GATE CS 2008

Question 21

Which of the following statements is true for every planar graph on n vertices?

• The graph has a vertex-cover of size at most 3n/4
  

• The graph is Eulerian
  

• The graph is connected
  

• The graph has an independent set of size at least n/3
  

Question 22

• P = Q - k
• P = Q + k
• P = Q
• P = Q +2 k

Question 23

A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve 3x⁴ - 16x³ + 24x² + 37

• 0
• 1
• 2
• 3

Question 24

If P, Q, R are Boolean variables, then (P + Q\')(PQ\' + PR)(P\'R\' + Q\') simplifies

• PQ\'
• PR\'
• PQ\' + R
• PR\'\' + Q

Question 25

Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is 0.6. If she studies mathematics on a day, then the probability that she studies computer science the next day is 0.4. Given that Aishwarya studies computer science on Monday, what is the probability that she studies computer science on Wednesday?

• 0.24

• 0.36

• 0.4

• 0.6

Question 26

How many of the following matrices have an eigenvalue 1?

• four
  

• three
  

• two
  

• one
  

Question 27

Let fsa and pda be two predicates such that fsa(x) means x is a finite state automaton, and pda(y) means that y is a pushdown automaton. Let equivalent be another predicate such that equivalent (a, b) means a and b are equivalent. Which of the following first order logic statements represents the following: Each finite state automaton has an equivalent pushdown automaton.

• A
• B
• C
• D

Question 28

For a magnetic disk with concentric circular tracks, the seek latency is not linearly proportional to the seek distance due to

• non-uniform distribution of requests
• arm starting and stopping inertia
• higher capacity of tracks on the periphery of the platter
• use of unfair arm scheduling policies

Question 29

Which of the following is/are true of the auto-increment addressing mode?

I.  It is useful in creating self-relocating code.
II. If it is included in an Instruction Set Architecture, 
    then an additional ALU is required for effective address 
    calculation.
III.The amount of increment depends on the size of the data
     item accessed.

• I only
• II only
• III Only
• II and III only

Question 30

P and Q are two propositions. Which of the following logical expressions are equivalent? 

• Only I, II and III
  

• Only I, II and IV
  

• All of I, II, III and IV
  

• Only I and II