#Q2 Let R be a commutative ring with unity and A and B any two ideals of R such that A+B = R. Then A.B =
Anonymous Quiz
27%
A∩B
35%
A∪B
29%
A×B
9%
A∆B
#Q3 Let mZ and nZ be two ideals of Z Then mZ and nZ are co maximal ideals if
Anonymous Quiz
10%
lcm (m,n)=m
76%
gcd (m,n)=1 ,and m & n are primes
6%
gcd (m,n)≠1
8%
For any m & n , and m & n are primes
#Q4 Which of the following statements is/are true
Anonymous Quiz
27%
<x> is maximal ideal in Z[ x ]
35%
<(X x X)+1> is not maximal ideal in Q[ x ]
31%
<x+1> is not maximal ideal in Q[ x ]
6%
(X x X x X) -x+1 is reducible over Q
#Q5 ( Z_6 ,+_6 ,×_6 ) is------ of ( Z_12 ,+_12 ,×_6 )
Anonymous Quiz
34%
Subring
23%
Ideal
32%
Not subring
11%
Left ideal
#Q6 Which of the following is true?
Anonymous Quiz
11%
Subring of a commutative ring need not to be commutative
43%
If a ring is without zero divisors, then subring may have zero divisors
13%
Centre of a division ring is not an integral domain
32%
There exist rings with unity 1 having a subring with unity not equal to 1
#Q7 Let I and J be two ideals of R then
Anonymous Quiz
25%
Union of two ideals is an ideal.
44%
Arbitrary intersection of ideals of R need not to be an ideal
16%
I+J is not an ideal
15%
I.J is an ideal
#Q8 Let R be a ring with unity 1 And I be an ideal of R. If 1∈I , then
Anonymous Quiz
0%
I≠R
45%
I ⊂ R
53%
I=R
2%
None of these
#Q9 Let R be a ring and I and J be the ideals of R then
Anonymous Quiz
8%
I ∪J is ideal
38%
I+J is generated by I∩J
52%
I∩J is ideal
2%
I-J is also an ideal
#Q10 Which of the following statement is true?
Anonymous Quiz
14%
Intersection of two left ideals of ring R is right ideal
24%
Intersection of left ideal and right ideal is left ideal
60%
Intersection of left ideal and right ideal may not be even one sided ideal of R
2%
Intersection of left ideal and right ideal is right ideal
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#Q1 Let 2x+1 in Z_4 [x] then multiplicative inverse of 2x+1 is
Anonymous Quiz
4%
3x+1
30%
2x+2
30%
3x-1
35%
2x+1
#Q2 Let <m>and<n> be the ideal of Z then
Anonymous Quiz
33%
<m>∩<n>=<b> , b=gcd(m ,n )
24%
<m>∩<n>=<b> , b=m .n
22%
<m>∩<n>=<b> , b=m/n
22%
<m>∩<n>=<b> , b=Lcm(m ,n )
#Q4 Which of the following is/are maximal ideals of Z× Z?
Anonymous Quiz
17%
4 Z× Z
21%
3 Z× 6 Z
25%
2 Z×4 Z
38%
Z× 3 Z
#Q5 A= {f∈C[0 ,1] ;f(1/2)=0=f(1/3)} is
Anonymous Quiz
16%
Maximal ideal
35%
Prime ideal
35%
Both
14%
None of these
#Q7 I= {(a,0);a∈Z} is an ideal of Z × Z which is
Anonymous Quiz
10%
Prime
40%
Maximal
23%
Both
27%
Neither prime nor maximal
#Q8 Let R be a commutative ring with unity and M be the maximal ideal of R, then
Anonymous Quiz
27%
R/M need not to be integral domain
36%
R/M has zero divisor
33%
R/M is division ring
4%
None of these
#Q9 Which of the following is/are true
Anonymous Quiz
5%
For any ring R, every maximal ideal is a prime ideal
44%
For any commutative ring with unity, every prime ideal is a maximal ideal
23%
For any finite commutative ring with unity, every prime ideal need not to be a maximal ideal
28%
For any commutative ring R, if R/P is an integral domain, p-Ideal, then P is prime ideal
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