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Solved 2025: MATHEMATICS: Mathematical Programming in C | FYUG 2025

Course No: MATSEC-151 | 2nd Semester
Full Marks: 50 | Pass Marks: 20 | Time: 2 Hours

UNIT-I: C Fundamentals

Question 1 (a)

1 Mark

Question: Write the syntax for variable declaration in C.

Solution:

data_type variable_name;

Example: int count; or float price;

Question 1 (b)

1 Mark

Question: Write the syntax to define a symbolic constant.

Solution:

#define CONSTANT_NAME value

Example: #define PI 3.14159

Question 1 (c)

1 Mark

Question: How will you write the arithmetic expression a² + 10a - 8 in C?

Solution:

a * a + 10 * a - 8;

Alternatively, using the math library: pow(a, 2) + 10 * a - 8;

Question 1 (d)

1 Mark

Question: How will you assign the value 100 to the variable x at the time of variable declaration?

Solution:

int x = 100;

Question 2 (a)

2 Marks

Question: Which of the following are valid variable names: Char, First_name, List one, 2int_type?

Solution:

  • Char: Valid (C is case-sensitive; char is a keyword, but Char is not).
  • First_name: Valid (contains letters and underscores).
  • List one: Invalid (contains a space).
  • 2int_type: Invalid (cannot start with a digit).

    • Question 3 (a)

    5 Marks

    Question: Write the rules for naming identifiers.

    Solution:

  • An identifier can only contain alphabets (uppercase and lowercase), digits, and underscores (_).
  • The first character must be an alphabet or an underscore. It cannot be a digit.
  • Keywords (like int, while, etc.) cannot be used as identifiers.
  • Identifiers are case-sensitive (e.g., Total and total are different).
  • No special characters or spaces are allowed except for the underscore.

    • UNIT-II: Operators and Control Flow

    Question 4 (a)

    1 Mark

    Question: What are the relational operators in C?

    Solution:

    Relational operators are used to compare two values. They are:

  • == (Equal to)
  • != (Not equal to)
  • > (Greater than)
  • < (Less than)
  • >= (Greater than or equal to)
  • <= (Less than or equal to)

    • Question 5 (a)

    2 Marks

    Question: What is the error in: int x=10; float y=4.25; x=y%x;?

    Solution:

    The error lies in the expression x = y % x;.
    Error: The modulo operator (%) can only be used with integer operands. Since y is a float, this operation is illegal in C.

    Question 6 (a)

    5 Marks

    Question: Write a C program to read two integers m and n and to decide and print whether m is a multiple of n.

    Solution:

    
#include 
int main() {
int m, n;
printf("Enter two integers (m and n): ");
scanf("%d %d", &m, &n);
if (n != 0 && m % n == 0) {
    printf("%d is a multiple of %d\n", m, n);
} else {
    printf("%d is not a multiple of %d\n", m, n);
}
return 0;

}

    UNIT-III: Loops and Logic

    Question 7 (a)

    1 Mark [span_30](start_span)

    Question: Write the general syntax of for loop.

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    Solution:

    
for (initialization; condition; increment/decrement) {
// Statements to be executed
}

    Question 9 (a)

    5 Marks [span_32](start_span)

    Question: Write the rules for switch statement.

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    Solution:

  • The switch expression must be an integral type (int or char).
  • Each case label must be a unique constant expression.
  • The break statement is optional but used to exit the switch block; otherwise, execution "falls through" to the next case.
  • The default case is optional and executes if no case matches.
  • Case labels must end with a colon (:).

    • UNIT-IV: Functions and Recursion

    Question 10 (a)

    1 Mark [span_39](start_span)

    Question: Every program must have a ______ function.

    [span_39](end_span)

    Solution:

    main

    Question 11 (b)

    2 Marks [span_41](start_span)

    Question: What is recursion?

    [span_41](end_span)

    Solution:

    Recursion is a programming technique where a function calls itself, either directly or indirectly, to solve a problem.

     It must have a base case to terminate the calls.

    Question 12 (a)

    5 Marks [span_45](start_span)

    Question: Write a C program to compute the sum of first n natural numbers using function.

    [span_45](end_span)

    Solution:

    
#include 
int findSum(int n) {
return (n * (n + 1)) / 2;
}
int main() {
int n;
printf("Enter a positive integer: ");
scanf("%d", &n);
printf("Sum of first %d natural numbers is %d\n", n, findSum(n));
return 0;
}

    UNIT-V: Arrays

    Question 13 (a)

    1 Mark

    Question: Write the syntax for declaring a two-dimensional array.

    Solution:

    data_type array_name[row_size][column_size];

    Example: int matrix[3][3];

    Question 13 (c)

    1 Mark

    Question: What is the first subscript of one-dimensional array in C?

    Solution:

    0

    Question 15 (a)

    5 Marks

    Question: Write a program to find the largest element in an integer array.

    Solution:

    
#include 
int main() {
int arr[100], n, i, max;
printf("Enter number of elements: ");
scanf("%d", &n);
printf("Enter %d elements:\n", n);
for(i = 0; i < n; i++) {
    scanf("%d", &arr[i]);
}

max = arr[0];
for(i = 1; i < n; i++) {
    if(arr[i] > max) {
        max = arr[i];
    }
}

printf("Largest element = %d\n", max);
return 0;

}

    Exam Focus Enhancements

    Exam Tips

  • When writing programs, always include #include <stdio.h> and basic indentation for full marks.
  • For short syntax questions, always provide an example.

    • Common Mistakes

  • Confusing = (assignment) with == (equality) in if conditions.
  • Forgetting that array indices start at 0, not 1.

    • Important Formulas List

  • Sum of n natural numbers: n(n+1)/2
  • Condition for multiple: m % n == 0
    • [span_57](start_span)Generated by Gemini for Knowlet Academic Solutions.[span_57](end_span)
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