Math for Computer science
Questions 41 to 50
41.

Find gof if
f(x) = ax + b and g(x) = cx + d when a,b,c,d are constants.
(a) ac + bc + d (b) ac + bcx + d (c) acx + bc + d (d)
ac + bc + dx (e) ax + bc + d.

42.

To show The
statement p(1) is true for a fixed +ve integer ‘1’, is called
(a) Inductive step (b) Inductive hypothesis (c) Basic
Step
(d) Strong induction (e) Rule of inference.

43.

The difference
of A and B denoted by A – B contains
(a) Those
elements in both A and B
(b) Those
elements in either A or B
(c) Those
elements purely in A but not B
(d) Those
elements in Set A, but not in universal set
(e) Those
elements in Set B, but not in set A.

44.

A fair coin
has been tossed for 3 times. What is the probability that all three times
head will be outcome.
(a) 3/8 (b) 1/3 (c) 1/8 (d) 3/3 (e) 0.

45.

Let G be
grammar with Vocabulary V = {s, 0,1}, Set of terminals T = {0,1} starting
symbol s, and production p = {s ®1s1, s® 0} then the language of the grammar, [L(G)] is
(a) {0, 110,
11110, 1011101, …………}
(b) {0, 110,
11101, 1111110, ……….}
(c) {0, 101,
11011, 1110111, …………}
(d) {0, 110,
11110, 1111101, …………}
(e) {0, 110,
11110, 1111110, ……….}.

46.

Let V = { S,
A, a, b} and T = {a, b} Let G = {V,T,S,P}. The language of G, L(G) is given
by L(G) = {bb, ba}then the production is given by
(a) P = {S ®a AB, A®Bb, B ® l } (b)
P = {S ®A,
A®B,
B ® l }
(c) P = {S ®b B, B®b, B ® a } (d) P = {S ®A Ba, AB®a}
(e) P = {S ®b A, A®B, B ® a }.

47.

Which of the
following statements is true?
(a) Sentence ® Noun Verb
(b) Sentence ® Noun Pronoun
(c) Sentence ® Noun Phrase Verb Phrase
(d) Sentence ® Verb Phrase Noun Phrase
(e) Sentence ® Noun Phrase Noun Phrase.

48.

Let R be a
relation from C to A and S be a relation from B to C. Then RoS defined by
(a) { (b, c) / b Î B, c Î C } (b) { (c, a) / c Î C, a Î A }
(c) { (a, b) / a Î A, b Î B } (d) { (a, c) / a Î A, c Î C }
(e) { (b, a) / b Î B, aÎA }.

49.

Let R = {
(1,1), (1,2), (2,2), (2,3),(2,4), (3,1), (3,2), (3,3), (3,4) } then R1 is
given by
(a) { (1,1),
(1,2), (2,2), (2,3), (3,1), (3,2), (3,3),(2,4), (4,3)}
(b) ( (1,1),
(2,1), (2,2), (3,2), (1,3), (2,3), (3,3),(4,2), (4,3)}
(c) { (1,1),
(2,1), (2,2), (3,2), (2,3), (3,1), (3,3), (4,2),(3,4)}
(d) { (1,1),
(1,2), (2,2), (2,3),(2,4) (3,1), (3,2), (3,3), (4,3)}
(e) { (1,1),
(4,1), (4,2), (3,2), (1,3), (2,3), (3,3), (3,4),(4,2) }.

50.

From a deck of
well shuffled pack of cards 4 cards are drawn. What is the probability that
all four are aces?
(a) 5/52C4 (b) 2/52C4 (c)
1/52C4 (d) 4/52C4 (e) 3/52C4.

Answers
41.

Answer : (c)
Reason: f(x)
= ax+b g(x) = cx+d
(gof)
(x) = g[f(x)]
=
g[ax+b]
=
C(ax+b) +d
=
acx+bc+d

42.

Answer : (c)
Reason: by
definition

43.

Answer : (c)
Reason: by
definition

44.

Answer : (c)
Reason: Let
E : getting all three times head
A
fair con is tossed for three times so the
Total
no. of cases are 23 = 8
These
will be only one case favorable to E.

45.

Answer : (c)
L
(G) = {0, 101, 11011, 1110111, …..}

46.

Answer : (c)
Reason: L(G)
= {bb, ba}

47.

Answer : (c)
Reason: Sentence
Noun phrase verb phrase

48.

Answer : (c)

49.

Answer : (b)
Reason: R1
= {(1,1) (2,1) (2,2) (3,2) (4,2) (1,3) (2,3) (3,3) (4,3)}

50.

Answer : (c)
Reason: In
a pack of cards these are 4 aces so all four aces can be selected in only one
way.
From the deck of well shuffled pack of
cards 4 cards are drawn, which can be selected in 52
E
: getting 4 aces

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