Jawaharlal Nehru Technological University Kakinada 2009 B.Tech Computer Science and Engineering Mathematics-1 - Question Paper

4.    (a) Form the differential equation by eliminating the arbitrary constants

y=e^x (acosx+bsinx).

(b)    Solve the differential equation y(2xy+e^X)dx-e^Xdy=0.

(c)    A body kept in air with temperature 25 ^oC cools from 140 ^oC to 80 ^oC in 20minutes. Find when the body cools down to 35 ^oC.    [4+6+6]

5.    (a) Solve the differential equation: (D² + 1)y = e^-x + x³ + e^x sinx.

(b) Solve (D² + 4)y = sec2x by the method of variation of parameters. [8+8]

OO___

6.    (a) Prove that L [[ 1 f (t)] = f f (s) ds where L [f(t) ] = f (s)

s

(b)    Find the inverse Laplace Transformation of ^3(sf ^-5²⁾

(c)    Evaluate / / (x² + y²) dxdy over the area bounded by the ellipse f² + =1

[5+6+5]

7.    (a) If = x²z, 0₂ = xy - 3z², then find V( V0i . V0₂ )

(b) Evaluate J F .dr where F = zi + xj + yk and C is x = a cost, y = a sint,

C

z = 2- from t = 0 to t = 1.    [8+8]

8.    Verify divergence theorem for F = 4xz i - y² j + yz k, where S is the surface of the cube bounded byx = 0, x = 1, y = 0, y = 1, z = 0 and z = 1.    [16]

I B.Tech Supplementary Examinations, November 2009 MATHEMATICS-I ( Common to Civil Engineering, Electrical & Electronic Engineering, Mechanical Engineering, Electronics & Communication Engineering, Computer Science & Engineering, Chemical Engineering, Electronics & Instrumentation Engineering, Bio-Medical Engineering, Information Technology, Electronics & Control Engineering, Mechatronics, Computer Science & Systems Engineering, Electronics & Telematics, Metallurgy & Material Technology, Electronics & Computer Engineering, Production Engineering, Aeronautical Engineering, Instrumentation & Control Engineering and Automobile Engineering)

Time: 3 hours    Max Marks: 80

Answer any FIVE Questions All Questions carry equal marks

Find the envelope of the family of ellipses X2 + y2 =1 where the two parameters are connected by the relation a + b = c where c is a constant.    [8+8]

Trace the Folium of Decartes : x³ + y³ = 3axy.

Find the surface area generated by rotating the arc of the catenary y = a cos(x/a) from x = 0 to x = a about the x-axis.    [8+8]

Form the differential equation by eliminating the arbitrary constant c: y = 1 + x² + c\/l + x².

Solve the differential equation:

dt using Laplace transforms

(c) Evaluate f f X+d²) by transforming into polar cordinates    [5+6+5]

o y

7.    (a) If a is a constant vector, evaluate curl((axr)/r³) where r=xi+yj+zk and r=|r|. (b) Evaluate //^A-ⁿ ds for A=(x+y²)i - 2xj + 2yzk and S is the surface of the

S

plane 2x+y+2z=6 in the first octant.    [8+8]

8.    (a) Apply Greens theorem to evaluate (2xy x²)dx + (x² + y²)dy,

C

where C is bounded by y = x² and y² = x.

(b) Apply Stokes theorem to evaluate J'(y dx + zdy + xdz)

C

where C is the curve of the intersection of the sphere x² + y² + z² = a² and x + z = a.    [8+8]

I B.Tech Supplementary Examinations, November 2009 MATHEMATICS-I ( Common to Civil Engineering, Electrical & Electronic Engineering, Mechanical Engineering, Electronics & Communication Engineering, Computer Science & Engineering, Chemical Engineering, Electronics & Instrumentation Engineering, Bio-Medical Engineering, Information Technology, Electronics & Control Engineering, Mechatronics, Computer Science & Systems Engineering, Electronics & Telematics, Metallurgy & Material Technology, Electronics & Computer Engineering, Production Engineering, Aeronautical Engineering, Instrumentation & Control Engineering and Automobile Engineering)

Time: 3 hours    Max Marks: 80

Answer any FIVE Questions All Questions carry equal marks

1.    (a) Test the convergence of the following series E xⁿ , x > 0.    [5]

(b)    Test the following series for absolute /conditional convergence

E(-1)"

n= 1

[5]

(c)    Verify cauchys mean value theorem for f(x) = e^x and g(x) = e^-x in [a,b] [6]

2.    (a) If u=x²-y², v=2xy where x=r cos0, y=rsin0 show that = 4r³.

d(r,l

PL

r

(b) For the cardioid r=a(1+cos0) prove that p is constant, where p is the radius of curvature.    [8+8]

3.    (a) Trace the curve y² = ^x .

(b) The part of the parabola y² = 4ax cut off by the latus-return revolves about the tangent at the vertex. Find the surface area of revolution.    [8+8]

4.    (a) Form the differential equation of the family of curves log (y+a) = x²+c , c is

the parameter.

(b)    Solve the differential equation: 3 - y cosx = y⁴(sin2x - cosx).

(c)    An object whose temperature is 75 ⁰C cools in an atmosphere of constant temperature 25 ⁰C at the rate k$ , d being the excess temperature of the body over the atmosphere. If after 10 minutes the temperature of the objects falls to 65⁰ C. Find its temperature after 20 minutes. Find the time required to cool down to 55 ⁰C.    [3+7+6]

5.    (a) Solve the differential equation: (D³ + 1)y = cos(2x - 1).

(b) Solve the differential equation: (D² + 1)y = cosx by the method of variation of parameters.    [8+8]

6.    (a) Find the Laplace Transformation of the following function: t e^-t sin2t.

(b)    Using Laplace transform, solve y+2y^/+5y = e ^- sint, given that y(0) = 0, y'(0) = 1.

5 x²

(c)    Evaluate J f x(x² + y²) dxdy    [5+6+5]

0 0

7.    (a) Show that F = (z² + 2x + 3y) i + (3x +2y + z) j + (y + 2zx) k is irrotational.

Hence find the corresponding scalar potential 0 such that F = V 0 .

(b) Evaluate Jj F .ds where F = xy i x² j + (x + z) k and S is the region of

S

the plane 2x + 3y + z = 6 bounded in the first octant.    [8+8]

8.    Verify divergence theorem for F =2xzi + yzj + z²k over upper half of the sphere x²+y²+z²=a².    [16]

I B.Tech Supplementary Examinations, November 2009 MATHEMATICS-I ( Common to Civil Engineering, Electrical & Electronic Engineering, Mechanical Engineering, Electronics & Communication Engineering, Computer Science & Engineering, Chemical Engineering, Electronics & Instrumentation Engineering, Bio-Medical Engineering, Information Technology, Electronics & Control Engineering, Mechatronics, Computer Science & Systems Engineering, Electronics & Telematics, Metallurgy & Material Technology, Electronics & Computer Engineering, Production Engineering, Aeronautical Engineering, Instrumentation & Control Engineering and Automobile Engineering)

Time: 3 hours    Max Marks: 80

Answer any FIVE Questions All Questions carry equal marks k k k k k

1.    (a) Test the convergence of the series

22 _ i V¹ + (3- - 3 V² + (44 - _

l² 1) + 23 2) + 3³ 3

(b)    Show that the series+..... converges absolutely. [5]

(c)    If f (x) = log 2 sin (nX) + log x, prove that f log 2 cos    f = 0 for some xe(1,2) *    [6]

2.    (a) Find the stationary points of the following function u and find the maximum

or the minimum value u = x² + 2xy + 2y² + 2x + y

(b) Find the envelope of the family of circles x² + y² - 2ax cos# - 2ay sin# = c² ( # is a parameter )    [8+8]

3.    (a) Trace the Cissoid of Diocles : y² (2a-x) = x³.

(b) Show that the surface area of the spherical zone contained between two parallel planes of distance h units apart is 2nah, where a is the radius of the sphere.

[8+8]

(b) Find the inverse Laplace Transformation of ^3(s2 5²⁾

(c) Evaluate / / (x² + y²) dxdy over the area bounded by the ellipse 2 + fr =1

[5+6+5]

7.    (a) Prove that F=(2x+yz)i +(4y+zx)j - (6z-xy)k is solenodal as well as orrota-

tional. Also find the scalar potential of F

(b) Evaluate J Fdt where F=(x-y)i+(y-2x)j and C is the closed curve in the xy

C

plane x=2cost, y=3sint from t=0 to 2 n    [8+8]

8.    Verify divergence theorem for F = x³ i + y³j + z³ k taken over the surface of the sphere x²+y²+z²= a².    [16]

I B.Tech Supplementary Examinations, November 2009 COMPUTER PROGRAMMING FOR BIOTECHNOLOGISTS

(Bio-Technology)

Time: 3 hours    Max Marks: 80

Answer any FIVE Questions All Questions carry equal marks

1.    (a) Draw the block diagram of an 8-bit, 8-word RAM system and explain briefly

its operations.

(b) Compare serial and parallel memory with respect to the speed of reading and writing.    [10+6]

2.    (a) Define the terms:

i.    Throughput

ii.    Turnaround time

iii.    Swapping.

(b) What are the main features of MS-DOS and UNIX operating system? [6+10]

3.    (a) Draw a Flowchart for the following

The average score for 3 tests has to be greater than 80 for a candidate to qualify for the interview. Representing the conditional logic for generating reject letters for all candidates who do not get the required average and interview call letters for the others.

(b) Explain the basic structure of C program.    [6+10]

4.    (a) In what way array is different from an ordinary variable?

(b)    What conditions must be satisfied by the entire elements of any given array?

(c)    What are subscripts? How are they written? What restrictions apply to the values that can be assigned to subscripts?

(d)    What advantage is there in defining an array size in terms of a symbolic constant rather than a fixed integer quantity?

(e)    Write a program to find the largest element in an array.    [2+2+4+4+4]

5.    What do you mean by functions? Give the structure of the functions and explain about the arguments and their return values.    [16]

6.    (a) Explain the different ways of passing structure as arguments in functions.

(b) Write a C program to illustrate the method of sending an entire structure as a parameter to a function.    [6+10]

7.    Declare two queues of varying length in a single array. Write functions to insert and delete elements from these queues.    [16]

8.    Write a bioperl program that takes a set of (related sequences) in FASTA format.

(a)    aligns them using ClustalW

(b)    converts them to PHYLIP format.

k k k k k

I B.Tech Supplementary Examinations, November 2009 COMPUTER PROGRAMMING FOR BIOTECHNOLOGISTS

(Bio-Technology)

Time: 3 hours    Max Marks: 80

Answer any FIVE Questions All Questions carry equal marks

1.    With a neat diagram explain the working of an execution unit of a CPU. [16]

2.    (a) What are time sharing systems? Explain time sharing using timing diagram.

(b) What is batch operating system? Explain batch mode of operation using timing diagrams.    [8+8]

3.    (a) What is the purpose of the if-else statement? In what way is this statement

different from the while, the do-while and the for statements.

(b) A cloth showroom has announced the following seasonal discounts on purchase of items:

Write a C program to read purchase extent and calculate discount. Also print the purchase amount and discount.    [6+10]

4.    (a) Write a program to sort the set of strings in an alphabetical order?

(b) How are multidimensional arrays defined? Compare with the manner in which one-dimensional arrays are defined.    [12+4]

5.    Write a C program that uses a function to sort an array of integers.    [16]

6.    (a) What is a structure? How is it declared? How it is initialized?

(b) Define a structure to represent a data. Use your structures that accept two different dates in the format mmdd of the same year. And do the following: Write a C program to display the month names of both dates.    [6+10]

7.    Write in detail about the following:

(a)    Recursion

(b)    Applications of Queues    [8+8]

8.    Write a bioperl script to identify restriction enzyme sites for a given sequence.[16]

I B.Tech Supplementary Examinations, November 2009 COMPUTER PROGRAMMING FOR BIOTECHNOLOGISTS

(Bio-Technology)

Time: 3 hours    Max Marks: 80

Answer any FIVE Questions All Questions carry equal marks

k k k k k

1.    (a) What are the types of voice recognition system? What does training such

a system, mean?

(b) What are transducers? Name any five physical properties that are commonly measured by transducers.    [8+8]

2.    (a) Distinguish between Windows 95 and Windows NT.

(b) Explain the important features of PC operating systems.    [6+10]

3.    (a) Describe the two different forms of the if-else statement. How do they differ?

(b)    Compare the use of the if-else statement with use of the ?: operator. In particular, in what way can the ?: operator be used in place of an if-else statement?

(c)    Admission to a professional course is subject to the following conditions:

i.    marks in maths >= 60.

ii.    marks in physics >= 50.

iii.    marks in chemistry >= 40.

iv.    total in all three subjects >= 200.

Given the marks in three subjects, write a C program to process the application to find whether eligible or not.    [6+4+6]

4.    (a) Write a C program to do Matrix Multiplications.

(b) Write in detail about one dimensional and multidimensional arrays. Also write about how initial values can be specified for each type of arrays? [10+6]

5.    What do you mean by functions? Give the structure of the functions and explain about the arguments and their return values.    [16]

6.    (a) What is a structure? How is it declared? How it is initialized?

(b) Define a structure to represent a data. Use your structures that accept two different dates in the format mmdd of the same year. And do the following: Write a C program to display the month names of both dates.    [6+10]

7.    Write a program to convert a postfix expression to a fully parenthesized infix expression. For example, AB+ would be transformed in to (A+B) and AB+C- would be transformed into ((A+B)-C).    [16]

8. Write a bioperl script that runs clustalw on a given protein FASTA file (use the any protein file as example).    [16]

I B.Tech Supplementary Examinations, November 2009 COMPUTER PROGRAMMING FOR BIOTECHNOLOGISTS

(Bio-Technology)

Time: 3 hours    Max Marks: 80

Answer any FIVE Questions All Questions carry equal marks

1.    With a neat diagram explain the working of an execution unit of a CPU. [16]

2.    Give a neat sketch showing major components of Unix OS and explain functions of each of them.    [16]

3.    (a) C program contains the following declarations and initial assignments.

int i=8, j=5, k;

float x=0.005, y = - 0.01, z;

char a,b,c=d,d=c;

Determine the value of each of the following assignment expressions.

ⁱ.    ^{i -}=^(j>⁰⁾ ? ^j:0; y

ii.    a = (y>=0)? y : 0

iii.    i += (j-2);

iv. z = (j ==5) ? i : j

(b) What are the increment and decrement operators? Explain with proper example with differentiates prefix and postfix operations.    [4+6+6]

4.    (a) Write a C program to do Matrix Multiplications.

(b) Write in detail about one dimensional and multidimensional arrays. Also write about how initial values can be specified for each type of arrays? [10+6]

5.    Write a C program that uses a function to sort an array of integers.    [16]

6.    (a) What is a structure? How is it declared? How it is initialized?

(b) Define a structure to represent a data. Use your structures that accept two different dates in the format mmdd of the same year. And do the following: Write a C program to display the month names of both dates.    [6+10]

7.    Declare two queues of varying length in a single array. Write functions to insert and delete elements from these queues.    [16]

8.    Write a bioperl program that takes a sequence and finds homologs from SwissProt using remoteMast.    [16]

I B.Tech Supplementary Examinations, November 2009 ENGINEERING GRAPHICS ( Common to Civil Engineering, Mechanical Engineering, Mechatronics, Metallurgy & Material Technology, Production Engineering, Aeronautical Engineering and Automobile Engineering)

Time: 3 hours    Max Marks: 80

Answer any FIVE Questions All Questions carry equal marks

1.    Draw a Diagonal scale of R.F 3:100, showing meters, decimeters and centimeters and to measure up to 5 meters. Show the length of 3.69 meters on it. [16M]

2.    A circle of 60 mm diameter rolls on a horizontal line for half a revolution clock -wise and then on a line inclined at 60 degrees to the horizontal for another half, clock - wise. Draw the curve traced by a point P on the circumference the circle, taking the top most point on the rolling circle as generating point in the initial position.    [16M]

3.    The front view of a line AB measures 65 mm and makes an angle of 45 degrees with xy . A is in the H.P. and the V.T. of the line is 15 mm below the H.P. The line is inclined at 30 degrees to the V.P. Draw the projections of AB and find its true length and inclination with the H.P. Also locate its H.T.    [16M]

4.    A cone of base diameter 60 mm and altitude 75mm lies on the HP on one of its generators. The plan of the axis is inclined at 45⁰ to the VP. Draw its projections.

[16M]

5.    A cone of base diameter 50 mm and axis length 70 mm rests with its base on HP. A section plane perpendicular to V.P and inclined at 35^o to HP bisects the axis of the cone. Draw the development of the truncated cone.    [16]

6.    Draw the isometric projection of a Frustum of hexagonal pyramid, side of base 30 mm the side of top face 15mm of height 50 mm.    [16]

7.    Convert the orthogonal projections shown in figure1 below into an isometric view of the actual picture.    [16M]

Figure 1:

8. Draw the perspective view of a right regular hexagonal prism, edge of base 25 mm and 60 mm long lying on ground on one of its rectangular faces such that its axis is inclined at 30^o to the picture plane and one of its vertical edges touching the picture plane. The station point is 80 mm in front of the picture plane, and lies in a central plane bisecting the axis. The horizon is in the level of the rectangular faces of the prism.    [16M]

I B.Tech Supplementary Examinations, November 2009 ELECTRONIC DEVICES AND CIRCUITS ( Common to Electrical & Electronic Engineering, Electronics & Communication Engineering, Computer Science & Engineering, Electronics

& Instrumentation Engineering, Bio-Medical Engineering, Information Technology, Electronics & Control Engineering, Computer Science & Systems Engineering, Electronics & Telematics, Electronics & Computer Engineering and Instrumentation & Control Engineering)

Time: 3 hours    Max Marks: 80

Answer any FIVE Questions All Questions carry equal marks

1.    (a) Derive the expression for the electro static deflection sensitivity in the case of

CRT.

(b) Compare electro static and electro-magnetic deflection sensitivity in all respects.    [8+8]

2.    (a) Explain the following terms

i.    Storage time

ii.    Transitive time

iii.    junction capacitance.

(b) Calculate the dynamic forward and reverse resistance of a p-n junction diode when the applied voltage is 0.25V at T=300K Given lo = 2A.    [8+8]

3.    (a) What is a rectifier? Show that a PN diode acts as a rectifier.

(b)    Draw the circuit diagram for a half wave rectifier and explain its operation.

(c)    Explain the various types of filters used in power supplies.    [4+6+4]

4.    (a) Explain the mechanism of current flow in a PNP and NPN Transistor

(b) In a transistor operating in active region, although the collector Junction is reverse - biased, the collector current is quite large Explain.    [10+6]

5.    (a) What is load line?. Discuss how the load line can be drawn on the Ic-Vce

characteristics for a bipolar transistor amplifier.

(b)    What is 0 of a transistor?.

(c)    Draw a graph showing the variation of a with emitter current in a BJT.

[8+4+4]

6.    (a) Draw the circuit diagram of CE amplifier with emitter resistance and obtain its

equivalent hybrid model and derive expressions for Aj, R₁, A_V use approximate analysis.

(b) Determine A_v, A_j,R_i, R_O for CE amplifier using n-p-n transistor with hi_e = 1200Q h_re = 0 hf_e = 36 h_oe = 2 x 10^-6mho R_L = 2.5&Q R_S = 500Q (neglect the effect of biasing circuit)    [8+8]

7.    (a) Explain the concept of feedback as applied to electronic amplifier circuits.

What are the advantages and disadvantages of positive and negative feedback?

(b)    With the help of general block diagram explain the term feedback.

(c)    Define the following terms in connection with feedback.    [6+4+6]

i.    Return difference feedback.

ii.    Closed loop voltage gain.

iii.    Open loop voltage gain.

8.    (a) Derive an expression for frequency of oscillation of transistorized Colpitts os

cillator.

(b) A quartz crystal has the following constants. L=50mH, C1=0.02PF, R=500Q and C₂=12PF. Find the values of series and parallel resonant frequencies. If the external capacitance across the crystal changes from 5PF to 6PF, find the change in frequency of oscillations.    [8+8]

k k k k k

I B.Tech Supplementary Examinations, November 2009 INTRODUCTION TO CHEMICAL ENGINEERING (Chemical Engineering)

Time: 3 hours    Max Marks: 80

Answer any FIVE Questions All Questions carry equal marks

1.    (a) Explain the water softening process lime soda process.

(b) Explain the Faradys laws qualitatively and quauitatively.    [8+8]

2.    (a) Explain a combined detailed flow diagram of a process.

(b)    State the different forms of energy associated with mass.

(c)    Write the general energy balance equation for a flow system.    [4+4+8]

3.    Explain how pressure drops can be calculated for isothermal viscous flow? [16]

4.    Write about the different methods of feeding with figures?    [16]

5.    (a) Write the relation between individual and overall mass transfer coefficients

and also mention units of each.

(b) Briefly explain design of packed adsorption column.    [6+10]

6.    (a) With a neat sketch briefly explain the construction and working principle of

Bubble - Cap plate column.

(b) Give some industrially important packing materials used in packed column.

[12+4]

7.    (a) Explain the term distribution coefficient with respect to liquid-liquid extrac

tion, for both dilute solutions and concentrated solutions.

(b) Describe the multistage extraction process for separation of a liquid mixture consisting of two components A and B.    [6+10]

8.    Discuss in detail about the various types of adsorption equipment.    [16]

1 of 1

1

   (a) Find the radius of curvature of x = ae⁴ [sin 9 cos 9] , y = ae⁶ [cos d sin 9]

at 0 = 0.

(b) Trace the curve y² (a-x) = x³, (a>0)    [8+8]

2

   (a) Find the surface area of the solid obtained by revolving the cycloid

x = a(t + sin t), y = a(1 + cos t) about its base(x axis)

4 2

(b) By changing the order of integration, evaluate J f ex dxdy.    [8+8]

⁰ Vv

3

   (a) Form the differential equation by eliminating the arbitrary constant

secy + secx = c + x²/2.

(b)    Solve the differential equation:

(2y sin x + cos y ) dx = (x siny + 2 cosx + tany ) dy.

(c)    Find the orthogonal trajectories of the family: rⁿ sin n# = bⁿ.    [3+7+6]

4

   (a) Examine the convergence of

Y, Vn tan ^- 1 ( 1/ n³ )

(b) Examine the convergence of

L ^{[ (n} + ^{1) /nP ]    [8}+^8]