Department of COMPUTER SCIENCE & ENGINEERING

COMPUTER PROGRAMMING

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 Application and System Software (5m)

(b). Explain about Procedure oriented programming languages in detail (5m)

4. (a) Explain about Object Oriented Programming languages in detail(5m)

(b) Discuss about different computer languages with examples (5m)

5. Explain the steps in software development process (10m)

UNIT – II

1. (a) (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)

(b) Explain the various data types available in C-language (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-language with suitable examples (5m)

(b) Explain about the various logical operators available in C-language with suitable examples (5m)

5. (a) Explain about the various relational and equality operators available in C-language with suitable

Examples (5m)

(b) Write a constant? Explain the different constants available in C-language with suitable examples

(5m)

UNIT – III

1. (a) a) What is meant by type conversion? Why is necessary? Explain about implicit and explicit

Type conversion with examples.

(b) Explain different relational operators available in C language with examples.(5m)

(b). Explain different looping statements with syntax and examples (5m)

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( )

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UNIT-1

1. (a) Construct a plain scale of RF 1:50000 TO show kilometers and hectometers and long enough to measure up to 7 kilometers. Measure a distance of 54 hectometers on your scale

(b) Draw an Octagon given the length of side 25mm

2.(a) Construct a plain scale to show meters when 1 cm represents 4 meters and long enough to

measure up to 50 meters . Find the R.F and mark on your scale a distance of 36 meters (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) Construct a DIAGONAL scale of RF 1:3200000TO show kilometers and long enough to measure

up to 400 km show distance of 257 km and 333 km on your 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.

1. (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) Construct A vernier scale to read meters, decimeters and centimeters and long enough to measure up to 4 mt . RF of the scale is 1/20 mark on your scale a distance of 2.28 mt

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 30

0 to HP. The end M is 20mm above

SUBJECT: ENGINEERING DRAWING(R-16)

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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 30

0 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 meters apart. The distance between the pegs measured parallel to the floor is 3.6 meters. 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 30

0to 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. The top view of a 75mm long line AB measures 65 mm, while the length of its front view is 50mm ITS one end

A is in the HP AND 12 mm in front of the VP. Draw the projections of AB and determine the inclinations with

the HP AND the VP.

2. A line CD measuring 80 mm is inclined at an angle of 300 to HP and 45

0 TO VP. The point C is 20 mm above

HP and 30mm in front of VP. Draw the projections of the straight line.

3. A line AB is 75mm long. A is 50 mm in front of VP and 15 mm above HP .B is 15mm in front of VP and is

above HP. TOP VIEW OF AB is 50 mm long. Find the front view length and the true inclinations

4.A line AB 65 mm long has its end A 20 mm above HP AND 25mm in front of VP. END B is 40 mm above HP

and 65mm in front of VP. Draw the projections of AB. find its inclinations with HP and VP.

5. The projections of a line measure 80mm in the top view and 70mm in the front view. The MID –POINT of the

line is 45mm in front of VP and 35mm above HP . One end is 10 mm in front of VP and nearer to it. Draw the

projections. Find the true length and true inclinations with reference planes.

6. A line AB 65 mm long has its end A, 15 mm above HP and 15mm in front of VP. It is inclined at 550 to HP

and 350 to VP draw its projections.

UNIT-IV

1. A regular pentagonal plate of side 28mm is placed with one side on HP such that the surface is

inclined at 450

to HP and perpendicular to VP. Draw its projections and traces.

2. A thin circular metal plate of 48 mm diameter, having its plane vertical and inclined at 400

to

VP its center is 33mm above HP and 25mm in front of VP. Draw its projections and locate its

traces.

3. A thin rectangular plate of sides 50mm x 25mm has its shorter side in the HP and inclined at an

angle of 300 to the VP. Project its front view when its top view is a perfect square of 25mm side.

4. A regular pentagonal lamina of 30mm sides has one edge in HP and inclined at an angle of 300

to VP. Draw its projections when its surface is inclined at 450

to HP

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

(i) The top view of the diameter AB making 300 angles with the V.P

(ii) The diameter AB making 300 angles with the V.P

6. A circular lamina of 60mm diameter rests on HP on a point 1 on the circumference. The lamina

is inclined to HP such that the top view of it is an ellipse of minor axis 35mm.The top view of

the diameter through the point 1 makes an angle of 450 with VP.

i) Draw the projections ii) Determine the angle made by the lamina with HP.

UNIT-V

1.Draw the projections of a cylinder, base 30mm diameter and axis 40mm long resting with a

point of its base circle on HP such that the axis is making an angle of 300 with HP and parallel to

VP.

2.A pentagonal prism side of base 25mm and axis 50mm long resting with one of its edges on HP

such that the base containing that edge makes an angle of 300 to HP and 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 300 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.Draw the projections of a cone of base 30mm diameter and axis 50mm long resting on HP on a

point of its base circle with the axis making an angle of 450 with HP and parallel to VP.

6.A cone 40 mm bases and axis 50mm long touches VP on a point of its base circle. The axis is

inclined at 300

to VP and the front view of the axis is inclined at 450 to HP. Draw it’s

projections?

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UNIT-VI

1. Draw the orthographic views as shown in fig 2. Draw the orthographic views as shown in fig

3. Draw the orthographic views as shown in fig 4. Draw the orthographic views as shown in fig

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

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Note: All Dimensions are in mm

Draw the isometric view as shown in fig

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(i) (ii)

Note: All Dimensions are in mm

1. Human beings migrate for various reasons. Write any five reasons for their

migration.(5M)

2. Why do people call Mr.Neave’s family as an 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 morning

1. What evidence do you find in the text to support the statement that Ramanujan was an

unusual mathematical genius? (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. What is a visa? Write any five eligibility requirements for H1-B visa. (5M)

2. Summarize the story, ‘An Ideal Family’. (3M)

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

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

b) She_____ (see) the movie many times.

1. What factors attract the Indian youth while selecting a job.(5M)

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

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

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

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

1. Write the telephonic conversation between you and your friend Mr. Kiran about your

return to your village from the city. (5M)

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

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

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

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

English –I QUESTION BANK – I B.TECH

Unit-I

1. Why rural people migrate to cities and why they plan to return to their village after

few months? (5M)

2. Explain the characters Mr.Neave and Harold? (3M)

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

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)

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

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

clouds 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)

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

fall 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)

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

clouds 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)

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)

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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

SUBJECT : MATHEMATICS-II

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

SUBJECT: MATHEMATICS-I

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

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. 4M

(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 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. 4M

UNIT—II

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

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

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

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 for Fraunhofer diffraction due to

‘N’parallel slits. 6M

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

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

experiment? Explain why? 6M

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

nm and 510 nm in 3rd

order. 4M

APPLIED PHYSICS QUESTION BANK(2018-19)

5(a)What is meant by Diffraction of light? Explain it on the basis of Huygen’s wave theory?4M

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

minima. 6M

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

determine the resolving power of the Telescope. 6M

(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. 4M

UNIT – III 1(a) What is a half wave plate and Quarter wave plate? Deduce an expression for its thickness.

6M

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

1.553 and μo= 1.544. 4M

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? 4M

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

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? 7M

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

UNIT-IV 1.(a)State the fundamental equations of electromagnetism. 4M

(b)Write the Maxwell’s electromagnetic equations in differential or integral form. 6M

2.(a)State and explain stokes and Gauss divergence theorems. 4M

(b) Write the Maxwell’s electromagnetic equations in differential or integral form. 6M

3.(a) Stat and prove Gauss’s theorem. 4M

(b) What is the curl of a vector? Show that it is related to net circulation integral. 6M

4.(a) Discuss the propagation of electromagnetic waves in dielectrics. 6M

(b)Discuss irrotational vector field. Show that it can be regarded as a field of the gradient of

a scalar 4M

5.(a) Derive Maxwell’s equations from the basic laws of electromagnetism. Explain physical

meaning of each equation. 6M

(b)What do you understand by the gradient of a scalar field? Explain its physical

significance. 4M

6.(a) State and explain Stoke’s theorem in its calculus form. 4M

(b) Write the Maxwell’s electromagnetic equations in differential or integral form. 6M

7.(a) What is the curl of a vector? Show that it is related to net circulation integral. 6M

(b) State and explain Stoke’s theorem in its calculus form. 4M

UNIT—V 1.(a) Derive time independent wave equation for a free particle. 5M

(b) Derive time dependent Schrodinger’s wave equation for a free particle. 5M

2.(a) Explain the energy of an electron in one dimensional square well potential box. 7M

(b) Calculate the minimum energy of free electron trapped in a one dimensional box of width

0.3 nm (given h = 6.63 X 10-34

J. S and me = 9.1 X 10-31

Kg). 3M

3.(a) What is Fermi level and explain the Fermi-Dirac distribution function of electron in a

metal. 4M

(b) Discuss the variation with temperature on the distribution. 6M

4.(a) What are the properties of Matter waves? 3M

(b) Derive Eigen values and Eigen functions for a particle in a one dimensional potential box.

7M

5.(a) Define valence band, conduction band and forbidden energy gap in the energy band

structure. 3M

(b) Explain the Kronig-penny model of solids and show that it leads to energy band

structure. 7M

6.(a) How matter waves are different from Electromagnetic waves?. 3M

(b) Based on classical free electron theory, derive an expression for electrical conductivity of metals.

7M

7.(a) Based on quantum free electron theory, derive an expression for current density of

metals. 6M

(b) Explain the salient features of Classical free electron theory. 4M

8 (a) Explain the concept of Effective mass and derive the expression for it 4M

(b) What is the most probable position for a particle in one dimensional potential box of

width ‘L’ in the first quantum state? Explain graphically. 6M

UNIT- VI 1 (a ) Distinguish between Intrinsic and Extrinsic semiconductors - 2M

(b) Derive the expression for concentration carriers in intrinsic semiconductor. 8M

2 (a) Distinguish between N- type and P- type extrinsic semiconductors 4M

(b) Derive the expression for Fermi energy in N-type extrinsic semiconductor. 6M

3 (a) Explain P- type extrinsic semiconductors. 4M

(b) Derive an expression for Fermi energy in extrinsic P-type semiconductor. 6M

4 (a) State and explain Hall Effect. 5M

(b) Derive an expression for Hall coefficient and Give any two of its applications.. 5M

5 (a) Define and explain drift current and diffusion currents 8M

(b) Explain the electronic transport mechanism for Photo Conductors. 2M

6 (a) Explain the concept of hole. 2M

(b) What do you understand by drift and diffusion currents in the case of a semiconductor?

Deduce Einstein’s relation relating to these currents. 8M

7 (a)How does the band theory of solids lead to the classification of solids into conductors,

semiconductors and insulators? 6M

(b) Establish Einstien’s relation between diffusion coefficient and mobility of charge carriers.

4M