1. Calculate the GCD of 1160718174 and 316258250 using Euclidean algorithm..
A. 882.
B. 770.
C. 1078.
D. 1225.
Answer= 1078
2. Calculate the GCD of 102947526 and 239821932 using Euclidean algorithm..
A. 11.
B. 12.
C. 8.
D. 6.
Answer= 6
3. Calculate the GCD of 8376238 and 1921023 using Euclidean algorithm..
A. 13.
B. 12.
C. 17.
D. 7.
Answer= 13
4. What is 11 mod 7 and -11 mod 7?.
A. 4 and 5.
B. 4 and 4.
C. 5 and 3.
D. 4 and -4.
Answer= 4 and -4
5. Which of the following is a valid property for concurrency?.
A. a = b (mod n) if n.
B. (a-b).
C. a = b (mod n) implies b = a (mod n).
D. a = b (mod n) and b = c (mod n) implies a = c (mod n).
Answer= All of the mentioned
6. [(a mod n) + (b mod n)] mod n = (a+b) mod n.
A. TRUE.
B. FALSE.
C. Nothing can be said.
D. None of the mentioned.
Answer= TRUE
7. [(a mod n) – (b mod n)] mod n = (b – a) mod n.
A. TRUE.
B. FALSE.
C. Nothing can be said.
D. None of the mentioned.
Answer= FALSE
8. 117 mod 13 =
A. 3.
B. 7.
C. 5.
D. 15.
Answer= 15
9. The multiplicative Inverse of 1234 mod 4321 is.
A. 3239.
B. 3213.
C. 3242.
D. Does not exist.
Answer= 3239
10. The multiplicative Inverse of 550 mod 1769 is.
A. 434.
B. 224.
C. 550.
D. Does not exist.
Answer= 434
11. The multiplicative Inverse of 24140 mod 40902 is.
A. 2355.
B. 5343.
C. 3534.
D. Does not exist.
Answer= Does not exist
12. (6x2 + x + 3)x(5x2 + 2) in Z_10 =
A. x3 + 2x + 6.
B. 5x3 + 7x2 + 2x + 6.
C. x3 + 7x2 + 2x + 6.
D. None of the mentioned.
Answer= 5x3 + 7x2 + 2x + 6
13. Is x3 + 1 reducible over GF(2).
A. Yes.
B. No.
C. Can't Say.
D. Insufficient Data.
Answer= Yes
14. Is x3 + x2 + 1 reducible over GF(2).
A. Yes.
B. No.
C. Can't Say.
D. Insufficient Data.
Answer= No
15. Is x4 + 1 reducible over GF(2).
A. Yes.
B. No.
C. Can't Say.
D. Insufficient Data.
Answer= Yes
16. The result of (x2 ? P), and the result of (x ? (x ? P)) are the same, where P is a polynomial..
A. TRUE.
B. FALSE.
C. Nothing can be said.
D. None of the mentioned.
Answer= TRUE
17. The GCD of x3+ x + 1 and x2 + x + 1 over GF(2) is.
A. 1.
B. x + 1.
C. x2.
D. x2 + 1.
Answer= 1
18. The GCD of x5+x4+x3 – x2 – x + 1 and x3 + x2 + x + 1 over GF(3) is.
A. 1.
B. x.
C. x + 1.
D. x2 + 1.
Answer= x + 1
19. The GCD of x3 – x + 1 and x2 + 1 over GF(3) is.
A. 1.
B. x.
C. x + 1.
D. x2 + 1.
Answer= 1
20. Find the 8-bit word related to the polynomial x6 + x + 1.
A. 1000011.
B. 1000110.
C. 10100110.
D. 11001010.
Answer= 1000011
21. If f(x)=x7+x5+x4+x3+x+1 and g(x)=x3+x+1, find f(x) + g(x)..
A. x7+x5+x4.
B. x7+x5+x4+x3+x.
C. x4+x2+x+1.
D. x6+x4+x2+x+1.
Answer= x7+x5+x4
22. If f(x)=x7+x5+x4+x3+x+1 and g(x)=x3+x+1, find f(x) x g(x)..
A. x12+x5+x3+x2+x+1.
B. x10+x4+1.
C. x10+x4+x+1.
D. x7+x5+x+1.
Answer= x10+x4+x+1
23. If f(x)=x7+x5+x4+x3+x+1 and g(x)=x3+x+1, find the quotient of f(x) / g(x)..
A. x4+x3+1.
B. x4+1.
C. x5+x3+x+1.
D. x3+x2.
Answer= x4+1
24. Primitive Polynomial is also called a ____i) Perfect Polynomialii) Prime Polynomialiii) Irreducible Polynomialiv) Imperfect Polynomial.
A. ii) and iii).
B. only iii).
C. iv) and ii).
D. None.
Answer= ii) and iii)
25. Which of the following are irreducible polynomials?i) X4+X3ii) 1iii) X2+1iv) X4+X+1.
A. i) and ii).
B. only iv).
C. ii) iii) and iv).
D. All of the options.
Answer= All of the options
26. The polynomial f(x)=x3+x+1 is a reducible..
A. TRUE.
B. FALSE.
C. Nothing can be said.
D. None of the mentioned.
Answer= FALSE
27. Find the HCF/GCD of x6+x5+x4+x3+x2+x+1 and x4+x2+x+1..
A. x4+x3+x2+1.
B. x3+x2+1.
C. x2+1.
D. x3+x2+1.
Answer= x3+x2+1
28. On multiplying (x5 + x2 + x) by (x7 + x4 + x3 + x2 + x) in GF(28) with irreducible polynomial (x8 + x4 + x3 + x + 1) we get.
A. x12+x7+x2.
B. x5+x3+x3.
C. x5+x3+x2+x.
D. x5+x3+x2+x+1.
Answer= x5+x3+x2+x+1
29. On multiplying (x6+x4+x2+x+1) by (x7+x+1) in GF(28) with irreducible polynomial (x8 + x4 + x3 + x + 1) we get.
A. x7+x6+ x3+x2+1.
B. x6+x5+ x2+x+1.
C. x7+x6+1.
D. x7+x6+x+1.
Answer= x7+x6+1
30. Find the inverse of (x2 + 1) modulo (x4 + x + 1)..
A. x4+ x3+x+1.
B. x3+x+1.
C. x3+ x2+x.
D. x2+x.
Answer= x3+x+1
31. Find the inverse of (x5) modulo (x8+x4 +x3+ x + 1)..
A. x5+ x4+ x3+x+1.
B. x5+ x4+ x3.
C. x5+ x4+ x3+1.
D. x4+ x3+x+1.
Answer= x5+ x4+ x3+1
32. A very common field in this category is GF(2) with the set {1, 2} and two operations, addition and multiplication..
A. TRUE.
B. FALSE.
C. Nothing can be said.
D. None of the mentioned.
Answer= FALSE
33. Multiplication / Division follow which operation?.
A. XOR.
B. NAND.
C. AND.
D. OR.
Answer= AND
34. What do the above numbers correspond to?0 1 2 3 40 4 3 2 10 1 2 3 4– 1 3 2 4.
A. Both Additive Inverses.
B. Both Multiplicative Inverses.
C. Additive and Multiplicative Inverse respectively.
D. Multiplicative and Additive Inverses respectively.
Answer= Both Multiplicative Inverses
35. How many numbers cannot be used in GF(p) in 2n where n=4?.
A. 2.
B. 5.
C. 3.
D. 1.
Answer= 3
36. If f(x)=x3+x2+2 and g(x)=x2-x+1, find: f(x) + g(x).
A. x3+2x2-x+3.
B. x3+x2+3.
C. x3+x+1.
D. x2+2x+4.
Answer= x3+2x2-x+3
37. If f(x)=x3+x2+2 and g(x)=x2-x+1, find: f(x) – g(x).
A. x3+x+4.
B. x3+x+1.
C. x3+x2+3.
D. x3+3x+2.
Answer= x3+x+1
38. If f(x)=x4+x3+2 and g(x)=x3-x+6, find: f(x) + g(x).
A. 2x4+2x3+x+8.
B. x4+2x3-x+8.
C. x4+x2+x+8.
D. x4+x3+8.
Answer= x4+2x3-x+8
39. If f(x)=x4+x2-x+2 and g(x)=x2-x+1, find: f(x) – g(x).
A. x4+1.
B. x2+1.
C. x2+2x+6.
D. x4-1.
Answer= x4+1
40. If f(x)=x3+x2+2 and g(x)=x2-x+1, find the quotient of f(x) / g(x).
A. x+3.
B. x2+4.
C. x.
D. x+2.
Answer= x+2
41. If f(x)=x3+x2+2 and g(x)=x2-x+1, find: f(x) x g(x).
A. x4+x2+2x+2.
B. x5+2x3+2x+3.
C. x5+3x2-2x+2.
D. x4+x2+x+1.
Answer= x5+3x2-2x+2
42. Find the 8-bit word related to the polynomial x5 + x2 + x.
A. 10011.
B. 1000110.
C. 100110.
D. 11001010.
Answer= 100110
43. Find the 8-bit word related to the polynomial x6 + x5 + x2 + x +1.
A. 10011.
B. 11000110.
C. 100110.
D. 1100111.
Answer= 1100111
44. If f(x)=x7+x5+x4+x3+x+1 and g(x)=x3+x+1, find f(x) – g(x)..
A. x7+x5+x4+x3.
B. x6+x4+x2+x.
C. x4+x2+x+1.
D. x7+x5+x4.
Answer= x7+x5+x4
45. 5/3 mod 7 =
A. 2.
B. 3.
C. 4.
D. 5.
Answer= 4
46. The polynomial x4+1 can be represented as
A. (x+1)(x3+x2+1).
B. (x+1)(x3+x2+x).
C. (x)(x2+x+1).
D. None of the mentioned.
Answer= None of the mentioned
47. -5 mod -3 =
A. 3.
B. 2.
C. 1.
D. 5.
Answer= 1
48. Multiply the polynomials P1 = x5 +x2+ x) by P2 = (x7 + x4 +x3+x2 + x) in GF(28) with irreducible polynomial (x8 + x4 + x3 + x + 1). The result is.
A. x4+ x3+ x+1.
B. x5+ x3+x2+x+1.
C. x5+ x4+ x3+x+1.
D. x5+ x3+x2+x.
Answer= x5+ x3+x2+x+1
49. Multiply 00100110 by 10011110 in GF(2^8) with modulus 100011011.The result is.
A. 101111.
B. 101100.
C. 1110011.
D. 11101111.
Answer= 101111
50. Find the inverse of (x7+x+1) modulo (x8 + x4 + x3+ x + 1)..
A. x7+x.
B. x6+x3.
C. x7.
D. x5+1.
Answer= x7
51. 7x = 6 mod 5. Then the value of x is.
A. 2.
B. 3.
C. 4.
D. 5.
Answer= 3
52. The product of monic polynomials is monic..
A. TRUE.
B. FALSE.
C. Can't Say.
D. None of the mentioned.
Answer= TRUE
53. The product of polynomials of degrees m and n has a degree m+n+1..
A. TRUE.
B. FALSE.
C. Can't Say.
D. None of the mentioned.
Answer= FALSE
54. The sum of polynomials of degrees m and n has degree max[m,n]..
A. TRUE.
B. FALSE.
C. Can't Say.
D. None of the mentioned.
Answer= Can't Say
55. (7x + 2)-(x2 + 5) in Z_10 =
A. 9x2 + 7x + 7.
B. 9x2+ 6x + 10.
C. 8x2 + 7x + 6.
D. None of the mentioned.
Answer= 9x2 + 7x + 7
56. GCD(a,b) = GCD(b,a mod b).
A. TRUE.
B. FALSE.
C. Nothing can be said.
D. None of the mentioned.
Answer= TRUE
57. All groups satisfy properties.
A. G-i to G-v.
B. G-i to G-iv.
C. G-i to R-v.
D. R-i to R-v.
Answer= G-i to G-iv
58. An Abelian Group satisfies the properties.
A. G-i to G-v.
B. G-i to R-iv.
C. G-i to R-v.
D. R-i to R-v.
Answer= G-i to G-v
59. A Ring satisfies the properties.
A. R-i to R-v.
B. G-i to G-iv.
C. G-i to R-v.
D. G-i to R-iii.
Answer= G-i to R-iii
60. A Ring is said to be commutative if it also satisfies the property.
A. R-vi.
B. R-v.
C. R-vii.
D. R-iv.
Answer= R-iv
61. An 'Integral Domain' satisfies the properties.
A. G-i to G-iii.
B. G-i to R-v.
C. G-i to R-vi.
D. G-i to R-iii.
Answer= G-i to R-vi
62. A Field satisfies all the properties above from G-i to R-vi..
A. TRUE.
B. FALSE.
C. Nothing can be said.
D. None of the mentioned.
Answer= TRUE
63. In modular arithmetic : (a/b) = b(a^-1).
A. TRUE.
B. FALSE.
C. Nothing can be said.
D. None of the mentioned.
Answer= FALSE
64. a.(b.c) = (a.b).c is the representation for which property?.
A. G-ii.
B. G-iii.
C. R-ii.
D. R-iii.
Answer= G-ii
65. a(b+c) = ac+bc is the representation for which property?.
A. G-ii.
B. G-iii.
C. R-ii.
D. R-iii.
Answer= R-iii
66. For the group Sn of all permutations of n distinct symbols, what is the number of elements in Sn?.
A. n.
B. n-1.
C. 2n.
D. n!.
Answer= n!
67. For the group Sn of all permutations of n distinct symbols, Sn is an abelian group for all values of n..
A. TRUE.
B. FALSE.
C. Nothing can be said.
D. None of the mentioned.
Answer= FALSE
68. Does the set of residue classes (mod 3) form a group with respect to modular addition?.
A. Yes.
B. No.
C. Can't Say.
D. Insufficient Data.
Answer= Yes
69. Does the set of residue classes (mod 3) form a group with respect to modular addition?.
A. Yes.
B. No.
C. Can't Say.
D. Insufficient Data.
Answer= No