Download OU B.Sc 2018 May-June 2nd Year 2nd Semester 7114E Mathematics Question Paper

Download OU (Osmania University)B.Sc (Bachelor of Science Maths, Electronics, Statistics, Computer Science, Biochemistry, Chemistry & Biotechnology) 2018 May-June 2nd Year 2nd Semester 7114E Mathematics Previous Question Paper

FIECULT-Y OF SFIENCE
3351; IV? Semester [CESC] Exan'ilnatin?. 1.111111111111112...? ._
Subject: Mathematics _
Paper: W Algebra
_"'|3in1111:..3 Hours Hal- ? I
SECHDN - A1115 )1. 4 = 2a Marks}
[Short Answer Type}
Nate: Answer any Five of the fallowing qua-
/ L111t G be any grpup and {aim}2 - 512112 far all a 1:1 e G then 5111 '
'33
Igroup.1\ 7",
?if'a,?esjandtx={12345).?= ?114532)thenevaluate1zx1i 111,13"1 111311.
is an abelian
3. If H and K are subgroups of a group G with |EIiE2?1J1K | = E?then SHOW thatH ['iK is
.11 7:
.""' _ _
'5 ?l_l:_|.ll'
an abelian group. 1.!
4 Deters'nine ail group homomorphism; 1113111 2?1?; to 2:11;.
XE} .
fl} ?ne zero diviE-ar in a ring R. F1111;- all zero divisors in the 11ng{Z12 +111. -12}
(6'. If 11 and [1 are 15111111111111: 1119;111:111 a1ing R. then shnwthai l1+ 13:11:11 + 1111r KE {1. 5! E11}
is 3111113115 an ideal of R
'H_
/8 13111 that ?x} - + 311+- ?1 has four zeros in Z 11.
?: 1R 5 be 11121111116 rings and 11:11 ?1 S is a homo morphism. If R' 15 communicative
th
en shm? th?tg 111(R)'1s- commutative
SECTION-B- {4:115:51} 111111115)
{Essay Answer Type] 1'
9. (i) Let G be a group and H' 15 non empty subset of G. Then 5111:1111 -thatH' 1; 9.1111111;
afG if and ianly ifab E H furall a. b E H.
{ii}. In the symmetric group 33 ?nd the elements which satiiafy- 1113? ? a: wha'
identity iia'nnutatian 111 $3

I
v
ii?ajtr' ?itary finite initiagral damain Is a ?aid. : _ __ . .5
Idempotant element in a ring R then show that d1?m " .' _.1.
- {I} ?e?na- M'attimai idea!" In a ring R
.?ij- L?t R be a cumulative ring with unity and A be 3% R then show
That quotient E is a fieid if and only if A' Is a maxim al I 331.
f
1-2. {a} Let D be an integral domain. Then shpMaL?-Iere exists a ?etd F that m?tal?s E
subring isomorphic to D. 3R??
1"}:th
)Enyet F be a ?eld and fix}. 9|: :f'b?x] with g(xh? a. That. show that tha?ra exists unique
polynomials g(x) and rfx):_i?r?E?J-su?h that f(x) = q(x)g{x} + rix) with either t(x} ==U m" dag
.. .-I F.
ruling g(xl- im?
ig??
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