#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
GATE Maths 2015 PYQ Paper With Answer Key.pdf
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โค2
#Q1 Let K (u)= K [ u] iff
Anonymous Quiz
8%
u is transcendental over K
39%
u is not a root of any polynomial over K
29%
u is algebraic over K
24%
K(u) is never equal to K[ u ]
#Q2 Let F be an extension field of K. Define L= {ฮฑ โF โถ ฮฑ is algebric over K} then
Anonymous Quiz
6%
L is never a subfield of K
54%
L is subfield of K
20%
L is only a subring of K
20%
L is a subfield of F
#Q3 Let K be a field and F is a subfield of K, then what should be the external composition between F and K such that K forms vector space over F.
Anonymous Quiz
23%
With multiplication of F
57%
With multiplication of k
13%
Addition of F
7%
None of these options
#Q4 Which of the following statement is/are true if (R,+,โ) be a ring and F < R and (F,+,โ) is a field and external composition is same as multiplication in R
Anonymous Quiz
15%
R over F always form a vector space
56%
R over F forms vector space if unity of R is same as unity of F
26%
R over F is vector space always if unity of R is not same as unity of F
3%
R over F never forms a vector space
#Q5 Let V={fโf:RโR} over R. Then which of the following is not a subspace of V over R
Anonymous Quiz
2%
W1={fโV:f is bounded}
31%
W2={fโV:f is continuous}
38%
W3={fโV:f is Monotonic}
29%
W4={fโV:f is of bounded variation}
#Q6 Which of the following is/are not a subspace of V={f:f:[a,b]โR} over R
Anonymous Quiz
16%
{fโV:f is periodic}
16%
{fโV:f is odd function}
26%
{fโV:f is even function}
42%
{fโV:f holds intermediate value property}