GATE|| DBMS || Functional Dependency And Normalizations || Pyq ( 2010 to 2025 )

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Question 1

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?
[GATE 2014 || SET-1 MCQ || 2-mark]

  • 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.

Question 2

In a relational data model, which one of the following statements is TRUE? [GATE 2022 || MCQ || 1-mark]

  • A relation with only two attributes is always in BCNF.

  • If all attributes of a relation are prime attributes, then the relation is in BCNF.

  • Every relation has at least one non-prime attribute.

  • BCNF decompositions preserve functional dependencies.

Question 3

Consider a relation R(A,B,C,D,E) with the following three functional dependencies.
AB→C;BC→D;C→E
The number of super keys in the relation R is . [GATE 2022|| NAT|| 2-mark]

  • 8

Question 4

Which one of the options given below refers to the degree (or arity) of a relation in relational database systems? [GATE 2023|| MCQ || 1-mark]

  • Number of attributes of its relation schema.

  • Number of tuples stored in the relation.

  • Number of entries in the relation.

  • Number of distinct domains of its relation schema.

Question 5

Which of the following statements about a relation R in first normal form (1NF) is/are TRUE ?
[GATE 2024 || SET-1 MSQ || 2-mark]

  • R can have a multi-attribute key

  • R cannot have a foreign key

  • R cannot have a composite attribute

  • R cannot have more than one candidate key

Question 6

The symbol → indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE?

[GATE 2024|| SET-1 MSQ || 2-mark]

  • (X,Y)→(Z,W) implies X→(Z,W)

  • (X,Y)→(Z,W) implies (X,Y)→Z

  • ((X,Y)→Z and W→Y) implies (X,W)→Z

  • (X→Y and Y→Z) implies X→Z

Question 7

Consider the following relational schema along with all the functional dependencies that hold on them.
R1(A,B,C,D,E):{D→E,EA→B,EB→C}
R2(A,B,C,D):{A→D,A→B,C→A} [GATE|| 2025 || SET- 2 MSQ || 2-mark]

  • R1 is in 3NF

  • R2 is in 3NF

  • R1 is NOT in 3NF

  • R2 is NOT in 3NF

Question 8

Consider a relational schema team(name , city , owner) with functional dependencies {name → city , name → owner} .
The relation team is decomposed into two relations,  t1(name , city) and t2(name , owner). Which of the following statement(s) is/are TRUE?

[GATE|| 2025|| MSQ SET-1 || 2-mark]

  • The relation team is NOT in BCNF.

  • The relations t1and t2 are in BCNF.

  • The decomposition constitutes a lossless join.

  • The relation team is NOT in 3NF.

Question 9

Which of the following is TRUE?
[GATE 2012|| MCQ || 1-mark]

  • 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

Question 10

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? [GATE 2013|| MCQ || 2-mark]

  • 3

  • 4

  • 5

  • 6

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