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10) A ring <R,+,>> is called as zero divisors if ab=0 implies a. a=0,b=0. b. a=0,b=0. c. a=0,b=0. d. a=0,b=0. 11) Every subgroup of a cyclic group is a/an a. Abelian. b. cyclic. c. normal. d. all the above. 12) Which of the following structures is NOT a field? a. <C,+,>> b. <Q,+,> c. <R,+,> d. <Z0​+,>>. 13) Which of the following structures is NOT a ring? a. <Q,+,> b. <R,+,> c. <Z0​+,+>. d. <N,+,>>. 14) Number of generators of a cyclic group G of order 8 is a. 1. b. 2 . c. 3 . d. 4 . 15) Let G be a group. If H is a subgroup of G with order 11 , and index of H in G is 7 . Then order of group G must be a. 77. b. 121 . c. 154 . d. 1078 .
16) If b is a unit ring R, then b is a. a zero divisor. b. a zero element. c. An identity element. d. an invertible element. 17) The number of elements in A6​ is a. 26. b. 6! c. 360 . d. None of the above. 18) H⋅a is a set of a. left cosets. b. right cosets. c. left and right cosets. d. none of the above. 19) A commutative ring with unity element and without zero divisor is called a/an a. field. b. subfield. c. subring. d. integral domain. 20) Which of the following statement is FALSE? a. Z is a subring of 2Z. b. 2Z is a subring of Z. c. Q is a subring of R. d. Z is a subring of Q.