#Q8 R= {0 ,2 ,4 ,6 ,8} ring with addition modulo 10 and multiplication modulo 10. Then unity of R is
Anonymous Quiz
20%
2
22%
4
19%
8
39%
6
#Q9 R= {a+ √p b ; p-prime,a &b ∈R} with ordinary addition and ordinary multiplication. Then unity of R is
Anonymous Quiz
6%
p
21%
√p
65%
1
8%
a+b
#Q10 Let R=(P(N),∆ ,∪ ) be the set, then R will be
Anonymous Quiz
17%
Ring
50%
Commutative Ring
24%
Integral Domain
9%
Not Ring
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#Q1 Let R=(P(N),∆ ,∩ ) then the zero element of R will be
Anonymous Quiz
14%
N
58%
𝜙
27%
A- N, N is the set of Natural numbers
2%
Ac
#Q2 R=(P(N),∆ ,∩ ) be the ring, then the unity of R is
Anonymous Quiz
24%
𝜙
55%
N, N = Natural numbers
18%
A ,A∈P(N)
4%
Ac ,A∈P(N)
❤1
#Q3 Unity of the zero ring for ( R ,+ ,∙ ) is
Anonymous Quiz
18%
0
32%
1
39%
Unity does not exist
11%
Infinite unity
#Q4 Let R be a commutative ring and a ,b are nilpotent element of R then
Anonymous Quiz
22%
a-b is nilpotent element
16%
a/b is nilpotent
51%
a.c is nilpotent ,∀ non-zero c in R
12%
a+c is nilpotent ,∀ c ∈ R
#Q5 Let a be a nilpotent element of index “r” in R Then 1-a is
Anonymous Quiz
29%
nilpotent
37%
idempotent
23%
Unit
12%
Zero divisor
❤1
❤1
#Q9 Let ∪(R) be the set of units in R and Z(R) be the set of units in zero divisor. And R be Ring with unity, then
Anonymous Quiz
6%
∪(R) ⊂Z(R)
38%
Z(R) ⊂ ∪(R)
31%
Z(R)∩ ∪(R)≠ϕ
25%
Z(R)∩ ∪(R)=ϕ
#Q10 Let (Z ,* ,∙ ) be the ring and a *b=a+b and a∙b=a+b-ab. Then unity of (Z ,* ,∙ ) is
Anonymous Quiz
18%
1
42%
0
28%
2
12%
-1
❤4
#Q1 List of zero divisors of Z_(m ) is
Anonymous Quiz
20%
{x∈Z_(m ) |gcd(x,m)≠1}
61%
{x∈Z_(m ) |gcd(x,m)=1}
13%
{x∈Z_(m ) |gcd(x,m)=2}
6%
{x∈Z_(m ) |gcd(x,m)≠2}
#Q5 Let R be an integral domain then
Anonymous Quiz
16%
R[x] is a field
16%
R[x] is a division ring
41%
R[x] has inverse of all non-zero elements
28%
R[x] does not have zero-divisor