𝐓𝐡𝐞𝐲 𝐰𝐞𝐫𝐞 𝐨𝐧𝐜𝐞 𝐢𝐧 𝐲𝐨𝐮𝐫 𝐞𝐱𝐚𝐜𝐭 𝐩𝐨𝐬𝐢𝐭𝐢𝐨𝐧. 𝐓𝐡𝐞𝐲 𝐚𝐜𝐜𝐞𝐩𝐭𝐞𝐝 𝐭𝐡𝐞 𝐜𝐡𝐚𝐥𝐥𝐞𝐧𝐠𝐞. 𝐓𝐡𝐞𝐲 𝐬𝐮𝐜𝐜𝐞𝐞𝐝𝐞𝐝. 𝐓𝐡𝐞 𝐨𝐧𝐥𝐲 𝐪𝐮𝐞𝐬𝐭𝐢𝐨𝐧 𝐢𝐬: 𝐖𝐢𝐥𝐥 𝐲𝐨𝐮?
𝐄𝐧𝐫𝐨𝐥𝐥 𝐍𝐨𝐰 :- https://bit.ly/49PVrCW
𝐄𝐧𝐫𝐨𝐥𝐥 𝐍𝐨𝐰 :- https://bit.ly/49PVrCW
𝐓𝐡𝐞𝐲 𝐰𝐞𝐫𝐞 𝐨𝐧𝐜𝐞 𝐢𝐧 𝐲𝐨𝐮𝐫 𝐞𝐱𝐚𝐜𝐭 𝐩𝐨𝐬𝐢𝐭𝐢𝐨𝐧. 𝐓𝐡𝐞𝐲 𝐚𝐜𝐜𝐞𝐩𝐭𝐞𝐝 𝐭𝐡𝐞 𝐜𝐡𝐚𝐥𝐥𝐞𝐧𝐠𝐞. 𝐓𝐡𝐞𝐲 𝐬𝐮𝐜𝐜𝐞𝐞𝐝𝐞𝐝. 𝐓𝐡𝐞 𝐨𝐧𝐥𝐲 𝐪𝐮𝐞𝐬𝐭𝐢𝐨𝐧 𝐢𝐬: 𝐖𝐢𝐥𝐥 𝐲𝐨𝐮?
𝐄𝐧𝐫𝐨𝐥𝐥 𝐍𝐨𝐰 :- https://bit.ly/49PVrCW
𝐄𝐧𝐫𝐨𝐥𝐥 𝐍𝐨𝐰 :- https://bit.ly/49PVrCW
#Q1 Under the ring homomorphism, which of the following is/are true?
Anonymous Quiz
9%
Nilpotent map to idempotent
19%
Idempotent map to nilpotent
62%
Idempotent to idempotent
9%
Any element can map to any element
❤2
#Q2 Let R be a ring with unity and I be any proper ideal of R. Then which of the following is/are true?
Anonymous Quiz
31%
I must be contained in a prime ideal of R
19%
I may not be contained in any ideal of R
43%
I is contained in some maximal ideal of R
7%
I is only contained in R
#Q3 Let R be any P. I. D and p∈R and P is a prime element. Then which of the following is/are true?
Anonymous Quiz
5%
<p> ≠0 is not a prime ideal of R
49%
<p> ≠0 may not be a maximal ideal of R
35%
p may not be an irreducible element
11%
<p> ≠0 is maximal ideal of R
#Q4 Let n be any prime element of R then n be irreducible if R is
Anonymous Quiz
24%
Integral domain
38%
P .I .D
24%
Not U.F.D
14%
For every ring R
#Q5 Let A and B be two non-zero ideals of PID R, generated by a and b respectively. Then A∙B ideal of R is generated by
Anonymous Quiz
11%
A⋅B= <a+b>
41%
A⋅B= <a∩b>
38%
A⋅B= A∩B
11%
A⋅B= <ab>
#Q6 Let R be a subring of Q containing 1, then
Anonymous Quiz
26%
R is a PID
21%
R contains infinitely many prime ideals
29%
R contains a prime ideal which is not maximal
24%
For every maximal ideal M in R, field R/M is finite
#Q7 Let ω be the nth root of unity then □dim dim [ Q[ ω ] ∶Q] is
Anonymous Quiz
18%
n
29%
N x N
18%
2n
36%
ϕ(n)
🎉2
#Q8 Let F=Q(√2) be the field, then number of subfields of F is
Anonymous Quiz
7%
4
33%
1
37%
2
24%
Infinite
#Q10 Which of the following statements are true?
Anonymous Quiz
31%
Subring of an I.D is I.D
31%
Subring of an U.F.D is U.F.D
13%
Subring of an PID is P.I.D
25%
Subring of an E.D is E.D
#Q1 Let ax≅b(mod n )be any equation then this equation have solution if
Anonymous Quiz
17%
If lcm (a ,n )= l ,then l/b
43%
If gcd (a ,b )= d ,then d/n
23%
If gcd (a ,n )= d ,then b/d
17%
If gcd (a ,n )= d ,then d/b
#Q3 Let a and b belong to some extension of F and Let b be algebraic over F. Then which of the following is true?
Anonymous Quiz
24%
[ F (a ,b) ∶F (a)]≥ [ F ( a ,b ):F ]
32%
[ F (a ,b) ∶F (a)]≤ [ F ( a ):F ]
21%
[ F (a ,b) ∶F (a)]≥ [ F ( a ):F ]
24%
[ F (a ,b) ∶F (a)]≤ [ F ( a ,b ):F ]
#Q4 Let E be a finite extension of R. As C is algebraically closed then
Anonymous Quiz
8%
E ≠ C and ∈≠R
28%
E =C but never equal to R
44%
E =R but never equal to C
19%
E =R or ∈ = C
#Q6 Let a and b be two elements of K. Then a and b are conjugate over F if
Anonymous Quiz
9%
a and b are only roots of same minimal polynomial over F
33%
a and b are algebraic over F
18%
a and b are not algebraic over F
39%
a and b are algebraic over F and they are roots of same minimal Polynomial over F