GATE-CS-2007

Question 1

Consider the following two statements about the function f(x)=|x|

P. f(x) is continuous for all real values of x
Q. f(x) is differentiable for all real values of x 

Which of the following is TRUE?

• P is true and Q is false.

• P is false and Qis true.

• Both P and Q are true

• Both P and Q are false.

Question 2

Let S be a set of n elements. The number of ordered pairs in the largest and the smallest equivalence relations on S are:

• n and n

• n² and n

• n² and 0

• n and 1

Question 3

What is the maximum number of different Boolean functions involving n Boolean variables?

• n²

• 2ⁿ

• 2²ⁿ

• 2ⁿ²

Question 4

Let G be the non-planar graph with the minimum possible number of edges. Then G has

• 10 edges and 6 vertices
  

• 10 edges and 5 vertices 
  

• 9 edges and 6 vertices
  

• 9 edges and 5 vertices 
  

Question 5

Consider the DAG with Consider V = {1, 2, 3, 4, 5, 6}, shown below. Which of the following is NOT a topological ordering? 

[caption width="800"] [/caption]

• 1 2 3 4 5 6

• 1 3 2 4 5 6

• 1 3 2 4 6 5

• 3 2 4 1 6 5

Question 6

Which of the following problems is undecidable? [2007]

• Membership problem for CFGs
• Ambiguity problem for CFGs.
• Finiteness problem for FSAs.
• Equivalence problem for FSAs.

Question 7

Which of the following is TRUE?

• Every subset of a regular set is regular.
• Every finite subset of a non-regular set is regular.
• The union of two non-regular sets is not regular.
• Infinite union of finite sets is regular.

Question 8

How many 3-to-8 line decoders with an enable input are needed to construct a 6-to-64 line decoder without using any other logic gates?

• 7
• 8
• 9
• 10

Question 9

Consider the following Boolean function of four variables: f(w,x,y,z) = ∑(1,3,4,6,9,11,12,14) The function is:

• independent of one variables.
• independent of two variables.
• independent of three variables.
• dependent on all the variables.

Question 10

Consider a 4-way set associative cache consisting of 128 lines with a line size of 64 words. The CPU generates a 20-bit address of a word in main memory. The number of bits in the TAG, LINE and WORD fields arerespectively:

• 9,6,5

• 7, 7, 6

• 7, 5, 8

• 9, 5, 6