Math for Computer science
Questions 10 to 20
11.

Let f(x) = x + 5 and g(x) = x^{2} then (fog)
(x) is
(a) x + 5 (b)
x^{2} (c)
x^{2}  5 (d) x^{2}
+ 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)}.


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) = x^{2}
(fog)
(x) = f [g (x)]
=
f [x^{2}]
=
x^{2} + 5.


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


Answer : (d)
Reason: 1
1 0 1 0 0 1 0 0 0 1
2^{10}
2^{9} 2^{8} 2^{7}
2^{6} 2^{5} 2^{4} 2^{3}
2^{2} 2^{1} 2^{0}
=
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}
= 4c_{0 }x^{4} y^{0} + 4c_{1}. x^{41}.
y + 4c_{2}. x^{42}, y^{2} + 4c_{3}. x^{43}
y^{3} + 4c_{4}. x^{44} y^{4}
(x+y)^{4}
= x^{4} + 4x^{3}y + 6x^{2}y^{2} + 4xy^{3}
+ y^{4}


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}.

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