GATE CS 2008

Question 1

• 1
• -1
• INF
• -INF

Question 2

If P, Q, R are subsets of the universal set U, then 

• Q^c U R^c
  

• P U Q^c U R^c
  

• P^c U Q^c U R^c
  

• U
  

Question 3

The following system of equations 

[caption width="800"] [/caption]

has a unique solution. The only possible value(s) for α is/are

• either 0 or 1
  

• any real number 
  

• 0
  

• any real number other than 5
  

Question 4

In the IEEE floating point representation, the hexadecimal value 0 × 00000000 corresponds to

• the normalized value 2^-127
• the normalized value 2^-126
• the normalized value +0 
• the special value +0 

Question 5

Let r denote number system radix. The only value(s) of r that satisfy the equation 

• decimal 10
• decimal 11
• decimal 10 and 11
• any value > 2

Question 6

In the Karnaugh map shown below, X denotes a don\'t care term. What is the minimal form of the function represented by the Karnaugh map?

A)   


B) 

C) 

D)  

• A

• B

• C

• D

Question 7

Given f₁, f₃ and f in canonical sum of products form (in decimal) for the circuit

A) m(4, 6)

B) m(4, 8)

C) m(6, 8)

D) m(4, 6, 8)

• A
• B
• C
• D

Question 8

Which of the following is true for the language

• It is not accepted by a Turing Machine
• It is regular but not context-free
• It is context-free but not regular
• It is neither regular nor context-free, but accepted by a Turing machine

Question 9

Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

• I and II
• I and IV
• II and III
• II and IV

Question 10

Which of the following describes a handle (as applicable to LR-parsing) appropriately?

• It is the position in a sentential form where the next shift or reduce operation will occur
• It is non-terminal whose production will be used for reduction in the next step
• It is a production that may be used for reduction in a future step along with a position in the sentential form where the next shift or reduce operation will occur
• It is the production p that will be used for reduction in the next step along with a position in the sentential form where the right hand side of the production may be found