GATE Maths 2017 PYQ Paper With Answer Key.pdf
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#Q1 Let 2x+1 in Z_4 [x] then multiplicative inverse of 2x+1 is
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4%
3x+1
30%
2x+2
30%
3x-1
35%
2x+1
#Q2 Let <m>and<n> be the ideal of Z then
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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?
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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
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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
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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
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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
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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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#Q1 Let R be a Boolean ring. Then
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21%
Every proper prime ideal need not to be a maximal ideal
40%
Every proper prime ideal P of R is maximal ideal
27%
Every maximal ideal is prime ideal
13%
None of these
#Q2 Let I=<2>and J=<3 > be the ideals of Z then
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38%
I∩J is prime ideal
16%
I.J is prime ideal
42%
I∩J is not maximal ideal
4%
I.J is maximal ideal
#Q4 Under a ring homomorphism, image of an ideal is an ideal if
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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 ----------
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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 ----------
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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
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44%
f(x)= [X x X]
22%
f(x)= 0
26%
f(a-ib)=a+ib
7%
f(a+ib)=a-ib