Flow of Control — NCERT Solutions

Concept: A year is a leap year if:

• It is divisible by 4 AND not divisible by 100, OR
• It is divisible by 400.

$$\text{Leap year condition: } (year \% 4 == 0 \text{ and } year \% 100 \neq 0) \text{ or } (year \% 400 == 0)$$

Program:

# Program to check leap year
year = int(input("Enter a year: "))

if (year % 4 == 0 and year % 100 != 0) or (year % 400 == 0):
    print(year, "is a Leap Year.")
else:
    print(year, "is NOT a Leap Year.")

Sample Output 1:

Enter a year: 2024
2024 is a Leap Year.

Sample Output 2:

Enter a year: 1900
1900 is NOT a Leap Year.

Sample Output 3:

Enter a year: 2000
2000 is a Leap Year.

Concept: Observe the pattern:

• The absolute values are multiples of 5: $5, 10, 15, 20, 25, \ldots$
• The signs alternate: negative for odd terms, positive for even terms.

We use a for loop and a sign variable that alternates between $-1$ and $+1$.

Program:

# Program to generate the sequence -5, 10, -15, 20, -25 ... upto n terms
n = int(input("Enter the number of terms (n): "))

sign = -1
for i in range(1, n + 1):
    term = sign * (5 * i)
    print(term, end=" ")
    sign = sign * -1   # Alternate the sign

print()  # For newline at the end

Sample Output:

Enter the number of terms (n): 6
-5 10 -15 20 -25 30

Given: The series is $\displaystyle\sum_{i=1}^{n} \frac{1}{i^3} = 1 + \frac{1}{8} + \frac{1}{27} + \cdots + \frac{1}{n^3}$

Concept: Use a for loop to iterate from 1 to n, adding $\dfrac{1}{i^3}$ to the sum in each iteration.

Program:

# Program to find sum of 1 + 1/8 + 1/27 + ... + 1/n^3
n = int(input("Enter the value of n: "))

total = 0
for i in range(1, n + 1):
    total = total + (1 / (i ** 3))

print("Sum of the series =", total)

Sample Output:

Enter the value of n: 3
Sum of the series = 1.1620370370370371

Verification: $1 + \dfrac{1}{8} + \dfrac{1}{27} = 1 + 0.125 + 0.037037\ldots \approx 1.162$ ✓

Concept: Repeatedly extract the last digit using the modulo operator (% 10) and remove it using integer division (// 10), adding each digit to a running sum.

Program:

# Program to find sum of digits of a number
num = int(input("Enter an integer number: "))

# Work with the absolute value to handle negative numbers
original = num
num = abs(num)
digit_sum = 0

while num > 0:
    digit = num % 10        # Extract last digit
    digit_sum = digit_sum + digit
    num = num // 10         # Remove last digit

print("Sum of digits of", original, "=", digit_sum)

Sample Output:

Enter an integer number: 4567
Sum of digits of 4567 = 22

Trace for 4567:

• digit = 7, sum = 7, num = 456
• digit = 6, sum = 13, num = 45
• digit = 5, sum = 18, num = 4
• digit = 4, sum = 22, num = 0 → loop ends
• Result: 22 ✓

Concept: A number is a palindrome if it reads the same forwards and backwards. We reverse the number by extracting digits one by one and compare the reversed number with the original.

Program:

# Function to check if a number is a palindrome
def is_palindrome(num):
    original = num
    num = abs(num)      # Handle negative numbers
    reversed_num = 0

    while num > 0:
        digit = num % 10
        reversed_num = reversed_num * 10 + digit
        num = num // 10

    if reversed_num == abs(original):
        return True
    else:
        return False

# Main program
number = int(input("Enter a number: "))

if is_palindrome(number):
    print(number, "is a Palindrome.")
else:
    print(number, "is NOT a Palindrome.")

Sample Output 1:

Enter a number: 12321
12321 is a Palindrome.

Sample Output 2:

Enter a number: 123421
123421 is NOT a Palindrome.

Trace for 12321:

• digit=1, rev=1, num=1232
• digit=2, rev=12, num=123
• digit=3, rev=123, num=12
• digit=2, rev=1232, num=1
• digit=1, rev=12321, num=0
• reversed_num (12321) == original (12321) → Palindrome ✓

**Pattern (i): Diamond shape with )*

# Pattern i: Diamond shape
n = 3   # number of rows in upper half (excluding middle)

# Upper half (including middle)
for i in range(1, 2*n, 2):
    print('*' * i)

# Lower half
for i in range(2*n-2, 0, -2):
    print('*' * i)

Output:

*
***
*****
***
*

*(Note: Based on the pattern shown — *, *, *, *, * — this is a diamond.)*

Pattern (ii): Number palindrome pattern

# Pattern ii: Number palindrome pattern
n = 5
for i in range(1, n + 1):
    # Print descending part: i, i-1, ..., 1
    for j in range(i, 0, -1):
        print(j, end=' ')
    # Print ascending part: 2, 3, ..., i
    for j in range(2, i + 1):
        print(j, end=' ')
    print()

Output:

1 
2 1 2 
3 2 1 2 3 
4 3 2 1 2 3 4 
5 4 3 2 1 2 3 4 5 

Pattern (iii): Descending number triangle

# Pattern iii: Descending number triangle
n = 5
for i in range(n, 0, -1):
    for j in range(1, i + 1):
        print(j, end=' ')
    print()

Output:

1 2 3 4 5 
1 2 3 4 
1 2 3 
1 2 
1 

**Pattern (iv): Right-angled triangle with * (hollow)**

# Pattern iv: Hollow right-angled triangle with *
n = 5
for i in range(1, n + 1):
    for j in range(1, i + 1):
        if j == 1 or j == i or i == n:
            print('*', end=' ')
        else:
            print(' ', end=' ')
    print()

Output:

* 
* * 
*   * 
*     * 
* * * * * 

Concept: Use if-elif-else ladder to compare the percentage with the given ranges and assign the appropriate grade.

Program:

# Program to find grade based on percentage
percentage = float(input("Enter the percentage of marks: "))

if percentage > 90:
    grade = 'A'
elif percentage >= 80:   # 80 to 90
    grade = 'B'
elif percentage >= 70:   # 70 to 80
    grade = 'C'
elif percentage >= 60:   # 60 to 70
    grade = 'D'
else:                    # Below 60
    grade = 'E'

print("Percentage:", percentage)
print("Grade:", grade)

Sample Output 1:

Enter the percentage of marks: 92.5
Percentage: 92.5
Grade: A

Sample Output 2:

Enter the percentage of marks: 75.0
Percentage: 75.0
Grade: C

Sample Output 3:

Enter the percentage of marks: 55.0
Percentage: 55.0
Grade: E

Concept: Use a while loop to keep showing the menu, if-elif-else for menu selection, and another if-elif-else ladder for grade calculation.

Program:

# SMIS - Student Mark Information System
# Menu driven program for Class X marks

marks = []   # List to store marks

while True:
    print("\n===== STUDENT MARK INFORMATION SYSTEM =====")
    print("1. Enter marks of 5 subjects and display them")
    print("2. Calculate and display percentage")
    print("3. Find and display grade")
    print("4. Exit")

    choice = int(input("Enter your choice (1-4): "))

    if choice == 1:
        marks = []   # Reset marks list
        subjects = ["Subject 1", "Subject 2", "Subject 3",
                    "Subject 4", "Subject 5"]
        print("\nEnter marks out of 100 for each subject:")
        for sub in subjects:
            m = float(input(sub + ": "))
            marks.append(m)
        print("\nMarks entered:")
        for i in range(5):
            print(subjects[i], ":", marks[i])

    elif choice == 2:
        if len(marks) == 0:
            print("Please enter marks first (Option 1).")
        else:
            total = sum(marks)
            percentage = total / 5
            print("\nTotal Marks =", total)
            print("Percentage  =", percentage, "%")

    elif choice == 3:
        if len(marks) == 0:
            print("Please enter marks first (Option 1).")
        else:
            total = sum(marks)
            percentage = total / 5
            print("\nPercentage =", percentage, "%")

            if percentage > 85:
                grade = 'A'
            elif percentage >= 75:   # < 85 and >= 75
                grade = 'B'
            elif percentage >= 50:   # < 75 and >= 50
                grade = 'C'
            elif percentage > 30:    # > 30 and <= 50
                grade = 'D'
            else:                    # < 30
                grade = 'Reappear'

            print("Grade =", grade)

    elif choice == 4:
        print("Exiting the program. Goodbye!")
        break

    else:
        print("Invalid choice! Please enter a number between 1 and 4.")

Sample Output:

===== STUDENT MARK INFORMATION SYSTEM =====
1. Enter marks of 5 subjects and display them
2. Calculate and display percentage
3. Find and display grade
4. Exit
Enter your choice (1-4): 1

Enter marks out of 100 for each subject:
Subject 1: 88
Subject 2: 76
Subject 3: 92
Subject 4: 81
Subject 5: 79

Marks entered:
Subject 1 : 88.0
Subject 2 : 76.0
Subject 3 : 92.0
Subject 4 : 81.0
Subject 5 : 79.0

Enter your choice (1-4): 2
Total Marks = 416.0
Percentage  = 83.2 %

Enter your choice (1-4): 3
Percentage = 83.2 %
Grade = B

Enter your choice (1-4): 4
Exiting the program. Goodbye!