#Q4 Under a ring homomorphism, image of an ideal is an ideal if
Anonymous Quiz
33%
It is one-one homomorphism
43%
It is onto homomorphism
22%
Its kernel is not equal to zero
2%
None of these
#Q5 Under ring Homomorphism; inverse image of a prime ideal ----------
Anonymous Quiz
40%
Need not to be a prime ideal
30%
Need not to be an ideal
11%
May be maximal ideal
19%
Is prime ideal
#Q6 Under any ring homomorphism, inverse image of maximal ideal is ----------
Anonymous Quiz
31%
Maximal ideal
33%
Need not to be ideal
19%
May be prime
17%
May not be maximal
#Q9 Which of the following is/are not a homomorphism from C→C
Anonymous Quiz
44%
f(x)= [X x X]
22%
f(x)= 0
26%
f(a-ib)=a+ib
7%
f(a+ib)=a-ib
GATE Maths 2016 PYQ Paper With Answer Key.pdf
1 MB
For More Pratice Question: https://bit.ly/3JYcZlS
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