1. GCD(a,b) = GCD(b,a mod b)

a) True

b) False

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Consider the Following properties Properties

G-i) Closure

G-ii) Associative

G-iii) Identity Element

G-iv) Inverse Element

G-v) Commutative

Consider the Following properties Properties

R-i) Closure under multiplication

R-ii) Associativity of multiplication

R-iii) Distributive Law

R-iv) Commutativity of multiplication

R-v) Multiplicative Identity

R-vi) No zero divisors

R-vii) Multiplicative Inverse

2. 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

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3. 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

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4. 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

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5. 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

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6. 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

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7. A Field satisfies all the properties above from G-i to R-vi.

a) True

b) False

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8. In modular arithmetic : (a/b) = b(a^-1)

a) True

b) False

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^{-1}).

9. a.(b.c) = (a.b).c is the representation for which property?

a) G-ii

b) G-iii

c) R-ii

d) R-iii

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10. a(b+c) = ac+bc is the representation for which property?

a) G-ii

b) G-iii

c) R-ii

d) R-iii

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11. 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!

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12. 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

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13. Is S a ring from the following multiplication and addition tables?

+ a b x a b

a a b a a a

b b a b a b

a) Yes

b) No

c) Can’t Say

d) Insufficient Data

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14. 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

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15. 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