GATE CSE 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?
A
P is true and Q is false.
B
P is false and Q is true.
C
Both P and Q are true.
D
Both P and Q are false.
Engineering Mathematics   Calculus
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:
A
n and n
B
n^{2} \; and \; n
C
n^{2} \; and \; 0
D
n and 1
Discrete Mathematics   Set Theory
Question 3
What is the maximum number of different Boolean functions involving n Boolean variables?
A
n^{2}
B
2^{n}
C
2^{2^{n}}
D
2^{n^{2}}
Digital Logic   Boolean Algebra
Question 4
Let G be the non-planar graph with the minimum possible number of edges. Then G has
A
9 edges and 5 vertices
B
9 edges and 6 vertices
C
10 edges and 5 vertices
D
10 edges and 6 vertices
Discrete Mathematics   Planar Graph
Question 5
Consider the DAG with V = {1,2,3,4,5,6}, shown below.

Which of the following is NOT a topological ordering?
A
1 2 3 4 5 6
B
1 3 2 4 5 6
C
1 3 2 4 6 5
D
3 2 4 1 6 5
Algorithm   Graph Traversal
Question 6
Which of the following problems is undecidable?
A
Membership problem for CFGs.
B
Ambiguity problem for CFGs.
C
Finiteness problem for FSAs.
D
Equivalence problem for FSAs.
Theory of Computation   Undecidability
Question 7
Which of the following is TRUE?
A
Every subset of a regular set is regular.
B
Every finite subset of a non-regular set is regular.
C
The union of two non-regular sets is not regular.
D
Infinite union of finite sets is regular.
Discrete Mathematics   Set Theory
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?
A
7
B
8
C
9
D
10
Digital Logic   Combinational Circuit
Question 9
Consider the following Boolean function of four variables:
f (w, x, y, z)=\Sigma(1,3,4,6,9,11,12,14)
The function is:
A
independent of one variables
B
independent of two variables.
C
independent of three variables.
D
dependent on all the variables
Digital Logic   Boolean Algebra
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 are respectively:
A
9, 6, 5
B
7, 7, 6
C
7, 5, 8
D
9, 5, 6
Computer Organization   Cache Memory
There are 10 questions to complete.

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