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

Code No: 7114/E/R
FACULTY OF SCIENCE
B.Sc. IV ~ Semester (CBSC) Examination. June 2018
Subject: Mathematics
Paper: IV Algebra
Time: 3 Hours Max. Marks: 80
SECTION ? A (5 x 4 = 20 Marks)
(Short Answer Type)
any Five of the following questions
up 230 and indicate their orders.
Note: Answer
1, . Write at! subgroups of the gro
2 For n>1. show that the aitem m
ating group An has order 7
3. If G is a QTOUP and H is a sub group of index 2 in G? then she ?@s a normal
subgroup of G. ?
,4? If G is an abelian group and H is a normal subgroup of G tl?e?sQ that ?ts also an
abelian group.
I
,5: De?ne idempotent element in a ring R. Find all idempotekements in the ring
.(210. +10 X10) /
\p?f [1 and I; are any two ideals in a ring R, then sh
f 4 w that h H I; is always an ideal of R.
1/7? if f(x) = 1+2x+3x2. g(x) = 2+3x+4x2+xJ then ?@e f(x)+g(x), f(x).g(x) in the ring
? 251*].
8. Let R be a commutative ring of charact ? then show that the mapping (3 : R ?> R
De?ned by ?(a) = a2 VaeR is a homomo . ism.
QB (4x15=60 Marks)
say Answer Type)
9. (a) (i) Let G be a 9% a V , K be two subgroups of G. Then show that
HK= {hklh t: , ts: } is a subgroup of G.
(5?) 1-64 G be a grgup and aEG is such that 0(a) = n then show that o(a?) = gchnJc)
(wh k 1 positive integer)
OR
M: (a, ,a2,a3 ..... am ) and [3 = (b, ,b2,b3 ..... b" )are any two disjoint permutations
- n show that 0:}? = [30:
/(ii) Let 04/3 6 Se and a = (124536),? = (143256) then evaluate 0:.[1,a,6",0:2 _
1 oyi/Let G be a group and ab 6 G and H is a subgroup of G then show that
(i) aH = bH aaebH
'(ii) ah is a sub group of Go ae H.
OR
/M.et G be a ?nite abelian group and P be a p?me that divides the order of G then show
that G has an element of order P.
1 (i) Show that every finite integral domain is a ?eld.
~ (ii) De?ne characteristics of a ring R with unity. Show that the characteristics of an
integral domain is either zero or a prime.
OR
Contd..2..