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 101

^{2 }is divisible by 4. 101 is divisible by 2. Consequently, 101^{2 }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 x

_{1}, x_{2}, x_{3}, ... of distinct elements is infinitely countable.
(B) Náµ¡N is infinitely countable

(C) Qáµ¡Q is infinitely countable

(D) (R\Q)áµ¡(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) P

_{1}=[{1}, {2,3,4}, {5,6}, {7}, {8,9}]
(B) P

_{2}=[{1,3,5}, {2,7}, {4,6,8,9}]
(C) P

_{3}=[{1,3,4}, {2,6,7,8,9}]
(D) P

_{4}=[{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(7n

^{2}+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=p

^{2}/4 (B) q>p^{2}/4
(C) q≤p

^{2}/4 (D) p^{2}=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 K

_{3,3}is planar.
(C) A simple graph that does contain a sub
graph homeomorphic to K

_{5}is planar.
(D) A simple graph that does contain a sub
graph homeomorphic to K

_{3,3}is planar.
Answer: B