# Engineering-Mathematics |Gate-2009| Previous Year Questions| Set-12

Engineering-Mathematics |Gate-2009|

1. Which one of the following is TRUE for any simple connected undirected graph with more than 2 vertices? [GATE – 2009]

a. No two vertices have the same degree.
b. At least two vertices have the same degree.
c. At least three vertices have the same degree.
d. All vertices have the same degree.

1. What is the chromatic number of an n-vertex simple connected graph which does not contain any odd length cycle? Assume n ≥ 2. [GATE – 2009]

a. 2
b. 3
c. n-1
d. n

1. Which one of the following in NOT necessarily a property of a Group? [GATE – 2009]

a. Commutative
b. Associative
c. Existence of inverse for every element
d. Existence of identity

1. Consider the binary relation R = {(x, y), (x, z), (z, x), (z, y)} on the set {x, y, z}. Which one of the following is TRUE? [GATE – 2009]

a. R is symmetric but NOT antisymmetric
b. R is NOT symmetric but antisymmetric
c. R is both symmetric and antisymmetric
d. R is neither symmetric nor antisymmetric

1. An unbalanced dice (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value is odd is 90% of the probability that the face value is even. The probability of getting any even numbered face is the If the probability that the face is even given that it is greater than 3 is 0.75, which one of the following options is closest to the probability that the face value exceeds 3? [GATE – 2009]

a. 0.453
b. 0.468
c. 0.485
d. 0.492

1. For the composition table of a cyclic group shown below :

hich one of the following choices is correct? [GATE – 2009]

a. a, b are generators
b. b, c are generators
c. c, d are generators
d. d, a are generators

1. Which one of the following is the most appropriate logical formula to represent the statement? “Gold and silver ornaments are precious”. The following notations are used: G(x): x is a gold ornament S(x): x is a silver ornament P(x): x is precious : [GATE – 2009]

a. ∀x(P(x) → (G(x) ∧ S(x)))
b. ∀x((G(x) ∧ S(x)) → P(x))
c. ∃x((G(x) ∧ S(x)) → P(x)
d. ∀x((G(x) ∨ S(x)) → P(x))

1. The binary operation □ is defined as follows

Which one of the following is equivalent to P Ú Q ? [GATE – 2009]

a. ¬Q□¬P
b. P□¬Q
c. ¬P□Q
d. ¬P□¬Q

1. Consider the following well-formed formulae: [GATE – 2009]
1. ¬∀x(P(x))
2. ¬∃x(P(x))
3. ¬∃x(¬P(x))
4. ∃x(¬P(x))

Which of the above are equivalent? [GATE – 2009]

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