Total No. a/ Pages 4

SECOND SEMESTER

END SEMESTER EXAMINATION

Roll No. .." ..

B.E. (IT)

M91Y-2009

IT-lli PRINCIPLES OF ELECTRICALENGINEERING

Time: 3 Hours

1[aJ Find mesh currents in the following circuit.';,-fl-

Max. Marks: 70

5

~ 12V

[b] Find Thevenin' s .equivalent resistance seen from terminals AB.

bJ"- '-t -"- '

IO'_~ '1ZE::5A 2---<)..,

2

[c1 Find the current in the load (I O-j7.5) when connected across ABterminals. 15"-ll. 5

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[b] A balanced three phase Y connected load requires 10 kVA at 0.5lagging pf. Find the kVAR size of a delta condenser bank which maybe parallel ed with the load to bring the pf to 0.866 lag. Also, computethe value of capacitor in each leg of delta connected bank. The supplyvoltage is 415 V at 50 Hz. 7

[c] Determine the range ofthe parameter K for stability. 4

If two such networks are cascaded, find ABCD parameters and Zparameter, of the equivalent network.

Deterrmne the transmi ssion parameters of the network given below.

) J.1 ~ ( 0 7

'VI lixc:-6 >< 0 ~"

4[a]

.!.. .[l..'-

rd] If v =.fi cos OJ! is applied as source to the circuit, find the currentdra~n from the source. . 2

2[a] A series RLC circuit is excited from a constant voltage variablefrequency source. The current in the circuit becomes max imum atfrequency of 0)0 = 600 rad/sec and falls to half of the maximum valueat OJ=400rad/sec. If the resistance in the circuit is 30 find val ues of L~C. 5

[b] Discuss briefly about Q of a resonant circuit and bandwidth of thecircuit. What are their significance. 2

[c] A toaster operates at 115 V, 60 Hz, l OA and absorbs 1150 W at unitypf. A choke coil is wound with a r~tio of X'/R = 5 so that if placed inseries with the toaster on 230 V, 50 Hz supply, the toaster will have115 V across its terminals. Draw the phasor diagram with and withoutconnection of the choke coil. 7

The power input to 500 volts, 50 HZ, 6 poles, 3 phase induction ~o.tor

running at 975 rpm is 40 kW. The stator losses are low, and frict ionand windage losses are 2 kW. Calculate (i) slip (i i) roto r copper losses(iii) net shaft power output (iv) efficiency. 7

6[a]

5[a] A 50 kVA, 23001230V, 50 Hz tran sformer has a high voltage windingresistance of 0.650 and low voltage wind ing resistance of 0.0065 O.Laboratory test showed the following results:OCtest: V =230VI =5.7A P =190WSC test : V = 41.5V I =21.7A {wattmeter reading not recorded}Compute the value of primary voltage needed to provide ratedsecondary voltage when transformer is connected in step up mode andis delivering 50 \<VA at a pf of 0.8 lagging. 7

[b] Draw a neat phasor diagram of transformer with pure resistive load .Deve lop an equivalent circuit for the same. Briefly explain thediagram. 7

+V2-

oT 1'h"lF

a

A volta ge pulse of unit height and width of T sec is applied to theseries RC circuit as shown in the figure given below. Determine thevol tage across the capacitor 'C' as a function "Of time. Assume thatcapacitor is uncharged. ~ 6

-t):\ _~'Is. y T c.

3[a]

[b] Determine the driving point impedance of the -ladder circuit shown infigure given below. I. 4

I '-1 H ""l..

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[b] With the help of mmf and emf phasor diagram explain the operation ofsynchronous machine as generator and motor. 3

[c] Draw the phasor diagram of synchronous generator under overexcitation! normal excitation! under excitation when operating atconstant load, with variable excitation and fixedterminal voltage.

47[a] A DC shunt motor runs at 1200 rpm on no load drawing SA from nov

de mains. Its armature and field resistances are 0.2Sn and lIOnrespectively. When loaded, the motor draws 62A from the mains.What would be its speed? Calculate shaft load torque delivered .by themachine. 7

[b] A separately excited generator running at IS00 rpm supplied 2S0 at12S V to a circuit of constant resistance. What will be the currentwhen the speed is dropped to 1200 rpm with field current unchanged?Assume armature resistance to be o.osn and the total drop at brushesto be l.SV. 7

8[a] The four arms of a wheatstone bridge is shown in the figure givenbelow. Work out the conditions for the balance and show that value ofinductance is independent offrequency. 4

[b] Discuss different types of digital voltmeters. Draw their neat diagramand explain their working. 5

[c] Draw a neat diagram of C.R.a. Explain its working. Discuss howimpedance is measured using C.R.a. 5

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Total No. of Pages 3

SECOND SEMESTER

END SEMESTER EXAMINATION

Roll No .

B.E. (IT)

!M9lY-2009

IT-1l2 MECHANICAL SCIENCES

Time: 3 Hours Max. Marks : 70

I [a](i) Explain principle oftransmissibility of force. 3(ii) State and prove Varignon's Theorem. 4

[b] Two smooth spheres each of radius lOa mm and weight lOON rests in ahorizontal channel having vertical walls, the distance between which is360 mm. Find the reactions at point of contact A,B,C and D as shownin Fig. l(b). 7

/;.

A!/

I r - - - - --,

g / /~- 2,(,o n.,,,, --l'l F,'d· 1( b)

2[a](i) What is efficiency of screw Jack? Also explain self locking. 3

(ii) Proof ~' = e" where the notation' s have their usual meanings. 4,[b] A block weighting 2000 N is to be raised by means of 15° wedge B

weighting 700 N. The co-efficient of friction of all contact surfaces is0.2. Calculate the minimum horizontal force that is required to raisethe block. (Fig.2b) 7

III

)

/ / / / / J

p,

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. 3[a] Determine the moment of Inertia of shaded area in Fig. shown belowabout x-axis and y-axis. :r: 7

6[a] Derive the expres sion for the centre of pressure and total pressure incase of an inclined submerged surface. 7

[b] A reactangular plate 3m x5 m is immersed vertically in water such thatthe 3m side is parallel to the water surface. Determine the hydraulicforce and the centre of pressure if the top edge of surface is(i) Flush with the water surface(ii) 2m below the water surface. 7

7[a] Explain follow ing:(i) Thermodynamic system, surroundings & Barometry. 3(ii) Thermodynamic equilibrium. 3

[b](i) State zeroth low of thermodynamics and also derive relation 'sbetween degree Fahrenheit and degree centigrade temperature scale . 5

(i i) Calculate the work done in piston cylinder arrangement duringexpansion where the process is given by equation.p = (V ' + 6V) bar, volume changes from 1m3 to 4m3

• 3

8[a](i) State the first law of thermodynamics for a closed systemundergoing a change of state. 3

(ii) Write both statements of second law of thermodynamics' with neatsketch. 4

[b] Derive the efficiency of Diesel with the help of P-V & T-s diagram .7

7f2-~ ,&{h)

Draw SFD & BMD for loading shown in Fig. 4(a).

ib

1o ~ ~ x

[b] Determine the force in all the members of the truss shown in Fig. 3(b).2 '~ 2m -:f"' ' '' ''-I 7

-rA ~ c

~ 5C'1 ~

~ ~ r

. . h"t4 (g,)[b] A bar of 30 mm diameter IS subjected to a pull of 60 kN. The

measured extension on a gauge length of 200 mm is 0.09 mm andchange is diameter is 0.0039 mm, Calculate the poisson ratio and threeelastic constants . 7

4[a]

5[a] Derive the Bending or flexure formulaMa E- = - = -I Y R

Where notations are haying their usual meanin gs. 7[b] State and explain the conditions of equil ibriums of a floating and

submerged body. 7

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Total No . ofPages 2

SECOND SEMESTER

END SEMESTER EXAMINATION

Roll No. ". ".

B.E. (IT)

M91Y-2009

IT-113 ENGINEERING MATHEMATICS-I

I [a] d iy dy < (..fix)Solve - , +3-+4y=e cos - .dx dx 2

[b] (i) Find the Laplace Transform of the following periodic function ofperiod 20

f(a) = { t]o ,(2a - t}/a,

O,;;t';;a

a ,;; t,;; 2a.

(1"1) F' d I I e. f 3s+ 5III nverse Lap ace Transform 0 as + 6s + 12

2[a] State Convolution Theorem for Laplace Transform. UsingConvolution Theorem solve the initial value problemd' d d-2::+ 32+ 2y = e-' , y(O)=0, 2(0) =-1.dt ' dt dt

[b] Solve the system of equationsdx dy

2- +3- -4x +5y = 3t +2dt dt

dx dy- +- - 2x +y =1dt dt

3[a] (I) Obtain the first order Taylor series appro ximation to the functionf (x, y)= e' In(x + y) about the point (I , 0).

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(ii) Evaluate the integral If, (a' -x' - y ') dxdy, where R is the

region x' + y' ~ a' .

[b] Obtain the Fourier series expansion of the following periodic functionj (x) =4 -x' , - 2 ~x ~2 of period 4. Hence show thatn ? 1 1 112=1- 2' + 3' - 4' + .........

4[a] (i) Find the volume of the solid under the surface az = x' + y ' and

whose base R is the circle x' + y ' = a' .

(ii) Test the functionj(x,y )= cos 2x + cos Y + cos(2x + y1 0 < x, Y < n, for relativemaximum and minimum.

[b] Find Fourier cosine series of the function

j(x)= {x, 0 < x < 22, 2 <x< 4.

5[a] Show that if the function j (z)=u(x,y)+iv(x,y) is analytic then thefirst order partial derivatives of u(x, y) and v(x, y ) exist and satisfy the

Cauchy-Riemann equations. Hence, show that j (z) = z ' :z is notanalytic at any point.

[b] Let D be the region bounded by the closed cylinderx' + y ' =16, z =0 and z =4. Verify the Gauss Divergence theoremifv=3x'T +6y 'J +zk.

6[a] State and prove Residue theorem. Using Residue theorem evaluate theintegral.

[b] Find the values of a, band c such that the maximum value of thedirectional derivative of j (x,y,z)= axy' +byz +cx'z' at (1, -I , I) is inthe direction parallel to the axis of y and has magnitude 6.

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Roll No.:BE (IT)

Tota l No. of Pages: 2SECOND SEMESTER

END SEMESTER EXAMINATION, May 2009IT-114: INTRODUCTION TO PROGRAMMING

Time: 3hrs. Max, Marks: 70Note : Question number I is compulsory. Attempt any FOURfrom the rest.

Assume suitable missing data, ifany.

I. Attempt any seven questions fro m the fo llowing:(i) Convert (A245F)J6 -> ( )10(ii) What is precedence operator and associativity.(iii) Explain the advantages of structured programming.(iv) What is the difference between Structure and Union.(v) What are primary and secondary storage?(vi) Can a function of 'C' return more than one value? Justi fy your answer.(vii) What is the difference between call by value and call by reference?(viii) Under what conditions can two pointer variables be subtracted.(ix) Differentiate between local variable and global variable.(x) Ex plain briefly the use of inline functions in'C'.

[2 x 7)2.

(a) What is the use oflogical operator in 'C'? Explain with the help of examples. [4)

(b) Wri te a program that reads from a file and counts and prints the number ofconsonant s, vowels, white spaces, digits and others till the end of the file. [6)

3.

(c) Explain the ind irection operator. [4)

(a) Write a funct ion using pointers to add two matrices and to return the resultant matr ixto the calli ng function . [6)

4.

(b) Explain the meaning and purpose of the fo llow ing:(i) Struct (ii) sizeof (i ii) typedef (iv) enum

(c) How does a structure differ from an array?

[4)

[4)

(a) What do you understand by the nested control structures? Exp lain with the help of anexample . [4)

(b) What is dynamic memory allocation? Explain the allocation and free ing of memory indynamic memory allocation. Justify with the help of an example. [4)

(c) Write the loop in three different ways:(i) Using a 'while' statement.

(ii) Using a ' do-while ' statement.

(i ii) Using a 'for' loop statement.

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5.(a) What is an algorithm? Also explain pseudocode and flowchart with the help of an

example . [4]

(b) What is the difference between the switch statement and if-else? Explain with the helpofan example. [6]

6.

(c) What is command-line argument? Explain with an example. [4]

(a) What are the various types oflanguages available in programm ing? Explain. [4]

(b) Differentiate between Top-down and Bottom-up programming. Explain. Also discussmodu lar programming in detail. [6]

(c) What is file handl ing in'C' ? Explain with its modes of operation.

7. Write short notes on any TWO of the following:(a) Object-oriented programming.(b) User-defined function.(c) Strings.(d) Preprocessor directives.(e) Pointers .

v

[4]

[7 x 2]

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Total No. of Pages 3

SECOND SEMESTER

END SEMESTER EXAMINATION

Roll Nu .

B.E. (IT)

MYlY-2009

IT-US DISCRETE STRUCTURES

Time: 3 Hours Max. M arks : 70

f:J.R~~.; ~t\.n.~'I,:'~r,:4l.~!; q u~sti ons se lect i ~g any TWO parts from each.h~"'i-r"',"\Assume s Ui table rrussm data, If an ;

I [aj Let G = {(a, b) :a.b e R,a ;< o}. Define a binary operation * on G by(a,b )*(e,d ) = (ae, be + d) for all (a,b), (e, d) e G. Show that (G,*) is agroup.

[b] Let G , and G, be two groups and let f :G, -> G2be a homomorphismfrom G, to G" then show that(i) feel) ~ e, where c. is the identify in G, and c, is the identity in G, .(ii) f(a"}= [j(a))" for ~ll a e G.(iii) IfH is a subgroup of G, then f(H) is a subg roup of G, .

[c] Prove that a non-empty subset S of a ring R is a subring iffa,b e S=> a - b e S anda.b e S.Also, prove that the intersection of two subr ings of a ring R is asubring of R.

2[a] Solve the recurrence relationan-6a"_1+8an_2 = nA'1 where uo=8, u/ ;:::;; 22.

[b] State and prove extended pigeonhole principle and hence show that ifany 26 people are selected then we may choose a subset of 4 so that all4 were born on the same day of the week.

[c] Using generating funct ion, solve the recurrence relationa ,l - 5all_1 + 6a""2= 2/1 + n, n :2: 2.

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3[~] Prove that the relation R defined on the set of integers Z byx Ry <:> x - y is a multiple of 3, is an equivalence relation. Also, findall the equivalence classes.

[b] By using definition of characteristic function show thatAn (Bv C)=(An B)v(A nC).

[c] What do you mean by a language generated by a gramm ar?Let G, =(V,,v,,S, p ) where V:, = {S, A,B}, VT= {a ,b} and

P= {S-,>AB, S-,>bA, A -'> a, B -,>ba} and G,= (VN,v" S, p) where

V, =Is,B} VT={a,b} and P ={S -'> aBa,B -'> aBa, B -'> h} S is thestart symbol in both the gramma r. Find L(G,) and L(G,) . Are thesetwo grammars equivalent?

4[a] Explain Dijkastra' s algorithm for finding the shortest path. By usingthis algorithm find the shortest path between a to z for the followinggraph:

b e. ~

)). ;'0

Cl C c " Z

l!- I. ?'i

ol (, .f.

[b] Determine minimal spannmg tree USlJ1g Kruskal' s algorithm of thefollowing graph:

~~V9 .<. Vt>'< \)7 3 V. (0 Vs-

Write the algorithm also.

[c] Define Eulerian circuit and Hamiltonian circuit. Give an example of agraph (i) that has an Eulerian circuit and a hamiltonian circuit, whichare distinct (ii) that has a hamiltonian circuit but not an Euleriancircuit.

5[a] (i) By using Algebra of propositions, show thatl- p /\ (- q /\r )v (q /\r )v (p /\r )]<:> r(ii) Define logical equivalent. Show that

- (p <:> q)=+ p <:> q)=(p <:>- q)[b] (i) Obtain the pdnf of (- pv -q)=::> (- p /\ r )and pcnf of

(- p=::>r) /\(q<:> p).(ii) Let K(x) : x is man, L(x) : x is mortal, M(x) : x is an integer,

N(x) : either positive or negative . Express the following usingquantifiers :

All men are mortalAny integer is either positive or negative.

[c] Check the validity of the follow ing argument:(i) If the computer was down saturday afternoon, then Mary went to

a matinee.Either Mary went to a matinee or took a nap saturday afternoon.Mary did not take a nap that aftemoon.

(ii) Babies are illogicalNobody is despised who can manage a crocodile.Illogical persons are despised.

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