Relational Algebra and SQL Queries Previous Year Questions (PYQs) for GATE DA: 9+ Solved Questions with Step-by-Step Solutions

Solve 9+ Relational Algebra and SQL Queries previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

Chapter Roadmap: Relational Algebra and SQL Queries

Your Learning Journey

Relational Algebra & Semantics

Formal query language using mathematical operations. Highest weightage topic.

SQL Joins, Aggregation & Grouping

Practical SQL implementation with table combinations and summary computations.

SQL Subqueries & Evaluation

Nested queries and execution semantics. Understand internal processing.

By the end of this chapter, you will:

Write queries in both relational algebra and SQL
Predict query results for any given database instance
Understand join semantics and aggregation behavior
Analyze nested queries and their execution order

What is Relational Algebra?

The Core Idea

Relational algebra is a procedural query language that operates on relations (tables) to produce new relations.

InputOne or two relations

OutputA new relation (table)

ProceduralSpecifies how to get the result

ComposableOutput becomes next input

The Six Fundamental Operations

Operation	Symbol	Purpose
Select	$σ$	Filter rows
Project	$π$	Filter columns
Union	$\cup$	Combine rows
Difference	$-$	Remove rows
Product	$\times$	All combinations
Rename	$ρ$	Rename attrs

Relational Algebra and SQL Queries: Solved Questions with Step-by-Step Explanations (5 Problems)

Question 1 · Database Management and Warehousing NAT

On a relation named Loan of a bank:

Loan
loan number	branch name	amount
L11	Banjara Hills	90000
L14	Kondapur	50000
L15	SR Nagar	40000
L22	SR Nagar	25000
L23	Balanagar	80000
L25	Kondapur	70000
L19	SR Nagar	65000

the following SQL query is executed.

SELECT L1.loan number
FROM Loan L1
WHERE L1.amount > (SELECT MAX (L2.amount)
                    FROM Loan L2
                    WHERE L2.branch name = ’SR Nagar’);

The number of rows returned by the query is (Answer in integer)

Question 2 · Database Management and Warehousing MCQ

Consider a database that includes the following relations:
Defender(name, rating, side, goals)
Forward(name, rating, assists, goals)
Team(name, club, price)
Which ONE of the following relational algebra expressions checks that every name
occurring in Team appears in either Defender or Forward, where

ϕ

denotes the
empty set?

A.
$Π_{nam e} (Team) ∖ (Π_{nam e} (Defender) \cap Π_{nam e} (Forward)) = ϕ$
B.
$(Π_{nam e} (Defender) \cap Π_{nam e} (Forward)) ∖ Π_{nam e} (Team) = ϕ$
C.
$Π_{nam e} (Team) ∖ (Π_{nam e} (Defender) \cup Π_{nam e} (Forward)) = ϕ$
D.
$(Π_{nam e} (Defender) \cup Π_{nam e} (Forward)) ∖ Π_{nam e} (Team) = ϕ$

Question 3 · Database Management and Warehousing MCQ

Consider the given relations

X, Y

and

Z

. The relation

X

has three columns

P, Q

and

R

. The relation

Y

has three columns

P, Q

and

S

. The relation

Z

has two columns

P

and

T

X

P

Q

R

P1 Q1 R1
P2 Q2 R2
P3 Q3 R2

Y

P

Q

S

P1 Q1 2
P1 Q2 5
P2 Q1 6
P3 Q3 1

Z

P

T

P1 T1
P3 T2
P4 T3
P4 NULL

Consider the relational algebra expression

P R S \prod [(σ_{(Q = Q 3 \lor R = R 2)} [X ⋈ Y]) ⋈ (σ_{(S > 1)} [Y ⋈ Z])]

where

⋈

denotes natural join operation.

Which of the following options is the correct output for the given expression?

A.
Two rows (P1, R1, 2) and (P1, R1, 5)
B.
Three rows (P1, R1, 2), (P1, R1, 5) and (P2, R2, 6)
C.
One row (P1, R1, 2)
D.
Zero rows

Question 4 · Database Management and Warehousing MCQ

Consider the following three relations:

Car (model, year, serial, color)
Make (maker, model)
Own (owner, serial)

A tuple in Car represents a specific car of a given model, made in a given year, with a serial number and a color. A tuple in Make specifies that a maker company makes cars of a certain model. A tuple in Own specifies that an owner owns the car with a given serial number. Keys are underlined; (owner, serial) together form key for Own. (

⋈

denotes natural join)

π_{o w n er} (O w n ⋈ (σ_{co l or = ‘‘ r e d^{''}} (C a r ⋈ (σ_{mak er = ‘‘ A B C^{''}} M ak e))))

Which one of the following options describes what the above expression computes?

A.
All owners of a red car, a car made by ABC, or a red car made by ABC
B.
All owners of more than one car, where at least one car is red and made by ABC
C.
All owners of a red car made by ABC
D.
All red cars made by ABC

Question 5 · Database Management and Warehousing NAT

Consider the following two tables named Raider and Team in a relational database
maintained by a Kabaddi league. The attribute ID in table Team references the
primary key of the Raider table, ID.

Raider
ID	Name	Raids	RaidPoints
1	Arjun	200	250
2	Ankush	190	219
3	Sunil	150	200
4	Reza	150	190
5	Pratham	175	220
6	Gopal	193	215

The SQL query described below is executed on this database:

SELECT *
FROM Raider, Team
WHERE Raider.ID=Team.ID AND City=“Jaipur” AND
RaidPoints > 200;

The number of rows returned by this query is ______.

Team
City	ID	BidPoints
Jaipur	2	200
Patna	3	195
Hyderabad	5	175
Jaipur	1	250
Patna	4	200
Jaipur	6	200

A question from this chapter

Question 1

On a relation named Loan of a bank: Loan loan number branch name amount L11 Banjara Hills 90000 L14 Kondapur 50000 L15 SR Nagar 40000 L22 SR Nagar 25000 L23 Balanagar 80000 L25 Kondapur 70000 L19 SR Nagar 65000 the following SQL query is executed. SELECT L1.loan number FROM Loan L1 WHERE L1.amount > (SELECT MAX (L2.amount) FROM Loan L2 WHERE L2.branch name = ’SR Nagar’); The number of rows returned by the query is (Answer in integer)

Question 2

Consider a database that includes the following relations: Defender(name, rating, side, goals) Forward(name, rating, assists, goals) Team(name, club, price) Which ONE of the following relational algebra expressions checks that every name occurring in Team appears in either Defender or Forward, where ϕ denotes the empty set?

Question 3

Consider the given relations X, Y and Z . The relation X has three columns P, Q and R . The relation Y has three columns P, Q and S . The relation Z has two columns P and T . X P Q R P1 Q1 R1 P2 Q2 R2 P3 Q3 R2 Y P Q S P1 Q1 2 P1 Q2 5 P2 Q1 6 P3 Q3 1 Z P T P1 T1 P3 T2 P4 T3 P4 NULL Consider the relational algebra expression P R S \prod [(σ_{(Q = Q 3 \lor R = R 2)} [X ⋈ Y]) ⋈ (σ_{(S > 1)} [Y ⋈ Z])] where ⋈ denotes natural join operation. Which of the following options is the correct output for the given expression?

Question 4

Consider the following three relations: Car (model, year, serial, color) Make (maker, model) Own (owner, serial) A tuple in Car represents a specific car of a given model, made in a given year, with a serial number and a color. A tuple in Make specifies that a maker company makes cars of a certain model. A tuple in Own specifies that an owner owns the car with a given serial number. Keys are underlined; (owner, serial) together form key for Own. (⋈ denotes natural join) π_{o w n er} (O w n ⋈ (σ_{co l or = ‘‘ r e d^{''}} (C a r ⋈ (σ_{mak er = ‘‘ A B C^{''}} M ak e)))) Which one of the following options describes what the above expression computes?

Question 5

Consider the following two tables named Raider and Team in a relational database maintained by a Kabaddi league. The attribute ID in table Team references the primary key of the Raider table, ID. Raider ID Name Raids RaidPoints 1 Arjun 200250 2 Ankush 190219 3 Sunil 150200 4 Reza 150190 5 Pratham 175220 6 Gopal 193215 The SQL query described below is executed on this database: SELECT * FROM Raider, Team WHERE Raider.ID=Team.ID AND City=“Jaipur” AND RaidPoints > 200; The number of rows returned by this query is ______. Team City ID BidPoints Jaipur 2200 Patna 3195 Hyderabad 5175 Jaipur 1250 Patna 4200 Jaipur 6200

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Relational Algebra and SQL Queries Previous Year Questions (PYQs) for GATE DA: 9+ Solved Questions with Step-by-Step Solutions

Chapter Roadmap: Relational Algebra and SQL Queries

Relational Algebra & Semantics

SQL Joins, Aggregation & Grouping

SQL Subqueries & Evaluation

What is Relational Algebra?

The Core Idea

The Six Fundamental Operations

Relational Algebra and SQL Queries: Solved Questions with Step-by-Step Explanations (5 Problems)

More previous year questions (pyqs) in this unit

A question from this chapter

Login to view the complete previous-year questions and solutions

Personalised first. High quality throughout.

Built around you, not around a syllabus PDF

Revision that hits your weak spots

Questions calibrated to the real exam

Notes written for recall, not for volume

One place for everything

Honest progress

Unlock the whole course