DADI INSTITUTE OF ENGINEERING & TECHNOLOGYdiet.edu.in/QuestionBanks/I BTECH I SEM/I_CSE A.pdf · DADI INSTITUTE OF ENGINEERING & TECHNOLOGY (Approved by A.I.C.T.E., New Delhi & Affiliated

DADI INSTITUTE OF ENGINEERING & TECHNOLOGY (Approved by A.I.C.T.E., New Delhi & Affiliated to JNTUK, Kakinada)

NAAC Accredited Institute

An ISO 9001:2008, ISO 14001:2004 & OHSAS 18001:2007 Certified Institute.

NH-5, Anakapalle – 531002, Visakhapatnam, A.P.

Phone: 08924-221111 / 221122/9963981111, www.diet.edu.in, E-mail: [email protected]

Department of COMPUTER SCIENCE & ENGINEERING

COMPUTER PROGRAMMING

Class – I CSE– I Semester (2018-19) Name of the Faculty-G.Pushpa

UNIT – I

1. (a) Explain About Various Input And Output Devices Of A Computer (5m)

(b). What Is Central Processing Unit (CPU) In A Computer? Explain About Various Components

And Their Functions of CPU. (5m)

2. (a) Explain About Algorithm And Its Characteristics (5m)

(b). Discuss The Steps In Program Development (5m)

3. (a) Explain About Object Oriented Programming Languages In Detail(5m)

(b) Discuss About Different Computer Languages with Examples (5m)

4. Explain the Steps in Software Development Process (10m)

5. (a) Explain About Application And System Software (5m)

(b). Explain About Procedure Oriented Programming Languages in Detail (5m)

UNIT – II

1. (a) List The Basic Data Types, Their Sizes And Range Of Values Supported By ‘C’ Language.

(b) What Do You Mean By Operator Precedence And Associativity? How One Can Override The

Precedence Defined By C Language? Give Illustrative Examples (5m)

2. (a) Explain All Arithmetic Operations Available In C-Language With Examples (5m)

(b) Explain About Type Conversion And Casting With Suitable Examples. Also Write The Type

Conversion Rules In C-Language (5m)

3. (a) Explain About Assignment Operator In C-Language With Suitable Examples (5m)

(b) Explain About Conditional Operator In C- Language With Suitable Examples (5m)

4. (a) Explain About The Various Unary Operators Available In C With Suitable Examples (5m)

(b) Explain About The Various Logical Operators Available In C-Language With Example(5m)

5. (a) Explain About The Various Relational And Equality Operators Available In C-Language With S

Suitable Examples (5m)

(b) Write A Constant? Explain The Different Constants Available In C-Language With Suitable

Examples (5m)

UNIT – III

1. (a)What Is Meant By Type Conversion? Why Is Necessary? Explain About Implicit and Explicit

Type Conversion with Examples.

(b). Explain Different Looping Statements With Syntax And Examples (5m)

mailto:[email protected]

2. (a) Differentiate Between Else-If And Switch? Explain With An Example? (5m)

(b) Write A C-Program To Swap The Given Two Numbers Without Using A Third Variable (5m)

3. (a) What Is The Purpose Of Do-While And While Loops? Discuss About Their Usage. Distinguish

Between Both of Them (5m)

(b) An Integer Is Divisible By 9 If The Sum Of Its Digits Also Divisible By 9. Write A C Program(5m)

4. (a) Write A Program To Verify Whether The Given Number Is Prime Number Or Not? (5m)

(b) Write A Program To Find The Single Digit Sum Of A Given Number (5m)

5. Explain The Switch –Case-Default Control Statements With Various Options Along With Suitable

Examples (10m)

UNIT – IV

1. (a) Explain The Terms User Defined Functions And Predefined Functions(5m)

(b) Differentiate Between Iteration And Recursion (5m)

2. (a) Explain The Auto And Register Storage Classes With Suitable Examples(5m)

(b) Explain The Static And Extern Storage Classes With Suitable Examples(5m)

3. (a) Explain About Recursive Functions With Suitable Examples (5m)

(b) Write A C Program To Find Factorial Of A Given Number Using Recursive Functions(5m)

4. (a) Write A Program To For Tower’s Of Hanoi Using Recursion? (5m)

(b) Define A Function For Determining Whether A Given Character Is A Vowel Or Not(5m)

5. (a) Write A Program To Find Largest Of Three Given Numbers Using Functions? (5m)

(b) Explain About Function Prototypes And Function Scope Rules With Suitable Examples? (5m)

UNIT – V

1. (a) Write A Program To Check Whether The Given String Is Palindrome Or Not? (5m)

(b) What Is An Array? How To Initialize 1D And 2D Arrays? Discuss About The Advantage And

Disadvantages Of Arrays (5m)

2. (a) Write A Program To Find The Biggest And Smallest Elements Of An Array With Their

Positions?5m)

(b) Explain About 2-Dim Array Initialization In C-Language With Suitable Examples(5m)

3. (a) Write A Program To Traverse A Single Dimensional Array (5m)

(b) Write A C Program For Matrix Multiplication With Sufficient Conditions(5m)

4. (a) Write A Program To Create An Array Of 10 Cells. Accept The Data Into The First 9 Cells And

Store The Sum In The 10th

Cell Using Functions (5m)

(b). Write A Program To Traverse A Two Dimensional Array (5m)

5. Explain The Following String Functions With Suitable Examples Or Programs

Strcat () , Strcmp(), Strcpy(), Strlen(), Strrev(). (10 M)

UNIT – VI

1 .(a) Write About Call By Value Mechanism With Suitable Example? (5m)

(b). Write About Call By Reference Mechanism With Suitable Example? (5m)

2. (a) Explain About Malloc() And Calloc() Functions With Suitable Example(5m)

(b). Explain About Realloc() And Free() Functions With Suitable Example(5m)

3. (a) Explain About Dangling Memory And Memory Leak With Suitable Examples (5m)

(b). Write A C Program To Explain The Concept Of Pointer Arithmetic 5m)

4. (a) Define A Structure In C Language? Explain The Storage Of Structure Elements In Memory(5m)

(b). Define A Union In C Language? Explain The Storage Of Union Elements In Memory (5m)

5. (a) Explain About Fread() And Fwrite() Functions With Suitable Example? (5m)

(b).Write A Program To Merge Any Two Files? (5m)

6. (a) Discuss Various Valid Arithmetic Operations That Can Be Performed On Pointers In C.

(b) Explain The Following Functions In File Operations:

(I) Getw( ) (Ii) Putw() (Iii) Fscanf( ) (Iv) Fprintf( )






I B.Tech I SEM QUESTION BANK

Branch : CSE-A Faculty : B.Usha Rani

Asst.professor

Sub: ENGINEERING DRAWING

UNIT-1

1.(a) Draw a vernier scale of RF=2:1 to show centimeters and millimeters and long enough to

measure up to 7cm. Measure a distance of 4.25cm on the scale. (b) Draw an Octagon given the length of side 25mm

2.(a) Construct a diagonal scale to read up to 1/100th

of a meter given RF=1/50 and to measure up to 7m. Indicate a distance of 5.45m.

(b) Construct a regular polygon of any number of sides, given the length of its sides equal to 25mm.

3.(a) The foci of an ellipse are 90mm apart and the minor axis is 72mm long. Determine the

length of the major axis. Construct the ellipse. Draw a tangent to the ellipse from any point.

(b) Construct a regular hexagon of side 28mm when one side is horizontal.

4. The major axis of an ellipse is 150mm long and the minor axis is 100m m long. Find the foci and draw the ellipse by arcs of circles method. Draw a tangent to the ellipse at a point on it 25mm above the major axis.

5 .(a) The area of a field is 50000 sq m. The length and the breadth of the field, on the map is 10

cm and 8 cm respectively. Construct a diagonal scale which can read up to one metre.

Mark the length of 235 meter on the scale. What is R.F of the scale? (b) The foci of an ellipse are 90 mm apart and the minor axis is 72 mm long. Determine the

length of the major axis. Construct the ellipse. 6. (a) Construct an ellipse when the major axis is 120 mm and the distance between the foci is

108 mm. Determine the length of the minor axis. (b) Draw a vernier scale of R.F = 1/25 to read centimeters up to 4 meters and on it, show lengths representing 2.39 m and 0.91 m.


UNIT-II 1.(a) Draw the orthographic projections of the following points:

(i) A, 20mm above HP and 30mm behind VP

(ii) B, 25mm below HP and 25mm in front of VP

(iii) C, 25mm below HP and 30mm behind VP

(iv) D, 30mm below HP and in VP (b) The top view of a 75mm long line measures 55mm. The line is in the VP; it’s one

end being 25mm above the HP. Draw its projections.

2. (a) A line MN 50mm long is parallel to VP and inclined at 300 to HP. The end M is

20mm above HP and 10mm in front of VP. Draw the projections of the line. (b) A point P is 20mm below HP and lies in the third quadrant. Its shortest distance from xy

is 40mm. Draw its projections. 3. A line AB 50mm long is perpendicular to VP and parallel to HP. Its end A is 20mm in front of VP and the line is 40mm above HP. Draw the projections of the line.

(i) A, 25mm above H.P and 35mm in front of V.P

(ii) B, 25mm above H.P and 40 mm behind V.P

4. (a) The front view of a line inclined at 300 to the V.P is 65 mm long. Draw the

projections of the line, when it is parallel to and 40 mm above the H.P, its one end being 30 mm in front of the V.P. (b) Mark the projections of the following points on a common reference line,

(i) C, 30mm below H.P and 45 mm behind V.P

(ii) D, 30 mm below H.P and 40 mm in front V.P 5. Two pegs fixed on a wall are 4.5 metres apart. The distance between the pegs measured parallel to

the floor is 3.6 metres. If one peg is 1.5 m above the floor, find the height of the second peg and the inclination of the line joining the two pegs with the floor.

6. (a) A line PQ 40 mm long is parallel to VP and inclined at an angle of 300to HP. The lower end P

is 15 mm above HP and 20 mm in front of VP. Draw the projections of the line.

(b) Draw the projections of a line EF 40 mm long parallel to HP and inclined at 350to VP. E is 20

mm above HP and 15 mm in front of VP.

UNIT-III

1. A line PQ, 100 mm long, is inclined at 450 to the H.P and at 30

0 to the V.P. Its end P is in

the second quadrant and Q is in the fourth quadrant. A point R on PQ, 40 mm from P is in both the planes. Draw the projections of PQ.

2. A line AB, 90 mm long, is inclined at 450 to the H.P and its top view makes an angle of 60

0 with the

V.P. The end A is in the H.P and 12 mm in front of the V.P. Draw its front view and finds its true inclination with the V.P.

3. The top view of a line is 65mm long and is inclined at 300 to the reference line. One end

is 20mm above HP and 10mm in front of VP. The other end is 60mm above HP and in front of VP. Draw the projections and find the true length of the line and its true inclinations to HP and VP.

4. A line AB, 50mm long, has its end A is both the HP and the VP. It is inclined at 300 to

the HP. and at 450

to the VP. Draw its projections.

5. A line AB 65mm long, has its end A 20 mm above HP and 25 mm in front of VP. End B

is 40 mm above HP and 65 mm in front of VP. Draw the projections of AB. Find its inclinations with HP and VP.

6. A line CD measuring 80 mm is inclined at an angle of 30

0to HP and 45

0 to VP. The

point C is 20 mm above HP and 30 mm in front of VP. Draw the projections of the straight line

UNIT-IV

1. A regular hexagonal lamina of 26mm side has a central hole of 30mm diameter. Draw the

front and top views when the surface of the lamina is inclined at 450 to HP. A side of

lamina is inclined at 350 to VP.

2. Draw the projections of a pentagonal sheet of 26mm side, having its surface inclined at

300 to VP. It’s one side is parallel to VP and inclined at 45

0 to HP.

3. A thin rectangular lamina EFGH of 60mm length and 36mm width is inclined at an angle

of 450 to VP. Its longer edge is making an angle of 30

0 with VP. Draw the projections.

4. A 600

set-square of 125 mm longest side is so kept that the longest side in the H.P

making an angle of 300

with the V.P and the set-square itself inclined at 450

to the H.P.

Draw the projections of the set- square.

5. Draw the projections of the circle of 50 mm diameter resting in the H.P on a point A on

the circumference, its plane inclined at 450 to the H.P and

(a) The top view of the diameter AB making 300

angle with the V.P

(b) The diameter AB making 300

angle with the V.P

6. Draw the projections of a regular hexagon of 25 mm side, having one of its sides in the

H.P and inclined at 600

to the V.P and its surface making an angle of 450with the H.P.

UNIT-V

1. A cylinder of diameter of base 50mm and height 60mm is suspended freely from a point on its circular rim. The projection of the axis on HP is parallel to the XY line. Draw the projections of the cylinder.

2. A pentagonal pyramid of base edge 25mm and altitude 60mm rests on one side of base on

HP such that the highest base corner is 20mm above HP. Its axis is parallel to VP. Draw its projections.

3. Draw the projections of a cylinder 75mm diameter and 100 mm long, lying on the ground with its axis inclined at 30

0 to the V.P and parallel to the ground.

4. Draw the projections of a cone, base 75 mm diameter and axis 100 mm long, lying on the

H.P on one of its generators with the axis parallel to the V.P.

5. A hexagonal pyramid side of base 25 mm axis 50 mm long lies with one of its

rectangular faces on the H.P and its axis is parallel o he V.P. Draw its projections. 6. A tetrahedron of 40 mm side rests with one of its edges on HP and

perpendicular to VP. The triangular face containing that edge is inclined at 300

to HP. Draw its projections.

UNIT-VI 1. Draw the isometric view as shown in fig

(Note: all dimensions are in mm)

2. Draw (i) Front View (ii)) Side View (iii) Top View as shown in fig


3. Draw (i) Front View (ii) Top View (iii) Side View as shown in fig


4. Draw the isometric view as shown in fig


5. Draw the isometric view as shown in fig

(Note: all dimensions are in mm) 6. Draw (i) Front View (ii) Top View (iii) Side View, as shown in fig.


7. Draw (i) Front View (ii) Side View from the right (iii) Top View as shown in fig


8. Draw the isometric view as shown in fig.


DADI INSTITUTE OF ENGINEERING & TECHNOLOGY (Approved by A.I.C.T.E., New Delhi& Affiliated to JNTUK, Kakinada)

NAAC Accredited Institute An ISO 9001:2008, 14001:2004 & OHSAS 18001:2007 Certified Institute

NH–5, Anakapalle, Visakhapatnam–531002, Andhra Pradesh

1

English QUESTION BANK FOR I B.TECH ECE

Unit-I

1) What is meant by “Human Resource”? Give examples from various professions. (5M)

2) What exactly is the problem with Mr. Neave‟s ideal family? (3M)

3) Fill the blank with the suitable verb.(2M)

a) The train had________(leave) before he reached the railway station.

b) She ______ (read) since morining

1) Write in detail how Srinivasa Ramanujan is an invaluable human resource, particularly to the

field of Mathematics. (5M)

2) What is the underlying irony in the story, „An Ideal Family‟? (3M)

3) Fill the blank with the suitable verb. (2M)

a) Summer________(come) after winter.

b) Malathi ______ (pay) the fee before the teacher announced.

1) Why human resource is considered invaluable? (5M)

2) Do you think Mr. Neave‟s family is an ideal family? Why/why not? (3M)


a) They______ (watch) T.V when the postman came.

b) She_____ (see) the movie many times.

1) How is human resource the backbone of every industry?5M)

2) What is the shadowy meaning Mr.Neave has at the end of the story? (3M)


a) She_____(write) a letter when her father came.

b) Kiran_______ (go) to the canteen just now.

1) Define the role of human resources in any industry. How can this resource strengthen the

industry? (5M)

2) Why do people call Mr.Neave‟s family an ideal family? (3M)


a) She______ (wait) for the principal for two hours when he came.

b) Kiran_____ (come) to the college on foot.




2

1) Justify Indian government‟s decision of celebrating 22 December as National Mathematics Day.

(5M)

2) Who do you think is the cause for conditions in Mr. Neave‟s family? Justify your answer with

suitable instances from the text. (3M)


a) They _____ (visit) Taj Mahal one year ago.

b) Krishna_______ (loss) the key just now.

Unit -II

1) You are an official from the Finance Department and are not very enthusiastic about

spending money on road safety schemes. You feel that a few road safety posters on the

main roads are sufficient. Explain your views to support your statement. (5M)

2) What is the central theme of the story, „War‟? (3M)

3) Write the meanings of the following phrases. (a) backdrop of pines (b) mists of the fall

morning. (2M)

1) You are an official from the Transport Department and want to spend money on

improving road intersections and on a new bypass. Explain your views to support your

statement. (5M)

2) What are the different views that passengers articulate regarding war? (3M)

3) Write the meanings of the following phrases. (a) checkerboard of farms (b) white clouds

of bloom (2M)

1) You are an official from the police department. You want to double the number of traffic

policemen so that laws can be enforced with on-the-spot fines. Explain your views to

support your statement. (5M)

2) What is the message that the author wishes to convey through this story? (3M)


morning.(2M)

1) You are a representative of the Citizen‟s Welfare Association, and would like to

introduce a road safety training week in all school, colleges, factories and offices.

Explain your views to support your statement. (5M)

2) What are the fat man‟s feelings towards sending children to war? (3M)




3


of bloom(2M)

1) Explain the reasons why there is a need to enforce traffic rules and regulations

strictly.(5M)

2) Summarize the story, „War‟. (3M)


morning. (2M)

1) Traffic hazards are increasing day after day. Suggest some ways by which these may be

countered. (5M)

2) Why was the woman who entered the carriage upset? How are the other passengers

affected by war? (3M)


of bloom(2M)

Unit-III

1) Does consumption of bio-mass affect forest resources? How? (5M)

2) What is the unexpected twist in the story, „Verger‟? (3M)

3) Write the synonyms for (a) Stringent (b) Hazard (2M)

1) It is sometime towards the end of the twenty-first century. Imagine you are living in an

Indian village. Write a paragraph describing what the village looks like under the impact

of technology over the years. (5M)

2) Explain the character of Albert Foreman. (3M)

3) Write the synonyms for (a) change (b) Hazard (2M)

1) What is the advantage of the new „Print and copy online‟ service? (5M)

2) Narrate the discussion between bank manager and Foreman. (3M)

3) Write the synonyms for (a) educate (b) mysterious (2M)

1) Elaborate the statement- „Mass production or production by the masses. (5M)




4

2) How does Mr. Foreman overcome all his obstacles in life? (3M)

3) Write the synonyms for (a) danger (b) advantage (2M)

1) Write the benefits of technology or on the problems created by it. (5M)

2) What is the central theme of the story, „Verger‟? (3M)

3) Write the synonyms for (a) direct (b) wander (2M)

1) Modern technology is a friend or foe. Explain with reasons? (5M)

2) How does Foreman expand his business? (3M)

3) Write the synonyms for (a) capital (b) urge (2M)

Unit-IV

1) Write a short note on Pedal Power. (5M)

2) Describe Mriganko Babu‟s reaction to the scarecrow? (3M)

3) Write the noun forms of (i) electricity (II) ferment.

1) Why is such intensive research being carried out to discover viable alternative sources of

energy? (5M)

2) Who was Mriganko Shekhar Mukhopadhyay? (3M)

3) Write the noun forms of (i) compose (II) protect.

1) List the problems involved in producing and using electricity in India. (5M)

2) Who was the scarecrow? (3M)

3) Write the noun forms of (i) construct (II) ferment.

1) You are a journalist writing a feature article on a village that makes use of alternative

energy sources. The people of the village are proud of their self-reliance. Prepare a list

of questions to ask the sarpanch of the village as well as a few other villagers. (5M)

2) Justify the title of the story „The Scarecrow”. (3M)

3) Write the noun forms of (i) pollute (II) destroy




5

1) What are DRE mini-grids? Describe some of its features and explain how they are

different from commercial grids. (5M)

2) Narrate the incident that occurred between Abhiram and Mriganko Babu? (3M)

3) Write the noun forms of (i) conserve (II) irrigate.

1) Write a short note on Solar Energy. (5M)

2) How did Mriganko Babu pass time while waiting for his driver? (3M)

3) Write the noun forms of (i) absorb (II) stimulate.

Unit- V

1) You and Student B live next door to each other. B is fond of dogs and has an Alsatian as

a pet. You want to tell B that it is not good to have pets in the house. Think of the points

you can make. (5M)

2) What is the message that the author conveys through the text- A Village Lost to the

Nation‟? (3M)

3) Write the synonyms for (i) annoying (ii) incessantly (2M)

1) Write a paragraph on Global warming. (5M)

2) What were the feelings of the author‟s parents regarding their village? (3M)

3) Write the synonyms for (i) catalyze (ii) resist(2M)

1) Humans are responsible for the destruction of animal species, both directly and

indirectly. Explain the statement. (5M)

2) How are the villages affected by the Hirakud Dam? (3M)

3) Write the synonyms for (i) invade (ii) umpteen(2M)

1) Write a paragraph on deforestation. (5M)

2) What were the people forced to do because their homes were submerged? (3M)

3) Write the synonyms for (i) yell (ii) whisper(2M)

1) In what ways are birds useful to humans? In what ways are they harmful?

2) What were the author‟s feelings for his lost home? (3M)




6

3) Write the synonyms for (i) teach (ii) danger(2M)

1) What are the efforts being made at present to preserve wildlife? (5M)

2) What is the theme of the passage- „A Village Lost to the Nation‟? (3M)

3) Write the synonyms for (i) build (ii) copious(2M)

Unit -VI

1) Imagine that you are the chief engineer of a company. Write a set of safety measures to be

adopted to avert industrial accidents. (5M)

2) What is Martin Luther King‟s second achievement according to the author? (3M)

3) Write the antonyms for (i) aggressive (ii) recluse (2M)

1) What are the objectives of training to employees? (5M)

2) What are the author‟s views on racism? (3M)

3) Write the antonyms for (i) collect (ii) diurnal (2M)

1) Write a paragraph about the importance of computer training today. (5M)

2) What is James Baldwin‟s view about African history? (3M)

3) Write the antonyms for (i) gather (ii) vanish (2M)

1) Describe the process of sedimentation. (5M)

2) According to author, Martin Luther King achieved two things. What is his first

achievement? (3M)

3) Write the antonyms for (i) tamed (ii) destroy (2M)

1) What is the need for training (i) a new employee, and (ii) an employee already in service?

(5M)

2) In what way did Mahatma Gandhi influence Martin Luther King? (3M)

3) Write the antonyms for (i) slimy (ii) detail (2M)

1) Write the unspoken rules of civility at the workplace. (5M)

2) How did Martin Luther King embrace his African roots? (3M)




7

3) Write the antonyms for (i) emit (ii) accessible (2M)






----------------------------------------------------------------------------------------------------------------------------- -----------

SUBJECT : MATHEMATICS-II YEAR : I SEM : I

NAME OF THE FACULTY : K MURALI BRANCHS: CSE- A

UNIT-I

1. (a) Find a real root of 𝑥3 − 4𝑥 − 9 = 0 , using Bisection method up to 4 stages. 5M

(b) Find a real root of the equation 𝑥𝑒𝑥 = 2 By using Regula-Falsi method 5M

2. (a) Using Regula-Falsi method, find the root of the equation 𝑥 log10 𝑥 = 1.2 5M

(b) Find the root of the equation 𝑥 log10 𝑥 = 1.2 by using Newton-Rapson method. 5M

3. (a) Using Newton-Raphson method, find the root of the equation x+log10 x =3.375 correct to four decimal

Places. 5M

(b) Find a real root of the equation cos 𝑥 − 𝑥2 − 𝑥 = 0 , using Newton- Raphson method. 5M

4. (a) Solve the system of equations by Newton Raphson method 𝑥2 + 𝑦2 − 1 = 0 𝑎𝑛𝑑 𝑦 − 𝑥2 = 0 5M

(b) Solve x3 − 2x − 5 = 0,for a positive root by iteration method. 5M

5. (a) Using Newton – Raphson method, find a root of the equation 2x- 3sinx =5 , near x=5

correct to three decimal places. 5M

(b) Find the real root of 2𝑥 − log 𝑥 = 6 correct to three decimal places, using Regula falsi method. 5M

6. (a) Solve the system of equations by Newton Raphson method 3𝑦𝑥2 − 10𝑥 + 7 𝑎𝑛𝑑 𝑦2 − 5𝑦 + 4 = 0

5M

(b) By using Newton-Raphson method, find the root of 𝑥4 − 𝑥 − 10 = 0, correct to three Decimal places.

5M


UNIT-II 1. (a) Find f (2.5) using Newton’s forward formula for the following table 5M

(b) The population of a town according to census is given below. Estimate the population of

a town for the year 1895. 5M

2. (a) Using Lagrange’s interpolation formula find the value of y(12) from the data 5M

(b) By using Lagrange’s interpolation formula, find a polynomial to the data. 5M

x 0 1 3 4

f(x) -12 0 6 12

3. (a) Given that f(6500) = 80.6084, f(6510) = 80.6846, f(6520) = 80.7456, f(6530) = 80.8084,

Find f(6526) using Newton’s backward interpolation formula. 5M

(b) Using a forward difference formula, find y(5) from the given table 5M

4. (a) Use Gauss backward interpolation formula to find f(32) given that

f (25) = 0.2707, f (30) = 0.3027, f (35) = 0.3386, f (40) = 0.3794

(b) Use Newton’s forward interpolation formula to find f(32) given that 5M

f (25) = 0.2707, f (30) = 0.3027, f (35) = 0.3386, f (40) = 0.3794.

5. (a) 𝑃𝑟𝑜𝑣𝑒 𝑡𝑕𝑎𝑡 1 (1 + ∆)(1 − ∇) = 1 (2) Evaluate ∆𝑛(𝑒𝑎𝑥+𝑏) 5M

(b) Given that y(3) = 6, y(5) = 24, y(7) = 58, y(9) = 108, y(11) = 174, find the polynomial 5M

using Lagrange’s formula.

6. (a) Prove that (i) 𝐸∇ = ∇𝐸 = ∆ (ii) 𝛿𝐸1

2 = ∆ . 5M

(b) If the interval of differencing is unity, find ∆(ex log2x) 5M

x 0 1 2 3 4 5

y 0 1 8 21 72 94

Year ( x) 1871 1881 1891 1901 1911

Population( y) 146 166 181 193 201

x 5 7 9 13

y 11 13 18 27

x 1 6 11 16 21 26

y 5 10 14 18 24 32

UNIT-III

1. (a) Using modified Euler method solve numerically the equation 2d y

x yd x

, with y(1)= 1

to find y(1.2). 5M

(b) Given s ind y

x yd x

, y(0) = 1, compute y(0.2) and y(0.4) using Euler’s modified method. 5M

2. (a) / 2

1 , (0 ) 1y x y y using Taylors method up to 3rd degree term and compute y(0.1). 5M

(b) Solve , 𝑦′ = 𝑦 − 𝑥2 , 𝑦 0 = 1 using Picard’s method up to 4th

approx. 5M

3. (a) Find y(0.1), using 4th

order Runge – Kutta method given that 𝑦/ = 𝑥 + 𝑥2𝑦 , 𝑦 0 = 1 5M

(b) Solve 𝑦′ = 𝑦 + 𝑥 , y(0) = 1using Picard’s method up to third approximation and hence

find the value of y(0.1). 5M

4. (a) Estimate y(0.2), given 𝑦′ = 3x + y , y(0) = 1 using Runge-Kutta 4th order . 5M

(b) Evaluate y(0.2) and y(0.4) correct to three decimals by Taylors method if y(x) satisfies

𝑦/ = 1 − 2𝑥𝑦 ,𝑦 0 = 0 5M

5. (a) Evaluate (𝑠𝑖𝑛𝑥 − 𝑙𝑜𝑔𝑥 + 𝑒𝑥) 𝑑𝑥1.4

0.2 by using Simpson’s 3/8

th rule 5M

(b) Evaluate 𝑑𝑥

1+𝑥

1

0 by using Trapezoidal rule. 5M

6. (a) Evaluate 𝑒−𝑥2𝑑𝑥

0.6

0 by using Simpson’s 1/3

rd rule , taking seven ordinates. 5M

(b) A cu.rve is observed to pass through the points given in the following table 5M

x 1.0 1.5 2.0 2.5 3.0 3.5 4.0

y 2 2.4 2.7 2.8 3 2.6 2.1

By using simpson’s rule find the area bounded by the curve and x axis between x=1 and x=4

UNIT IV

1. (a) Obtain the Fourier series for 𝑓 𝑥 = 𝑒𝑥 in the interval 0 < 𝑥 < 2𝜋. 5M

(b) Find a Fourier series to represent the function f(x) = 𝑥 − 𝑥2 from 𝑥 = −𝜋 𝑡𝑜 𝑥 = 𝜋 5M

2. (a) Expand 𝑓 𝑥 = 𝑥 sin𝑥 as a Fourier series in the interval −𝜋 < 𝑥 < 𝜋. 5M

And show that 1

1.3−

1

3.5+

1

5.7−

1

7.9 … . =

𝜋−2

4

(b) Find the Fourier series of 𝑓 𝑥 = 0 ,−𝜋 < 𝑥 < 0𝜋

4 , 0 < 𝑥 < 𝜋

5M

3. (a) Obtain the Fourier series to represent 𝑓 𝑥 = 1

4 𝜋 − 𝑥2 , 0 < 𝑥 < 2𝜋 . 5M

(b) Find the Fourier series of the periodic function defined as 𝑓 𝑥 = −𝜋 , − 𝜋 < 𝑥 < 0𝑥 , 0 < 𝑥 < 𝜋

Hence , deduce that 1

12 +1

32 + 1

52 + … =𝜋2

8 5M

4. (a) Find Fourier cosine series of the function 𝑓 𝑥 = sin𝑥 𝑖𝑛 0,𝜋 and hence show that

1

4𝑛2−1 =

1

2∞𝑛=1 5M

(b) Find the half range sine series of 𝑓 𝑥 =

𝜋

2 , 0 < 𝑥 <

𝜋

2

𝜋 − 𝑥 , 𝜋

2< 𝑥 < 𝜋

5M

5. (a) Find the Fourier series of the function 𝑓 𝑥 = 0 , 0 < 𝑥 < 1

𝑥2 , 1 < 𝑥 < 2 5M

(b) Find Fourier cosine series for 𝑓 𝑥 = 𝑥 𝑥 − 2 , 𝑖𝑛 0 ≤ 𝑥 ≤ 2 and hence find the sum of the

series

1

12 −1

22 + 1

32 −1

42 + ⋯ 5M

6. (a) Find the Fourier series of periodicity 2 for 𝑓 𝑥 = 𝑥 + 𝑥2 , 𝑖𝑛 0 < 𝑥 < 2 5M

(b) Find the half range cosine series of 𝑓 𝑥 = 1, 0 < 𝑥 <

𝜋

2

−1, 𝜋

2< 𝑥 < 𝜋

5M

UNIT -V

1. (a) Using the method of separation of variables, solve 𝜕𝑢

𝜕𝑥= 2

𝜕𝑢

𝜕𝑡+ 𝑢 𝑤𝑕𝑒𝑟𝑒 𝑢 𝑥, 0 = 6 𝑒−3𝑥 .5M

(b) Using the method of separation of variables, solve

4 𝜕𝑢

𝜕𝑥+

𝜕𝑢

𝜕𝑦= 3𝑢,𝑔𝑖𝑣𝑒𝑛 𝑡𝑕𝑎𝑡 𝑢(0,𝑦) = 3 𝑒−𝑦 − 𝑒−5𝑦 5M

2. A tightly stretched string with fixed end points x=0 and x=1is initially in a position given by

𝑦 = 𝑦0 𝑠𝑖𝑛3 𝜋𝑥

𝑙 . If it is released from this position, find the displacement y(x, t). 10M

3. Solve the equation 𝜕𝑢

𝜕𝑡=

𝜕2𝑢

𝜕𝑥 2 𝑤𝑖𝑡𝑕 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 𝑢 𝑥 , 0 = 3 sin 𝑛𝜋𝑥 ,𝑢 0 , 𝑡 =

0 𝑎𝑛𝑑 𝑢 1 , 𝑡 = 0,𝑤𝑕𝑒𝑟𝑒 0 < 𝑥 < 1 , 𝑡 > 0. 10M

4. Solve the laplace equation 𝜕2𝑢

𝜕𝑥 2 + 𝜕2𝑢

𝜕𝑦 2 = 0 subject to the conditions 𝑢 0 , 𝑦 = 𝑢 𝑙 , 𝑦 =

𝑢 𝑥 , 0 = 0 𝑎𝑛𝑑 𝑢 𝑥 , 𝑎 = 𝑠𝑖𝑛 𝑛𝜋𝑥/𝑙 . 10M

5. A string of length 100 cm is tightly stretched between x=0 and x=100 and is displaced from it

equilibrium positions by imparting each of its points an intial velocity given by

𝑔 𝑥 = 𝑥 , 𝑖𝑓 0 ≤ 𝑥 ≤ 50

100 − 𝑥 , 𝑖𝑓 50 ≤ 𝑥 ≤ 100

Then find the displacement at any subsequent time . 10M

6. Find the solution of the wave equation 𝜕2𝑢

𝜕𝑡 2 = 𝑎2 𝜕2𝑢

𝜕𝑥 2 , if the intial defiection is

𝑓 𝑥 =

2𝑘

𝑙 𝑥 , 𝑖𝑓 0 < 𝑥 <

𝑙

22𝑘

𝑙 𝑙 − 𝑥 , 𝑖𝑓

𝑙

2< 𝑥 < 𝑙

and intial velocity equal to 0. 10M

UNIT VI

1. (a) Using Fourier integral , Show that cos 𝜆𝑥

𝜆2+𝑎2

∞

0=

𝜋

2𝑎 𝑒−𝑎𝑥 ,𝑎 > 0 , 𝑥 ≥ 0 . 5M

(b) Find the Fourier transform of 𝑓 𝑥 = 𝑥 , 𝑖𝑓 𝑥 ≤ 1

0 , 𝑖𝑓 𝑥 > 1 5M

2. (a) Find the Fourier transform of 1

𝑥 5M

(b) Find the Fourier sine transform of 𝑒−𝑎2𝑥2

5M

3. (a) Find the Fourier cosine transform of 1

𝑎2+𝑥2. 5M

(b) Find the Fourier sine and cosine transforms of 2𝑒−5𝑥 + 5𝑒−2𝑥 5M

4. (a) Find the Fourier sine transform of 𝑓 𝑥 = 𝑒−𝑎𝑥 ,𝑎 > 0 and deduce the inversion formula.5M

(b) Find the inverse Fourier sine transform of 𝑓 𝑥 𝑜𝑓 Fs(p) = 𝑝

1+𝑝2. 5M

5. (a) Find the Fourier Cosine transform of 𝑒−𝑎𝑥

𝑥 5M

(b) Find the inverse Fourier sine transform 𝑓 𝑥 𝑜𝑓 Fs(p) = 𝑒−𝑎𝑝

𝑝; and show that Fs

-1(1/p) =1. 5M

6. (a) Prove that 𝐹 𝑥𝑛 𝑓(𝑥) = (−𝑖)𝑛 𝑑𝑛

𝑑𝑝 𝑛 𝐹 𝑝 . 5M

(b) Prove that 𝐹 𝑑𝑛

𝑑𝑥 𝑛 𝑓(𝑥) = −𝑖𝑝 𝑛 𝐹 𝑝 .𝑤𝑕𝑒𝑟𝑒 𝐹 𝑓 𝑥 = 𝐹(𝑝). 5M






QUESTION BANK

SUBJECT: MATHEMATICS-I

CLASS: B.TECH YEAR/ SEM: I/I BRANCH: CSE-A & B

NAME OF THE FACULTY: B.CH.K.PREETHI, ASST.PROF , DEPARTMENT OF MATHEMATICS

UNIT- I

1.(a) Solve the D.E 𝒙𝟐 + 𝒚𝟐 𝒅𝒙 + 𝟐𝒙𝒚 𝒅𝒚 = 𝟎. 𝟓𝑴

(b) Find the Orthogonal trajectories of the family of circles 𝒙𝟐 + 𝒚𝟐 + 𝟐𝒇𝒚 + 𝟏 = 𝟎, 𝒇 being

the parameter. 𝟓𝑴

2.(a) Solve the D.E 𝒚 𝒙𝟒𝒚𝟒 + 𝒙𝟐𝒚𝟐 + 𝒙𝒚 𝒅𝒙 + 𝒙 𝒙𝟒𝒚𝟒 − 𝒙𝟐𝒚𝟐 + 𝒙𝒚 𝒅𝒚 = 𝟎 𝟓𝑴

(b) Find the orthogonal trajectory of 𝒓 = 𝒂 𝒔𝒆𝒄𝜽 + 𝒕𝒂𝒏𝜽 𝟓𝑴

3.(a) Solve 𝒅𝒚

𝒅𝒙+ 𝒙𝒔𝒊𝒏𝟐𝒚 = 𝒙𝟑𝒄𝒐𝒔𝟐𝒚 . 𝟓𝑴

(b) Find the orthogonal trajectory of 𝒓𝟐 = 𝒂𝟐𝒔𝒊𝒏𝟐𝜽 𝟓𝑴

4.(a) The temperature of a cup of coffee is 𝟗𝟐°𝑪, when freshly poured the room temperature

being 𝟐𝟒°𝑪. In one minute it was coaled to 𝟖𝟎°𝑪. How long a period

must elapse, before the temperature of the cup becomes 𝟔𝟓°𝑪. 𝟓𝑴

(b) The number of N of bacteria in a culture grew at a rate proportional to N. The value of N was initially 100 and increased to 332 in one hour. What was the value of N after 3/2 hours? 𝟓𝑴

5.(a) Find the orthogonal trajectory of 𝒓 =𝟐𝒂

𝟏+𝒄𝒐𝒔𝜽 . 𝟓𝑴

(b) Suppose that an object is heated to 𝟑𝟎𝟎° 𝑭 and allowed to cool in a room maintained at

𝟖𝟎° 𝑭. If after 10 minutes, the temperature of the object is 𝟐𝟓𝟎° 𝑭, what will be its temperature after 20 minutes? 𝟓𝑴 6(a) Solve the D.E 𝒙𝟑𝒚𝟐 + 𝒙 𝒅𝒚 + 𝒙𝟐𝒚𝟑 − 𝒚 𝒅𝒙 = 𝟎. 𝟓𝑴 (b) Write (i) RC circuit (ii) Newton’s law of cooling. 𝟓𝑴


UNIT-II

1. (a) Solve 𝑫𝟐 + 𝟗 𝒚 = 𝒄𝒐𝒔𝒆𝒄 𝟑𝒙 by the method Variation of parameters. 𝟓𝑴

(b) Solve 𝑫𝟐 + 𝟏 𝒚 = 𝒔𝒆𝒄𝟐𝒙 by the method Variation of parameters. 𝟓𝑴 2. S olve 𝑫𝟑 + 𝟏 𝒚 = 𝒄𝒐𝒔 𝟐𝒙 − 𝟏 + 𝒙𝟐𝒆−𝒙 𝟏𝟎𝑴 3. (a) Solve 𝑫𝟐 + 𝟐𝑫 + 𝟏 𝒚 = 𝒙𝒄𝒐𝒔𝒙. 𝟓𝑴

(b) Solve 𝑫𝟐 + 𝟐 𝒚 = 𝒆𝒙𝒄𝒐𝒔𝟐𝒙 + 𝒙𝟐𝒆𝟑𝒙. 𝟓𝑴

4. (a) Solve 𝒚′′ − 𝟐𝒚′ + 𝟐𝒚 = 𝒆𝒙 + 𝒄𝒐𝒔𝒙 + 𝒙𝟐. 𝟓𝑴 (b) Solve 𝒚′′ − 𝟐𝒚′ + 𝒚 = 𝒆𝒙 𝒙 𝒔𝒊𝒏𝒙. 𝟓𝑴 5 .(a) Solve 𝑫𝟐 + 𝟒 𝒚 = 𝒄𝒐𝒔𝟐𝒙 + 𝒄𝒐𝒔𝒉𝟑𝒙. 𝟓𝑴

(b) Solve 𝑫𝟐 + 𝟐𝑫 + 𝟏 𝒚 = 𝒆−𝒙 + 𝒙 + 𝒔𝒊𝒏𝟐𝒕. 𝟓𝑴

6. (a) The charge q(t) on the capacitor is giving by D.E 𝟏𝟎 𝒅𝟐𝒒

𝒅𝒕𝟐+ 𝟏𝟐

𝒅𝒒

𝒅𝒕+ 𝟏𝟎𝟎𝟎𝒒 = 𝟏𝟕 𝒔𝒊𝒏𝟐𝒕

.At time zero the current in zero and the charge on the capacitor is 1/2000 coulomb. Find the charge on the capacitor for t >0 . 𝟓𝑴 (b) In an L-C-R circuit, the charge q on a plate of the condenser is given by

𝑳 𝒅𝟐𝒒

𝒅𝒕𝟐+ 𝑹

𝒅𝒒

𝒅𝒕+

𝒒

𝑪= 𝑬 𝒔𝒊𝒏𝝎𝒕, 𝒘𝒉𝒆𝒓𝒆 𝒊 =

𝒅𝒒

𝒅𝒕. The circuit is tuned to resonance so that

𝝎𝟐 = 𝟏

𝑳𝑪 .If 𝑹𝟐 <

𝟒𝑳

𝑪 𝒂𝒏𝒅 𝒒 = 𝟎, 𝒊 = 𝟎 𝒘𝒉𝒆𝒏 𝒕 = 𝟎, show that

𝒒 =𝑬

𝑹𝑾 −𝒄𝒐𝒔𝝎𝒕 + 𝒆

−𝑹𝒕

𝟐𝑳 𝒄𝒐𝒔𝒑𝒕 +𝑹

𝟐𝑳𝑷 𝒔𝒊𝒏𝒑𝒕 . 𝟓𝑴

UNIT-III

1. (a) Using the expression 𝒔𝒊𝒏 𝒙 = 𝒙 − 𝒙𝟑

𝟑!+

𝒙𝟓

𝟓!−

𝒙𝟒

𝟕!+ ⋯… .. show that

𝑳 𝒔𝒊𝒏 𝒕 = 𝝅

𝟐 𝒔𝟑/𝟐 𝒆−𝟏/𝟒𝒔 𝟓𝑴

(b) (i) Show that the function 𝒇 𝒕 = 𝒕𝟐 is of exponential order 3. 𝟐𝑴

(ii) Find the Inverse Laplace Transform of 𝒔−𝟏

𝒔𝟐+𝟓𝟐 𝟑𝑴

2. (a) Show that 𝒔𝒊𝒏𝟐𝒕+𝒔𝒊𝒏𝟑𝒕

𝒕𝒆𝒕

∞

𝟎 𝒅𝒕 =

𝟑𝝅

𝟒 . 𝟓𝑴

(b) Evaluate 𝒆−𝟓𝒕 𝜹 𝒕 − 𝟐 𝒅𝒕.∞

𝟎 𝟓𝑴

3.(a) Solve the D.E 𝒚′′ − 𝟔𝒚′ + 𝟗𝒚 = 𝒕𝟐𝒆𝟑𝒕 if 𝒚 𝟎 = 𝟐, 𝒚′ 𝟎 = 𝟔 using Laplace transforms method. 𝟓𝑴

(b) Solve the D.E 𝒚′′ + 𝟐𝒚′ + 𝟓𝒚 = 𝟖𝒔𝒊𝒏𝒕 + 𝟒𝒄𝒐𝒔𝒕, if 𝒚 𝟎 = 𝟏, 𝒚′ 𝝅

𝟒 = 𝟐 using

Laplace transforms method. 𝟓𝑴

4. (a) Find 𝒊 𝑳−𝟏 𝟏

(𝒔𝟐+𝟏)(𝒔𝟐+𝟗) 𝒊𝒊 𝑳−𝟏

𝟑

(𝒔−𝝅

𝟐)𝟒 𝟓𝑴

(b) Find 𝒊 𝑳−𝟏 𝒔

𝒔𝟒+𝒔𝟐+𝟏 𝒊𝒊 𝑳−𝟏 ( 𝒕 −

𝟏

𝒕)𝟑 𝟓𝑴

5. (a) Solve the following differential equation by the transform method

𝑫𝟐 + 𝒏𝟐 𝒙 = 𝒂 𝒔𝒊𝒏 𝒏𝒕 + 𝜶 , 𝒙 = 𝟎 𝒂𝒕 𝒕 = 𝟎 . 𝟓𝑴

(b) Find 𝑳[𝒇 𝒕 ] where 𝒇 𝒕 = 𝒆𝒕 𝒊𝒇 𝟎 < 𝒕 < 1

𝟎 𝒊𝒇 𝒕 > 1 . 𝟓𝑴

6. (a) Find 𝑳−𝟏 𝟏

(𝒔𝟐(𝒔𝟐+𝟏)𝟐 using convolution theorem. 𝟓𝑴

(b) State convolution theorem and use it to evaluate 𝑳−𝟏 𝟏

𝒔𝟐+𝟒𝒔+𝟏𝟑 𝟐 𝟓𝑴

UNIT-IV

1.(a) Find 𝒙𝝏𝒖

𝝏𝒙+ 𝒚

𝝏𝒖

𝝏𝒚 if 𝒖 =

𝒙𝟑𝒚𝟑

𝒙𝟑+𝒚𝟑 𝟓𝑴

(b) Find the extreme values of 𝒇 𝒙,𝒚 = 𝒙𝟑 + 𝟑𝒙𝒚𝟐 − 𝟑𝒙𝟐 − 𝟑𝒚𝟐 + 𝟕. 𝟓𝑴

2. (a) Expand 𝒇 𝒙,𝒚 = 𝒙𝒚𝟐 + 𝒄𝒐𝒔 𝒙𝒚 in powers of 𝒙 − 𝟏 , 𝒚 −𝝅

𝟐 upto second

degree term. 𝟓𝑴 (b) Discuss the Maxima and Minima of 𝒇 𝒙,𝒚 = 𝒙𝟑𝒚𝟐 𝟏 − 𝒙 − 𝒚 . 𝟓𝑴

3. (a) Show that the functions u= 𝒙

𝒚, 𝒗 =

𝒙+𝒚

𝒙−𝒚 are functinally dependent and

find the relation between them. 𝟓𝑴 (b) Find the dimensions of a rectangular parallelopipid box open at the top of max capacity whose surface area is 108 sq inches. 𝟓𝑴

4.(a)Prove that 𝐽𝐽′ = 1 If 𝒖 =𝒚𝒛

𝒙, 𝒗 =

𝒛𝒙

𝒚, 𝒘 =

𝒙𝒚

𝒛. 𝟓𝑴

(b) Find the point in the plane 𝟐𝒙 + 𝟑𝒚 − 𝒛 = 𝟓 which is nearest to the origin. 𝟓𝑴

5. (a) If u = 𝒇 𝒓 and x= r𝐜𝐨𝐬 𝜽, 𝒚 = 𝒓 𝐬𝐢𝐧 𝜽 prove that 𝝏𝟐𝒖

𝝏𝒙𝟐 +𝝏𝟐𝒖

𝝏𝒚𝟐 = 𝒇′′ 𝒓 +𝟏

𝒓 𝒇′(𝒓).

𝟓𝑴

(b) Find the maximum and minimum values of 𝒇 = 𝟑𝒙𝟒 − 𝟐𝒙𝟑 − 𝟔𝒙𝟐 + 𝟔𝒙 + 𝟏.

𝟓𝑴

6. (a) If 𝒙 = 𝒗𝒘, 𝒚 = 𝒘𝒖 ,𝒛 = 𝒖𝒗 ,𝒙 = 𝒓𝒔𝒊𝒏𝜽𝒄𝒐𝒔𝝋, 𝒚 = 𝒓𝒔𝒊𝒏𝜽𝒔𝒊𝒏𝝋, 𝒛 = 𝒓𝒄𝒐𝒔𝜽

Then find 𝑱 𝒙,𝒚,𝒛

𝒓,𝜽,𝝋 . 𝟓𝑴

(b) Expand 𝒆𝒙 𝐬𝐢𝐧 𝒚 in powers of 𝒙,𝒚 . 𝟓𝑴

UNIT-V

1. (a) Form the Partial differential equation by eliminating arbitrary constants from

𝒊 𝒛 = 𝒂𝒙 + 𝒃𝒚 + 𝒂𝒃, 𝒊𝒊 𝒛 = 𝒂𝒙 + 𝒃𝒚 + 𝒂𝟐 + 𝒃𝟐 𝟓𝑴

(b) Form the Partial differential equation by eliminating 𝒇 & 𝑔 from

𝒛 = 𝒇 𝒚 + 𝒈(𝒙 + 𝒚). 𝟓𝑴

2. (a) Solve the PDE 𝒙 𝒚 − 𝒛 𝒑 + 𝒚 𝒛 − 𝒙 𝒒 = 𝒛(𝒙 − 𝒚). 𝟓𝑴

(b) Solve the PDE (𝒑

𝟐+ 𝒙)𝟐 + (

𝒒

𝟐+ 𝒚)𝟐 = 𝟏. 𝟓𝑴

3. (a) Solve 𝒙 + 𝟐𝒛 𝒑 + 𝟒𝒛 − 𝒚 𝒒 = 𝟐𝒙 + 𝒚 . 𝟓𝑴

(b) Solve the PDE 𝒛𝟐 𝒑𝟐 + 𝒒𝟐 = 𝟏. 𝟓𝑴

4. (a) Solve 𝒙 𝒚𝟐 + 𝒛 𝒑 − 𝒚 𝒙𝟐 + 𝒛 𝒒 = 𝒛 𝒙𝟐 − 𝒚𝟐 . 𝟓𝑴

(b) Solve the PDE 𝒑𝟐𝒒𝟐 + 𝒙𝟐𝒚𝟐 = 𝒙𝟐𝒒𝟐 𝒙𝟐 + 𝒚𝟐 . 𝟓𝑴

5. (a) Solve the PDE 𝒙𝟐𝒑𝟐 + 𝒚𝟐𝒒𝟐 = 𝟏. 𝟓𝑴

(b) Solve the PDE 𝒚 + 𝒛 𝒑 − 𝒛 + 𝒙 𝒒 = 𝒙 − 𝒚 𝟓𝑴

6. (a) Solve the PDE 𝒑𝐜𝐨𝐬 𝒙 + 𝒚 + 𝒒𝒔𝒊𝒏 𝒙 + 𝒚 = 𝒛. 𝟓𝑴

(b) Solve the PDE 𝒙𝟐

𝒑+

𝒚𝟐

𝒒= 𝒛. 𝟓𝑴

UNIT-VI

1. (a) Solve 𝑫𝟐 + 𝟐𝑫𝑫′ − 𝟖𝑫′𝟐 𝒛 = 𝟐𝒙 + 𝟑𝒚. 𝟓𝑴

(b) Solve 𝑫𝟐 + 𝑫𝑫′ − 𝟔𝑫′𝟐 𝒛 = 𝒙𝟐𝒔𝒊𝒏 𝒙 + 𝒚 . 𝟓𝑴

2. (a) Solve 𝑫𝟐 − 𝑫𝑫′ 𝒛 = 𝒔𝒊𝒏𝒙 𝒄𝒐𝒔𝟐𝒚. 𝟓𝑴

(b) Solve 𝑫𝟐 − 𝑫𝑫′ − 𝟐𝑫 𝒛 = 𝒔𝒊𝒏 𝟑𝒙 + 𝟒𝒚 . 𝟓𝑴

3. (a) Solve 𝝏𝟐𝒛

𝝏𝒙𝟐 − 𝟔𝝏𝟐𝒛

𝝏𝒙𝝏𝒚+ 𝟗

𝝏𝟐𝒛

𝝏𝒚𝟐 = 𝟏𝟐𝒙𝟐 + 𝟑𝟔𝒙𝒚 + 𝒆𝒙+𝒚 𝟓𝑴

(b) Solve 𝝏𝟐𝒛

𝝏𝒙𝟐 −𝝏𝟐𝒛

𝝏𝒙𝝏𝒚− 𝟐

𝝏𝟐𝒛

𝝏𝒚𝟐 = (𝒚 − 𝟏)𝒆𝒙 𝟓𝑴

4.(a) Solve 𝑫𝟑 − 𝑫′𝟑 𝒛 = 𝒙𝟑𝒚𝟑. 𝟓𝑴

(b) Solve 𝑫𝟐 − 𝟐𝑫𝑫′ 𝒛 = 𝒆𝟐𝒙 + 𝒙𝟑𝒚. 𝟓𝑴

5.(a) Solve 𝑫𝟐 − 𝟐𝑫𝑫′ + 𝑫′𝟐 𝒛 = 𝟐𝒙𝒄𝒐𝒔𝒚. 𝟓𝑴

(b) Solve 𝑫𝟐 − 𝑫′𝟐 𝒛 = 𝒄𝒐𝒔 𝒙 + 𝒚 . 𝟓𝑴

6.(a) Solve 𝝏𝟐𝒛

𝝏𝒙𝟐 + 𝟐𝝏𝟐𝒛

𝝏𝒙𝝏𝒚+

𝝏𝟐𝒛

𝝏𝒚𝟐 = 𝟐𝒔𝒊𝒏𝒚 − 𝒙𝒄𝒐𝒔𝒚. 𝟓𝑴

(b) Solve 𝝏𝟑𝒛

𝝏𝒙𝟑 − 𝟑𝝏𝟑𝒛

𝝏𝒙𝟐𝝏𝒚+ 𝟒

𝝏𝟑𝒛

𝝏𝒚𝟑 = 𝒆𝒙+𝟐𝒚. 𝟓𝑴






APPLIED PHYSICS QUESTION BANK, MID-I (2018-19)

Class – I CSE (A) – I Semester Name of the Faculty- APPA RAO.P

UNIT-I

1 (a ) State and explain the Principle of superposition of waves.- 4M

(b Explain the formation of Newton’s rings and obtain an expression for the diameter of the

dark rings in reflected system..– 6M

2 (a) In Newton’s rings experiment, diameter of the tenth dark ring due to wavelength 6000Å

in air is 0.5 cm. Find the radius of curvature of the lens.– 4 M

(b) If the air film in the Newton’s rings apparatus is replaced by an oil film, then how does

the radius of the rings change? Explain.– 6M

3 (a) What are the necessary conditions to get clear and distinct interference fringes – 4M

( b ) Describe principle ,construction and working of Michelson Interferometer. - 6M

4( a ) Explain the colours in a thin film when exposed it to a sun light – 4M

( b ) Explain why the centre of Newton’s rings is dark in the reflected system. Why are they

circular – 6M

5 (a) Distinguish between Monochromatic and Polychromatic light sources, Give one

example for each –3M


(b) With a ray of diagram, discuss the theory of thin films and the condition constructive

and destructive interference in the case of reflected light.—7M

6 (a) ) Derive cosine law and write down the conditions for brightness & darkness in the

reflected system. - 6M

(b) In Newton’s rings experiment, diameter of 10th

dark ring due to wavelength 6000 A in

air is 0.5 cm. Find the radius of curvature of lens.

UNIT—II

1 (a) What are the types of diffraction and give the difference between them ? 4 M

(b) Obtain the condition for primary maxima in Fraunhofer diffraction due to single slit

and derive an expression for width of the central maxima - 6 M

2 (a) What is the difference between interference and diffraction –4M

(b) Explain the diffraction due to two parallel slits and obtain the Intensity of light on the

screen.—6M

3 (a) Define the grating and Explain with necessary theory, the Fraunhofer diffraction due

to ‘N’parallel slits.– 6 M

(b) Calculate the maximum number of order possible for a tranmission grating - 4 M

4 (a) What happens to the diffraction fringes, if the slit width is reduced in single slit

experiment? Explain why?.- 6 M

(b) A grating has 6000 lines/cm.Find the angular separation between two wavelengths of 500

nm and 510 nm in 3rd

order – 4M

5 (a) What is meant by Diffraction of light? Explain it on the basis of Huygen’s wave theory ?

4 M

(b) Explain the theory of plane transmission grating abd derive equations for maxima and

minima.- 6M

6 (a) Define resolving power of grating and explain Rayliegh criterion for resolution and

determine the resolving power of the Telescope - 6 M

(b) How many orders will be visible ,if wave length of light is 5000 A ? Given that the

number of lines per centimeter on the grating is 6655. .- 4 M

UNIT – III

1(a) What is a half wave plate and Quarter wave plate? Deduce an expression for its

thickness-6 M

(b) Calculate the thickness of half wave plate of quartz for a wavelength 500nm.

Here μe= 1.553 and μo= 1.544..- 4 M

2 (a ) Write the difference between Spontaneous and Stimulated Emissions.– 4M

(b) Explain the working of Ruby laser with the help of neat energy level diagram..– 6M

3 (a) What is population inversion and how can it be achieved ?.- 4 M

(b) Explain the working of He-Ne gas laser with the help of neat energy level diagram.- 6 M

4 (a) Distinguish between polarized and unpolarized lights –3M

(b) State and explain Brewsters law? Discuss how to produce the plane,Circular and

Elliptical polarized lights?

5 (a) Explain Einstein’s coefficients. Derive the relation between them.-5M

(b) What are the characteristics and applicatios of LASER beam.-5M

6(a) Write a note on double refraction? 4M

(b) Explain the principle ,construction and working of a Nicol prism.-6M

polarized light can be produced-7M

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