1
GATE CSE 1998
MCQ (Single Correct Answer)
+1
-0.3
Which of the following statements is false?
A
A tree with a n nodes has (n – 1) edges
B
A labeled rooted binary tree can be uniquely constructed given its postorder and preorder traversal results.
C
A complete binary tree with n internal nodes has (n + 1) leaves.
D
The maximum number of nodes in a binary tree of height h is ( 2h+1 - 1 ).
2
GATE CSE 1998
MCQ (Single Correct Answer)
+1
-0.3
Which normal form is considered adequate for normal relational database design?
A
$$2$$ $$NF$$
B
$$5$$ $$NF$$
C
$$4$$ $$NF$$
D
$$3$$ $$NF$$
3
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.

4
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
$$\pi_{A_1} \left(\sigma_{C_1}\left(R_1\right)\right) \to \sigma_{C_1} \left(\pi_{A_1}\left(R_1\right)\right)$$