GATE CSE 2008

Question 1
\lim_{x\rightarrow \infty }\frac{x-sin x}{x+cos x} equals
A
1
B
-1
C
\infty
D
-\infty
Engineering Mathematics   Calculus
Question 2
If P, Q, R are subsets of the universal set U, then (P\cap Q\cap R)\cup (P^{C} \cap Q \cap R)\cup Q^{C} \cup R^{C} is
A
Q^{C} \cup R^{C}
B
P \cup Q^{C} \cup R^{C}
C
p^{C}\cup Q^{C} \cup R^{C}
D
U
Discrete Mathematics   Set Theory
Question 3
The following system of equations
x_{1}+x_{2}+2x_{3}=1
x_{1}+2x_{2}+3x_{3}=2
x_{1}+4x_{2}+\alpha x_{3}=4
has a unique solution. The only possible value(s) for \alpha is/are
A
0
B
either 0 or 1
C
one of 0, 1 or -1
D
any real number other than 5
Engineering Mathematics   Linear Algebra
Question 4
In the IEEE floating point representation the hexadecimal value 0x00000000 corresponds to
A
The normalized value 2^{-127}
B
The normalized value 2^{-126}
C
The normalized value +0
D
The special value +0
Digital Logic   Number System
Question 5
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
\bar{b}\cdot \bar{d}+\bar{a}\cdot \bar{d}
B
\bar{a}\bar{b}+\bar{b}\cdot \bar{d}+\bar{a}b\cdot \bar{d}
C
\bar{b}\cdot \bar{d}+\bar{a}b\cdot \bar{d}
D
\bar{a}\bar{b}+\bar{b}\cdot \bar{d}+\bar{a}\cdot \bar{d}
Digital Logic   Boolean Algebra
Question 6
Let r denote number system radix. The only value(s) of r that satisfy the equation \sqrt{121_{r}}=11_{r} is / are
A
decimal 10
B
decimal 11
C
decimal 10 and 11
D
any value \gt 2
Digital Logic   Number System
Question 7
The most efficient algorithm for finding the number of connected components in an undirected graph on n vertices and m edges has time complexity
A
\Theta (n)
B
\Theta (m)
C
\Theta (m+n)
D
\Theta (mn)
Algorithm   Graph Traversal
Question 8
Given f1, f3 and f in canonical sum of products form (in decimal) for the circuit

f_{1}=\sum m(4,5,6,7,8)
f_{3}=\sum m(1,6,15)
f=\sum m(1,6,8,15)

then f_{2} is
A
\summ(4,6)
B
\summ(4,8)
C
\summ(6,8)
D
\summ(4,6,8)
Digital Logic   Boolean Algebra
Question 9
Which of the following is true for the language{ a^{p}|p is a prime} ?
A
It is not accepted by a Turing Machine
B
It is regular but not context-free
C
It is context-free but not regular
D
It is neither regular nor context-free, but accepted by a Turing machine
Theory of Computation   Context Free Language
Question 10
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
A
I and II
B
I and IV
C
II and III
D
II and IV
Theory of Computation   Undecidability
There are 10 questions to complete.

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