University of Mumbai 2005-1st Sem B.E Computer Science FE - Question Paper
First year papers of November 2005
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(REVISED COURSE)
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[ Total Marks : 100
(3 Hours)
N.B. (1) Question No. 1 is compulsory.
(2) Answer any four out of remaining six questions. .
(3) Assume suitable data wherever required. .
1. (a) The amplifier of figure utilizes an n-channel FET for which Vp = -2-0 V, gmo = 1 -60 mA/V and lpSS = 1 -65 mA. It is desired to bias the circuit at lD = 0-8 mA using VDD = 24 V. Assume rd Rd.
12
Find (i) VQS, (ii) gm , (iii) Rs, Rs by passed with a very large capacitance.
(iv) Rd> such that voltage gain is atleast 20 dB,. with
(b) What method is used to bias an FET against device and temperatue variation ? Explain how this is 8 effective.
2. (a)' Draw and explain current-mirror circuit. ' 8
(b) For the circuit shown in figure, determine the following 12
(i) lE, lEl. IE2
(ii) Collector to ground voltage
(iii) base-voltage.
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VBE = 0-7 V [3=100 both the transistors are matching. |
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plS'how ,o construct basic instrumentation ampiitler trom general purpose OP-aMP.
Derive an expression for Voul.
4 (a) Give its Irequency 1 =
response curve. Give practical application of this filter. - 5
(b) Compare active and passive filters.
5 Draw and explain phase-shilt oscillator using OP-AMP. De*. expression ,or treguenc, o. oscillation
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7 (a) Explain monostable operation using IC 555 Draw the wavetorms at trigger, V. and across capacitor. 15
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//-cjs/ pfa /// ~ 'J (REVISED COURSE)
(3 Hours) [Total Marks : 100
N.B.: (1) Question No. 1 is compulsory.
(2) Attempt any four out of remaining six questions.
(3) Figures to the right indicate full marks.
(4) Answers to sub-questions of Individual questions should be answered one below the other.
(5) Use a blue/black ink pen to write answers.
1. (a) If x = CiS show that lim x.x.x,.......x =-1.
20
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(b) If y = eax cos (bx + c), prove that
e3* cos I bx + c + n tan- I and hence find n1 derivative of e5x cos x cos 3x.
(c) A particle moves along a plane curve such that its linear velocity is perpendicular to the radius vector, show that the path of the particle is a circle.
(d) If u = exVz show that - = (1 + 3xyz + x2y2z2. exyz).
Sxdydz
2. (a) Prove that 8
cos8 0 + sin 6 = -t [cos 80 + 28 cos 40 + 35] By using complex numbers.
04
(b) Find all the roots of the equation z3 = i (z - 1 )3. 6
(c) Prove that cosh5x = [cos h 5x + 5 cos h 3x + 10 cos hx] 6
16
3. (a) If sin (0 + i<(>) = tan a + iseca, prove that cos 20 cos h $ = 3. 8
(b) Prove that i log~| = 7t-2tan~1x. 6
(c) Test whether Rolle's theorem hold for the function ex (sin x-cos x). - 6
1 1
4. (a) If ym + y m= 2x, prove that(x2 - 1) yn + 2 (2n + 1) xyn + n2 - m2) yn = 0. 8
(b) If y = sin-1 find n,h differential coefficients, then convert it into polar form. 6
(c) If lim sin 2x + a sin x f[ncj va|UQ 0f a ancj hence the limit. 6
x -0 xJ
5. (a) For the space curve x = e* cos t, y = e' sin t, z = e*. Find the radius of curvature and radius of torsion. 8
(b) Calculate the value of VlO correct to four decimal places by using Taylors theorem. 6
(c) Using Lagrange's mean value theorem, prove that 6
1 + b2 1 + a2
Hence deduce that
7t 3 -4 ;t 1 - + -rrr- < tan 1 -<-+-.
4 25 3 4 6
(a) State and prove that the Eulers theorem on homogeneous function of three variables. Hence if 8
f(x, y, z) = x2yz - 4y2z2 + 2xz3
OL L. . 3f 3f .,
Show that x-~ + y- + z = 4f.
9x ! 3y 3z
(b) Show that minimum value of 6
a3 a3 2 u = xy + + is 3a\ x
(c) Find [(3-82)2 + 2(2-1 )3]5 by using the theory of approximations. 6
(a) If u = log (x3 + y3 + z3 - 3xyz) show that (-Jj- + )2 u =
8
(x + y + ;
(b) If log 0 = r x where r2 - x2 + y2, show that = 6 (x ry ) 6
dyd r3
(c) Find the equation of the osculating plane to the curve x = 2 abt, y = a2 log t, z = b2t2 at t = 1. Also, find the 6 equation of the principle normal at t = 1.
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(REVISED COURSE)
{3 Hours) [Total Marks : 100
Section I
N.B.: (1) Question No. 1 is compulsory.
(2) Attempt any four questions from remaining six questions.
(3) Assume any suitable data if required and justify the same.
1. (a) An electron is projected horizontally with an initial velocity 'V0' in to an uniform electric field acting vertically 5
upwards. Show that the trajectory of an electron with in field is a parabola.
(b) Describe working of P-N-P transistor in common base configuration. 5
2. (a) Proton and Deuteron are accolcratod by the same potential. Compare their De-Broglie wavelengths. 5
[Given data mp = -i- md]
(b) Density of CaF2 is 3180 kg/m3, A unit ccli contains four Ca++ and eight F~ ions. Atomic wt. of Ca = 40 and F = 19. 5 Calculate the lattice constant of this crystal.
3. (a) An electron of energy 40 c.V. is circulating in a plane at right angles to a uniform magnetic field of strength 5
10-6 wb/m2. Calculate the radius of orbit and frequency of revolution.
(b) Show that packing efficiency in BCC monoatomic structure is 68%. 5
4. (a) Calculate the thickness of quartz plate needed to produce ultrasonic waves of frequencies (i) 3-8 MHz (ii) 300 KHz. 5
(where density of quartz crystal = 2650 kg/m3 and Youngs modulus = 8 x1010 N/m2)
(b) If a stream of electrons with average velocity of 1 -6 x 107 m/sec. is deflected by 0-3 m in travelling a distance of 5
0-5 m through an electric field of 3500 volts/m perpendicular to its path then estimate e/m ratio for electron.
5. (a) A CRT is designed to have dellection sensitivity of 0-3 mm per volt. The plates are required to be 3 cm long and 5
6 mm apart. The distance of the screen from the centre of the plate is 20 cm. What should be final anode voltage ? What will be the deflection sensitivity for a charged particle which is 2500 times heavier than electron but having same charge.
(b) At what velocity the De-Broglie wave length of an alpha particle is equal to the wavelength of 1-8 KeV x-ray 5 photons ? [mp = 1-67 x 10~27 kg]
6. (a) Show that in a crystal of cubic structure the distance between the planes with miller indices (hkl) is equal to 5
V h + k + r where a : lattice parameter.
(b) A crystal lattirs plane (326) makes an intercept of 1 -5 A on x-axis in a crystal having lattice constant 1 -5 A, 2 A, 5 4 A, on x, y, z crystallographic axis respectively. Find y and z axes intercept.
7. (a) Explain use of CRO to measure phase and frequency ol electrical signal. 5 (b) Explain Cavitation effect when ultrasonic wave is passed through a liquid. 5
Section II
N.B.: (1) Question No. 8 is compulsory.
(2) Attempt any four out of remaining six questions.
(3) Assume any suitable data.
(4) Figures to the right indicate full marks.
(5) Answer two sections on different answer-sheets.
At. Wt.: Ca = 40, H = 1,0 = 16, S = 32, N = 14, C = 12, Cl = 35-5, Fe = 55-8, Mg = 24, Si = 28.
8. Answer any five of the following : 10
(a) Fatty oils are no more used as lubricants on the large scale. Why ?
(b) Define Pollution and mention its any two causes.
(c) What is the repeat unit of natural rubber ? (with structure)
(d) Define BOD with its significance.
(e) Name the indicator used in EDTA titration. What is the colour change at the end point of titration ?
(f) Define copolymer and give one example.
9. (a) Which TYPE of film/lubrication required for HIGH SPEED, LOW LOAD Machines ? 4 (b) Calculate amount of Lime (90% pure) and Soda (100% pure) for 1 million lit of water containing the following impurities : 6
CaS04 = 136 ppm. H2SOd = 49 ppm, MgCI2 = 95 ppm, MgS04 = 60 ppm, Si02 = 50 ppm.
10. (a) Which type of moulding is used for coating the wires used for insulation ? 4 (b) Explain Reactions of Lime and Soda used for softening. 6
11. (a) Define flash point of lubricant. How is it determined by Pensky-Martens Apparatus ? 5 (b) Differentiate: (i) Thermoplastic and Thermosetting resins (any 3 points) 3
(ii) LDPE and HDPE (any 2 points) 2
12. (a) Explain any three moulding constituents of plastics (With 2 ex. of each) 6 (b) Write a note on Photochemical smog. 4
13. (a) A zeolite softener was completely exhausted and was regenerated by passing 150 lit. of NaCI soln., containing 6
50 g/lit. of NaCI. How many litres of water of hardness 450 ppm can be softened by this container ?
(b) Give an account of Phosphate conditioning in case of boilers as internal treatment method. 4
14. (a) Give the sources and effects of the air pollutants Ozone and SOx.
(b) 16 gm of blended oil was heated with 50 ml KOH. This mixture then required 31 -5 ml of 0-5 N HCI-50 ml KOH 6 required 45 ml 0-5 N HCI. Find % cottonseed oil, if saponification value = 192 mg. 4
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(REVISED COURSE)
[Total Marks : 100
(3 Hours)
N.B. (1) Question No. 1 is compulsory.
(2) Solve any four questions out of remaining six questions.
(3) Assume suitable data if necessary.
(4) Figures to the right indicate marks.
(5) Take value of g = 9-81 m/s.
20
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-I' Solve the tWQ buckets in the equilibrium position shown in figure. Determine the weight of bucket B. Bucket A has a weight of 60 N. |
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(b) A force of 200 N acting on a bracket as shown in figure. Determine. An equivalent force and couple at A. ft)
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(c) A stone dropped into a well is heard to strike the water in 4 seconds. Find the depth of the well, assumina the velocity of sound to be 335 m/sec. .
(d) The path of projectile is a parabola. Justify this statement with the help of mathematical derivation, e A paS moves in a x-y plane with an acceleration, a = -3i - 16tj m/s*. If it starts at the ongin with
a starting velocity 50 m/s directed at 30 C to the x-axis, compute at t = 2 sec., (i) Radius of curvature of path, (ii) Tangential acceleration,, (iii) Normal acceleration.
V a.
(Vx
Hint:
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(a) The Truss is loaded and supported as shown in figure. Determine the following
12
(i) Identify the zero force member.
(ii) Find forces in members EF, ED and FC by method of joints.
(iii) Find forces in members GF, GC and BC by method of section.
(b) Bar AB is acted upon by forces as shown in the figure. Find F to be applied at P for the system in
(b:i
(a) The Rectangular block as shown in figure is acted upon by the following forces P = 500 kN acting from B to C Q = 480 kN acting from C to E T = 270 kN acting from F to G.
Replace the specified set of forces by single resultant force acting at 0 and a couple.
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(b) What force P must be applied to the weightless wedges shown in figure to start them under the 1000 kN 8 block ? The angle of friction at all contact surfaces is 10. ;
(a) Find the length L of a portion of bent up wire shown in figure. The C.Q. of a whole figure is at point O. 8
(b) Find the Moment of Inertia of ashaded area shown in figure with respect to the centroidal axis parallel to AB. 8
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the components of forces acting at points B, C and E. Assume that the pulley is smooth. 10
5. (a) Determine
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(b) A boy throws a ball with an initial velocity 24 m/s knowing that the boy throws the ball from a distance of 30 m 10
from the building. Determine (i) the maximum heighththat can be reached by the ball and (ii) the
corresponding angle a.
6. (a) Figure shows below a plot of a-t curve for a particle moving along straight line. Draw v-t and s-t curve and 10
determine the speed and distance covered by the particle after 50 sec. Find also the maximum speed and time at which the speed is attained by the particle.
(b) In the mechanism shown in figure. Piston C is constrained to move in a vertical slot. A and B moves on 10 horizontal surface. Rods CA and CB are connected with smooth hinges. If VA = 0-45 m/sec. to the right.
Find velocity of C and B. Also find angular velocity of two rods.
7 (a) A mass of 8 kg can slide freely on a smooth vertical rod as shown in figure. The mass is released from rest at a distance of 500 mm from the top of the spring. The spring constant is 60 N/mm. Determine the velocity of A when the spring has compressed through 20 mm. The free length of the spring is 400 mm.
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(b) The magnitude and direction of two identical smooth balls before central oblique impact are as shown in figure. Assuming e = 0-90. Determine the magnitude and direction of velocity of each ball after impact.
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(c) A 15 kg siender rod AB is 1 -5 m long and pivoted about point O which is 0-3 m from end B. The other end is pressed against a spring of constant. K = 300 kN/m. Until the spring is compressed 25 mm. The rod is then in a horizontal position. If the rod is released from this position. Determine the angular velocity when the rod has rotated through 60 and 90.
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(REVISED COURSE)
[ Total Marks : 100
( 3 Hours )
B. (1) Question No. 1 is compulsory .
(2) Attempt any four questions out of remaining six questions.
(3) Assume any suitable data wherever required.
(a) In the circuit-diaqram shown below what is the finai voltage drop across capacitor.
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(b) A wire has a resistance of 12 2. It is bent in the form of circle. Calculate the resistance between any two points on its diameter.
(c) The resistance of a wire of uniform diameter d and length is 'H' Q. Calculate the resistance of another wire of same material but diameter 2d and length '41'.
(d) Find Rvv in the following circuit. IB
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(e) Calculate the power dissipated in the circuit when supply voltage u = 5 cos (wt) and i = sin (wt).
(f) Find lc in the following circuit if B = 200.
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(g) An Impedence Z is connected to the secondary of an ideal transformer, having primary and
\2
secondary turns as N1 and N2, Show that Z seen from primary is equal to
(h) State Flemings right hand and left hand rules.
(i) Calculate the current flowing thro 2-2 kn Resistor in the following circuit. Both diodes are ideal.
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(j) Calculate the impedence of the circuit given below :
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2. (a) Derive the expressions for the following parameters of Full Wave Rectifier:
(l)!d= {ID U (III) pdc (IV) pac (V) Etficicr
(b) What is ripple factor and derive for the ripple factor of fuil wave rectifier.
(c) With neat circuit dia and waveform explain capacitor input filter.
3. (a) Compare BJT configurations (CE, CB, CC) w.r.t.
(i) Input resistance (iv) Current gain
(ii) Output resistance (v) Applications.
(iii) Voltage gain .
(b) Discuss the operation of JFET.
(c) Calculate the RMS and Average values of the waveform shown below :
4. (a) Calculate the current thro' 10 2 resistor by
(i) Superposition theorem (ii) Thevenins theorem.
(b) An RLC series circuit with resistance of 10 n, inductance of 0-2H and capacitance of 40 |iF is 8 supplied with a 100 V supply at variable frequency.
Find(i) Resonating frequency (v) Voltage across R,L,C
(ii) Current at resonance (vi) Quality factor
(iii) Power (vii) B.W.
(iv) Power factor
(c) Define (i) Conductance (ii) Susceptance. 2
5. (a) A 230 V DC shunt motor takes no load current of 3A and runs at 1100 rpm. If the full load current 4
is 41 Amps. Find the speed on full load if Ra = 0-25 2. and Rsh = 230 1.
(b) Why 1-ph Induction motors are not self starting ? and HenCe explain the construction and working 6 principle of shaded pole Induction motor.
(c) Discuss the effect of p.f. on regulation of transformer. 4
(d) Draw and explain the vector diagram of transformer with leading p.f. load. 6
6. (a) Discuss the measurement of 3-ph power by two wattmeters method. Draw phasor and 8
circuit-diagram '
(b) Discuss the graphical representation of series resonance. 8
(c) Define the following terms : 4
(i) Latching current (iii) dv/dt
(ii) Holding current (iv) di/dt.
7. Write short notes on : 20
(a) Gravity and Spring Control Instruments
(b) Temperature Sensors
(c) Star-Delta transformations
(d) Double-field revolving theory.
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[ REVISED CCXJRSE ]
( 3 Hours ) [ Total Marks : 100
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N.B. : (1) Question No.l is compulsory. (2) Attempt any four out of remaining six questions. (3) All programs in C programming language. Q |
No |
Detailed and framed questions |
Max. Marks |
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Q1 |
a |
Suppose you place a given sum of money, A, into a savings account at the beginning of each year for n years. If the account earns interest at the rate of i percent annually, then the amount of money that have accumulated after n years, F is given by F=A[(1+i/100) + (1+i/100)2 +(1+i/100)3 +.........+(1 + i/100)n] |
10 |
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b |
Write an interactive C program to determine the following i) Money gets accumulated at the end of n years ii) how much money needs to be deposited at the beginning of the first year to get an amount Famt Theres a recursive function called Ackermans function, which is popular with lecturers of computer science course and can be defined like this if m and n are integers. Ack(m,n) = n + 1 if m=0 Ack(m,n)=Ack((m-1,1) if (n=0) and m>0 Ack(m.n)=Ack(m-1 ,ack(m,n-1)) otherwise Where m>=0 and n>=0 - Write a recursive function for the aforesaid Ackermans function |
To | |
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Q2. |
a |
Write a program which finds four digit perfect squares , where the number represented by the first two digits and last two digits are also perfect squares e.g. 1681= 4I2 , 16= 42 , 81=92 |
10 |
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b |
A famous conjecture holds that all positive integers converges to 1 (one) when treated in the following fashion. Step 1. If the number is odd, it is multiplied by three and one is added 2. If the number is even , it is divided by two 3. Continuously apply above operations to the intermediate results until the number converges to one Write a program to read an integer number from key board and implement the above mentioned algorithm and display all the intermediate values until the number converges to 1. Also count and display the number pf iterations require for the convergence |
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Q3. |
a |
Write a program to read the name and total marks of a class of 50 students. Arrange this data (names and marks) in the descending order of total marks and print the outputs with proper headings. |
10 |
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b |
Write a program for computing mean, variance and standard deviation of a sot of numbers using the following formula n Mean = 1/n Z Xi i-1 ' n Variance - 1/n I (Xi-Xmean)2 i-1 Standared Deviation = '/Variance |
10 1 |
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