11.
|
Let f(x) = x + 5 and g(x) = x2 then (fog)
(x) is
(a) x + 5 (b)
x2 (c)
x2 - 5 (d) x2
+ 5 (e) x – 5.
|
|
|
Which of the following is the encrypt of the menage
"Do Not Pass go" by translating the letters into numbers applying
the caesar cipher f(p) = (p + 3) mod 26.
(a) GR QWR SDVV JR (b)
GR QRW SVDV JR
(c) GR QRW SDVV RJ (d)
GR QRW SDVV JR
(e) GR QWR SDVV RJ.
|
|
|
Binary equavalent of the decimal number 645 is
(a) 1 1 0 0 0 0 0 1 0 1 (b)
1 0 1 0 0 0 0 1 0 1 (c) 1 0 1
0 0 0 1 0 0 1
(d) 1 0 1 0 0 0 0 0 1 1 (e)
0 1 0 1 1 1 1 0 1 0.
|
|
|
Decimal equivalent of the Binary notation 1 1 0 1 0 0
1 0 0 0 1 is
(a) 1673 (b)
1809 (c) 1682 (d) 1681 (e) 1697.
|
|
|
How many positive integers less than 100 are
divisible by either 7 or 11
(a) 2 (b)
22 (c) 20 (d) 23 (e) 19.
|
|
|
The pigeonhole principle is stated as
(a) If
K + 1 or more objects are placed into K boxes. then there is at least one box
containing two or more of the objects.
(b) If
K + 1 or more objects are placed into K boxes then there is at most one box
containing two or more of the objects
(c) If
K + 1 or more objects are placed into K boxes then there is exactly one box
containing two or more of the objects
(d) If
K + 1 or more objects are placed into K boxes then there is no box containing
two or more of the objects
(e) If
K + 1 or more objects are placed into K boxes then all the boxes containing
two or more of the objects.
|
|
|
Probability of the sample space of a Random
Experiments always equals to
(a) 0 (b)
1 (c) 1/2 (d) 1/4 (e) a.
|
|
|
A relation R is said to be symmetric Relation
(a) if (a, b) Î R whenever (b, a) Î R (b) if (a,
b)Ï R whenever (b, a) Ï R
(c) if (b, a) Î R whenever (a, b) Î R (d) if (h,
a) Î R whenever (a, b) Ï R
(e) if (b, a) Ï R whenever (a, b) Î R.
|
|
|
Let R = {(a, a) (a, c) (b, a) (b,
b)} and S = {(a, b) (b, c) (c, a) (c, c)}
then SoR is given by
(a) {(a, a) (b, a) (a, c) (b, b)
(b, c)} (b) {(a, a)
(a, b) (a, c) (b, c) }
(c) {(a, a) (a, b) (a, c) (b, b)
(c, b)} (d) {(a, a)
(a, b) (a, c) (b, b) (b, c)
(e) {(a, a) (a, b) (c, a) (b, b)
(b, c)}.
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|
|
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® a A, A®a, B ® ba
(a) L(G) = {ab, aba} (b) L(G) ba, aba}
(c) L(G) = {aa, aab} (d) L)G) = {aa, bba} (e) L(G) = {Iaa, aba}.
|
Answers
11.
|
Answer : (d)
Reason: f
(x) = x + 5
g
(x) = x2
(fog)
(x) = f [g (x)]
=
f [x2]
=
x2 + 5.
|
|
|
Answer : (d)
Reason: f
(p) = (p + 3) mod 26
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
L
|
M
|
N
|
O
|
P
|
Q
|
R
|
S
|
T
|
U
|
V
|
W
|
X
|
Y
|
Z
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
21
|
22
|
23
|
24
|
25
|
D O N O T
P A S S G O
3
14 13 14 19 15 0 18 18 6 14
 (+3)
6
17 16 17 22 18 3 21 21 9 17
G
R Q R W S D V V J R
Code is GR QRW SDVV JR
|
|
|
Answer : (d)
Reason: 1
1 0 1 0 0 1 0 0 0 1
210
29 28 27
26 25 24 23
22 21 20
=
1024 + 512 + 128 + 16 + 1
=
1681
(110
1001 0001)2 = (1681)10
|
|
|
Answer : (b)
Reason: The
numbers less than 100 divisible by 7 are
7,
14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98
the no - of numbers divisible by 7 are 14
The
numbers divisible by 11 are
11,
22, 33, 44, 55, 66, 77, 88, 99
The no - of numbers divisible by 11 are 6
The
no - of numbers divisible by both 7 and 11 are 1
The + ve integers less than 100 divisible by
7 or 11
=
14 + 9 – 1 = 23 – 1 = 22.
|
|
|
Answer : (a)
Reason: By
definition.
|
|
|
Answer : (e)
Reason: (x+y)4
= 4c0 x4 y0 + 4c1. x41.
y + 4c2. x42, y2 + 4c3. x43
y3 + 4c4. x44 y4
(x+y)4
= x4 + 4x3y + 6x2y2 + 4xy3
+ y4
|
|
|
Answer : (b)
Reason: By
definition of probability of sample spare.
|
|
|
Answer : (c)
Reason: By
definition of symmetric Relation.
|
|
|
Answer : (d)
Reason: R
= {(a, a) (a, c) (b, a) (b, b)}
S
= {(a, b) (b, c) (c, a) (c, c)}
SoR
= S[R(x)] " x Î {a, b, c}
={(a,
a) (a, b) (a, c) (b, b) (b, c)}.
|
|
|
Answer : (c)
Reason: S
® AB, S ® aA, A® a B® ba
L(G)
= {aa, aba}.
|
21.
|
A sentence is made up of
(a) Noun
phrase proceeded by a verb phrase
(b) Noun
phrase followed by verb phrase
(c) Noun
phrase followed by Noun phrase
(d) Verb
phrase followed by Noun phrase
(e) Verb
phrase followed by a verb phrase.
|
|
|
Let a set A has a4 elements then P(A) denotes the
powerset of the set A. Now cardinality of P(A) is
(a) 16 (b)
81 (c) 256 (d) 1 (e) 4.
|
|
|
A function from set A to set B is one - to -one and
onto, then the ferniction is known as
(a) Sujection (b)
Injection (c)
Bijection
(d) Homomorphism (e)
Automorphism.
|
|
|
(pÙØq)®p is a
(a) Contingency (b) Contradiction (c) Tautology
(d) Contrapositive (e) Inverse.
|
25.
|
The fallacy of
denying the antecedent is denoted by
(a) [(p®q)Ù p] ®q (b)
[(p®q)Ù Øp] ®Øq
(c) [(p®q)Ù q] ®p (d)
(p®q)Ù Øq] ® Øp
(e) [(p®q)Ù Ør] ® Øq.
|
26.
|
For which of
the following ‘2’ is an element.
(a) {2, {2}} (b) {{2}, {{2}}} (c)
{{2}, {{2, {2}}
(d) {f, {2}} (e) {{2}}.
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27.
|
Let F(x) : x
is a pearl, P(x) : x is soft.
The statement “All pearls are soft” equivalent
(a) "x[F(x) Ù P(x)] (b) "x[F(x) Ú P(x)] (c) "x[F(x) « P(x)]
(d) "x[F(x) ® P(x)] (e) "x[F(x), P(x)].
|
28.
|
Suppose that U
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The bit string for the set A = {1, 3, 6,
10} is
(a) 00 1110 0111 (b) 10 1001 0101 (c) 11 0110 0111
(d) 10 1001 0001 (e) 00 1010 1010.
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29.
|
Suppose that U
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The element of the set for which the bit
string is 11 1100 1111
(a) {0, 1, 2, 3, 5, 7, 8, 9, 10} (b) {1, 2, 3, 4, 7, 8, 9, 10}
(c) {1, 3, 5, 6, 7, 8, 9, 10} (d) {2, 3, 4, 7, 8, 9, 10}
(e) {1, 3, 4, 5, 6, 7, 8, 9, 10}.
|
30.
|
Find the value
of éë1/2û + é1/2ù + 1/2ù
(a) 1 (b) 2 (c) 0 (d) 0.5 (e)
1.5.
|
Answers
21.
|
Answer : (b)
Reason: By
definition of the sentence.
|
|
|
Answer : (a)
Reason: n(A)
= |A| = 4 = cordinality of A
|P(A)|
= cardinality of power set of A
=
24
=
16.
|
|
|
Answer : (c)
Reason: By
definition of bijection.
|
|
|
Answer : (c)
Reason:
P
|
Q
|
ùQ
|
P
Lù Q
|
(P
Lù Q) ®P
|
F
|
F
|
T
|
F
|
T
|
F
|
T
|
F
|
F
|
T
|
T
|
F
|
T
|
T
|
T
|
T
|
T
|
F
|
F
|
T
|
\ (PLùq) ® P is a Toutology.
|
25.
|
Answer : (b)
Reason: by
definition
|
26.
|
Answer : (a)
Reason: by
definition
|
27.
|
Answer : (d)
Reason: for
all x
If x is a pearl then x is soft
\ "x, [f(x) ® P(x)]
|
28.
|
Answer : (d)
Reason: Bit
string of A = {1,3,6,10} in U = {1,2,3,4,5,6,7,8,9,10} is 1010010001
|
29.
|
Answer : (b)
Reason: U
= {1,2,3,4,5,6,7,8,9,10} the elements for which bit string is 1111001111 is
{1,2,3,4, 7,8,9,10}
|
30.
|
Answer : (b)
Reason: éë1/2û + é1/2ù +1/2ù = éë0.5û + é0.5ù +1/2ù
= é0 + 1 +1/2ù
= é3/2ù = é1.5ù = 2
|
31.
|
Let f(x) = ëx2/2û. Find f(s) if S= {1, 2, 3, 4}
(a) {1, 2, 4, 4, 8} (b) {1, 2, 5, 8} (c) {0, 2, 4, 8} (d)
{0, 2, 5, 8} (e) {0, 2, 4, 9}.
|
32.
|
Which of the
following statements is false?
(a) fÎ{f} (b)
fÎ{f, {f}} (c)
{f}Î{f}
(d) {f}Î{{f}} (e)
{f} Ì{{f}, {f}}.
|
33.
|
From the
following, choose the decimal expansion of the integer that has (101011010)2
as its binary expansion.
(a) 338 (b) 344 (c) 346 (d) 330 (e) 340.
|
34.
|
From the
following, choose the binary expansion of 246.
(a) 1111 0011 (b) 1111 0110 (c) 1111 0101 (d)
1111 1100 (e) 1111 1001.
|
35.
|
The
r-combination from a set with “n” elements when repetitions of elements are not
allowed is
(a) C(n+r+1, r) (b) C(n+r-1, r) (c) C(n, r)
(d) C(n+r-1, r- 1) (e) C(n+r+1, r+1).
|
36.
|
Which of the
following statements is true in a year?
(a) Among any
group of 366 people there must be at least one with the same birthday.
(b) Among any
group of 366 people there must be at least two with the same birthday
(c) Among any
group of 366 people there must be at most one with the same birthday
(d) Among any
group of 366 people there must be at most none with the same birthday
(e) Among any
group of 366 people there must be exactly 2 with the same birthday.
|
37.
|
What is the
probability that a card selected from a deck is a king?
(a) 1/4 (b) 1/52 (c) 4/52 (d) 2/52 (e) 3/52.
|
38.
|
What is the
probability that a positive integer less than 100 selected at random is
divisible by 25?
(a) 3/100 (b) 4/100 (c) 2/100 (d) 5/100 (e) 1/100.
|
39.
|
What is the
probability that a positive integer selected at random from the set of
positive integers not exceeding 21 is divisible by 5 or 3?
(a) 11/20 (b) 10/20 (c) 11/21 (d) 10/21 (e) 12/21.
|
40.
|
Let A = {0,11}
and B = {1,10,101} then AB is given by [concatenation of A and B is AB]
(a) {01, 010,
0110, 110, 1110, 11110}
(b) {01, 010,
0111, 111, 1110, 11110}
(c) {01, 010,
0101, 111, 1110, 11101}
(d) {01, 010,
0111, 111, 1110, 11111}
(e) {01, 010,
0110, 111, 1110, 11010}.
|
Answers
31.
|
Answer : (c)
Reason: Let
f(x) = ëx2/2û if S= {1,2,3,4}
f(s)
= f({1,2,3,4})
f(1)
= ë12/2û = ë1/2û = ë0.5û = 0
f(2)
= ë22/2û = ë4/2û = ë2û = 2
f(3)
= ë32/2û = ë9/2û = ë4. 5û = 4
f(4)
= ë42/2û = ë16/2û = ë8û = 8
\ f(s) = {0,2,4,8}
|
32.
|
Answer : (c)
Reason: by
definition
|
33.
|
Answer : (c)
Reason: (1010
11010)2
=
1x28+ 0x27 + 1x26 + 0x25 + 1x24 + 1x23 + 0x22 + 1x21 +0x20
=
256 +0 +64+ 0 + 16 +8 +0 +2 +0
=
346
|
34.
|
Answer : (b)
Reason: 2|246
2|123-0
2|61-1
2|30-1
2|15-0
2|7-1
2|3-1
2|1-1
(11110110)2
|
35.
|
Answer : (c)
Reason: by
definition
|
36.
|
Answer : (b)
Reason: In
a year there are 365 days, if we distribute every day one pessons birthday
then at least two with the same birthday.
|
37.
|
Answer : (c)
Reason: E:
Selecting a king
|
38.
|
Answer : (a)
Reason: E:
A positive integer less than 100 in divisible by 25
|
39.
|
Answer : (d)
Reason: Positive
integer not exceeding 21 divisible by 5 or 3
|
40.
|
Answer : (c)
Reason: A={0,11}
B={1, 10, 101}
AB
= {01, 010, 0101, 111, 1110, 11101}
|
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 R-1 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: R-1
= {(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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