#Q3 Let R be any P. I. D and pโR and P is a prime element. Then which of the following is/are true?
Anonymous Quiz
5%
<p> โ 0 is not a prime ideal of R
49%
<p> โ 0 may not be a maximal ideal of R
35%
p may not be an irreducible element
11%
<p> โ 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 AโB ideal of R is generated by
Anonymous Quiz
11%
Aโ
B= <a+b>
41%
Aโ
B= <aโฉb>
38%
Aโ
B= AโฉB
11%
Aโ
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 ฯ be the nth root of unity then โกdim dim [ Q[ ฯ ] โถQ] is
Anonymous Quiz
18%
n
29%
N x N
18%
2n
36%
ฯ(n)
๐2
#Q8 Let F=Q(โ2) 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 axโ
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
#Q2 Find the degree of minimal polynomial for โ(-3)+โ2 over Q
Anonymous Quiz
9%
2
58%
4
21%
6
12%
8
#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) โถF (a)]โฅ [ F ( a ,b ):F ]
32%
[ F (a ,b) โถF (a)]โค [ F ( a ):F ]
21%
[ F (a ,b) โถF (a)]โฅ [ F ( a ):F ]
24%
[ F (a ,b) โถF (a)]โค [ F ( a ,b ):F ]
#Q4 Let E be a finite extension of R. As C is algebraically closed then
Anonymous Quiz
8%
E โ C and โโ R
28%
E =C but never equal to R
44%
E =R but never equal to C
19%
E =R or โ = 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
#Q9 Let F be any finite field and F* be the group with multiplication. Then all the finite subgroups of F*
Anonymous Quiz
5%
Not normal
33%
Non-cyclic
21%
Only one will be cyclic
42%
Abelian
#Q10 Let GF(1024) be any field then No. of subfields of order 32 is
Anonymous Quiz
34%
4
23%
7
23%
9
20%
1
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