1
GATE CSE 1998
Subjective
+2
-0

Suppose we have a database consisting of the following three relations.

FREQUENTS (student, parlor) giving the parlors each student visits.

SERVES (parlor, ice-cream) indicating what kind of ice-creams each parlor serves.

LIKES (student, ice-cream) indicating what ice-creams each student likes.

(Assume that each student likes at least one ice-cream and frequents at least one parlor)

Express the following in SQL:
Print the students that frequent at least one parlor that serves some ice-cream that they like.

2
GATE CSE 1998
MCQ (Single Correct Answer)
+2
-0.6
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, C2 are selection conditions and A1, A2 are attributes of R1?
A
$$\sigma_{C_1} \left(\sigma_{C_2}\left(R_1\right)\right) \to \sigma_{C_2} \left(\sigma_{C_1}\left(R_1\right)\right)$$
B
$$\sigma_{C_1} \left(\pi_{A_1}\left(R_1\right)\right) \to \pi_{A_1} \left(\sigma_{C_1}\left(R_1\right)\right)$$
C
$$\sigma_{C_1} \left(R_1 \cup R_2\right) \to \sigma_{C_1}\left(R_1\right) \cup \sigma_{C_1} \left(R_2\right)$$
D
$$\pi_{A_1} \left(\sigma_{C_1}\left(R_1\right)\right) \to \sigma_{C_1} \left(\pi_{A_1}\left(R_1\right)\right)$$
3
GATE CSE 1998
MCQ (Single Correct Answer)
+1
-0.3

There are five records in a database.

Name Age Occupation Category
Rama 27 CON A
Abdul 22 ENG A
Jennifer
28 DOC B
Maya 32 SER D
Dev 24 MUS C

There is an index file associated with this and it contains the values 1, 3, 2, 5 and 4. Which one of the fields is the index built from?

A
Age
B
Name
C
Occupation
D
Category
4
GATE CSE 1998
MCQ (Single Correct Answer)
+2
-0.6
Consider the following determinant $$$\Delta = \left| {\matrix{ 1 & a & {bc} \cr 1 & a & {ca} \cr 1 & a & {ab} \cr } } \right|$$$

Which of the following is a factor of $$\Delta $$ ?

A
$$a + b$$
B
$$a - b$$
C
$$a + b + c$$
D
$$abc$$
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