as in (a) that each node can hold up to 5 keys.

(c) In general, suppose a B+-tree node can hold a maximum of m keys, and you insert a long sequence of keys in increasing order. Then what approximately is the average number of keys in each leaf level node.
(i) In the normal case, and
(ii) With the insertion as in (b).

Theory Explanation is given below.
Question 42 Explanation: 


Question 43

Consider a bank database with only one relation
transaction (transno, acctno, date, amount)
The amount attribute value is positive for deposits and negative for withdrawals.

(a) Define an SQL view TP containing the information.
(acctno,, T2.amount)
for every pair of transactions T1, T2 such that T1 and T2 are transaction on the same account and the date of T2 is ≤ the date of T1.

(b) Using only the above view TP, write a query to find for each account the minimum balance it ever reached (not including the 0 balance when the account is created). Assume there is at most one transaction per day on each account, and each account has had atleast one transaction since it was created. To simply your query, break it up into 2 steps by defining an intermediate view V.

Theory Explanation is given below.
Question 44

Consider a schema R(A,B,C,D) and functional dependencies A → B and C → D. Then the decomposition of R into R1(AB) and R2(CD) is

dependency preserving and lossless join
lossless join but not dependency preserving
dependency preserving but not lossless join
not dependency preserving and not lossless join
Question 44 Explanation: 
If the given relations are to be lossless then
R1∩R2 ≠ 0
Given R1(A,B), R2
R1∩R2 = 0
Not lossless.
The given relation decomposed into R1(A,B) and R2(C,D) and there are only two functional dependencies A→B and C→D. So the given decomposition is dependency preserving.
Question 45

Suppose the adjacency relation of vertices in a graph is represented in a table Adj(X,Y). Which of the following queries cannot be expressed by a relational algebra expression of constant length?

List of all vertices adjacent to a given vertex
List all vertices which have self loops
List all vertices which belong to cycles of less than three vertices
List all vertices reachable from a given vertex
Question 45 Explanation: 
(a) Finding a adjacency vertex for the given vertex is too simple i.e., Adj(X,Y).
(b) Finding a self loop is also simple (Oop(X,X))
(c) If a → b, b → c then c!=a, finding this is also simple.
(d) List all the elements reachable from a given vertex is too difficult in Relational Algebra.
Question 46

Let r and s be two relations over the relation schemes R and S respectively, and let A be an attribute in R. Then the relational algebra expression σA=a(r⋈s) is always equal to

σA=a (r)
σA=a (r)⨝s
None of the above
Question 46 Explanation: 
(a) A=a for all r
(b) Display table
(c) A=a for all Tables r and s
Question 47

R(A,B,C,D) is a relation. Which of the following does not have a lossless join, dependency preserving BCNF decomposition?

A → B, B → CD
A → B, B → C, C → D
AB → C, C → AD
Question 47 Explanation: 
We have, R (A, B, C, D) and the Functional Dependency set = {AB→C, C→AD}. We decompose it as R1(A, B, C) and R2(C, D). This preserves all dependencies and the join is lossless too, but the relation R1 is not in BCNF. In R1 we keep ABC together otherwise preserving {AB→C} will fail, but doing so also causes {C→A} to appear in R1. {C→A} violates the condition for R1 to be in BCNF as C is not a super key. Condition that all relations formed after decomposition should be in BCNF is not satisfied here.
Question 48

Which of the following relational calculus expressions is not safe?

{t|∃u ∈ R1 (t[A] = u[A])∧ ¬∃s ∈ R2 (t[A] = s[A])}
{t|∀u ∈ R1 (u[A]= "x" ⇒ ∃s ∈ R2 (t[A] = s[A] ∧ s[A] = u[A]))}
{t|¬(t ∈ R1)}
{t|∃u ∈ R1 (t[A] = u[A])∧ ∃s ∈ R2 (t[A] = s[A])}
Question 49

Consider a relation geq which represents “greater than or equal to”, that is, (x,y) ∈ geq only if y >= x.

create table geq
(  Ib integer not null
   ub integer not null
   primary key 1b
   foreign key (ub) references geq on delete cascade ) 

Which of the following is possible if a tuple (x,y) is deleted?

A tuple (z,w) with z > y is deleted
A tuple (z,w) with z > x is deleted
A tuple (z,w) with w < x is deleted
The deletion of (x,y) is prohibited
Question 50

Consider the relation examinee (regno, name, score), where regno is the primary key to score is a real number.
(a) Write a relational algebra using (∏,σ,ρ,×) to find the list of names which appear more than once in examinee.
(b) Write an SQL query to list the regno of examinees who have a score greater than the average score.
(c) Suppose the relation appears (regno, centr_code) specifies the center where an examinee appears. Write an SQL query to list the centr_code having an examinee of score greater than 80.

Theory Explanation is given below.
There are 50 questions to complete.

Access subject wise (1000+) question and answers by becoming as a solutions adda PRO SUBSCRIBER with Ad-Free content

Register Now