# Relational Algebra · Database Management System · GATE CSE

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## Marks 1

GATE CSE 2022
Consider the following three relations in a relational database. Employee ( $$\underline {eld}$$ , Name), Brand ( $$\underline {bld}$$ , bName), Own...
GATE CSE 2014 Set 3
What is the optimized version of the relation algebra expression $$\pi_{A1}(\pi_{A2}(\sigma_{F1}(\sigma_{F2}(r))))$$, where $$A1, A2$$ are sets of att...
GATE CSE 2008
Which of the following tuple relational calculus expression(s) is/are equivalent to $$\forall t \in r \left(P\left(t\right)\right)$$? I. $$\neg \exist... GATE CSE 2006 Consider the relations r1(P, Q, R) and r2(R, S, T) with primary keys P and R respectively. The relation r1 contains 2000 tuples and r2 contains 2500 t... GATE CSE 2006 Which of the following relational query languages have the same expressive power? I) Relational algebra II) Tuple relational calculus restricted to sa... GATE CSE 2005 Let r be a relation instance with schema R = (A, B, C, D). We define$${r_1} = {\pi _{A,B,C}}\left( r \right)$$and$${r_1} = {\pi _{A,D}}\left( r \ri...
GATE CSE 2004
Let R1 (A, B, C) and R2 (D, E) be two relation schema, where the primary keys are shown underlined, and let C be a foreign key in R1 referring to R2. ...
GATE CSE 2003
Consider the following SQL query: Select distinct a1, a2, ..., an From r1, r2, ..., rm Where P; For an arbitrary predicate P, this query is equi...
GATE CSE 2002
With regard to the expressive power of the formal relational query languages, which of the following statements is true?
GATE CSE 2000
Given the relations employee (name, salary, deptno), and department (deptno, deptname, address) Which of the following queries cannot be expressed u...
GATE CSE 1999
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 ...
GATE CSE 1999
The relational algebra expression equivalent to the following tuple calculus expression: $$\left\{ {t|t \in r \wedge \left( {t\left[ A \right] = 10 \w... GATE CSE 1994 Give a relational algebra expression using only the minimum number of operators from$$\left( { \cup ,\, - } \right)$$which is equivalent to$$R \cap...
GATE CSE 1994
An instance of a relational scheme R(A, B, C) has distinct values for attribute A. Can you conclude that A is a candidate key for R?

## Marks 2

GATE CSE 2021 Set 1
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 ...
GATE CSE 2019
Consider the following relations P(X,Y,Z), Q(X,Y,T) and R(Y,V). How many tuples will be returned by the following relational algebra query? ...
GATE CSE 2018
Consider the relations $$r(A, B)$$ and $$s(B, C),$$ where $$s.B$$ is a primary key and $$r.B$$ is a foreign key referencing $$s.B.$$ Consider the quer...
GATE CSE 2015 Set 2
Consider two relations $${R_1}\left( {A,B} \right)$$ with the tuples $$(1,5), (3,7)$$ and $${R_2}\left( {A,C} \right) = \left( {1,7} \right),\left( {4... GATE CSE 2014 Set 3 Consider the relational schema given below, where eId of the relation dependent is a foreign key referring to empId of the relation employee. Assume t... GATE CSE 2014 Set 2 Consider a join (relation algebra) between relations r(R)and s(S) using the nested loop method. There are 3 buffers each of size equal to disk block s... GATE CSE 2012 Suppose R1 (A, B) and R2 (C, D) are two relation schemas. Let r1 and r2 be the corresponding relation instances. B is a foreign key that refers to C i... GATE CSE 2012 Consider the following relations A, B and C: A .tg {border-collapse:collapse;border-spacing:0;} .tg td{font-family:Arial, sans-serif;font-size:14px;... GATE CSE 2012 Consider the following relations A, B and C: A .tg {border-collapse:collapse;border-spacing:0;} .tg td{font-family:Arial, sans-serif;font-size:14px;... GATE CSE 2011 Consider a relational table r with sufficient number of records, having attributes A1, A2,....., An and let 1$$ \le $$p$$ \le $$n. Two queries Q1 ... GATE CSE 2010 The following functional dependencies hold for relations R(A, B, C) and S(B, D, E):$$\eqalign{ & B \to A \cr & A \to C \cr} The re...
GATE CSE 2008
Let R and S be two relations with the following schema R (P, Q, R1, R2, R3) S (P, Q, S1, S2) Where {P, Q} is the key for both schemas. Which of the fo...
GATE CSE 2007
Information about a collection of students is given by the relation studInfo(studId, name, sex). The relation enroll(studId, courseId) gives which stu...
GATE CSE 2007
Consider a selection of the form σA ≤ 100(r), where r is a relation with 1000 tuples. Assume that the attribute values for A among the tuples are unif...
GATE CSE 2007
Consider the relation employee(name, sex, supervisorName) with name as the key, supervisorName gives the name of the supervisor of the employee under ...
GATE CSE 2007
Consider the following relation schemas : b-Schema = (b-name, b-city, assets) a-Schema = (a-num, b-name, bal) d-Schema = (c-name, a-number) Let branch...
GATE CSE 2005
A table ‘student’ with schema (roll, name, hostel, marks), and another table ‘hobby’ with schema (roll, hobbyname) contains records as shown below: Ta...
GATE CSE 2004
Consider the relation Student (name, sex, marks), where the primary key is shown underlined, pertaining to students in a class that has at least one b...
GATE CSE 2001
Which of the following relational calculus expressions is not safe?
GATE CSE 1998
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...
GATE CSE 1996
A library relational database system uses the following schema USERS (User #, User Name, Home Town) BOOKS (Books # Book Title, Author Name) ISSUED (Bo...
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