In the group G = <Zn*, ×>, when the order of an element is the same as order of the group (i.e. f(n)), that element is called the Non – primitive root of the group.
a) True
b) False
Q.6.
In the order of group G= <Z20*, x>, what is the order of element 17?
a) 16
b) 4
c) 11
d) 6
Q.7.
The order of group G= <Zx> , primitive roots of the group are –
a) 8 , Primitive roots- 2,3
b) 6 , Primitive roots- 5
c) 6 , Primitive roots- 2,5
d) 6 , Primitive roots- 5,7
Q.8.
Which among the following values: anddoes not have primitive roots in the group G = <Zn*, ×>?
a) 17
b) 20
c) 38
d) 50
Q.9.
Find the number of primitive roots of G=<Z11*, x>?
a) 5
b) 6
c) 4
d) 10
Q.10.
Find the primitive roots of G=<Z11*, x>?.
a) {2, 6, 8}
b) {2, 5, 8}
c) {3, 4, 7, 8}
d) {2, 6, 7, 8}
Q.11.
If a group has primitive roots, it is a cyclic group
a) True
b) False
Q.12.
Find the primitive roots of G = <Z10*, ×>.
a) {2, 6, 8}
b) {3,6 ,9}
c) {3, 7, 8}
d) {3, 7}
Q.13.
The group G = <Zp*, ×> is always cyclic.
a) True
b) False
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