In a B⁺ tree, if the search-key value is 8 bytes long, the block size is 512 bytes and the block pointer size is 2 bytes, then the maximum order of the B⁺ tree is _________.

Which one of the following statements is NOT correct about the B⁺ tree data structure used for creating an index of a relational database table?

A relational database contains two tables Student and Performance as shown below:

The primary key of the Student table is Roll_no. For the Performance table, the columns Roll_no. and Subject_code together from the primary key. Consider the SQL query given below:

SELECT S.Student_name, sum (P.Marks)
       FROM Student S, Performance P
       WHERE P.Marks > 84
       GROUP BY S.Student_name;

The number of rows returned by the above SQL query is _____.

Let the set of functional dependencies F = {QR → S, R → P, S → Q} hold on a relation schema X = (PQRS). X is not in BCNF. Suppose X is decomposed into two schemas Y and Z, where Y = (PR) and Z = (QRS).

Consider the two statements given below.

• I. Both Y and Z are in BCNF

II. Decomposition of X into Y and Z is dependency preserving and lossless

Which of the above statements is/are correct?

In an Entity-Relationship (ER) model, suppose R is a many-to-one relationship from entity set E1 to entity set E2. Assume that E1 and E2 participate totally in R and that the cardinality of E1 is greater than the cardinality of E2.

Which one of the following is true about R?

Consider the following two tables and four queries in SQL.

Query 1:    SELECT B.isbn, S.copies
            FROM Book B INNER JOIN Stock S
            ON B.isbn = S.isbn;

Query 2:    SELECT B.isbn, S.copies
            FROM Book B LEFT OUTER JOIN Stock S
            ON B.isbn = S.isbn;

Query 3:    SELECT B.isbn, S.copies
            FROM Book B RIGHT OUTER JOIN Stock S
            ON B.isbn = S.isbn;

Query 4:    SELECT B.isbn, S.copies
            FROM Book B FULL OUTER JOIN Stock S
            ON B.isbn = S.isbn;

Which one of the queries above is certain to have an output that is a superset of the outputs of the other three queries?

Consider the following four relational schemas. For each schema, all non-trivial functional dependencies are listed. The underlined attributes are the respective primary keys.

Schema I: Registration(rollno, courses)
          Field ‘courses’ is a set-valued attribute containing the set of 
          courses a student has registered for.
          Non-trivial functional dependency
          rollno → courses

Schema II: Registration (rollno, coursid, email)
          Non-trivial functional dependencies:
          rollno, courseid → email
          email → rollno
 	
Schema III: Registration (rollno, courseid, marks, grade)
          Non-trivial functional dependencies:
          rollno, courseid, → marks, grade
          marks → grade
 	
Schema IV: Registration (rollno, courseid, credit)
          Non-trivial functional dependencies:
          rollno, courseid → credit
          courseid → credit

Which one of the relational schemas above is in 3NF but not in BCNF?

Consider a database that has the relation schema EMP (EmpId, EmpName, and DeptName). An instance of the schema EMP and a SQL query on it are given below.

The output of executing the SQL query is ___________.

Consider a database that has the relation schema CR(StudentName, CourseName). An instance of the schema CR is as given below.

The following query is made on the database.

         T1 ← πCourseName(σStudentName='SA'(CR))
         T2 ← CR ÷ T1

The number of rows in T2 is ____________.

An ER model of a database consists of entity types A and B. These are connected by a relationship R which does not have its own attribute. Under which one of the following conditions, can the relational table for R be merged with that of A?

Consider the following tables T1 and T2.

In table T1, P is the primary key and Q is the foreign key referencing R in table T2 with on-delete cascade and on-update cascade. In table T2, R is the primary key and S is the foreign key referencing P in table T1 with on-delete set NULL and on-update cascade. In order to delete record 〈3,8〉 from table T1, the number of additional records that need to be deleted from table T1 is _________.

Consider the following database table named top_scorer.

SELECT ta.player FROM top_scorer AS ta
WHERE ta.goals > ALL (SELECT tb.goals
                  FROM top_scorer AS tb
                  WHERE tb.country = 'Spain')
AND ta.goals > ANY (SELECT tc.goals
                  FROM top_scorer AS tc
                  WHERE tc.country = 'Germany')

The number of tuples returned by the above SQL query is _____.

Which of the following is NOT a superkey in a relational schema with attributes V, W, X, Y, Z and primary key VY?

B⁺ Trees are considered BALANCED because

Suppose a database schedule S involves transactions T₁, …, T_n. Construct the precedence graph of S with vertices representing the transactions and edges representing the conflicts. If S is serializable, which one of the following orderings of the vertices of the precedence graph is guaranteed to yield a serial schedule?

Consider the following database table named water_schemes :

The number of tuples returned by the following SQL query is _________.

with total(name, capacity) as
   select district_name, sum(capacity)
   from water_schemes
   group by district_name
with total_avg(capacity) as
   select avg(capacity)
   from total
select name
   from total, total_avg
   where total.capacity ≥ total_avg.capacity

SELECT operation in SQL is equivalent to

Consider an Entity-Relationship (ER) model in which entity sets E₁ and E₂ are connected by an m:n relationship R₁₂, E₁ and E₃ are connected by a 1:n (1 on the side of E₁ and n on the side of E₃) relationship R₁₃.

E₁ has two single-valued attributes a₁₁ and a₁₂ of which a₁₁ is the key attribute. E₂ has two single-valued attributes a₂₁ and a₂₂ is the key attribute. E₃ has two single-valued attributes a₃₁ and a₃₂ of which a₃₁ is the key attribute. The relationships do not have any attributes.

If a relational model is derived from the above ER model, then the minimum number of relations that would be generated if all the relations are in 3NF is ___________.

Consider the following relations:

Consider the following SQL query.

SELECT S. Student_Name, sum(P.Marks)
     FROM Student S, Performance P
     WHERE S.Roll_No = P.Roll_No
     GROUP BY S.Student_Name

The number of rows that will be returned by the SQL query is _________.

Consider the following transaction involving two bank account x and y.

The constraint that the sum of the accounts x and y should remain constant is that of

With reference to the B⁺ tree index of order 1 shown below, the minimum number of nodes (including the Root node) that must be fetched in order to satisfy the following query:”Get all records with a search key grater than or equal to 7 and less than 15″ is ___________.

Consider two relations R₁(A,B) with the tuples (1,5), (3,7) and R₂(A,C) = (1,7), (4,9). Assume that R(A,B,C) is the full natural outer join of R₁ and R₂. Consider the following tuples of the form (A,B,C): a = (1.5,null), b = (1,null,7), c = (3,null,9), d = (4,7,null), e = (1,5,7), f = (3,7,null), g = (4,null,9). Which one of the following statements is correct?  

Consider a simple checkpointing protocol and the following set of operations in the log.

(start, T₄); (write, T₄, y, 2, 3); (start, T₁); (commit, T₄); (write, T₁, z, 5, 7);
(checkpoint);
(start, T₂); (write, T₂, x, 1, 9); (commit, T₂); (start, T₃); (write, T₃, z, 7, 2);

If a crash happens now and the system tries to recover using both undo and redo operations, what are the contents of the undo list and the redo list

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?

Consider the following relation

  Cinema (theater, address, capacity)

Which of the following options will be needed at the end of the SQL query

SELECT P1. address
FROM Cinema P1

Such that it always finds the addresses of theaters with maximum capacity?

The value of is

Suppose X_i for i = 1, 2, 3 are independent and identically distributed random variables whose probability mass functions are Pr[X_i = 0] = Pr[X_i = 1]=1/2 for i = 1, 2, 3. Define another random variable Y = X₁X₂ ⊕ X₃, where ⊕ denotes XOR. Then Pr[Y = 0|X₃ = 0] = _______________.

Consider the relation scheme R = (E, F, G, H, I, J, K, L, M, N) 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?

Given the following statements:

    S1: A foreign key declaration can always 
        be replaced by an equivalent check
        assertion in SQL.
    S2: Given the table R(a,b,c) where a and
        b together form the primary key, the 
        following is a valid table definition.
        CREATE TABLE S (
            a INTEGER,
            d INTEGER,
            e INTEGER,
            PRIMARY KEY (d),
            FOREIGN KEY (a) references R)

Which one of the following statements is CORRECT?

Consider the following four schedules due to three transactions (indicated by the subscript) using read and write on a data item x, denoted by r(x) and w(x) respectively. Which one of them is conflict serializable?

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?

Given the following schema:

     employees(emp-id, first-name, last-name, hire-date, dept-id, salary)
     departments(dept-id, dept-name, manager-id, location-id)

You want to display the last names and hire dates of all latest hires in their respective departments in the location ID 1700. You issue the following query:

SQL> SELECT last-name, hire-date
     FROM employees
     WHERE (dept-id, hire-date) IN ( SELECT dept-id, MAX(hire-date)
                                     FROM employees JOIN departments USING(dept-id)
                                     WHERE location-id = 1700
                                     GROUP BY dept-id); 

What is the outcome?

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

Given the STUDENTS relation as shown below.

For (StudentName, StudentAge) to be the key for this instance, the value X should not be equal to

Consider the following schedule S of transactions T1, T2, T3, T4:

Which one of the following statements is CORRECT?

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 size, out of which one buffer is reserved for intermediate results. Assuming size(r(R)) < size(s(S)), the join will have fewer number of disk block accesses if

SQL allows tuples in relations, and correspondingly defines the multiplicity of tuples in the result of joins. Which one of the following queries always gives the same answer as the nested query shown below:

    select * from R where a in (select S.a from S)

What is the optimized version of the relation algebra expression π_A1(π_A2(σ_F1(σ_F2(r)))), where A1, A2 are sets of attributes in  with A1 ⊂ A2 and F1, F2 are Boolean expressions based on the attributes in r?

A prime attribute of a relation scheme is an attribute that appears