# 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:
 Question 6
The minterm expansion of f(P,Q,R)=PQ+QR'+PR' is
 A $m_{2}+m_{4}+m_{6}+m_{7}$ B $m_{0}+m_{1}+m_{3}+m_{5}$ C $m_{0}+m_{1}+m_{6}+m_{7}$ D $m_{2}+m_{3}+m_{4}+m_{5}$
Digital Logic   Boolean Algebra
Question 6 Explanation:
 Question 7
A main memory unit with a capacity of 4 megabytes is built using 1Mx1-bit DRAM chips. Each DRAM chip has 1K rows of cells with 1K cells in each row. The time taken for a single refresh operation is 100 nanoseconds. The time required to perform one refresh operation on all the cells in the memory unit is
 A 100 nanoseconds B 100 *$2^{10}$ nanoseconds C 100*$2^{20}$ nanoseconds D 3200*$2^{20}$ nanoseconds
Computer Organization   Memory Chip Design
Question 7 Explanation:
 Question 8
P is a 16-bit signed integer. The 2's complement representation of P is $(F87B)_{16}$. The 2's complement representation of 8*P is
 A $(C3D8)_{16}$ B $(187B)_{16}$ C $(F878)_{16}$ D $(987B)_{16}$
Digital Logic   Number System
Question 8 Explanation:
 Question 9
The Boolean expression for the output f of the multiplexer shown below is A $\overline{P\bigoplus Q\bigoplus R}$ B $P\bigoplus Q\bigoplus R$ C P+Q+R D $\overline{P+Q+R}$
Digital Logic   Combinational Circuit
Question 9 Explanation:
 Question 10
In a binary tree with n nodes, every node has an odd number of descendants. Every node is considered to be its own descendant. What is the number of nodes in the tree that have exactly one child?
 A 0 B 1 C (n-1)/2 D n-1
Data Structure   Binary Tree
Question 10 Explanation:
There are 10 questions to complete.