oe GX-10003

[Total Marks : 80

3

3

(e)

(0

2. (a)

(b)

a+iy -B+iSlp+i6 "-iv_l

4

4

6

6

Z3 : (z- 1)3, then show that z = +* |.ot $ *n.r. e = 20 +.Find the non-singular matrices P and Q such that PAQ is in Normal Forrn. Alsot-rind rank ofA.

I + 3 1 6le=l 2 4 2 2ll_r2 14 s 16 l

(c) State and Prove Euler's theorem for homogeneous functions in two variables

^) ^') ^)

and hence find the value of *2 #.'*, #. r' #*-# *rS ro'

u : e-* + r' + log (*3 + y3 - xzy- xy2)

/i.

3. (a)

(b)(c)

'*'?:-"", ,Qrnl Enc 2ol3 I cBc^sl-

'Do(-1-(REVISED COURSE)

(3 Hours)

\ ts. :, I r QuestionNo. 1 is compulsory.1) Solve any three from the remaining'

( .:t) . r. (a) Ifcr+iB:tanh Ir*tZJ, provethatu]- B:: l.

6lu 6lu(b) If u: x2y * e*Y2 show that *n =

4,ar.

6(u, r', u') .)

(c) If u:1-x,v:x(1 -y),w:xy(1 -z) showthat 7,r r,, = x-)"

(d) Provethatlog (1 -x+x2) :-x . + - +-

Express the relation in ct, 0, y, 6 for which A: IFind nth derivative of 2*cos2x sin x.

is unitary.

F,,':',,.'hrr r alues of 7. the s1'stem of equations have X non-trivial solution'/ Obtain 6

r.: -r;1:rion lbrrealr'alues offuu'here3x+y-)"x:0,4x-2y-32:0,2),x+ 4y-)"2:0.Fr:J the stetionary values of sin x sin y sin(x + y). 6

Iicrsrr - il )cos(u+ir): 1,rvhereX,y, u, v arereal.thenshou,thattanh2ycosh2v:sir-r2u. 8

ITURN OVER

V-A4-II-Ex- 13-F- 12

Con. 7380-GX-10003-13.

rrux+w:&, +. += r,Showthat +(*), . +(*)= o.

If (l + i tanq)(r + itanP) is real then one of the principal values is (seccr)""2P.

solve by crout's Method the system of equaitons 2x + 3y + z- - 1, 5x + y + z:9,3x+ 2y + 4z:11

If sinae cos3e : a cos e + bcofe * ccos 5e * dcos 7e then find a, b, c, d.

Use Taylor theorem and arrange the equaiton in powers of x.

7 +(x+ 2)+3(x+2)3 +(x+ 2)4-(x+2)s

(c) Ify: cos (m sin-lx)prove that (1-*2)Yn+2- Qn+ 1) xyn*r * (m2-n2;rn:0'

6. (a) Solve correctly upto three iterations the follou'ing equations by Gauss-Seidel method.

10x- 5y -22:3,4x- 10:' - 3z: -3, X * 6)'+ l0z: -3'

+. (a)

(b)

(c)

s. (a)

(b)

(b)

(c)

If u : sin(x2 + y2) and a2x2- blr'l : c:find {!. 6

8Fit a curve y : ax + bx2 tbr the data :

x I 2 J 4 5 6

v 2.51 5 .82 9.93 11.81 20.55 27.06

v-

-

(:,

S

6

6

26-t0-13-DT'P6_ PM_l

Con.5552 -I3

(Revised Course)

(2 Hours)

N.B. : (1) Question No.l is compulsary,(2) Attempt any three questions from euestion No. 2 to 6.(2) Use suitale data wherever required.(3) F'igupes to tLe right indicate full marks.t-

nE l="€rr) I 'q oec :-otJfsCch{"t;Aff

APrs€sL'GX-l0030

I Total Marks : 60

1. Solve any five from the following :-

(a) Define the term space raffice, unit cell and lattice qarameter.(b) Find the interplaner spacing between the family of planes (l l l) in a crystal of

lattice constant 3Ao.

(c) Represent the following in the cubic unit cell :-(tT2),(002), u2tl

(d) Define drift current, diffusion current and mobility of charge carriers.(e) Explain the use of p-Irl junction as a solar cell.(0 State with neat diagram direct and inverse Piezoelectric effect.(8) W-hat is magnetic circuit ? Explain Ohm's Law in case of magnetic circuit.

(a) Explain the Hall effect in metal ? Derive the formulae to determine the densityand mobilifv of the electrons.

(b) Define ligeancy and critical radius ratio in case of ionic solid. Write the conditionsfor siabilify of ionic crystal in 3-D ? Determine critical radius ratio for trigancy 6.

(a) Explain with neat diagram construction of Bragg's X-ray spectrometer ? Write theprocedure to determine crystal skucture" Calculate the maxirnum orcler of diffractionifX-ra1''s of wavelength 0'8 19 Ao is incident on a crystal of lattice spacing 0.2g2 nm.(b) Calculate the nurnber of,turns required to produce a magnetic flux clf 4 x 105 wb,if an iron rod of length 50 crn and cross sectional area 4 cmz carrying an electriccurrent 1A is in the fbrm of ring. (perweability of iron is 65 x l0-4 H/rnS,-

x5

2.

3.

4. (a)

(b)

What is mesomoqphic state of matter ? Explain with neat rliagrarn cholesteric phase.What is dielectric polarization and dieiectric susceptibility ? Find the relarionbetween them ?

5

5

I TUI{I\* GL'ER

25-10-13-DTP6-PM-2

Con. 5552-GX-10030-13.

(c) The resistivity of intrinsic InSb at room termperatrue is 2 x lOaO cm. If the 5

mobility of electron is 6 m2lV-sec and mobility of hole is 0.2 m2lv-sec. Calculate

its instrinsic carrier dentsitY.

5. (a) Identify the crystal structure if its density is 9'6 x 102 kglm3,lattice constant is 5

4'3 A" and atornic weight is23.5(b) Explain the formation of depletion region in P-N junction.

(c) Define reverberation time ? State Sabine's formula and explain the terms involved 5

init?

6. (a) What are soft and Hard magnetic material ? State their properties and applications. 5

(b) What is Fermi level in semiconductor ? Show that in intrinsic semiconductor Fermi 5

level always at the middle between the forbiddon energy gap ?

(c) An Ultrasonic sound wave is used to detect the position of defect in a steel bar of 5

thickness 50 cm. If the echo times are 40 and 90 p-sec. Locate the position of

defect.

28-10-20 13-DTP-P-7-MU- l6

Con.5769-13,

12 Fiours)

GX - 10010

I Total Marks : 60

N. B. : (1) Question No. 1 is compulsory'

tZ}Answeranythreequestionsfromtheremainingfllve.(3) AII questio&s carr]'equal marks'

(4)Atomicweight:-Mg:24,Ca:4A,Si:28,N:14'0:16'C:12

I. Solvs any livs:- 15

(a) What happens *.hen temporary hard water is boiied? Give equations to explain.

(b) Give the preparation and Llses of Silica refractory'

(c) Defir:e Gibbs Phase Rule. State the number of Phases' Components and

Degtees of freedorn for the foilowing equatiotr-

CaCOr,,, ;l Cao,,, * Cor,*,

(d) What is ihe function of plasticiser in the compouading of plastic? Give two

e:iamPles.

(e) Ti,go samples of water A and B wers anaiysed for their salt eontent:

(i) Sample A was found to contain 168 mg MgCO, per iitre.

(ii) Sample B was found to coatain 820 mg Ca(l'{Or), per litre and 2 mg

SiO, per iitre. Calculate the total hardness of each sample and state which

sarnple is more hard.

(0 Diseuss the conditions under which semisolid lubricants are used.

(g) Distinguish between thennoplastic and thermosetting resins.

2. {a) 50 ml of standard hard water containing I mg of pure CaCO, Fer ml consumed 6

Z0 tnlof EDTA. 50 nd of the water sample consumed 30 mt of same EDTAsoluti.on

using Erichrome Elack T indicator. After boiiing and filtering, 50 mtr of the water

sample required 10 ml of the sarae EDTA for titration. Calculate the total and

permanent hardness of water sample'

(b) Draw a neat phase diagrarn of the one component water system and explain with 5

referenoe to (i) curves (ii) Triple point' '

(c) &hat are carbon nano tubes? What are their types? Discuss their Electrical and 4

Mechanical ProPerties.

6

I TURN OYER

3. (a) Discuss the mechanism of thick-film lubrication.

28- 1G.201 3-DTP-P-7-MU- I 7

Con. 5769-GX - 10040-13.

(b) Define moulding and discuss the Injection moulding method of fabrication of plastic' 5

(c) Discuss the limitations of phase rule. 4

4. (a) Give the preparation, properties and uses of: (i) PMMA (ii) Buna-S. 6

(b) Give well balanced equations of the reactions that take place in the Lime soda 5

process.

(c) Find the saponification value of an oil sample weighing 1.5 g, refluxed with 25 4

ml of 0.5 N KOH, required 15 ml of 0.5 N HCI for the residual titration. The

blank titration reading was 25 ml of 0.5 N HCI'

5. (a) Discuss the setting and hardening of portland cement as well as the function of 6

gypsum with balanced equations'

(b) What is glass transition temperature? What are the factors that affect it and what 5

is the significance of it-

(c) An exSausted zeolite softener was regenerated by passing 150 litres of NaCl solution 4

having a sgength of 150 glL ofNaCl. If the hardness of the water is 600 ppm'

Calculate the total volume of water that is softened by the softener.

6. (a) Write short notes on any two:- 6

(i) Reverse osmosis

(ii) ElectrodialYsis s

(iii) Ultrafiltration

(b) Define conducting polymers. Explain Intrinsic and Doped conducting polymerwith 5

appropriate examPles-

(c) Define and discuss the signif,rcance of the following properties of lubricant (any 4

two):-

(i) Acid value of oil

(ii) Cloud and Pour Point

(i) Flash and Fire Point

F-E (eaO / tt"-'I l3 oe( *t3E ['1

€€ (cb6,, fi,t

GX-l0020I Total Marks ; 80

[04j

[04]

[04]

6 Cotr{ode 3-JP

Con. 5808-13. SEYTSEB COURSE)

i3 Hours)

N,B" (1) Question No. 1 is cCImpulsory.

tZ) Answsr any three questions out of remaining questions.(3) Use accetreration due.to gravity g = 9"81 m/sz.(.1) Use of electronic calculator is permitted"

Q.1. {a) A ring is pulled by t}uee f,orces as

sho.arn irl fig'we. Find the fbrce Fur{C ttr. ffiie 0 if resultant ofthese three f,*rces isi 100 N actingin veiticai direction.

Q.2.

I04j

F

(b) State and prove Lami's Theorem.

(c) Laws of friction

(d) A motorist is tavelling at 90 kmph, when he observes a traffic signal250 m atread of him turns red. The traffic signal is timed to stay redfar 12 sec. If the motorist wishes"to pass the signal without stoppingjust as it tums green. Determine (i) The required uniform decelerationof the motor. (ii) The speed of motor as it passes the signal.

(e) A 50 kg block kept on a 150 inclined plane is pushed down the planewith an initial velocity of 2A m/s. If lL,*= 0.4, detennine the distancetraveled by the block and the time it will take.as it comes to rest.

(a) A member ABC is loaded by distibuted load and pure moment as

shown in the Figure. Find the (i) magnitude and (ii) position alongAC ofthe resultant.

[04]

l06l

25 kl.'l-rn

ITURN O!.ER

N

7 Con-code 3-JP

Con.5808-GX-10020-13 2

(b) A cylinder weighing 1000 N and 1.5 m diameter is supported by a

beam AB of iength 6 m and weight 400 N as shown i, Iry.Neglecting friction at the surfaces of contacts, determine (i) Wallreaction at D. (ii) Tension in"the cable BC and (iii) Hinged reaction at

support A.

(c) A particle of mass 1 kg is acted upon by a force F which varies as

shown in fieure. If initial velocity of the particle is 10 m/s determine

(i) what is tfri maximum velocity attained by the particle. (ii) Time

when particle will be at the point of reversal.

[08j

[06]

f (see)

8 Con-code 3-JP

Con. 5808-GX-10020-13. 3

Q.3. (a) Locate the centroid of the shadded area.

(b) A prole is held in place bythree eables. If the force ofeach eable acting on thepoie is as shown in figuredeterrsrne the resultant.

At-18,-16,0)m"

(ei Two blocks IEa:10 kg andrilB=5 kg are connected withcord and puliey system as

shown in figure. Deterrninethe veiocity of each blockrvhen system is started fromrest and blook B gets

displacement by 2 m. Take

$x:A.Z befween block A andHorizontal surface.

{08I

[06]

'aa

D{0,0,24)m

E{15,-20,S}m

I TURN OYER

9 Con-code 3-JP

Con. 580rcX-10020-13.

Q.4' (a) Find the support reactions at A.and B for the beam shown i" flgg. i,J6 j

(b) A ball is thrown from horizontal level, such that it clears a wall 6 mhigh, situated at a horizontal distance of 35 m. If the angle ofprojection is 600 with respect'to the horizontal, what should be theminimum velocity of projection?

(c) 'C' is a unifsrm cylinder to which a rod 'AB' is pinned at ,A, and theother end of the rod 'B' is moving along a vertical wall as shown in&gure. If the end 'B' of the rod is moving upward arong the wall at aspeed of 3.3 m/s find the angular velocity of the cylinder assumingthat it is rolling without shpping.

[061

Irlb.l

8G kN/rn

n0f*,

l0 Con-code 3-JP

Con" 5808*GX-10020-13. 5

Q.5. (a) Find the forces in members BD, BE and CE by method of section

only.for the truss shown in the flgqfe. Also find The forces in other

rnembers by method ofjoints.

(b) In Asian games, for 100 m event an athlete accelerates uniformly [06]

from the start to his maximum veiocity in a distance of 4 rn and runs

the remaining distance with that velocity. If the athlete finishes the

race in 10.4 sec, determine (i) his initiat acceleration, (ii) his maximum velocity.

(c) In Erofe collar C slides on a horizontal rod. In the position shown rod to6l

AB is horizontal and has angular velocity of 0.6 rad/sec clockwise.Determine angular velocity of BC and velocity of collar C.

Q.6. (a) A force of 10 klrl acts at a point P(2,3,5) m and has its line of action [041

passing through Q(10,-3,4) m. Calculate moment of this force about apoint S(1,-10,3) m.

[08]

I

I

ITURN O\IER

l1 Con-code 3-JP

Con. 5808-GX-10020-13, 6

(b) Find the necessan' force to raise a heavy stone block of 2000 N" Take [08]

coeffieient oi friction as 0.25 for al1 surfaces. Neglect the weight of__-_ s _\\ eugc. r a(e angle of wedge as 15"

(c)

(d)

[04]

a velocity of 18 km/hr and ship B travels in the East with a velocity of9 km/hr. Find the relative velocity of B w.r.t. ship A.A body of mass 25 kg resting on a horizontal table is connected by [041

string passing over a smooth pulley at the edge of the table to anotherbody of mass 3.75 kg and hanging vertically as shown. Initiallir, thefriction between the mass A and the table is just sufficient to preventthe motion. If an additional 1.25 kg is added to the 3.75 kg mass, findthe acceleration of the masses.

A

A ship A travels in the north making an angle of 450 to the West with

26-|0-13-DTP6-AK-12

. con. se18-13, F,. r { t grern I

Bc#.,s J df ec zc, ( 3

GX-10011(Revised Cburse)

( 3 Hours )

N.B. : (1) Question No. 1 are compulsory.(2) Solve an,v three questions out of the remaining five questions.(3) Assume data if required, clearly stating the assumptions.

1. (a) Using source transformation find Lo -c'lL

[Total Marks : 80

(b)(c)

(d)(e)

(0(e)

2. (a)

State and Erplain Norton's theorem.Derive an expression for the average value of a sinusoidally varying current interms of Peak Value.Derive the condition for resonance in a series circuit.Give relation between line current and phase current, line voltage and phase voltagein balanced star and delta connected load.\\'hat are assumptions for an ideal transformer ?

Drau'and explain circuit diagram for half wave rectifier.

Find the currents Ip12,I, in the given circuit by node voltage method.

3r)- trt-

\20\ -l\o\

For the circuit shown determine the(i) Supply frequency (f).(ii) Coil resistance (r)(iii) Supply voltage (v)

T.=O-3\sh R

Aov

33

3

2

4

2

5q

I

8(b)

C= ZO{\F

\, \H=

zsv 55V

I TURN OVER

3

z.CL

- g'stl

26-t0-13-DTP6-AK-t3

Con. 5918-GX-10011-13 )

J.

(c) Draw and explain Phasor diagram of l-Phase practical transformer when(i) on no load(ii) Leading power factor load.

(a) Find the values of circuit elements and reactive voltampere drawn for a balanced3 phase load connected in delta and draws a power of l2kW at 440y.The powerfactor is 0.7 leading.

(b) The following results were obtained on a 40 KVA, 2400/120V transformer.O. C. test : 120V, 9.654 and396 W (on L.V. side)S. C. test :92Y,20.8A and 810 W (on H.V. side)Calculate the parameters of approximate equivalent circuit referred to H. V. side.(c) Explain series inductor filter.

(d) Explain circuit diagram and working of cE configuration of BJT.

(a) Determine current through 20o resistor in the following circuit.

\s.ci-- ,

36-<2_

2oo V(b) Two currents are represented by I, =l5Sin1**fl and I, =25 Sinl**f,1. These

currents are fed into common conductor. Find the total current. If the conductorhas resistance 50f), what will be energy loss in 10 hours.(c) In a three phase power measurement by two waltmeter method, both the wattmetersread the same value. What is the power factor of the load ? Justify your answer.(d) Explain the circuit diagram and waveforms of Bridge rectifier.

(a) For the given circuit find the value of 'Rr' so the maximum power dessipated in it.Also find Pmax.

\sV

)1

4.

5.

2.1-

\ZV

E\

2.6-10 -1 _? -DTP6-AK- 1 4

Con.591S-GX-10011-13

Withproperphase diagrams, explain behaviour of apure capacitor in anAC circuit.Derive condition for maximum efficiency of a transformer. Also derive equationfor load at maximqm efficiency.

6. (a) Determine current in 1A resistor using superposition theorem.

ltu 2-fL

(b) An inductive coil of resistance 1OCt and inductance 0.lH is connected in parallelwith 150 pF capacitor to a variable frequency, 200V supply. Find the resonancefrequency at which the total current taken from supply is in Phase with supplyvoltage. Also find value of this current. Draw the phasor diagram.

(c) Two wattmeters are connected to measure power in a three phase circuit. Thereading of one of the wattmeter is 7 kW when load power factor is unity. If the' power factor of the load is changed to 0.707 lagging without changing the totalinputpower, calculate the readings ofthe two wattmeters.

(b)(c)

4

8

7

f gl13e"^J cLax5-DlData-4

Con. 9026-13.

Bc,s I D"t z'al3 {-E fcaaQ f/-i

tr{s I

(REVISED COURSE)

(2 Hours)

GX-100s3

I Total Marks : 50

N.B. : (l) Questlons No. I is compulsory.(2) Answer any three from Question ]'{os. 2 to 6.

(3) Figures to right indicate full marks.

(4) Draw neat diagrarns wherever necessary.

l. Attempt any five from the following :- 15

i

(a) With thp help of suitabie example explain the concept of food-web.

(b) \Yhy there is need for sustainable development ?

(c) Explain briefly causes and effects of Ozone layer depletion.

(d) Explain briefly the role played by Ministry of Environment and Forest in the

conservation of environment.

(e) \l,h,v mpre emphasis is given on the development of renewable energy resources ?

(fl Exptain the concept of 'Carbon Credit'.

(g) What are the source$ and effects of noise pollution?

(a) In wha! way appropriate technology cao lead to better sustainable development.

(b) Draw suitable diagram and explain rvorking of Bag House Filter.

(c) What is hydel energy? Explain briefly the process of hydropower generation.

(a) How Solid waste managernent can be carried out by landfilling ?

(b) Explain briefly the important features of environmental clearance and authorizatian

mechanism

(c) What role is played by the technolory for better human health and environment ?

(a) Explain what are the reasons and impact of depleting nature of natural forest

resources.

Wkiat are the irrportant functions and powers of Central Poilution Control Board ?

*rarv rough sketch and explain how electricity can be generated f-rom wind energl".

I TURN OVER

2.

J.

A+.

5

5

5

(b)

(c)

La:t5-D:5ara-5

Con. e026-GX-10053-13. 2

5. (a) In what way environmental education and awareness can help in sustainable 5

develoPment ?

(b) Draw rough sketch and explain how flat-plate coliector can be usef*l in tapping 5

solar energy.

(c) How E- pollution is caused? what are its adverse eff,ects ?. 5

6. (a) How disaster management techniques can be imptemented in the event of Tsunami ? 5

(b) Explain the global environrnental crisis caused on account of growing population' 5

(c) What are the reasons and effects of global Warming ?

F€-l l-13-DTP7-RM-l

Con. 8055-13.

1 n, e rnlDtc zo11] LbWF.F (lL) Ny.D

(Revised course)GX-10120

[Total Marks : 80

N.B.: (1) Question No. I is compulsory.

(2) Answer any three questions from question nos' 2 to 6'

(3) Figures to the right indicate full marks.

(4) Programming Calculators are not allowed.

1. (a)

(b)

(c)

(d)

(e)

Evaluate f *'z-r d*

Solve (D4+4)y = 0

ProvethatEV= A=VE

Solve (x + zv') *=v.

3

3

3

3

4

6.

6-

8,

Evaluate II ,' O.Ut over the region between the circles r : 2 sin 0 , r : 4 sin 0 'R

4

2. (a)

(b)

6

6

8'

3.

(b)

(c)

if ,(fl Evaluate J J .- ,-O= dl'dx

0 / (l-y){y-x-

Solve :- (x3ya + x2y3 + xy2 + y) d1+ (xay3-x3y2-x2y+x)dy : 0

Change the order ofintegral and hence evaluate I' i'***fr x2 dx rr dx lt

(c) Prove that Jo 1;7 J" 1;7=75(a) Evaluate f; l, X- xdxdydz.

(b) Find the area of one loop of the lemniscate r2:a2 .cos2 0

(c) Solve (D3+2p2+D)y : x2e3x*sin2x*2x.

(a) Show that the length ofarc ofthe parabolay2 = 4ax cut offby the line 3y = 8x is

't 5a (log2+6 )

.Using the method of variation of parameters solve $ *+y : tun Z*'

dvCompute y(0.2) given fr+y+xy'=0, y(0)=1 by taking h = 0.1 using Runge-Kutta

method of fourth order correct to 4 decimals'

ITURNOVER

6

8

r3-t 1-13-DTP7-RM-2

Con, 8055-GX-10120-13,

5. (a) Solve fl+ x(x + y;= x' (x + y)3 - 1.

(b) solve $|-zy=:"*,r(0)=0 usingTaylorseriesmethod.Findapproximatevalue

ofy for x: 1 and 1.1.

.d Av(c) Evaluate Jo 1ft using

(i) Trapezoidal rule

/r\'d(ii) Simpson's [i.] rrl.una

/ e\6(iii) Simpson's li I rule.\ "./

(a) The current in a circuit containing an inductance L, registance R and voltageE sin wt is given by

.JiL fr+Ri= Esinwt

Ifi :0 at t: 0, find i.

(b) Evaluate JJ "" " dxdy overthetriangleboundedbyx+y:1, x= 1,y= 1.

(c) (i) Find the volume of solid bounded by the surfaces y2: 4ax, x2: 4ay and theplanes Z:0,2:3.

(ii) Change to polar co-ordinates and evaluate

| ^ lE-' dxdy

{ J.f-., .t^, _", -y,

6

6.

6

4

2