Math for Computer science Questions and Answers 131 to 140

Math for Computer science

Questions  131 to 140



131.
A function from set A to set B is one-to-one but not onto, then the function is known as
(a)
Sujection
(b)
Injection
(c)
Bijection
(d)
Homomorphism
(e)
Automorphism.
132.
What is the probability that the numbers on two dice are odd when they are rolled?
(a)
8 / 36
(b)
18 / 36
(c)
13 / 36
(d)
9 / 36
(e)
12 / 36.
133.
The member of the set {x/x is a cube of an integer less than 100}
(a)
{1, 2, 3, 4}
(b)
{1, 8, 27, 64}
(c)
{1, 8, 26, 64}
(d)
{1, 8, 26, 63}
(e)
{1, 8, 27, 125}.
134.
is given by
(a)
P(F|E) . P(F)
(b)
P(F|E) . P(E)
(c)
P(E|F) . P(E)
(d)
P(E|F) . P(F)
(e)
P(E|F) . P(F|E).
135.
Probability of the impossible event of a Random Experiments always equals to
(a)
0
(b)
1
(c)
½ 
(d)
¼
(e)
a.
136.
A relation R is said to be antisymmetric Relation
(a)
if (a, b) Î R and (b, a) Π R Þ a = b
(b)
if (a, b)Ï  R and (b, a) Ï R Þ a ¹ b
(c)
if (b, a) Π R and (a, b) Î R Þ a < b
(d)
if (b, a) Π R and(a, b) Ï R Þ b > a
(e)
if (b, a) Ï R and (a, b) Î R Þ a º b.
137.
The elements of the relation whose matrix is given by MR =  defined on a set A = {a, b, c} is
(a)
R = {a, b) (b, a)  (b, c) (c, b)}
(b)
R = {a, a) (a, c)  (b, b) (c, a) (c, c)}
(c)
R = {a, a) (b, b)  (c, c)}
(d)
R = {a, c) (b, b)  (c, a)}
(e)
R = {a, b) (b, a)}.
138.
Let R = {(a, a) (c, a) (b, a) (b, b)} and S = {(a, b) (b, c) (c, a) (c, c)} then RoS is given by
(a)
{(a, a) (b, a) (a, c) (a, b)}
(b)
{(a, a) (a, b) (a, c) (b, c)}
(c)
{(a, a) (a, b) (a, c) (b, b)}
(d)
{(a, a) (a, b) (a, c) (c, c)}
(e)
{(a, a) (a, b) (c, a) (b, a)}.
139.
Let V = {S, A, B, a, b} and T = {a, b} Find the language generated by the grammer {V, T, S, P} when the set p of production consists of S® aBA, B®b, S ® aA, A®a.
(a)
L(G) = {ab, aba}
(b)
L(G) = {ba, aba}
(c)
L(G) = {aa, aab}
(d)
L(G) = {aa, bba}
(e)
L(G) = {aa, aba}.
140.
The G.C.D of relatively prime numbers is
(a)
0
(b)
(c)
Greatest of the two numbers
(d)
Lowest of the two numbers
(e)
Average of the two numbers.

Answers

131.
Answer : (b)
Reason : By definition of injenction function
132.
Answer : (d)
Reason : There are 9 favourable cases for the given event and there are 36 total numbers of cases in the experiment. So, the probability is 9/36.
133.
Answer : (b)
Reason : {13 = 1, 23 = 8, 33 = 27, 43 = 64}
134.
Answer : (d)
Reason : By definition of multiplication theorem of probability
135.
Answer : (a)
Reason : By definition of impossible event.
136.
Answer : (a)
Reason : By definition of Anti symmetric relation.
137.
Answer : (d)
Reason : By definition of Matrix representation of a relation.
138.
Answer : (e)
Reason : RoS = R[S(x)] " x Î S
RoS = {(a, a) (a, b), (b,a), (c,a)}
139.
Answer : (e)
Reason :
L (G) = {aba, aa}
140.
Answer : (b)
Reason  :       by  the definition of relatively primes



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