# GATE CSE 2010

 Question 1
Let G=(V, E) be a graph. Define $\xi (G)=\sum_{d}i_{d}*d$ , where $i_{d}$ is the number of vertices of degree d in G. If S and T are two different trees with $\xi (S)=\xi (T)$ , then
 A |S|= 2|T| B |S|=|T|-1 C |S|=|T| D |S|=|T|+1
Discrete Mathematics   Graph Theory
Question 1 Explanation:
 Question 2
Newton-Raphson method is used to compute a root of the equation $x^{2} -13=0$ with 3.5 as the initial value. The approximation after one iteration is
 A 3.575 B 3.676 C 3.667 D 3.607
Engineering Mathematics   Numerical Method
Question 2 Explanation:

 Question 3
What is the possible number of reflexive relations on a set of 5 elements?
 A $2^{10}$ B $2^{15}$ C $2^{20}$ D $2^{25}$
Discrete Mathematics   Set Theory
Question 3 Explanation:
 Question 4
Consider the set S = {1, $\omega ,\omega ^{2}$}, where $\omega$ and $\omega ^{2}$ are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) forms
 A A group B A ring C An integral domain D A field
Discrete Mathematics   Group Theory
Question 4 Explanation:
 Question 5
What is the value of $\lim_{n\rightarrow \infty }(1-\frac{1}{n})^{2n}$?
 A 0 B $e^{-2}$ C $e^{-1/2}$ D 1
Engineering Mathematics   Calculus
Question 5 Explanation:

There are 5 questions to complete.