GATE CS 2010

Question 1

Let G = (V,E) be a graph. Define ξ(G) = Σd id x d, where id is the number of vertices of degree d in G. If S and T are two different trees with ξ(S) = ξ(T),then

• |S| = 2|T|
• |S| = |T|-1
• |S| = |T|
• |S| = |T|+1

Question 2

Newton-Raphson method is used to compute a root of the equation x²-13=0 with 3.5 as the initial value. The approximation after one iteration is

• 3.607
  

• 3.667
  

• 3.676
  

• 3.575
  

Question 3

What is the possible number of reflexive relations on a set of 5 elements?

• 2²⁵
  

• 2²⁰
  

• 2¹⁵
  

• 2¹⁰
  

Question 4

Consider the set S = {1, ω, ω2}, where ω and w² are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) forms

• A group
• A ring
• An integral domain
• A field

Question 5

What is the value of Lim_n->∞(1-1/n)²ⁿ ?

• 1
  

• e^-2
  

• e^-1/2
  

• 0
  

Question 6

The minterm expansion of f(P, Q, R) = PQ + QR\' + PR\' is

• m2 + m4 + m6 + m7
• m0 + m1 + m3 + m5
• m0 + m1 + m6 + m7
• m2 + m3 + m4 + m5

Question 7

A main memory unit with a capacity of 4 megabytes is built using 1M × 1-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.100×2¹⁰ nanoseconds
C.100×2²⁰ nanoseconds
D.3200×2²⁰ nanoseconds

• A

• B

• C

• D

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

• (C3D8)₁₆
  

• (187B)₁₆
  

• (F878)₁₆
  

• (987B)₁₆
  

Question 9

The Boolean expression for the output \'f\' of the multiplexer shown below is:

[caption width="800"] [/caption]

• (P(XOR)Q(XOR)R)\'

• P(XOR)Q(XOR)R

• (P+Q+R)\'

• P+Q+R

Question 10

Two alternative packages A and B are available for processing a database having 10^k records. Package A requires 0.0001n² time units and package B requires 10nlog₁₀n time units to process n records. What is the smallest value of k for which package B will be preferred over A?

• 12

• 10

• 6

• 5