Q. 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?

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Q. 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?

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Q. 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?

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Q. The maximum number of superkeys for the relation schema R(E,F,G,H) with E as the key is

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Q. Which one of the following statements about normal forms is FALSE?

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Q. 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?

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Q. 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?

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Q. 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

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Q. 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:

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Q. 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.

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Q. With regard to the expressive power of the formal relational query languages, which of the following statements is true?

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Q. 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).

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Q. 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

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Q. 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

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Q. 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?

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

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Q. 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?

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Q. 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? (GATE CS 2000)

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Q. Consider the relation X(P, Q, R, S, T, U) with the following set of functional dependencies

F = {
{P, R} → {S,T},
{P, S, U} → {Q, R}
}

Which of the following is the trivial functional dependency in F+ is closure of F?

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Q. A relational database contains two tables student and department in which student table has columns roll_no, name and dept_id and department table has columns dept_id and dept_name. The following insert statements were executed successfully to populate the empty tables:

Insert into department values (1, 'Mathematics')
Insert into department values (2, 'Physics')
Insert into student values (l, 'Navin', 1)
Insert into student values (2, 'Mukesh', 2)
Insert into student values (3, 'Gita', 1)

How many rows and columns will be retrieved by the following SQL statement?

Select * from student, department

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