# 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 1 Explanation:
 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 2 Explanation:
 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 3 Explanation:
 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 4 Explanation:
 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 5 Explanation:
 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 6 Explanation:
 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 7 Explanation:
 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 $\sum$m(4,6) B $\sum$m(4,8) C $\sum$m(6,8) D $\sum$m(4,6,8)
Digital Logic   Boolean Algebra
Question 8 Explanation:
 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 9 Explanation:
 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
Question 10 Explanation:
There are 10 questions to complete.