1 A non empty set A is termed as an algebraic structure ________ A with respect to binary operation * B with respect to ternary operation ? C with respect to binary operation + D with respect to unary operation – View Answer Answer: with respect to binary operation * 2 Condition for monoid is __________ A (a+e)=a B (a*e)=(a+e) C a=(a*(a+e) D (a*e)=(e*a)=a View Answer Advertisement 3 A group (M,*) is said to be abelian if ___________ A (x+y)=(y+x) B (x*y)=(y*x) C (x+y)=x D (y*x)=(x+y) View Answer 4 Matrix multiplication is a/an ____ property. A Commutative B Associative C Additive D Disjunctive View Answer 5 How many properties can be held by a group? View Answer 6 {1, i, -i, -1} is _____ A semigroup B subgroup C cyclic group D abelian group View Answer 7 The set of all real numbers under the usual multiplication operation is not a group since A multiplication is not a binary operation B multiplication is not associative C identity element does not exist D zero has no inverse View Answer Answer: zero has no inverse 8 The inverse of - i in the multiplicative group, {1, - 1, i , - i} is View Answer 9 If (G, .) is a group, such that (ab)2 = a2 b2 ∀ a, b ∈ G, then G is a/an A commutative semi group B abelian group C non-abelian group D none of these View Answer 10 If A = (1, 2, 3, 4). Let ~= {(1, 2), (1, 3), (4, 2)}. Then ~ is A not anti-symmetric B transitive C reflexive D symmetric View Answer 11 If the binary operation * is deined on a set of ordered pairs of real numbers as (a, b) * (c, d) = (ad + bc, bd) and is associative, then (1, 2) * (3, 5) * (3, 4) equals A (74,40) B (32,40) C (23,11) D (7,11) View Answer 12 Match the following A. Groups I. Associativity B. Semi groups II. Identity C. Monoids III. Commutative D. Abelian Groups IV Left inverse Codes. A B C D A IV I II III B III I IV II C II III I IV D I II III IV View Answer 13 An algebraic structure ____ is called a semigroup. A (P, *) B (Q, +, *) C (P, +) D (+, *) View Answer 14 A monoid is called a group if _______ A (a*a)=a=(a+c) B (a*c)=(a+c) C (a+c)=a D (a*c)=(c*a)=e View Answer 15 A cyclic group can be generated by a/an _____ element. A singular B non-singular C inverse D multiplicative View Answer 16 A cyclic group is always _________ A abelian group B monoid C semigroup D subgroup View Answer 17 If (G, .) is a group such that (ab)- 1 = a-1b-1, ∀ a, b ∈ G, then G is a/an A commutative semi group B abelian group C non-abelian group D None of these View Answer 18 If (G, .) is a group such that a2 = e, ∀a ∈ G, then G is A semi group B abelian group C non-abelian group D none of these View Answer 19 The set of integers Z with the binary operation "*" defined as a*b =a +b+ 1 for a, b ∈ Z, is a group. The identity element of this group is View Answer 20 In the group (G, .), the value of (a- 1 b)- 1 is A ab-1 B b- 1a C a-1b D ba-1 View Answer Advertisement |
