Bharathiar University 2009-2nd Year B.Sc Mathematics Maths s- - Question Paper
2 nd year ques. papers
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(b)
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(*)
//1
(s2 -t- 4s -f 5f
C* V yy
Solve the cquntion -72 + 23.y = sint
dy
given Unit y = = 0 when f = 0. at
Kind 1
s(s2 i 9)
dy
t - 0 srgih Gurrg y = = 0 craftcu f/2v dy
Y + 2 -3,y 8in* fcTWrp u>afuinl.au_& dt dt
, 1 1
L -r-ipa arrears.
s(s2 + 9)
D 1599 Q.P. Code : [07 DMA 041
(For the candidates admitted from 2007 onwards)
li.Sc. DEGREE EXAMINATION, DECEMBER 2009.
Sccond Year
Iart III Mathematics
DIFFERENTIAL EQUATIONS AN!) IAILACE TRANSFORMS
Time : Three hours Maximum ; 100 marks
Answer any FIVE questions.
(5 x 20 = 100)
1. (u) Solve : (.va * x)p* <tfa +je-2xy-y)
p + y2-xy 0.
(b) Solve: p2 \ pxy = y2 logy.
(**l) (x2 \ x)p2 \ (x2+x-2xy-y)
p + ~xy = 0.
(-%) ff.fr, p* ( pxy = yalugy.
2. (a) Solve : y + px -p2xi.
(b) Solve: (D2 + 2D (5)y = xe\
(5>f) y i p.X = p2XA .
(J&) (D2 +2D i-5)y = xe* .
3. (a) Solve: (I)2 -4D + 3).y = cx cos2x .
(b) Solve : t y- secx. dx4
(*) jSrittA (Dz - 41) + 3)y =e* cos2x
. .... dly (*-%) -TT+y ecx ax
4. (a) Korm tho partial differential equation by
eliminating f and # from
% **x /"(-j + U).
(b) Solve -. = a*z, given that x 0, ax
fe , dz n
= (i sin y and = 0. flv dy
() Z = x f
ujQj|iia>rD cni_&0Lb u0$ajo>**
Qa(ipa auJOTUfnlfiDi, oha.
USb) x = 0. = a sin y uimfraib- = 0 tt* cbe dy
(?Z
Qsnwr j-a2z cratrg *u>njfTL.6i>u f,a
dx
(b) Solve : z = px + qy + l + p2 +q2
() #rr* : x2- + y* = (x + y)z . dx dy
(%) $fr&A : z px \ qy + yjl ( pz +q2
(tt) Prove that UHO) = .v2/,(/*</))-a/(0)-s/*r(0) and then find /.(cob /j at).
(b) IVovo that /*(ln)~and thon find
b
(*0 UrU)) = suLlfU))-sf(0)-snQ)
CiugMib (coh /iut)arrcRn.
(v?t) (*") = crdjifiji Ciogwd)
o
Liain3 2t)f&s> jrcwi&.
(a) Kind the Laplaco transform of (t + 2)2 e*. h + 2
(b) Find /, 1
(s2 +4s ( 5 J
D 1600 Q.P. Code : [07 DMA 05]
(For the candidates admitted from 2007 onwards) B.Sc. DECREE EXAMINATION, DECEMBER 2009. Second Year Part III Mu thematic*
MECHANICS
Time : 'I*hrcc hours Maximum : 100 mark#
Answer any KIVK questions.
AH qucHtions carry equal marks/'*"'
1. (a) Stale and prove Lamia theorem.
(b) State and prove Varigons theorem.
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() (fejrflawbnoneru
2. (a) If two couples, whose momenta are equal and
opposite, act in the same plane upon a rigid body, prove that they balance are another.
(b) Obtain the equation to the line of action of the resultant to the system of coplanar forces acting on a rigid body.
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3. (a) AHCDEF is regular hexagon, forces P,2Pt 3Pf2P, 5P, 6P act along
Ali. BC\ DC. ED, EF, AF respectively. Show that the Bix forces are equivalent to a couple and find the moment of the couple.
(b) A uniform ladder is in equilibrium with are end resting on the ground and the other againHt a vertical wall; if the ground and wall be both rough, the coefficients of friction being ft and fi' respectively and if the ladder be on the point of slipping at both ends, show that 0, the inclination of the ladder to the horizon is given by
(c) Find the C.G. of a uniform solid hemisphere.
D 1600
2
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2//
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(a) State and prove the principle of virtual work for a system of coplanar forces acting on a body.
(b) The speed of a train increases at a constant rate a from 0 to v and then remains constant for an interval and finally decreases to 0 at a constant rate p. If / be the total distance described, prove that the total Lime
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OiDn&Ggih + ii.I- + JLj ctor
5. (a) Stale and prove the principle of conservation of energy.
(b) Prove that the path of a projectile is a parabola.
(c) Find the law of force towards the pole under which the curve r"a',co snO can be described.
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6. (a) Obtain the differential equation of the
contral orbit.
(b) A particle is projected at an angle a to the horizontal, so an to clear two walls of equal height a at a distance 2a from each other. Show that the range is 2acota/2.
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crfld> cfitf* 2a cot a! 2 *ii
7. (a) A parLicle moves in an ellipse under a force
which is always directed towards its focus. Kind the law of force, the velocity at any poinL of the path and its periodic time.
(b) Prove that the resultant motion of two simple harmonic motion of same period along two perpendicular direction is along on ellipse.
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8. (a) A particle executing a S.H.M. has velocities Vj and o2 when its distance from mean positions are dx and d2 respectively. Kind the amplitudes, period and the velocity when its distance from the moan position is
2
(b) Discuss the oblique impact of two smooth spheres. Kind its loss of kinetic energy.
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t
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(For the candidates admitted from 2007 onwards)
B.Sc. DEGREE EXAMINATION, DECEMBER 2009. Second Year Part III Mathematics Allied ACCOUNTANCY
Time : Three hours Maximum : 100 marks
Separato answer shoots for probloms Answer any FIVE questions.
(5 x 20 = 100)
1. Journalise the following transactions and post to
proper accounts :
2006 to.
Jan. 1 Balan (started buuinona with a capital of 10,000
Jan. 4 Bought goods from Velan 6,750
Jan. 7 Cash purchases 3,000
Jan. 10 Cash Sales 4,000
Jan. 13 Bought goods from Velan 2,000
Jan. 16 Sold goods to Gurunath 5,000
| ||||||||||||||||||||||||
{b}b&. GuCgil waAaxnuii) uj<tit |
Ofluja. 2006 | ||
JgOWUfH. 1 |
uiKuat Qprtftw |
10.000 |
gpMCurf). 4 |
CoKuafk. icufnw4)<u0 |
6.750 |
ggascuri) 7 |
QqrAa Oaaat(yMV |
3.000 |
5taKuA) 10 |
QgriAa sduoMB |
4.000 |
tgaiaiiti 13 |
Caj<aRt~ij9(3jigj <9*9 cuwii&up |
2.000 |
garcuifl. 16 |
"V** &* |
5.000 |
jgi<urfl 18 |
CJua>fp* QpirA*u> Q*&p>4l\u& |
2.850 |
jgataifl. 19 |
a*"**** #*<5 cfijpgt |
500 |
24 |
CajflMB aarakp GUgsugj |
2.400 |
jgwuifl. 26 |
Qg*4*u> Gupffgi |
1.650 |
gfoiajifi 27 |
ii>uonb Qg&}uj0 |
1.250 |
gpucufl. 30 |
Q$o**ib Qu$0 |
200 |
2. What is the difference between trade discount and cosh discount?
cfilujffunp en<g5uu|.&{$ib. Qrjn&& 0aT<gutq.($ib @ni_<3iu fiQTor Geuguufi ctotbp?
3. The position of a businessman who keeps his books on single entry was as under on 31.12.90 and 31.12.91.
1990 |
1991 | |
R a. |
Rs. | |
Cmth in hnnd |
400 |
480 |
Ctmh nl Bank |
0,000 |
2,600 |
Stock |
6,500 |
6,000 |
Debtor** |
4,000 |
5,200 |
Furniture |
300 |
350 |
Sundry croditors |
4,100 |
3,100 |
He withdraws Rs. 7,500 from business on 2.1.91 out of which he spent Rs. 5,200 for purchase of a motor truck for the business.
Adjustments :
(a) Depreciation on closing balance of furniture and truck at 10%
(b) Write off Rs. 220 as bad debts
(c) 5% Provision for bad and doubtful debts is needed. Find out the profit or loss for the year.
0 GS)iurrumf)u9ar jSansu 31.12.90 iDtbgyu)
31.12.91 c_ncmjk}. fDflDQ)
(ipGr)(Dii9Qj &Q\p Qn@*AuuiLaTar.
1990 |
1991 | |
- | ||
a>Au90uu| QprtAaib |
400 |
480 |
Cuiiji3a90uH Qprwaii) |
6.000 |
2.500 |
0ul| |
6.500 |
5.000 |
auairpfyim |
4.000 |
5.200 |
300 |
350 | |
4.100 |
3.100 |
2.1.91 (gnpr 0. 7.500 cfitununa) tr(9$&j.
(npa)u> 0. 5.200 &0 efi)ujfrungip*a4 Cionuujm iq.pa euafuciJibArra Qffa>6n Qoujpi
(9l) Gjsiuiorraiib 10% OHSffi @<9*ji9b
ia>n>&Q>oi iDfbjitb C#LDfTUL.niT (3i>) - 20 cucfrrsauCTJ CurrsQ<tg!.
(S) 6U7/T&AUOI LDjPglli) >UJML.ai $g*A<$6.
5Tiq.T @jrrUL) iO)a>$| pL_l-D0 SCflLf$5.
4. On lHt January, 1974, Rajesh draws a bill for Rs. 6,000 on Suresh payable after 3 months which duly accepts. Rajesh discounts the bill for Rs. 5,910. On the same date Suresh draws a bill for Rs. 6,000 for 3 months on Rflgesh. Suresh gets the bill discounted with his bankers at 6%. Per annum. On the due dato, Rajesh meets his acceptance, but Suresh fails to honour his acceptance. The bank has paid Rs. 20 as noting charges. Give journal entries in the books of Rajesh and Suresh.
ggarcuif) i, 197 *1 tb prrCggero CTOiuaiir
. 6,000/*afTOJ 3LprryEt Cta a.shi u>frpjp*JL.>i_ crcnuftinr Gldco Giiaoi/)pniT. *(Si7Ct}
<yp0lQffTTtfijDrrrr. i/rrtfgjcru ercwuojrr
U>fTfl)g)|*L.>L- 0. S91Oa(0) 6UL.L.U3 QtftuiJjDrm.
6TnuQjrr Cu9d> 0. 6000*frer
3-u)ir$ ilqtctt )0 LorrpgBtf Lg?)l_ 0IT<*gJCiu CtOft)
ajGnijdPjDirit. *Girr% jbp, Luirjptf JiLtini_ 6% euilk}.a( cufcufluSUu uili_ih Q*iu)fDmT. (p$)ii9q) ijrrCggcfu j5G5Tgunt_iij irjrrjDgijatftLctDL. iaipniT. enrra) ftCSpo} ig)jiL_tLi lorrLlcni. uasefflcucwD. ajru<fi 0. 20/- <&uyn$, QfTn*ujiT
(p<5>ojLjrr6in @(#uGutl(uu$6).|5;es>OT ijrrGgg6ro u>/i>gjib *Ggi% ffiR!T<S0 q*ftg>)d) uIgL| Quja.
5. Kumaran of Tirupur sends 40 cases of Hosiery goods worth Rs. 20,000 to Go kale of Bombay to be sold on consignment basis on lrt April 1974. Kumaran pays Rs. 500 towards Freight charges. The goods arc received by Gokale and he accepts a hill drawn on him by Kumaran at 3 months, for Rs. 10,000 on 6th April, 1974. The bill was discounted on the next day by Kumaran at 6% per annum. On 5th July 1974, Gokale sends an account sales to Kumaran showing that sales of the entire stock have been effected totalling Rs. 24,800. His expenses are : Godown rent Rs. 500 and Insurance Rs. 250. Gokale is entitled to a commission of 6% on sales proceeds. Gokale sent a bank draft for the balance duo to Kumaran and settled his account.
Prepare the account sales to be submitted by Gokale to Kumaran, Also pass Journal entries and show ledger accounts in the books of Kumaran and
Gokale.
0U>pai crchu&jn 40 QuLacdota Qarrovrt- 0. 20,000 LDuLjarar i9 ora: curran l_ ruija> 1, 1974ii>
Qpcn{0u9o) Qpibflnu&uji Gs/rCa><$
g$fi)*na QiApai 500 GauLidDjDnrr. <5Tj&(2r4a'/crr (JawraCo) crasuajfr QufhgjM*
GfT5T q-uyw 5. 1974U5 3J,6WT . 10,000ssfTT 3-iorr Q(5 e_7n iDrrp>jpitLc5>L_ gHunjDmr, 0iD7Gn **$>?> lanfogitf&Laou 6% <3ts3r cuLujj 6urij3u9fiu eutluib QtfujrfPjDfw. gpno 5. 1974) GfT*G<y $OTfgH)L.UJ c6)|t)Ufl)9Tffa9T9> U>P@I*(5 vWgxuMprrrf. ceiuu.
0. 24,0OO*(g, Gfilfba.uu@dQiiDgj. ,<&j(A<5
9(buui_ Q*q>qjaot i_rug) cunuaMt 0. 500/uoDgjrt-b ajtulSi!* Oojgli 0. 250. C&rraGa)A($ 6% cfljbut5>63Tu9y 6upruAuu4){Dgf. d$(y>ncn Qjbnayir.&Q (JaitaCJg) curui) sucoGcurrcncofiOUJ 0idgga *Wg)|uiS) abt*)<a CpiT OoujDcinjparr.
&K{T(a> (jiflrrg)!* efi)(bucncnAasTa>A
pujnrt Q*iuuj&jti>. Gld?jld @iopeji u>pjpii> Caita&o AOBTaof)<l) Ca>cuiunc*i 0j$lu(2ijAa)cnuju>. GuGijl (Acnr0Aa>0nijm) (u$)cijA>nujii>) $<$
Give the specimen journal entries appearing in Joint ventures in tho books of both the parties
A and B.
A, B @0ai0Lh @6?>wrefila>657uS]d> g)a>wrjbrr Qartewi *Wfl)( e-wi_n6n u>a$ifl (jtffluCuil u$MA>t @aj0$) sr@>flgyii> $(&&.
7. From the following particulars ascertain the bank balance as would appear in the pass book as on
31* December, 1974 :
(a) The bank overdrat (credit balance) as per cash book on 31* December, 1974 was Rs. 6,000.
(b) Interest on overdraft, six months ending 31"1 December, 1974 amounting to Rs. 200 is debited in the pass book.
(c) Bank charges for the above period also debited in the pass books which amounted to
Rs. 50.
(d) Cheques issued but not presented for payment beforo 31* December, 1974 amounted to Rs. 1,500.
(e) Cheques paid into the bank, but not cleared and credited before 31* December, 1974 were
Rs. 2,600.
(f) Interest on Govt. Securities collected by the bank and credited in the pass book amounted
to Rs. 1,800.
y>*ai5iL_ eStajijryaawrr Q&rrtifey &jf&iu90ua>u linear utq. e-ensn g)0ua>u 31 trtbuiir. 1974.
(<dl) Qfjn&s, 7L.tq.c9t ub|. eur/ foocbAJwyuufpgj (ajij&j @ul|) 31 iq.tfibuiir. 1974 (j. 6.000.
' Cc$b) <2uxb eucnpuujDga \5pnen euLiq.. giiin(ipb).e)ot jSlowuSleu 31 tiburr, 1974 Qrrena 0. 200.
Q9wQcdC\i\.G} ujpfpi neuouuil0OT0Ti.
(@) euruQ Cinrpaniluj rTCorbjaHCT5@ifluj
Qp,na>& 0. 50 Qffa)COilb ujbgj
6&UUL.dT0T&|.
(ff) rr(rr6S)cu erflgjib anna) rgijib curiii)u9b QffgHUi_fild)w. (jpTT0rTtt 31 uj.*rii>uiTt 1974 Q$rro)s 0. 1.500.
(b_) *nGfi>a> 6urw$uSlft) G#gy$)iL|ib, ama gggj&jGnijuStcu 31, btfihurr. 1974 QpemmfinA &nr*di)cbewjajira'sfiJcbflwo Qp>n&)9,0. 2,500.
(finr) Qjnjjl CiajrrA upfitjpflm t5$rri
aiL.iq.a>uj (Govt. Securities) Offa>C?a>ild) &i(ga> Qaujgi <aji/j meujhfhtJj) 0. 1.600
8. Prom Iho following particulars, preparo Income and expenditure account.
Ka. Rs.
Poo collected, including Meeting expenses 18,000
Rs. 80,000 on account of Travelling expenses 6,000
previous year 3,80,000
Pee for the year 10,000 Purchases of books and outstanding
Salary paid, including periodicals (including
Rs. 3,000 on account of 28,000 Re. 19,000 for purchase 29,000
the previous year at hooks)
Salary outstanding at Ront 10,000
the ond of the year Entertainment expenses 20,000 Q*fT6BT Tournament expanses Q&rr(&AuuL.@aTOT Gfi&jgru&tiMrrs J06unuj-Qu66)j* acctacds tunn Q*uj&. hUL-tb QfOMJMfa 3.90.000 IMDOVt (0. 80.000 (pjMnptLi fH_uun*.<b j9gaw>aiA 18.000 6. COO #ibi>nib Qga ( 3.000 Qppmpuj 29.000 10.000 15.000 4.000 20.000 fiUp# (PgUiwu* iiMJ<nd) QuifQflp CunA$ 0<MM*h <Aa>TitintLQA *L.i.rtb |
Rs. Rs. 1.000 Hostage 15.000 3.000 Printing and stationary 4,000 12,000 Donations received 10.000 y4w* u>(bptb AMf I0ff { 19.000-ai4t&j 28000 oiiuom 1.000 0u* Q*ttxg<n 3.000 - <>($0Qu0m 12.000 Qug |
D 1599
Attachment: |
Earning: Approval pending. |