GATE-CS-2001

Question 21

Consider a virtual memory system with FIFO page replacement policy. For an arbitrary page access pattern, increasing the number of page frames in main memory will

• always decrease the number of page faults
• always increase the number of page faults
• sometimes increase the number of page faults
• never affect the number of page faults

Question 22

Which of the following requires a device driver?

• Register
• Cache
• Main memory
• Disk

Question 23

Consider a schema R(A,B,C,D) and functional dependencies A->B and C->D. Then the decomposition of R into R1(AB) and R2(CD) is

• dependency preserving and lossless join
• lossless join but not dependency preserving
• dependency preserving but not lossless join
• not dependency preserving and not lossless join

Question 24

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?

• List of all vertices adjacent to a given vertex
• List all vertices which have self loops
• List all vertices which belong to cycles of less than three vertices
• List all vertices reachable from a given vertex

Question 25

Let r and s be two relations over the relation schemes R and S respectively, and let A be an attribute in R. then the relational algebra expression is always equal to

• A
• B
• C
• D

Question 26

How many 4-digit even numbers have all 4 digits distinct?

• 4536
  

• 2620
  

• 2296
  

• 2240
  

Question 27

Consider the following statements:

S1: There exists infinite sets A, B, C such that 
    A ∩ (B ∪ C) is finite.
S2: There exists two irrational numbers x and y such
    that (x+y) is rational.

Which of the following is true about S1 and S2?

• Only S1 is correct
• Only S2 is correct
• Both S1 and S2 are correct
• None of S1 and S2 is correct

Question 28

Let f: A→B be a function, and let E and F be subsets of A. Consider the following statements about images.

S1: f (E ∪ F) = f (E) ∪ f (F)
S1: f (E ∩ F) = f (E) ∩ f (F) 

Which of the following is true about S1 and S2?

• Only S1 is correct
• Only S1 is correct
• Both S1 and S2 are correct
• None of S1 and S2 is correct

Question 29

Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day?

• 1/7⁷
• 1/7⁶
• 1/2⁷
• 7/2⁷

Question 30

Consider a DFA over ∑ = {a, b} accepting all strings which have number of a’s divisible by 6 and number of b’s divisible by 8. What is the minimum number of states that the DFA will have?

• 8
• 14
• 15
• 48