GATE CS Databases questions

Consider three data items $D1, D2,$ and $D3,$ and the following execution schedule of transactions $T1, T2,$ and $T3.$ In the diagram, $R(D)$ and $W(D)$ denote the actions reading and writing the data item $D$ respectively. …

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 …

Consider the following functional dependencies in a database. …

Consider the following $2-3-4$ tree (i.e., B-tree with a minimum degree of two) in which each data item is a letter. The usual alphabetical ordering of letters is used in constructing the tree. What is the result of inserting $G$ in the above tree?

Consider the following SQL query Select distinct $a_1, a_2, …, a_n$ from $r_1, r_2, …, r_m$ where P For an arbitrary predicate P, this query is equivalent to which of the following relational algebra expressions?

Which of the following scenarios may lead to an irrecoverable error in a database system?

From the following instance of a relation schema $R(A,B,C)$, we can conclude that: $$\begin{array}{|l|l|}\hline \textbf{A} & \textbf{B} & \textbf{C} \\ \hline \text{1} & \text{1} & \text{1} \\ \text{1} & \text{1} & \text{0} \\ \text{2} & \text{3} & \text{2} \\ \text{2} & \text{3} & \text{2} \\ \hline \end{array}$$

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 $\text{BCNF}$, 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 …

A $B^+$ - tree index is to be built on the Name attribute of the relation STUDENT. Assume that all the student names are of length $8$ bytes, disk blocks are of size $512$ bytes, and index pointers are of size $4$ bytes. Given the scenario, what would be the best choice of the degree (i.e. number of pointers per node) of the $B^+$ - tree?

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

Relation $R$ with an associated set of functional dependencies, $F$, is decomposed into $\text{BCNF}$. The redundancy (arising out of functional dependencies) in the resulting set of relations is

Consider a relation geq which represents "greater than or equal to", that is, $(x,y) \in$ geq only if $y \geq x$. create table geq ( ib integer not null, ub integer not null, primary key ib, foreign key (ub) references geq on delete cascade ); Which of the following is possible if tuple (x,y) is deleted?

Which of the following relational calculus expression is not safe?

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

Let r and s be two relations over the relation schemes R and S respectively, and let A be an attribute in R. The relational algebra expression $\sigma_{A=a}(r \bowtie s)$ is always equal to

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?

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?

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.

Given the following relation instance. $$\begin{array}{|l|l|}\hline \text{X} & \text{Y} & \text{Z} \\ \hline \text{1} & \text{4} & \text{2} \\ \text{1} & \text{5} & \text{3} \\ \text{1} & \text{6} & \text{3} \\ \text{3} & \text{2} & \text{2} \\ \hline \end{array}$$ Which of the following functional dependencies are …

Given the relations employee (name, salary, dept-no), and department (dept-no, dept-name,address), Which of the following queries cannot be expressed using the basic relational algebra operations $\left(\sigma, \pi,\times ,\Join, \cup, \cap,-\right)$?