# 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:

There are 5 questions to complete.