Math for Computer science
Questions 10 to 20
11.
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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.
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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.
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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.
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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.
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How many positive integers less than 100 are
divisible by either 7 or 11
(a) 2 (b)
22 (c) 20 (d) 23 (e) 19.
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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.
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Probability of the sample space of a Random
Experiments always equals to
(a) 0 (b)
1 (c) 1/2 (d) 1/4 (e) a.
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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.
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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}.
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Answers
11.
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Answer : (d)
Reason: f
(x) = x + 5
g
(x) = x2
(fog)
(x) = f [g (x)]
=
f [x2]
=
x2 + 5.
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Answer : (d)
Reason: f
(p) = (p + 3) mod 26
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
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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
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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.
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Answer : (a)
Reason: By
definition.
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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
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Answer : (b)
Reason: By
definition of probability of sample spare.
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Answer : (c)
Reason: By
definition of symmetric Relation.
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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)}.
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Answer : (c)
Reason: S
® AB, S ® aA, A® a B® ba
L(G)
= {aa, aba}.
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