Bharathiar University 2009-2nd Year B.Sc Mathematics Maths s- - Question Paper

(?Z

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dx

(b) Solve : z = px + qy + l + p² +q²

() #rr* : x²- + y* = (x + y)z . dx dy

(%) $fr&A : z px \ qy + yjl ( p^z +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

L(9m¹2/).

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CiugMib (coh /iut)arrcRn.

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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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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,2P_t 3P_f2P, 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

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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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jQgU&A

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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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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 d_x and d₂ respectively. Kind the amplitudes, period and the velocity when its distance from the moan position is

(<W₂)

2

(b) Discuss the oblique impact of two smooth spheres. Kind its loss of kinetic energy.

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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

Uia

2.    What is the difference between trade discount and cosh discount?

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3.    The position of a businessman who keeps his books on single entry was as under on 31.12.90 and 31.12.91.

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.

HI IhM

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31.12.91    c_ncmjk}. fDflDQ)

(ipGr)(Dii9Qj &Q\p Qn@*AuuiLaTar.

2.1.91 (gnpr 0. 7.500 cfitununa) tr(9$&j.

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4. On l^Ht 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.

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. 6,000/*afTOJ 3LprryEt Cta a.shi u>frpjp*JL.>i_ crcnuftinr Gldco Giiaoi/)pniT.    *(Si7Ct}

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ILMrai

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 l^rt 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 6^th April, 1974. The bill was discounted on the next day by Kumaran at 6% per annum. On 5^th 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.

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Give the specimen journal entries appearing in Joint ventures in tho books of both the parties

A and B.

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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.

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Qp,na>& 0. 50 Qffa)COilb ujbgj

6&UUL.dT0T&|.

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(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

1

   D 1599