Loyola College B.Sc. Statistics April 2004 Numerical Methods Using ‘C’ Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.Sc., DEGREE EXAMINATION – STATISTICS

FOURTH SEMESTER – APRIL 2004

ST-4202/STA202 – NUMERICAL METHODS USING ‘C’

14.04.2004                                                                                                           Max:100 marks

9.00 – 12.00

 

SECTION -A

 

Answer ALL questions                                                                               (10 ´ 2 = 20 marks)

 

  1. What is an assignment statement? What is the relationship between an assignment statement and an expression statement?
  2. Mention the difference between pre-increment and post-increment operator.
  3. Give the syntax of ternary operator.
  4. What is the output of the following program segment?

for (i = 0, j = 0; i < = 5; i ++, j ++)

print f (” %d\ n”, i+j);

  1. Mention the difference between break and continue statement.
  2. What is an array?
  3. Comment on the following statement:

” scanf () and get char() functions are equivalent”.

  1. Find the value of f (10) using Lagrange’s linear interpolation for the following function:

x:   7    19

f:  15    35.

 

  1. Evaluate using Trapezoidal rule where f(x) is defined as

 

x: 0.8 0.9 1.0 1.1 1.2
f: 0.71736 0.78333 0.84147 0.92314 0.96356

 

  1. Give the steps to find the root of an equation by Newton-Raphson method.

 

SECTION – B

 

Answer any FIVE questions                                                                          (5 ´ 8 = 40 marks)

 

  1. a) Explain the data types available in C.
  2. b) What are type qualifiers? (6+2)

 

  1. Explain the concept of branching and looping with examples.

 

  1. Explain the syntax of the following:
  2. a) printf() b) toupper() c) pow()           d) floor()

 

 

 

 

 

  1. Give the output of the following program segments:
  2. a) i = x = 0; b) x = 0;

do                                                   for (i = 0; i<5; i++)

{                                                                 {

if (i% 5 = =0)                                  for (j = 0; j<i;j++)

{                                                                 {

x++;                                                switch (i+j-1)

printf(“%d \n”, x);                         {

}                                                     case -1:

i++;                                                case 0: x = x+1;

}while (i<20);                                             break;

printf (“%d’1′ x);                             case 1:

case 2:

case 3:  x = x+2;

break;

default:  x = x+3;

break;

}

printf (“%d\n”, x);

}

}                                                                         (3+5)

 

  1. a) Write a program to accept an integer and display it in reverse order.

 

  1. b) Write a program using function to find the factorial of a given positive integer. (4+4)

 

  1. Find the determinant of the following matrix by pivotal condensation method.

 

 

 

  1. Write a program to solve the equation x2+3x-5=0 using bisection method.

 

  1. Write a program to find the largest eigen vector by the method of iteration.

 

SECTION – C

 

Answer any TWO questions                                                                       (2 ´ 20 = 40 marks)

 

  1. a) Explain the structure of a C program.
  2. b) Write a program to find the maximum among ‘n’ given integers.
  3. c) Explain the concept of arrays with an example. (6+6+8)

 

  1. a) Write a program to find the roots of a quadratic equation of the form ax2+bx+c=0.
  2. b) Write a program to find the sum of 2 square matrices of order mxm.
  3. c) What are user defined functions? Explain the method of declining and defining a user

defined function.                                                                                                  (6+6+8)

 

 

 

  1. a) Explain the Gauss-elimination method to solve a given set of simultaneous equation

and write a program for the same.

 

  1. b) Evaluate using simpson’s 1/3 rule by taking h as 0.1. (12+8)

 

  1. a) Write a program using Lagrange’s interpolation method to evaluate f(y) where ‘f’ is a function defined as

x    :  x1    x2   ……..xn

f(x):  f1  f2  ……..fn

Assume that x1, x2…..xn,   f1,  f2,……fn are known values.

 

  1. b) Find the inverse of the following matrix by Gauss-Jordon elimination method.

 

A =                                                                                         (12+8)

 

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Loyola College B.Sc. Statistics April 2006 Numerical Methods Using C Question Paper PDF Download

             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AC 11

FOURTH SEMESTER – APRIL 2006

                                              ST 4202 – NUMERICAL METHODS USING C

(Also equivalent to STA 202)

 

 

Date & Time : 29-04-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

SECTION A

Answer ALL questions                                                                              [10×2 =20]

  1. Distinguish between a compiler and an interpreter
  2. Explain the importance of #define directive
  3. Define a] a variable b] a constant
  4. What is initialization? Why it is important?
  5. Mention any four C’s fundamental data types?
  6. Write the importance of bitwise operators
  7. What is an array? Define an array to store six subjects marks for 100 students.
  8. Distinguish between an array and a structure.
  9. What are different categories of functions?
  10. Define Interpolation .

SECTION B

 Answer any FIVE questions                                                                          [5×8 =40]

  1. Write a program to find the mean and standard deviation of n numbers.
  2. Using Newton-Raphson’s method , write a C program to evaluate a real root for the  equation:
    X3 + 2 X2 + 2 X +5 =0.
  3. Write a program to the maximum of N numbers
  4. Distinguish between do and while statements with an example.
  5. Write a C program for Lagrange’s interpolation formula.
  6. Explain the following operators in C with suitable examples
    a)arithmetic operators b) increment and decrement operators
  7. Write a C program to arrange n numbers of an array in the ascending order.
  8. Write a program that uses an user defined function namely Mystrlen() which counts and returns the length of a string .

SECTION C

Answer any TWO questions                                                                         [2 x 20 =40]

  1. Write a program to read the values of matrices viz. Am x l and Bl x n  and compute the product of the matrices and store the results in the matrix Cmxn.
  2. a] Write a program in C to find the roots of a quadratic equation.

b]   Using Trapezoidal rule, Write a program to evaluate the integral                           [12]

21         Write a C program to solve the system of linear equations by GAUSS’s elimination    method.

  1. a] Write a program that prints first n-fibonacci numbers in the series.

b]   Using Newton’s backward formula, find the annual premium at the age of 33 from the            following data:  Age in years              : 24           28          32           36           40

Annual premium in Rs.             : 28.06     30.19      32.75      34.94      40

 

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Loyola College B.Sc. Statistics April 2007 Numerical Methods Using C Question Paper PDF Download

           LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AC 12

 

FOURTH SEMESTER – APRIL 2007

ST 4202 – NUMERICAL METHODS USING C

 

 

 

Date & Time: 26/04/2007 / 9:00 – 12:00 Dept. No.                                            Max. : 100 Marks

 

 

 

SECTION A

Answer all questions.                                                                        (2×10=20)

 

  1. Mention the difference between float and double data type in C.
  2. Write the syntax of scanf() and getc() function.
  3. What is meant by nested loop?
  4. What are recursive functions?
  5. Mention any two library functions available in C with their use.
  6. Find the characteristic root of the matrix
  7. Mention any two iterative methods to find the root of a polynomial equation.
  8. What is Simpson’s 3/8 rule?
  9. Mention the use of Gauss Seidal iteration method.
  10. Find the inverse of the matrix

 

SECTION B

Answer any five questions.                                                         (5×8=40)

 

  1. What is a structured programming language? Explain the structure of a C program.
  1. Explain the syntax of if – else and if – else – if statements with examples.
  2. What are arrays? Explain the concept of single dimension and two dimension

arrays with examples.

  1. Write a program in C using function to display all the prime numbers between 1 and 100.
  2. Explain the regula – falsi method to find the real root of an equation f(x) = 0.
  3. Solve the following equations by Gauss – Jordan method:

10x + y + z = 12; 2x + 10y + z = 13; x + y + 5z = 7.

  1. Use Newton’s forward interpolation formula to find the value of f(142) based on the following data:.

x:         140      150      160      170      180

f(x):         3.685   4.854   6.302   8.076   10.225

  1. Obtain the value of f ¢(90) using Stirling’s formula based on the following data:

x:         60        75        90        105      120

f(x):         28.2     38.2     43.2     40.9     37.7

 

 

 

 

 

 

 

 

SECTION C

Answer any TWO questions.                                                          (2×20=40)

  1. a.) Mention the various input and output statements available in C.

b.) What are control statements? Explain the syntax of the ‘go to’ and

‘switch – case’ statements with examples.                       (8+12)

 

 

  1. Explain the Lagrange’s Interpolation method and hence find the value of y when

x=10 based on the following data:

x:         5          6          9          11

y:         12        13        14        16

  1. Find the inverse of the following the matrix using Gauss elimination method.

 

22.. a.) Write a program in C for finding  using Simpson’s 1/3 rule.

b.) Evaluate  by using Trapezoidal rule.                               (12+8)

 

 

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Loyola College B.Sc. Statistics April 2012 Numerical Methods Using C Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – APRIL 2012

CS 3203 – NUMERICAL METHODS USING C

 

 

Date : 02-05-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A  

                                                                       

ANSWER ALL THE QUESTIONS:                                                                       (10 X 2 =20)

 

  1. What is meant by identifier?
  2. Give the syntax for conditional operator in C.
  3. How will you declare a variable in C?
  4. List out any four built in functions in C.
  5. Write a transpose of a given matrix.

15   16   17

13   15   16

15   15   18

  1. State the formula for Newton’s backward interpolation.
  2. Differentiate the equation 5X5+2X 4+ 2X3 + 14X +45.
  3. What is the use of Newton- Raphson method?
  4. Give the formula for Simpson 3/8 rule.
  5. What is the use of power method?

 

PART – B  

                          

ANSWER ALL THE QUESTIONS:                                                                         (5 X 8 =40)

 

  1. a) Explain all types of if statements in C with suitable example.

(Or)

  1. b) Write a C program to find out sum and average of n numbers.

 

  1. a) Write a C program to find out factorial of n numbers using recursion.

(Or)

  1. b) Discuss about all the operators used in C.

 

  1. a) Solve the system of equation using Gauss Jordan method.

 

2x + 4y – 6z =  -8

x + 3y +  z  = 10

2x  – 4y – 2z = -12

 

(Or)

  1. b) Write a C program to solve the system of equation using Gauss elimination

method.

 

  1. a) Write a C program to implement Simpson’s 1/3 rule.

(or)

b). Evaluate the following integral using trapezoidal rule.

F(x) = 1/ (1+x2) with n = 10 on the interval [0-1].

 

  1. a) Write a C program to find out root of the equation using Regula –Falsi method.

(Or)

  1. b) Estimate theg given equation u’ = -2tu2 with h = 0.2 on the interval [0-1] using

Euler’s method.
PART – C

 

ANSWER ANY TWO QUESTIONS:                                                               (2 X 20 =40)

 

  1. a) Explain scanf() and printf() statement in C with suitable example.
  2. b) Illustrate the use of user defined function in C.
  3. a) Write a C program to find out biggest of any three given numbers .
  4. b) Estimate the value of y at x = 6 using Newton’s forward interpolation formula with the help of

the following table.

 

x 3 7 9 10
Y 168 120 72 63

 

  1. a) Write a C program to implement Runge –kutta IVth order method.
  2. b) Compute the root of the given equation using Bisection method.

X3 – 5X + 1 = 0 with the initial value a0 =0 and b0 =0

 

 

 

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Loyola College B.Sc. Statistics April 2016 Numerical Methods Using C Question Paper PDF Download

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Loyola College B.Sc. Computer Science April 2007 Numerical Methods Using C Question Paper PDF Download

            LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

HC 05

 

THIRD SEMESTER – APRIL 2007

CS 3200 – NUMERICAL METHODS USING C

 

 

 

Date & Time: 26/04/2007 / 9:00 – 12:00 Dept. No.                                                Max. : 100 Marks

 

 

PART-A

Answer all questions                                                                         10 x 2 = 20

  1. What is Compiler?
  2. Identify the valid variable

Interest, char, FILE, pi

  1. What is an array?
  2. List any four back-slash character constants in C.
  3. List an Gaussian methods
  4. Write a trapezoidal rule?
  5. Write a formula for Runge-Kutta 4th order method?
  6. Write a Simpson’s 1/3 and 3/8 rule.
  7. Define Numerical Integration.
  1. Find the determinant of the following matrix?

│    4   2   │

│    1   3   │

PART-B

Answer all Questions                                                                                    5 x 8 = 40

  1. (a)  Elucidate the structure of C Program                                         (or)

(b) Write a C program to generate Fibonacci series

  1. (a) Explain if.,else and switch statements in C language (or)

(b) Write a C Program to calculate a factorial of given value.

  1. (a) Explicate different categories of functions. (or)

(b) Write a C program for n x n matrix addition

  1. (a) Apply Newton’s Forward Problem for interpolation.

X(year)                  1891    1901    1911    1921    1931

Y(population)                        46      66        81        93      101

Estimate the population for the year 1895.                                   (or)

(b) Explain for, while and do..while statements with an example

 

  1. (a) Write a C program for Runge-Kutta 2nd order method              (or)

(b) Write a C program to find a determinant of a matrix.

PART-C

Answer any two Questions                                                               2 x 20 = 40

 

  1.  a) Explain various types of operators in C Language. (10 Marks)
  1. b) Elucidate Recursive function.                               (10 Marks)
  1.  Write a C program to evaluate 0 ò1 Sqrt(1+x^2) by
  1. a) Trapezoidal method                                (7 Mark)
  2. b) Simpson’s 1/3 and 3/8 method               (13 Mark)

 

  1.  Write a C program t to solve the system of equations by Gauss Elimination Method (20Marks)

 

 

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Loyola College B.Sc. Computer Science Nov 2012 Numerical Methods Using C Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – NOVEMBER 2012

CS 3203 – NUMERICAL METHODS USING C

 

 

Date : 09/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

PART – A

ANSWER ALL THE QUESTIONS:                                                                                  (10 X 2 =20)

 

  1. List out any four header files in C.
  2. Give the syntax for conditional operator.
  3. What is the use of switch case statement?
  4. What is file?
  5. What is the use of Power method?
  6. Find out the determinant of the given matrix.

5   6  1

3   2  3

5   5  5

  1. Give the formula for Simpson’s 3/8 rule
  2. What is the use of Newton’s Interpolation Method?
  3. State the formula for Newton Raphson Method.
  4. List out any two methods used to find out the roots of the non-linear equation.

PART – B

ANSWER ALL THE QUESTIONS:                                                                                 (5 X 8 =40)

 

  1. a) Write short notes on operators used in C.

(Or)

  1. b) Explain scanf() statement with suitable example.

 

12.a) Write a C program to find out whether the given number is even or odd.

(Or)

  1. b) What is meant by recursion? Write a C program to find out factorial of n numbers using recursion.

 

13.a) Solve the system of equation using Gauss Elimination method.

X + Y + Z = 6

2X – Y = 3Z = 4

4X +5Y – 10Z = 13

(Or)

  1. b) Write a C program to find out Eigen value and Eigen vector.

 

 

  1. a) Write a C program to implement Simpson’s 1/3 rule .

(or)

  1. b) Write a C program to implement Lagrange’s Interpolation Method.

 

 

 

 

  1. a) Evaluate the following integral using trapezoidal rule.

dx/1+x2 with n = 4

(Or)

  1. b) Write a C program to implement Runge – kutta IInd order method.

PART – C

ANSWER ANY TWO QUESTIONS:                                                                    (2 X 20 =40)

 

  1. a) Write a C program to find out sum and average of n numbers.
  2. b) Explain the looping statements in C with suitable example
  3. a) Write a C program to solve the system of equation using Gauss Jordan method.
  4. b) Estimate the value of Cos θ at θ =1.15 using Newton forward interpolation formula with the help of the following table.

 

Θ 1.0 1.1 1.2
Cos θ 0.5403 0.4536 0.3624

 

  1. a) Write a C program to find out transpose of a given matrix.
  2. b) Compute the root of the given equation using Bisection method.

X2 – 4X -10 = 0 with the initial value -1 & -2

 

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