Math for Computer science
Questions 61 to 70
61.

Which
one of the following statements is false?
(a) ∅x
A = ∅ (b) AXB = BXA
(c) R^{–1
}= {(y, x), (x, y) ∈R} (d) Domain of R^{1}= Range of
R.
(e) A
relation on A is a subset of AXA.

62.

List the ordered pairs in the relation R
from A={0,1,2,3,4} and B={0,1,2,3} where (a,b) ∈ R iff lcm(a,b) = 2.
(a) {(1,2),
(2,1),(2,2)} (b) {(1,2), (2,1)}
(c) {(1,2),
(2,1),(2,4)} (d) {(1,2),
(2,1),(2,2),(2,4)}
(e) {(2,1),(2,2),(2,4)}.

63.

Which
one of the following properties is not satisfied by the divides relation on the set of integers?
(a)
Reflexive (b)
Not symmetric
(c) Not
antisymmetric (d)
Transitive (e) Antisymmetric.

64.

Which
one of the collection of sets given below is the partition of the set Z×Z ?
(a) The set of pairs (x,y) where x or y is odd;
The set of pairs (x,y) where y is even.
(b) The set of pairs (x,y) where x and y are
odd; The set of pairs (x,y) where exactly one of x and y is odd; The set of
pairs (x,y) where x and y are even.
(c) The set of pairs (x,y) where x is positive;
The set of pairs (x,y) where y is positive; The set of pairs (x,y) where both
x and y are positive.
(d) The set of pairs (x,y) where x ≠ 0 and y≠
0; The set of pairs (x,y) where x=0 and y≠ 0; The set of pairs (x,y) where x
≠ 0 and y= 0.
(e) None of the above.

65.

A
function f(x) = x+1/x–1 will not be defined for x = ________.
(a) 0 (b) 1 (c) ½ (d) 2 (e) –1.

66.

The
domain and range of the function that assigns to each nonnegative integer
its last digit are
(a) 0Z,
Z (b) Z, Z+ (c) Z+,Z+ (d) Z+,{0..9} (e) Z+,Z.

67.

According
to RSA encryption algorithm the encryption key consists of modulus n = pq
where p and q are large primes and exponent e. Here e is relatively
prime to _________.
(a) pq where p,q are
large prime numbers
(b) p(q1) where p,q are
large prime numbers
(c) (p1)q where p,q
are large prime numbers
(d) (p1)(q1) where p,q
are large prime numbers
(e) (p+1)(q+1) where p,q
are large prime numbers.

68.

A
composite integer n that satisfies the congruence __________
for all positive integers b with gcd(b,n) = 1 is called a Carmichael number.
(a) b^{n–1}
≡ 1 (mod n) (b) b^{n }≡
1 (mod n)
(c) b^{n–1 }≡
b(mod n) (d) b^{n+1 }≡ 1 (mod n) (e) b^{n–1 }≡ 1
(mod n+1).

69.

a=
(1110)_{2 }and b= (1011)_{2, }a+b = ?
(a) 1111 (b) 10001 (c) 11001 (d) 10011 (e) 10111.

70.

If
a student has to select one project from three lists, first containing 23
projects second containing 15 projects and third containing 19 projects, the
total number ways to select the projects is
(a) 57 (b) 6555 (c) 6554 (d) 56 (e) 58.

Answers
61.

Answer : (c)
Reason : =
18 + 7 – 20 = 25 – 20 = 5.

62.

Answer : (b)
Reason : Cartesian
product is not commutative.

63.

Answer : (a)
Reason : The
lcm of 1,2 ; 2, 1 ; 2,2 is 2. So the answer is a.

64.

Answer : (e)
Reason : the
divides relation on the set of integers is not antisymmetric since 1–1 and
–1 1 but 1 ≠ –1.

66.

Answer : (b)
Reason : The
function f(x) = x+1/x–1 will not be defined for x = 1.

67.

Answer : (d)
Reason : The
answer is evident.

68.

Answer : (d)
Reason : As
per RSA encryption algorithm.

69.

Answer : (a)
Reason : According
to the definition of Carmichael number.

70.

Answer : (c)
Reason : 1 1
1 1 1 0
(+) 1 0 1 1
Result=
1 1 0 0 1

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