**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