GATE-CS-2002

Question 41

Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is :

• 1/16
• 1/8
• 7/8
• 15/16

Question 42

The binary relation S = ф (empty set) on set A = {1, 2, 3} is :

• Neither reflexive nor symmetric
• Symmetric and reflexive
• Transitive and reflexive
• Transitive and symmetric

Question 43

The C language is:

• A context free language

• A context sensitive language

• A regular language

• Parsable fully only by a Turing machine

Question 44

To evaluate an expression without any embedded function calls :

• As many stacks as the height of the expression tree are needed

• One stack is enough

• Two stacks are needed

• A Turing machine is needed in the general case

Question 45

Dynamic linking can cause security concerns because:

• Security is dynamic
• The path for searching dynamic libraries is not known till runtime
• Linking is insecure
• Cryptographic procedures are not available for dynamic linking

Question 46

Which combination of the following features will suffice to characterize an OS as a multi-programmed OS?

(a) More than one program may be loaded into main memory 
   at the same time for execution. 
(b) If a program waits for certain events such as I/O, 
   another program is immediately scheduled for execution. 
(c) If the execution of program terminates, another program 
   is immediately scheduled for execution. 

• a
• a and b
• a and c
• a, b and c

Question 47

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

• 16

• 42

• 43

• 44

Question 48

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 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 used on the decompositions? (Assume that the closures of F and G are available).

• Dependency-preservation
• Lossless-join
• BCNF definition
• 3NF definition

Question 49

From the following instance of a relation scheme R (A, B, C), we can conclude that :

A	B	C
1	1	1
1	1	0
2	3	2
2	3	2

• A functionally determines B and B function­ally determines C
• A functionally determines B and B does not functionally determine C
• B does not functionally determine C
• A does not functionally determine B and B does not functionally determine C

Question 50

In the index allocation scheme of blocks to a file, the maximum possible size of the file depends on :

• the size of the blocks, and the size of the ad­dress of the blocks.

• the number of blocks used for the index, and the size of the blocks.

• the size of the blocks, the number of blocks used for the index, and the size of the address of the blocks.

• None of these