1191. R+ is a group of non-zero positive real number under multiplication . Then which of the following group under addition is isomorphic to R +:

A. Z
B. Q
C. R *
D. C

1192. Any group G can be embedded in a group of bijective mappings of certain set is a statement of :

A. Lagrange’s theorem
B. Cauchy’s theorem
C. Cayley’s theorem *
D. Isomorphism theorem

1193. Let G and H be two cyclic group of order m and n respectively .if G and H are isomorphic then :

A. m<n
B. m>n
C. m=n *
D. m+n

1194. Let G be a cyclic group .Then which of the following is also cyclic :

A. Subgroup of G
B. Homomorphic image of G
C. Centre of G
D. All of them *

1195. For any set of points S in a plane , the set of distance preserving injective mappings of a plane which leave the point of S invariant is called :

A. Mapping
B. Invarient Mappings
C. Symmetries *
D. Permulations

1196.The symmertries of a rectangle form a :

A. Kleins four group, V4 *
B. Dihedral group of order 8, d4
C. Optic group
D. Permutation group of order 3, s3

1197. The symmetries of an equilateral traingle form a :

A. Klein’s four group v4
B. Dihedral group of order 8, d4
C. Optic group
D. Permutation group of order 3, s3 *

1198. The smallest non-cyclic group is :

A. V4 *
B. s3
C. D4
D. None

1199. Let G be a cyclic group .Then which of the following can be order of G :

A. 17
B. 107
C. 1,000,000,007 *
D. All of the above

1200. Let C be a group of complex number w.r.to addition . The Z(c)=

A. Q
B. R
C. C *
D. Z