Sunday, 28 February 2016

Vocational Teacher in Computer Science (98/2013) Solved Paper 26/07/2013 - Part 10

91.       If p and q are statements, then the compound proposition ¬p˅¬q is logically equivalent to:
(A) ¬p˅¬q          (B) ¬p˄¬q
(C) ¬p˄q            (D) ¬(p˄q)
Answer: X
92.       Give the English translation of the following statement:
∃x∀y∀z((F(x,y)˄F(x,z)˄(y≠z)→ ¬F(y,z))), where F(a,b) means a and b are friends and the universe of discourse for x, y and zis the set of all students in Maharajas college.
(A) There is a student none of whose friends are also friends with each other
(B) There is a student whose friends are also friends with each other
(C) There is a student whose two friends are also friends with each other
(D) There is a student whose friends, except two, are also friends with each other
Answer: A
93.       Which one of the following mathematical argument is not valid?
(A) If you answer every question in this booklet, then you will get highest score. You got highest score. There fore, you answered every question in this booklet
(B) If 101 is divisible by 2, then 1012 is divisible by 4. 101 is divisible by 2. Consequently, 1012 is divisible by 4.
(C) It is not sunny this afternoon and it is raining. We will go to the beach only if it is sunny. If we do not go to the beach we will be at home. Then, we will be at home.
(D) None of the above.
Answer: A
94.       N denotes the set of natural numbers; Q the set of rational numbers and R the set of real numbers. Pick the false statement.
(A) An infinite sequence x1, x2, x3, ... of distinct elements is infinitely countable.
(B) NᵡN is infinitely countable
(C) QᵡQ is infinitely countable
(D) (R\Q)ᵡ(R\Q) is infinitely countable
Answer: D
95.       Which one of the following is not a partition of the set S={1, 2, 3, ...... 8, 9}?
(A) P1=[{1}, {2,3,4}, {5,6}, {7}, {8,9}]
(B) P2=[{1,3,5}, {2,7}, {4,6,8,9}]
(C) P3=[{1,3,4}, {2,6,7,8,9}]
(D) P4=[{1,3,5}, {2,4,6}, {7,8,9}]
Answer: C

96.       Consider the relation.
R={(1,1),(2,2),(2,3),(3,2),(4,2),(4,4)} on the set A={1,2,3,4} then which one of the following is true?
(A) R is reflexive                      (B) R is symmetric
(C) R is anti symmetric           (D) R is not transitive
Answer: D
97.       Which one of the following is false?
(A) For any integer n greater 2, n(n+1)(2n+1)/6 is an integer.
(B) For any integer greater 1, n(7n2+5) is an integer and is a multiple of 6.
(C) The square of an odd integer is of the form 5p or 5p±2, where p is some integer.
(D) The cube of any integer is of the form 7p or 7p±1, where p is some integer.
Answer: C
98.       The linear congruence 7x≡4(mod 14) has:
(A) Infinitely many integral solutions
(B) No integral solutions
(C) Exactly six solutions
(D) Exactly 3 solutions
Answer: B
99.       Let G be a bigraph (bipartite graph) with p points and q lines. Then:
(A) q=p2/4          (B) q>p2/4
(C) q≤p2/4          (D) p2=4(q-1)
Answer: C
100.    Pick the true statement:
(A) Peterson graph is a planar graph
(B) A simple graph that does not contain sub graph homeomorphic to K3,3 is planar.
(C) A simple graph that does contain a sub graph homeomorphic to K5 is planar.
(D) A simple graph that does contain a sub graph homeomorphic to K3,3 is planar.
Answer: B



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