Gate MCQ Quiz Hub

1. Which of the following statements are TRUE about an SQL query? P : An SQL query can contain a HAVING clause even if it does not have a GROUP BY clause Q : An SQL query can contain a HAVING clause only if it has a GROUP BY clause R : All attributes used in the GROUP BY clause must appear in the SELECT clause S : Not all attributes used in the GROUP BY clause need to appear in the SELECT clause
P and R
P and S
Q and R
Q and S

2. Table A Id Name Age ---------------- 12 Arun 60 15 Shreya 24 99 Rohit 11 Table B Id Name Age ---------------- 15 Shreya 24 25 Hari 40 98 Rohit 20 99 Rohit 11 Table C Id Phone Area ----------------- 10 2200 02 99 2100 01 Consider the above tables A, B and C. How many tuples does the result of the following SQL query contains? SELECT A.id FROM A WHERE A.age > ALL (SELECT B.age FROM B WHERE B. name = "arun")
4
3
0
1

3. Consider a database table T containing two columns X and Y each of type integer. After the creation of the table, one record (X=1, Y=1) is inserted in the table. Let MX and My denote the respective maximum values of X and Y among all records in the table at any point in time. Using MX and MY, new records are inserted in the table 128 times with X and Y values being MX+1, 2*MY+1 respectively. It may be noted that each time after the insertion, values of MX and MY change. What will be the output of the following SQL query after the steps mentioned above are carried out? SELECT Y FROM T WHERE X=7;
127
255
129
257

4. Database table by name Loan_Records is given below. Borrower Bank_Manager Loan_Amount Ramesh Sunderajan 10000.00 Suresh Ramgopal 5000.00 Mahesh Sunderajan 7000.00 What is the output of the following SQL query? SELECT Count(*) FROM ( (SELECT Borrower, Bank_Manager FROM Loan_Records) AS S NATURAL JOIN (SELECT Bank_Manager, Loan_Amount FROM Loan_Records) AS T );
3
9
5
6

5. A relational schema for a train reservation database is given below. Passenger (pid, pname, age) Reservation (pid, class, tid) Table: Passenger pid pname age ----------------- 0 Sachin 65 1 Rahul 66 2 Sourav 67 3 Anil 69 Table : Reservation pid class tid --------------- 0 AC 8200 1 AC 8201 2 SC 8201 5 AC 8203 1 SC 8204 3 AC 8202 What pids are returned by the following SQL query for the above instance of the tables? SELECT pid FROM Reservation , WHERE class ‘AC’ AND EXISTS (SELECT * FROM Passenger WHERE age > 65 AND Passenger. pid = Reservation.pid)
1, 0
1, 2
1, 3
1, 5

6. Consider the following relational schema: Suppliers(sid:integer, sname:string, city:string, street:string) Parts(pid:integer, pname:string, color:string) Catalog(sid:integer, pid:integer, cost:real) Consider the following relational query on the above database: SELECT S.sname FROM Suppliers S WHERE S.sid NOT IN (SELECT C.sid FROM Catalog C WHERE C.pid NOT IN (SELECT P.pid FROM Parts P WHERE P.color<> 'blue')) Assume that relations corresponding to the above schema are not empty. Which one of the following is the correct interpretation of the above query?
Find the names of all suppliers who have supplied a non-blue part.
Find the names of all suppliers who have not supplied a non-blue part.
Find the names of all suppliers who have supplied only blue parts.
Find the names of all suppliers who have not supplied only blue parts.

7. 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”)
Q1 is the correct query
Q2 is the correct query
Both Q1 and Q2 produce the same answer
Neither Q1 nor Q2 is the correct quer

8. Given the following statements: S1: A foreign key declaration can always be replaced by an equivalent check assertion in SQL. S2: Given the table R(a,b,c) where a and b together form the primary key, the following is a valid table definition. CREATE TABLE S ( a INTEGER, d INTEGER, e INTEGER, PRIMARY KEY (d), FOREIGN KEY (a) references R) Which one of the following statements is CORRECT?
S1 is TRUE and S2 is FALSE
Both S1 and S2 are TRUE
S1 is FALSE and S2 is TRUE
Both S1 and S2 are FALSE

9. Given the following schema: employees(emp-id, first-name, last-name, hire-date, dept-id, salary) departments(dept-id, dept-name, manager-id, location-id) You want to display the last names and hire dates of all latest hires in their respective departments in the location ID 1700. You issue the following query: SQL> SELECT last-name, hire-date FROM employees WHERE (dept-id, hire-date) IN (SELECT dept-id, MAX(hire-date) FROM employees JOIN departments USING(dept-id) WHERE location-id = 1700 GROUP BY dept-id); What is the outcome?
It executes but does not give the correct result
It executes and gives the correct result
generates an error because of pairwise comparison
It generates an error because the GROUP BY clause cannot be used with table joins in a subquery

10. SQL allows tuples in relations, and correspondingly defines the multiplicity of tuples in the result of joins. Which one of the following queries always gives the same answer as the nested query shown below: select * from R where a in (select S.a from S)
select R.* from R, S where R.a=S.a (D)
select distinct R.* from R,S where R.a=S.a
select R.* from R,(select distinct a from S) as S1 where R.a=S1.a
select R.* from R,S where R.a=S.a and is unique R

11. Consider the following relational schema: employee(empId, empName, empDept) customer(custId, custName, salesRepId, rating) salesRepId is a foreign key referring to empId of the employee relation. Assume that each employee makes a sale to at least one customer. What does the following query return? SELECT empName FROM employee E WHERE NOT EXISTS (SELECT custId FROM customer C WHERE C.salesRepId = E.empId AND C.rating <> ’GOOD’);
Names of all the employees with at least one of their customers having a ‘GOOD’ rating.
Names of all the employees with at most one of their customers having a ‘GOOD’ rating.
Names of all the employees with none of their customers having a ‘GOOD’ rating.
Names of all the employees with all their customers having a ‘GOOD’ rating.

12. The statement that is executed automatically by the system as a side effect of the modification of the database is
backup
assertion
recovery
trigger

13. Which of the following command is used to delete a table in SQL?
delete
truncate
remove
drop

14. Consider the relation "enrolled(student, course)" in which (student, course) is the primary key, and the relation "paid(student, amount)" where student is the primary key. Assume no null values and no foreign keys or integrity constraints. Given the following four queries: Query1: select student from enrolled where student in (select student from paid) Query2: select student from paid where student in (select student from enrolled) Query3: select E.student from enrolled E, paid P where E.student = P.student Query4: select student from paid where exists (select * from enrolled where enrolled.student = paid.student) Which one of the following statements is correct?
All queries return identical row sets for any database
Query2 and Query4 return identical row sets for all databases but there exist databases for which Query1 and Query2 return different row sets.
There exist databases for which Query4 will encounter an integrity violation at runtime.
There exist databases for which Query3 returns strictly fewer rows than Query2

15. The following table has two attributes A and C where A is the primary key and C is the foreign key referencing A with on-delete cascade. A C ----- 2 4 3 4 4 3 5 2 7 2 9 5 6 4 The set of all tuples that must be additionally deleted to preserve referential integrity when the tuple (2,4) is deleted is:
(3,4) and (6,4)
(5,2) and (7,2)
(5,2), (7,2) and (9,5)
(3,4), (4,3) and (6,4)

16. The relation book (title, price) contains the titles and prices of different books. Assuming that no two books have the same price, what does the following SQL query list? select title from book as B where (select count(*) from book as T where T.price > B.price) < 5
Titles of the four most expensive books
Title of the fifth most inexpensive book
Title of the fifth most expensive bookTitles of the five most expensive books
Titles of the five most expensive books

17. Consider the following relation schema pertaining to a students database: Student (rollno, name, address) Enroll (rollno, courseno, coursename) where the primary keys are rollno,courseno. The number of tuples in the Student and Enroll tables are 120 and 8 respectively. What are the maximum and minimum number of tuples that can be present in (Student * Enroll), where '*' denotes natural join ?
8, 0
120, 8
960, 8
960, 120

18. The employee information in a company is stored in the relation Employee (name, sex, salary, deptName) (name is primary key ) Consider the following SQL query select deptName from Employee where sex = 'M' group by deptName having avg (salary) > (select avg (salary) from Employee) It returns the names of the department in which
the average salary is more than the average salary in the company
the average salary of male employees is more than the average salary of all male employees in the company
the average salary of male employees is more than the average salary of employees in the same department
the average salary of male employees is more than the average salary in the company

19. Consider the set of relations shown below and the SQL query that follows. Students: (Roll_number, Name, Date_of_birth) Courses: (Course number, Course_name, Instructor) Grades: (Roll_number, Course_number, Grade) select distinct Name from Students, Courses, Grades where Students. Roll_number = Grades.Roll_number and Courses.Instructor = Korth and Courses.Course_number = Grades.Course_number and Grades.grade = A Which of the following sets is computed by the above query?
Names of students who have got an A grade in all courses taught by Korth
Names of students who have got an A grade in all courses
Names of students who have got an A grade in at least one of the courses taught by Korth
None of the above

20. 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

21. 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 AND not(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

22. Consider the following three table to store student enrollements in different courses. Student(EnrollNo, Name) Course(CourseID, Name) EnrollMents(EnrollNo, CourseID) (EnrollNo,CourseID are primary keys) What does the following query do? SELECT S.Name FROM Student S, Course C, Enrollments E WHERE S.EnrollNo = E.EnrollNo AND C.Name = "DBMS" AND E.CourseID = C.CourseID AND S.EnrollNo IN (SELECT S2.EnrollNo FROM Student S2, Course C2, Enrollments E2 WHERE S2.EnrollNo = E2.EnrollNo AND E2.CourseID = C2.CourseID C2.Name = "OS")
Name of all students who are either enrolled in "DBMS" or "OS" courses
Name of all students who are enrolled in "DBMS" and "OS"
Name of all students who are either enrolled in "DBMS" or "OS" or both
None of the above

23. Consider the following Employee table ID salary DeptName 1 10000 EC 2 40000 EC 3 30000 CS 4 40000 ME 5 50000 ME 6 60000 ME 7 70000 CS How many rows are there in the result of following query? SELECT E.ID FROM Employee E WHERE EXISTS (SELECT E2.salary FROM Employee E2 WHERE E2.DeptName = 'CS' AND E.salary > E2.salary)
0
4
5
6

24. Select operation in SQL is equivalent to
the selection operation in relational algebra
the selection operation in relational algebra, except that select in SQL retains duplicates
the projection operation in relational algebra
the projection operation in relational algebra, except that select in SQL retains duplicates

25. Consider the following relation Cinema (theater, address, capacity) Which of the following options will be needed at the end of the SQL query SELECT P1. address FROM Cinema P1 Such that it always finds the addresses of theaters with maximum capacity?
WHERE P1. Capacity> = All (select P2. Capacity from Cinema P2)
WHERE P1. Capacity> = Any (select P2. Capacity from Cinema P2)
WHERE P1. Capacity > All (select max(P2. Capacity) from Cinema P2)
WHERE P1. Capacity > Any (select max (P2. Capacity) from Cinema P2)

26. A company maintains records of sales made by its salespersons and pays them commission based on each individual's total sales made in a year. This data is maintained in a table with following schema: salesinfo = (salespersonid, totalsales, commission) In a certain year, due to better business results, the company decides to further reward its salespersons by enhancing the commission paid to them as per the following formula: If commission < = 50000, enhance it by 2% If 50000 < commission < = 100000, enhance it by 4% If commission > 100000, enhance it by 6% The IT staff has written three different SQL scripts to calculate enhancement for each slab, each of these scripts is to run as a separate transaction as follows: T1 Update salesinfo Set commission = commission * 1.02 Where commission < = 50000; T2 Update salesinfo Set commission = commission * 1.04 Where commission > 50000 and commission is < = 100000; T3 Update salesinfo Set commission = commission * 1.06 Where commission > 100000; Which of the following options of running these transactions will update the commission of all salespersons correctly?
Execute T1 followed by T2 followed by T3
Execute T2, followed by T3; T1 running concurrently throughout
Execute T3 followed by T2; T1 running concurrently throughout
Execute T3 followed by T2 followed by T1

27. A table 'student' with schema (roll, name, hostel, marks), and another table 'hobby' with schema (roll, hobbyname) contains records as shown below: Table: Student ROLL NAME HOSTEL MARKS 1798 Manoj Rathod 7 95 2154 Soumic Banerjee 5 68 2369 Gumma Reddy 7 86 2581 Pradeep Pendse 6 92 2643 Suhas Kulkarni 5 78 2711 Nitin Kadam 8 72 2872 Kiran Vora 5 92 2926 Manoj Kunkalikar 5 94 2959 Hemant Karkhanis 7 88 3125 Rajesh Doshi 5 82 Table: hobby ROLL HOBBYNAME 1798 chess 1798 music 2154 music 2369 swimming 2581 cricket 2643 chess 2643 hockey 2711 volleyball 2872 football 2926 cricket 2959 photography 3125 music 3125 chess The following SQL query is executed on the above tables: select hostel from student natural join hobby where marks > = 75 and roll between 2000 and 3000; Relations S and H with the same schema as those of these two tables respectively contain the same information as tuples. A new relation S’ is obtained by the following relational algebra operation: S’ = ∏hostel ((σs.roll = H.roll (σmarks > 75 and roll > 2000 and roll < 3000 (S)) X (H)) The difference between the number of rows output by the SQL statement and the number of tuples in S’ is
6
4
2
0

28. In an inventory management system implemented at a trading corporation, there are several tables designed to hold all the information. Amongst these, the following two tables hold information on which items are supplied by which suppliers, and which warehouse keeps which items along with the stock-level of these items. Supply = (supplierid, itemcode) Inventory = (itemcode, warehouse, stocklevel) For a specific information required by the management, following SQL query has been written Select distinct STMP.supplierid From Supply as STMP Where not unique (Select ITMP.supplierid From Inventory, Supply as ITMP Where STMP.supplierid = ITMP.supplierid And ITMP.itemcode = Inventory.itemcode And Inventory.warehouse = 'Nagpur'); For the warehouse at Nagpur, this query will find all suppliers who
do not supply any item
supply exactly one item
supply one or more items
supply two or more items

29. Consider the relations r1(P, Q, R) and r2(R, S, T) with primary keys P and R respectively. The relation r1 contains 2000 tuples and r2 contains 2500 tuples. The maximum size of the join r1⋈ r2 is :
2000
2500
4500
5000

30. Student (school-id, sch-roll-no, sname, saddress) School (school-id, sch-name, sch-address, sch-phone) Enrolment(school-id sch-roll-no, erollno, examname) ExamResult(erollno, examname, marks) What does the following SQL query output? SELECT sch-name, COUNT (*) FROM School C, Enrolment E, ExamResult R WHERE E.school-id = C.school-id AND E.examname = R.examname AND E.erollno = R.erollno AND R.marks = 100 AND S.school-id IN (SELECT school-id FROM student GROUP BY school-id HAVING COUNT (*) > 200) GROUP By school-id
for each school with more than 200 students appearing in exams, the name of the school and the number of 100s scored by its students
for each school with more than 200 students in it, the name of the school and the number of 100s scored by its students
for each school with more than 200 students in it, the name of the school and the number of its students scoring 100 in at least one exam
nothing; the query has a syntax error

31. Consider a join (relation algebra) between relations r(R)and s(S) using the nested loop method. There are 3 buffers each of size equal to disk block size, out of which one buffer is reserved for intermediate results. Assuming size(r(R)) < size(s(S)), the join will have fewer number of disk block accesses if
relation r(R) is in the outer loop
relation s(S) is in the outer loop
join selection factor between r(R) and s(S) is more than 0.5
None of These

32. Let E1 and E2 be two entities in an E/R diagram with simple single-valued attributes. R1 and R2 are two relationships between E1 and E2, where R1 is one-to-many and R2 is many-to-many. R1 and R2 do not have any attributes of their own. What is the minimum number of tables required to represent this situation in the relational model?
2
3
4
5

33. In a schema with attributes A, B, C, D and E following set of functional dependencies are given A → B A → C CD → E B → D E → A Which of the following functional dependencies is NOT implied by the above set?
CD → AC
BD → CD
BC → CD
AC → BC

34. A database of research articles in a journal uses the following schema. (VOLUME, NUMBER, STARTPGE, ENDPAGE, TITLE, YEAR, PRICE) The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following functional dependencies exist in the schema. (VOLUME, NUMBER, STARTPAGE, ENDPAGE) -> TITLE (VOLUME, NUMBER) -> YEAR (VOLUME, NUMBER, STARTPAGE, ENDPAGE) -> PRICE The database is redesigned to use the following schemas. (VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE) (VOLUME, NUMBER, YEAR) Which is the weakest normal form that the new database satisfies, but the old one does not?
1NF
2NF
3NF
BCNF

35. Which of the following relational query languages have the same expressive power? 1.Relational algebra 2.Tuple relational calculus restricted to safe expressions 3.Domain relational calculus restricted to safe expressions
II and III only
I and II only
I and III only
I, II and III

36. A Relation R with FD set {A->BC, B->A, A->C, A->D, D->A}. How many candidate keys will be there in R?
1
2
3
4

37. What is the min and max number of tables required to convert an ER diagram with 2 entities and 1 relationship between them with partial participation constraints of both entities?
Min 1 and max 2
Min 1 and max 3
Min 2 and max 3
Min 2 and max 2

38. Relation R has eight attributes ABCDEFGH. Fields of R contain only atomic values. F = {CH -> G, A -> BC, B -> CFH, E -> A, F -> EG} is a set of functional dependencies (FDs) so that F+ is exactly the set of FDs that hold for R. How many candidate keys does the relation R have?
3
4
5
6

39. Consider the FDs given in above question. The relation R is
in 1NF, but not in 2NF
in 2NF, but not in 3NF
n 3NF, but not in BCNF
in BCNF

40. Which of the following is TRUE?
Every relation in 3NF is also in BCNF
A relation R is in 3NF if every non-prime attribute of R is fully functionally dependent on every key of R
Every relation in BCNF is also in 3NF
No relation can be in both BCNF and 3NF

41. Consider a relational table with a single record for each registered student with the following attributes. 1. Registration_Num: Unique registration number of each registered student 2. UID: Unique identity number, unique at the national level for each citizen 3. BankAccount_Num: Unique account number at the bank. A student can have multiple accounts or join accounts. This attribute stores the primary account number. 4. Name: Name of the student 5. Hostel_Room: Room number of the hostel Which one of the following option is INCORRECT?
BankAccount_Num is candidate key
Registration_Num can be a primary key
UID is candidate key if all students are from the same country
If S is a superkey such that S∩UID is NULL then S∪UID is also a superkey

42. Consider a relational table with a single record for each registered student with the following attributes. 1. Registration_Num: Unique registration number of each registered student 2. UID: Unique identity number, unique at the national level for each citizen 3. BankAccount_Num: Unique account number at the bank. A student can have multiple accounts or join accounts. This attribute stores the primary account number. 4. Name: Name of the student 5. Hostel_Room: Room number of the hostel Which one of the following option is INCORRECT?
BankAccount_Num is candidate key
Registration_Num can be a primary key
UID is candidate key if all students are from the same country
If S is a superkey such that S∩UID is NULL then S∪UID is also a superkey

43. Consider the following relational schema: Suppliers(sid:integer, sname:string, city:string, street:string) Parts(pid:integer, pname:string, color:string) Catalog(sid:integer, pid:integer, cost:real) (sid,pid are primary keys) Assume that, in the suppliers relation above, each supplier and each street within a city has a unique name, and (sname, city) forms a candidate key. No other functional dependencies are implied other than those implied by primary and candidate keys. Which one of the following is TRUE about the above schema?
The schema is in BCNF
The schema is in 2NF but not in 3NF
The schema is in 2NF but not in 3NF
The schema is not in 2NF

44. Consider the following relational schemes for a library database: Book (Title, Author, Catalog_no, Publisher, Year, Price) Collection (Title, Author, Catalog_no) with in the following functional dependencies: I. Title Author --> Catalog_no II. Catalog_no --> Title, Author, Publisher, Year III. Publisher Title Year --> Price Assume {Author, Title} is the key for both schemes. Which of the following statements is true?
Both Book and Collection are in BCNF
Both Book and Collection are in 3NF only
Book is in 2NF and Collection is in 3NF d.
Both Book and Collection are in 2NF only

45. Consider the following relational schemes for a library database: Book (Title, Author, Catalog_no, Publisher, Year, Price) Collection (Title, Author, Catalog_no) with in the following functional dependencies: I. Title Author --> Catalog_no II. Catalog_no --> Title, Author, Publisher, Year III. Publisher Title Year --> Price Assume {Author, Title} is the key for both schemes. Which of the following statements is true?
Both Book and Collection are in BCNF
Both Book and Collection are in BCNF
Both Book and Collection are in 3NF only
Both Book and Collection are in 2NF only

46. Consider the relation scheme R = {E, F, G, H, I, J, K, L, M, M} and the set of functional dependencies {{E, F} -> {G}, {F} -> {I, J}, {E, H} -> {K, L}, K -> {M}, L -> {N} on R. What is the key for R?
{E, F}
{E, F, H}
{E, F, H, K, L}
{E}

47. Given the following two statements: S1: Every table with two single-valued attributes is in 1NF, 2NF, 3NF and BCNF. S2: AB->C, D->E, E->C is a minimal cover for the set of functional dependencies AB->C, D->E, AB->E, E->C. Which one of the following is CORRECT?
S1 is TRUE and S2 is FALSE
Both S1 and S2 are TRUE
S1 is FALSE and S2 is TRUE
Both S1 and S2 are FALSE

48. The maximum number of superkeys for the relation schema R(E,F,G,H) with E as the key is
5
6
7
8

49. Which one of the following statements about normal forms is FALSE?
BCNF is stricter than 3NF
Lossless, dependency-preserving decomposi­tion into 3NF is always possible
Lossless, dependency-preserving decomposi­tion into BCNF is always possible
Any relation with two attributes is in BCNF

50. Let r be a relation instance with schema R = (A, B, C, D). We define r1 = ΠA, B, C (r) and r2 = ΠA.D (r). Let s = r1 * r2 where * denotes natural join. Given that the decomposition of r into r1 and r2 is lossy, which one of the following is TRUE?
s ⊂ r
r ∪ s
r ⊂ s
r * s = s

51. r ⊂ s
s ⊂ r
r ∪ s
r ⊂ s
r * s = s

52. Consider a relation scheme R = (A, B, C, D, E, H) on which the following functional dependencies hold: {A–>B, BC–>D, E–>C, D–>A}. What are the candidate keys of R?
AE, BE
AE, BE, DE
AEH, BEH, BCH
AEH, BEH, DEH

53. The relation scheme Student Performance (name, courseNo, rollNo, grade) has the following functional dependencies: name, courseNo → grade rollNo, courseNo → grade name → rollNo rollNo → name The highest normal form of this relation scheme is
2 NF
3 NF
BCNF
4NF

54. Consider the following functional dependencies in a database: Data_of_Birth → Age Age → Eligibility Name → Roll_number Roll_number → Name Course_number → Course_name Course_number → Instructor (Roll_number, Course_number) → Grade The relation (Roll_number, Name, Date_of_birth, Age) is:
In second normal form but not in third normal form
In third normal form but not in BCNF
In BCNF
None of the above

55. Relation R with an associated set of functional dependencies, F is decomposed into BCNF. The redundancy (arising out of functional dependencies) in the resulting set relations is.
Zero
More than zero but less than that of an equivalent 3NF decomposition
Proportional to the size of F+
Indeterminate

56. With regard to the expressive power of the formal relational query languages, which of the following statements is true?
Relational algebra is more powerful than relational calculus
https://compsciedu.com/mcq-questions/DBMS/GATE-cse-question-paper/6#:~:text=Relational%20algebra%20has%20the%20same%20power%20as%20relational%20calculus
Relational algebra has the same power as safe relational calculus
None of the above

57. Relation R is decomposed using a set of functional dependencies, F and relation S is decomposed using another set of functional dependencies G. One decomposition is definitely BCNF, the other is definitely 3NF, but it is not known which is which. To make a guaranteed identification, which one of the following tests should be used on the decompositions? (Assume that the closures of F and G are available).
Dependency-preservation
Lossless-join
BCNF definition
3NF definition

58. From the following instance of a relation scheme R (A, B, C), we can conclude that : A B C 1 1 1 1 1 0 2 3 2 2 3 2
A functionally determines B and B functionally determines C
A functionally determines B and B does not functionally determine C
B does not functionally determine C
A does not functionally determine B and B does not functionally determine C

59. 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

60. 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