# Math for Computer science Questions and Answers 11 to 20

## Math for Computer science

### Questions 10 to 20

 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. 12 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. 13 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. 14 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. 15 How many positive integers less than 100 are divisible by either 7 or 11 (a) 2                        (b) 22                      (c) 20                      (d) 23                      (e) 19. 16 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. 17 Probability of the sample space of a Random Experiments always equals to (a) 0                        (b) 1                        (c) 1/2                     (d) 1/4                     (e) a. 18 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. 19 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)}. 20 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.
12.
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
13.
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
14.
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.
15.
Answer : (a)
Reason:  By definition.
16.
Answer : (e)
Reason:  (x+y)4 = 4c0 x4 y0 + 4c1. x41. y + 4c2. x42, y2 + 4c3. x43 y3 + 4c4. x44 y4
(x+y)4 = x4 + 4x3y + 6x2y2 + 4xy3 + y4
17.
Answer : (b)
Reason:  By definition of probability of sample spare.
18.
Answer : (c)
Reason:  By definition of symmetric Relation.
19.
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)}.
20.
Answer : (c)
Reason:  S ® AB, S ® aA,   A® a       B® ba
L(G) = {aa, aba}.

#### No comments :

What you think about these Questions and Answers ? Let me know in comments.