GATE-CS-2007

Question 21

How many different non-isomorphic Abelian groups of order 4 are there

• 2
• 3
• 4
• 5

Question 22

Let Graph(x) be a predicate which denotes that x is a graph. Let Connected(x) be a predicate which denotes that x is connected. Which of the following first order logic sentences DOES NOT represent the statement: “Not every graph is connected”?

• A
• B
• C
• D

Question 23

Which of the following graphs has an Eulerian circuit? 

• The complement of a cycle on 25 vertices 
  

• A complete graph on 90 vertices
  

• Any k-regular graph where kis an even number.
  

• None of the above 
  

Question 24

Suppose we uniformly and randomly select a permutation from the 20! Permutations of 1, 2, 3 ,…..,20. What is the probability that 2 appears at an earlier position than any other even number in the selected permutation?

• 1/2
• 1/10
• 9!/20!
• Node of the above

Question 25

Let A be a 4 x 4 matrix with eigenvalues -5, -2, 1, 4. Which of the following is an eigenvalue of

[A  I]
[I  A] 

where I is the 4 x 4 identity matrix?

• -5
• -7
• 2
• 1

Question 26

Consider the set S = (A, B, C, D}. Consider the following 4 partitions π1, π2, π3, π4 on S : π1 = {ABCD}'  , π2 = {AB}' , {CD}' , π3 = {ABC}' , {D}' ,  π4 = A' , B' , C' , D'.  Let P be the partial order on the set of partitions S' = {π1, π2, π3, π4} defined as follows : πi P πj if and only if πi refines πj. The poset diagram for (S', P ) is :

• [caption width="800"] [/caption]
• [caption width="800"] [/caption]
• [caption width="800"] [/caption]
• [caption width="800"] [/caption]

Question 27

• A
• B
• C
• D

Question 28

Consider the series X_n+1 = X_n/2 + 9/(8 X_n), X₀ = 0.5 obtained from the Newton-Raphson method. The series converges to

• 1.5
• sqrt(2)
• 1.6
• 1.4

Question 29

A minimum state deterministic finite automaton accepting the language L={w | w ε {0,1} *, number of 0s and 1s in w are divisible by 3 and 5, respectively} has

• 15 states

• 11 states

• 10 states

• 9 states

Question 30

The language L= {0ⁱ21ⁱ | i≥0 } over the alphabet {0,1, 2} is:

• not recursive

• is recursive and is a deterministic CFL.

• is a regular language.

• is not a deterministic CFL but a CFL.