# Engineering-Mathematics |Gate-2010| Previous Year Questions| Set-11

Engineering-Mathematics |Gate-2010|

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  : [GATE – 2010]

a. |S| = 2|T|
b. |S| = |T| – 1
c. |S| = |T|
d. |S| = |T| + 1

1. 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 : [GATE – 2010]

a. 3.575
b. 3.676
c. 3.667
d. 3.607

1. What is the possible number of reflexive relations on a set of 5 elements? [GATE – 2010]

a. 210
b. 215
c. 220
d. 225

1. Consider the set S = {1, ω, ω2}, where ω and ω2 are cube roots of unity. If * denotes the multiplication operation, the structure (S,  *) forms : [GATE – 2010]

a. A group
b. A ring
c. An integral domain
d. A field

1. Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of q. What is the probability of a computer being declared faulty? [GATE – 2010]

a. pq + (1 – p)(1 – q)
b. (1 – q)p
c. (1 – p)q
d. pq

1. What is the probability that divisor of 1099 is a multiple of 1096? [GATE – 2010]

a. 16/625
b. 4/625
c. 12/625
d. 1/625

7. The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph? [GATE – 2010]

``````(I) 7, 6, 5, 4, 4, 3, 2, 1
(II) 6, 6, 6, 6, 3, 3, 2, 2
(III) 7, 6, 6, 4, 4, 3, 2, 2
(IV) 8, 7, 7, 6, 4, 2, 1, 1
``````

a. I and II
b. III and IV
c. IV only
d. II and IV

1. Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time t. Which one of the statements below expresses best the meaning of the formula ∀x∃y∃t(¬F(x, y, t))?[GATE – 2010]

a. Everyone can fool some person at some time
b. No one can fool everyone all the time
c. Everyone cannot fool some person all the time
d. No one can fool some person at some time