LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – NOVEMBER 2010

    PH 3812  – NUMERICAL METHODS AND C PROGRAMMING

 

 

 

Date : 03-11-10                 Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

Answer ALL questions.                                                                                            (10 x 2 = 20)

1. Dsitingush between Trapezoidal and Simpson’s rules of integration.
2. Reduce y = ae^bx to linear form.
3. Give the use of the comma operator in C.
4. Write a simple C program to find whether a given number is even or odd.
5. List the logical operators in C.
6. Explain operator precedence in C language.
7. With an example explain “array initialization”.
8. Explain the use of break statement in C with an example.
9. Mention any two advantages of pointers.
10. Give the general format of a union.

 

PART – B

Answer any FOUR questions.                                                                                             (4 x 7.5 = 30)

11. Evaluate using Lagrange’s interpolation formula the value of f (9) from the following table:

X	2	5	8	11
f(x)	94.8	87.9	81.3	75.1

12. Evaluate the integral using Trapezoidal rule with h=0.05.
13. Solve by Modified Euler’s method, dy/dx = 1 – y, for x=0.2, given y(0)=0, h=0.1.
14. Solve the following simultaneous equations by Gauss-Jordan method:

2x  +  3y  –    z  =  5

4x  +  4y  –  3z  =  3

2x  –   3y +  2z  =  2

15. Use the method of least squares to fit a straight line to the following data:

X	0	1	2	3	4
Y	1	1.8	3.3	4.5	6.3

Hence estimate the value of Y when X=2.5.

 

PART – C

Answer any FOUR questions.                                                                                             (4 x 12.5 = 50)

16. Develop a program to compute a missing value using Lagrange’s Interpolation.
17. Write a program in C to solve a differential equation using the fourth order Runge-Kutta method.
18. Develop C programs to
    1. find the greatest of three numbers             (5)
    2. to find whether a number is Armstrong (7)
19. Design a C program to multiply two 3 x 3 matrices.
20. Using switch…case design a program in C to determine the overall grade obtained by a student

based on scores in 5 subjects.

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – APRIL 2012

PH 3812 – NUMERICAL METHODS AND C PROGRAMMING

 

 

Date : 26-04-2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

Answer ALL the questions                                                                                                    (10 X 2 = 20)

1. List any two salient features of C Language.
2. Discuss the various arithmetic operators available in C.
3. What are Input and Output functions?
4. Reduce y=ae^bx to linear form.
5. Mention any two uses of Pointers.
6. Write down the first approximation in Regula-falsi method?
7. Given that, f(0)=8,f(1)=68 and f(5)=123,construct a divided difference table. Using the table determine the value of f(2).
8. Evaluate with h=0.25 using trapezoidal rule.
9. Write a C program to sum the series 1+2+3+…+100.
10. How are arrays declared in C?

PART – B

Answer any FOUR questions                                                                                                            (4 X 7.5 =30)

11. Write a short note on data storage classes.
12. Explain the use of switch case statement in C.
13. Find the positive root of x³-5x+3=0 by using Newton’s method.
14. Solve the linear equations by Gauss elimination method.

2x₁+4x₂+2x₃=15 ;        2x₁+x₂-2x₃=-5;             4x₁+x₂-2x₃=0

15. The temperature T (in ^oc) and lengths l(in nm) of heated rod is given. If l=a_o+a₁T, Find the best values for a_o and a₁.

T	20	30	40	50	60	70
l	800.3	800.4	800.6	800.7	800.9	801

 

PART – C

Answer any FOUR questions                                                                                                            (4 X 12.5 =50)

16. Develop a ‘C’ program to accept two 4×4 matrices from the keyboard and to display the sum and difference matrices in matrix form.
17. Develop a ‘C’ program to copy the contents of a file into another.
18. Write a C program to implement a numerical integration using Simpson’s 3/5^th rule.
19. Apply fourth order Runge-Kutta method to find the approximate value of y(0.2) from
    y’=y-x, y(0)=2 taking h=0.1.
20. The values of tan x for x is given, find
21. a) tan(0.12) b) tan(0.4) c) tan (0.5)

x	0.1	0.15	0.2	0.25	0.3
Y=tan x	0.1003	0.1511	0.2027	0.2553	0.3093

 

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – NOVEMBER 2012

PH 3812 – NUMERICAL METHODS AND C PROGRAMMING

 

 

Date : 06/11/2012            Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

Answer ALL questions:                                                                                                               (10×2=20)

 

1. Describe the structure of a C program.
2. Distinguish between main() and void main(void).
3. Write a C program to output the multiplication table.
4. Check whether the following numeric constants are valid. Give reason.
5. a) 67845L b) 25,000        c) +5.0E3        d) 7.1e 4          e) $ 285
6. How do variables and symbolic names differ?
7. Develop a C program to convert lowercase letter to upper case and vice-versa.
8. Apply Simpson’s 1/3 ^rd rule to estimate the value of the integral by dividing the interval (1,2) into four equal parts.
9. Given that f(0)=8, f(1)=68 and f(5)=123 ,construct a divided difference table. Using the table determine the value of f(2).
10. Differentiate between break and continue statements.
11. Briefly explain the various data types in C language.

PART – B

Answer any FOUR questions            :                                                                                                    (4×7.5=30)

11. Using Newton’s formula for interpolation with x and y given values and find f(7.5) for the data given below.

X	1	2	3	4	5	6	7	8
F(x)	1	8	27	64	125	216	343	512

12. Using Newton-Raphson’s method find correct to four decimal places, the roots lying in the interval 0 and 1 for the equation x³-6x+4=0.
13. Write a C program to evaluate the sum of the digits of a given number.

14 Determine y by Lagrange’s formula when x=35, for the data given below.

x	25	30	40	50
y	52	67.3	84.1	94.4

15. Write a C program to perform integration of a function using Trapezoidal rule.

PART – C

Answer any FOUR questions            :                                                                                                   (4×12.5=50)

16. Given that dy/dx=1+y², where y=0, when x=0, Find y(0.2) and y(0.4) by using Runge-Kutta method of order four.
17. Develop a C program to find the transpose of a matrix.
18. Find the value of y for x=0.2 when dy/dx=log(x+y) with the initial condition that y=1 for x=0 by using Euler’s modified method.
19. Solve the following simultaneous equations by Gauss-Jordan method

x₁+2x₂+x₃=8;                    2x₁+3x₂+4x₃=20;                     4x₁+3x₂+2x₃=16.

20. i) Discuss the various storage classes in C with suitable examples.
21. ii) Write a C program to accept a sequence of characters and find the number of vowels and consonants using switch statement.

 

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