Functions — NCERT Solutions

# Play and Learn program for toddlers
import random

def two_letter_words():
    """
    Function to quiz children on two-letter words.
    """
    words = ["at", "in", "on", "up", "go", "do", "be", "me", "he", "we"]
    word  = random.choice(words)
    # Display word with one letter missing
    pos   = random.randint(0, 1)
    hint  = list(word)
    hint[pos] = "_"
    print(f"\nComplete the two-letter word: {''.join(hint)}")
    answer = input("Your answer: ").strip().lower()
    if answer == word:
        print("Correct! Well done!")
    else:
        print(f"Oops! The correct word is: {word}")

def three_letter_words():
    """
    Function to quiz children on three-letter words.
    """
    words = ["cat", "bat", "hat", "dog", "pig", "hen", "sun", "run", "fun", "cup"]
    word  = random.choice(words)
    pos   = random.randint(0, 2)
    hint  = list(word)
    hint[pos] = "_"
    print(f"\nComplete the three-letter word: {''.join(hint)}")
    answer = input("Your answer: ").strip().lower()
    if answer == word:
        print("Correct! Well done!")
    else:
        print(f"Oops! The correct word is: {word}")

def addition_quiz():
    """
    Function to quiz children on addition of single digit numbers.
    """
    a = random.randint(1, 9)
    b = random.randint(1, 9)
    print(f"\nWhat is {a} + {b} ?")
    try:
        answer = int(input("Your answer: "))
        if answer == a + b:
            print("Correct! Great job!")
        else:
            print(f"Oops! The correct answer is: {a + b}")
    except ValueError:
        print("Please enter a valid number.")

# Main program
print("=== Welcome to Play and Learn ===")
while True:
    print("\n1. Two-letter words")
    print("2. Three-letter words")
    print("3. Addition of numbers")
    print("4. Exit")
    choice = input("Choose an activity (1-4): ")
    if choice == '1':
        two_letter_words()
    elif choice == '2':
        three_letter_words()
    elif choice == '3':
        addition_quiz()
    elif choice == '4':
        print("Goodbye! Keep learning!")
        break
    else:
        print("Invalid choice. Please try again.")

# Program to generate Fibonacci sequence using user defined function

def fibonacci(n):
    """
    Function to generate and display Fibonacci sequence up to n terms.
    Parameter: n - number of terms to generate
    """
    if n <= 0:
        print("Please enter a positive integer.")
        return
    elif n == 1:
        print("Fibonacci sequence:")
        print(1)
        return

    # Initialize first two terms
    first  = 1
    second = 1
    print("Fibonacci sequence:")
    print(first, end=" ")
    print(second, end=" ")

    # Generate remaining terms
    for i in range(3, n + 1):
        next_term = first + second
        print(next_term, end=" ")
        first  = second
        second = next_term
    print()  # newline at end

# Main program
terms = int(input("Enter the number of terms: "))
fibonacci(terms)

Sample Output:

Enter the number of terms: 10
Fibonacci sequence:
1 1 2 3 5 8 13 21 34 55

Explanation:

• The function starts with first = 1 and second = 1.
• Each subsequent term is computed as next_term = first + second.
• The variables are then shifted: first = second, second = next_term.
• This continues for n total terms.

# Menu-driven calculator using user defined functions
import math

def add(a, b):
    """Returns sum of a and b"""
    return a + b

def subtract(a, b):
    """Returns difference of a and b"""
    return a - b

def multiply(a, b):
    """Returns product of a and b"""
    return a * b

def divide(a, b):
    """Returns quotient of a divided by b"""
    if b == 0:
        return "Error: Division by zero!"
    return a / b

def log10_val(x):
    """Returns log base 10 of x"""
    if x <= 0:
        return "Error: log undefined for non-positive values!"
    return math.log10(x)

def sin_val(x):
    """Returns sine of x (x in degrees)"""
    return math.sin(math.radians(x))

def cos_val(x):
    """Returns cosine of x (x in degrees)"""
    return math.cos(math.radians(x))

# Main program
print("========== CALCULATOR ==========")
while True:
    print("\n--- MENU ---")
    print("1. Addition (+)")
    print("2. Subtraction (-)")
    print("3. Multiplication (*)")
    print("4. Division (/)")
    print("5. log10(x)")
    print("6. sin(x)")
    print("7. cos(x)")
    print("8. Exit")

    choice = input("\nEnter your choice (1-8): ")

    if choice in ['1', '2', '3', '4']:
        a = float(input("Enter first number : "))
        b = float(input("Enter second number: "))
        if choice == '1':
            print(f"Result: {a} + {b} = {add(a, b)}")
        elif choice == '2':
            print(f"Result: {a} - {b} = {subtract(a, b)}")
        elif choice == '3':
            print(f"Result: {a} * {b} = {multiply(a, b)}")
        elif choice == '4':
            print(f"Result: {a} / {b} = {divide(a, b)}")

    elif choice in ['5', '6', '7']:
        x = float(input("Enter the value of x: "))
        if choice == '5':
            print(f"Result: log10({x}) = {log10_val(x)}")
        elif choice == '6':
            print(f"Result: sin({x}°) = {sin_val(x):.4f}")
        elif choice == '7':
            print(f"Result: cos({x}°) = {cos_val(x):.4f}")

    elif choice == '8':
        print("Exiting calculator. Goodbye!")
        break
    else:
        print("Invalid choice! Please enter a number between 1 and 8.")

Sample Output:

--- MENU ---
1. Addition (+)
...
Enter your choice (1-8): 6
Enter the value of x: 90
Result: sin(90°) = 1.0000

# Program to check divisibility of a number by 7

def check_divisibility(num):
    """
    Function to check if num is divisible by 7.
    Parameter: num - the number to check
    """
    if num % 7 == 0:
        print(f"{num} is divisible by 7.")
    else:
        print(f"{num} is NOT divisible by 7.")

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

Sample Output 1:

Enter a number: 49
49 is divisible by 7.

Sample Output 2:

Enter a number: 20
20 is NOT divisible by 7.

# Program to prefix Mr/Ms based on gender

def display_name(name, gender):
    """
    Function to display name with appropriate prefix.
    Parameters: name   - person's name
                gender - 'M' for Male, 'F' for Female
    """
    gender = gender.upper()
    if gender == 'M':
        print(f"Hello, Mr. {name}")
    elif gender == 'F':
        print(f"Hello, Ms. {name}")
    else:
        print("Invalid gender entered. Please enter M or F.")

# Main program
person_name   = input("Enter name  : ")
person_gender = input("Enter gender (M/F): ")
display_name(person_name, person_gender)

Sample Output 1:

Enter name  : Arjun
Enter gender (M/F): M
Hello, Mr. Arjun

Sample Output 2:

Enter name  : Priya
Enter gender (M/F): F
Hello, Ms. Priya

Concept: For a quadratic equation $ax^2 + bx + c = 0$, the discriminant (determinant) $D = b^2 - 4ac$ determines the nature of roots:

• $D > 0$: Two distinct real roots
• $D = 0$: Two equal real roots
• $D < 0$: No real roots (complex roots)

# Program to find discriminant of a quadratic equation
import math

def quadratic_discriminant(a, b, c):
    """
    Function to calculate discriminant and determine nature of roots.
    Parameters: a, b, c - coefficients of quadratic equation ax^2 + bx + c = 0
    """
    if a == 0:
        print("Coefficient 'a' cannot be 0 for a quadratic equation.")
        return

    discriminant = b**2 - 4*a*c
    print(f"\nQuadratic Equation: {a}x² + {b}x + {c} = 0")
    print(f"Discriminant D = b² - 4ac = {b}² - 4×{a}×{c} = {discriminant}")

    if discriminant > 0:
        root1 = (-b + math.sqrt(discriminant)) / (2*a)
        root2 = (-b - math.sqrt(discriminant)) / (2*a)
        print("D > 0: Two distinct real roots exist.")
        print(f"Root 1 = {root1:.2f}")
        print(f"Root 2 = {root2:.2f}")
    elif discriminant == 0:
        root = -b / (2*a)
        print("D = 0: Two equal real roots exist.")
        print(f"Root = {root:.2f}")
    else:
        print("D < 0: No real roots. Roots are complex/imaginary.")

# Main program
print("Enter coefficients of quadratic equation ax² + bx + c = 0")
a = float(input("Enter a: "))
b = float(input("Enter b: "))
c = float(input("Enter c: "))
quadratic_discriminant(a, b, c)

Sample Output:

Enter a: 1
Enter b: -5
Enter c: 6

Quadratic Equation: 1.0x² + -5.0x + 6.0 = 0
Discriminant D = b² - 4ac = -5.0² - 4×1.0×6.0 = 1.0
D > 0: Two distinct real roots exist.
Root 1 = 3.00
Root 2 = 2.00

# Program to automate lucky draw for ABC School Annual Day
import random

def lucky_draw():
    """
    Function to randomly select a winner from token IDs 1 to 600.
    Returns: winning token ID
    """
    winner = random.randint(1, 600)
    return winner

def display_result(winner_id):
    """
    Function to display the lucky draw result.
    Parameter: winner_id - the winning token number
    """
    print("\n========================================")
    print("   ABC SCHOOL ANNUAL DAY LUCKY DRAW")
    print("========================================")
    print(f"  🎉 Congratulations! 🎉")
    print(f"  The Lucky Winner is Token ID: {winner_id}")
    print("========================================")

# Main program
print("Welcome to ABC School Annual Day Lucky Draw!")
print("Token IDs range from 1 to 600.")
input("\nPress ENTER to draw the lucky winner...")

winning_token = lucky_draw()
display_result(winning_token)

Sample Output:

Welcome to ABC School Annual Day Lucky Draw!
Token IDs range from 1 to 600.

Press ENTER to draw the lucky winner...

========================================
   ABC SCHOOL ANNUAL DAY LUCKY DRAW
========================================
  🎉 Congratulations! 🎉
  The Lucky Winner is Token ID: 347
========================================

Formula:
$$A = P \times \left(1 + \frac{r}{n}\right)^{n \times t}$$
$$CI = A - P$$

Where:

• $P$ = Principal Amount
• $r$ = Annual Rate of Interest (in decimal, e.g., 5% = 0.05)
• $t$ = Time in years
• $n$ = Number of times interest is compounded per year

# Program to calculate Compound Interest

def compound_interest(P, r, t, n):
    """
    Function to calculate compound interest.
    Parameters:
        P - Principal Amount
        r - Annual Rate of Interest (in %)
        t - Time in years
        n - Number of times interest compounded per year
    """
    r = r / 100          # Convert percentage to decimal
    A  = P * (1 + r/n) ** (n * t)   # Amount after interest
    CI = A - P                        # Compound Interest

    print(f"\nPrincipal Amount (P)        : Rs. {P:.2f}")
    print(f"Annual Rate of Interest (r) : {r*100:.2f}%")
    print(f"Time (t)                    : {t} years")
    print(f"Compounded (n)              : {n} times/year")
    print(f"Amount (A)                  : Rs. {A:.2f}")
    print(f"Compound Interest (CI)      : Rs. {CI:.2f}")

# Main program
P = float(input("Enter Principal Amount       : Rs. "))
r = float(input("Enter Annual Rate of Interest: % "))
t = float(input("Enter Time (in years)        : "))
n = int(input("Enter number of times compounded per year: "))
compound_interest(P, r, t, n)

Sample Output:

Enter Principal Amount       : Rs. 10000
Enter Annual Rate of Interest: % 5
Enter Time (in years)        : 2
Enter number of times compounded per year: 12

Principal Amount (P)        : Rs. 10000.00
Annual Rate of Interest (r) : 5.00%
Time (t)                    : 2.0 years
Compounded (n)              : 12 times/year
Amount (A)                  : Rs. 11049.41
Compound Interest (CI)      : Rs. 1049.41

# Program to swap two numbers if first is less than second

def swap_if_less(num1, num2):
    """
    Function to swap num1 and num2 if num1 < num2.
    Parameters: num1, num2 - two numbers
    Returns: (num2, num1) if num1 < num2, else (num1, num2)
    """
    if num1 < num2:
        # Swap: return num2 in place of num1 and num1 in place of num2
        return num2, num1
    else:
        # No swap needed
        return num1, num2

# Main program
a = float(input("Enter number 1: "))
b = float(input("Enter number 2: "))

result1, result2 = swap_if_less(a, b)

print(f"\nOriginal : Number 1 = {a}, Number 2 = {b}")
if a < b:
    print("Since Number 1 < Number 2, numbers are swapped.")
else:
    print("Since Number 1 >= Number 2, no swap needed.")
print(f"Returned : Number 1 = {result1}, Number 2 = {result2}")

Sample Output 1 (swap occurs):

Enter number 1: 5
Enter number 2: 10

Original : Number 1 = 5.0, Number 2 = 10.0
Since Number 1 < Number 2, numbers are swapped.
Returned : Number 1 = 10.0, Number 2 = 5.0

Sample Output 2 (no swap):

Enter number 1: 15
Enter number 2: 8

Original : Number 1 = 15.0, Number 2 = 8.0
Since Number 1 >= Number 2, no swap needed.
Returned : Number 1 = 15.0, Number 2 = 8.0

Step 1: Create a module file named shapes.py

# shapes.py — Module containing functions for various shapes
import math

def square_area(side):
    """Returns area of a square. Formula: side²"""
    return side ** 2

def square_perimeter(side):
    """Returns perimeter of a square. Formula: 4 × side"""
    return 4 * side

def rectangle_area(length, breadth):
    """Returns area of a rectangle. Formula: l × b"""
    return length * breadth

def rectangle_perimeter(length, breadth):
    """Returns perimeter of a rectangle. Formula: 2(l + b)"""
    return 2 * (length + breadth)

def triangle_area(base, height):
    """Returns area of a triangle. Formula: 0.5 × base × height"""
    return 0.5 * base * height

def triangle_perimeter(a, b, c):
    """Returns perimeter of a triangle. Formula: a + b + c"""
    return a + b + c

def circle_area(radius):
    """Returns area of a circle. Formula: π × r²"""
    return math.pi * radius ** 2

def circle_perimeter(radius):
    """Returns circumference of a circle. Formula: 2πr"""
    return 2 * math.pi * radius

def cylinder_surface_area(radius, height):
    """Returns total surface area of a cylinder. Formula: 2πr(r + h)"""
    return 2 * math.pi * radius * (radius + height)

Step 2: Create the main program file

# main.py — Main program that imports and uses shapes module
import shapes

print("===== SHAPE CALCULATOR =====")
print("1. Square")
print("2. Rectangle")
print("3. Triangle")
print("4. Circle")
print("5. Cylinder")

choice = int(input("\nEnter your choice (1-5): "))

if choice == 1:
    s = float(input("Enter side of square: "))
    print(f"Area      = {shapes.square_area(s):.2f}")
    print(f"Perimeter = {shapes.square_perimeter(s):.2f}")

elif choice == 2:
    l = float(input("Enter length: "))
    b = float(input("Enter breadth: "))
    print(f"Area      = {shapes.rectangle_area(l, b):.2f}")
    print(f"Perimeter = {shapes.rectangle_perimeter(l, b):.2f}")

elif choice == 3:
    base   = float(input("Enter base: "))
    height = float(input("Enter height: "))
    a      = float(input("Enter side a: "))
    b      = float(input("Enter side b: "))
    c      = float(input("Enter side c: "))
    print(f"Area      = {shapes.triangle_area(base, height):.2f}")
    print(f"Perimeter = {shapes.triangle_perimeter(a, b, c):.2f}")

elif choice == 4:
    r = float(input("Enter radius: "))
    print(f"Area          = {shapes.circle_area(r):.2f}")
    print(f"Circumference = {shapes.circle_perimeter(r):.2f}")

elif choice == 5:
    r = float(input("Enter radius: "))
    h = float(input("Enter height: "))
    print(f"Total Surface Area = {shapes.cylinder_surface_area(r, h):.2f}")

else:
    print("Invalid choice!")

Sample Output:

Enter your choice (1-5): 4
Enter radius: 7
Area          = 153.94
Circumference = 43.98

# GK Quiz Program with random questions, score and remarks
import random

# GK Questions: list of [question, option_a, option_b, option_c, option_d, correct_answer]
questions = [
    ["What is the capital of India?",
     "A. Mumbai", "B. New Delhi", "C. Kolkata", "D. Chennai", "B"],
    ["Which planet is known as the Red Planet?",
     "A. Venus", "B. Jupiter", "C. Mars", "D. Saturn", "C"],
    ["Who wrote the national anthem of India?",
     "A. Bankim Chandra", "B. Rabindranath Tagore", "C. Sarojini Naidu", "D. Mahatma Gandhi", "B"],
    ["What is the chemical symbol for Gold?",
     "A. Go", "B. Gd", "C. Au", "D. Ag", "C"],
    ["How many continents are there on Earth?",
     "A. 5", "B. 6", "C. 8", "D. 7", "D"]
]

def score(user_answers, correct_answers):
    """
    Function to calculate the quiz score.
    Parameters: user_answers    - list of answers given by user
                correct_answers - list of correct answers
    Returns: total score
    """
    total = 0
    for i in range(len(correct_answers)):
        if user_answers[i].upper() == correct_answers[i]:
            total += 1
    return total

def remark(scorevalue):
    """
    Function to display remark based on score.
    Parameter: scorevalue - the final score
    """
    print(f"\nYour Score: {scorevalue} / 5")
    if scorevalue == 5:
        print("Remark: Outstanding")
    elif scorevalue == 4:
        print("Remark: Excellent")
    elif scorevalue == 3:
        print("Remark: Good")
    elif scorevalue == 2:
        print("Remark: Read more to score more")
    elif scorevalue == 1:
        print("Remark: Needs to take interest")
    else:
        print("Remark: General knowledge will always help you. Take it seriously.")

# Main program
print("========== GK QUIZ ==========")
print("Answer each question with A, B, C, or D.\n")

# Shuffle questions for random display
random.shuffle(questions)

user_answers    = []
correct_answers = []

for idx, q in enumerate(questions):
    print(f"Q{idx+1}. {q[0]}")
    print(f"   {q[1]}")
    print(f"   {q[2]}")
    print(f"   {q[3]}")
    print(f"   {q[4]}")
    ans = input("   Your answer: ").strip().upper()
    user_answers.append(ans)
    correct_answers.append(q[5])
    print()

# Calculate and display score and remark
final_score = score(user_answers, correct_answers)
remark(final_score)

Sample Output:

========== GK QUIZ ==========
Q1. Which planet is known as the Red Planet?
   A. Venus
   B. Jupiter
   C. Mars
   D. Saturn
   Your answer: C
...
Your Score: 4 / 5
Remark: Excellent

Note: This question refers to the SMIS (Student Management Information System) developed in Chapters 5 and 6. The general approach to convert any functionality into user defined functions is shown below.

Concept: Each menu option or logical task should be wrapped in its own user defined function. The main program then calls these functions based on user choice.

General Structure:

# SMIS - Student Management Information System
# Using User Defined Functions

def input_student_details():
    """
    Function to accept and store student details.
    """
    name    = input("Enter student name   : ")
    roll_no = int(input("Enter roll number    : "))
    marks   = float(input("Enter marks obtained : "))
    return name, roll_no, marks

def display_student_details(name, roll_no, marks):
    """
    Function to display student details.
    """
    print("\n--- Student Details ---")
    print(f"Name        : {name}")
    print(f"Roll Number : {roll_no}")
    print(f"Marks       : {marks}")

def calculate_grade(marks):
    """
    Function to calculate grade based on marks.
    Parameter: marks - marks obtained by student
    Returns: grade as a string
    """
    if marks >= 90:
        return 'A+'
    elif marks >= 80:
        return 'A'
    elif marks >= 70:
        return 'B'
    elif marks >= 60:
        return 'C'
    elif marks >= 33:
        return 'D'
    else:
        return 'F'

def display_result(name, marks):
    """
    Function to display result with grade.
    """
    grade = calculate_grade(marks)
    print(f"\nResult for {name}:")
    print(f"Marks : {marks}")
    print(f"Grade : {grade}")
    if grade != 'F':
        print("Status: PASS")
    else:
        print("Status: FAIL")

# Main Menu
def main():
    while True:
        print("\n===== SMIS MENU =====")
        print("1. Enter Student Details")
        print("2. Display Student Details")
        print("3. Display Result")
        print("4. Exit")
        choice = input("Enter choice: ")

        if choice == '1':
            name, roll_no, marks = input_student_details()
        elif choice == '2':
            display_student_details(name, roll_no, marks)
        elif choice == '3':
            display_result(name, marks)
        elif choice == '4':
            print("Exiting SMIS. Goodbye!")
            break
        else:
            print("Invalid choice!")

main()

Key Principle: Each distinct operation (input, display, grade calculation, result) is encapsulated in its own function, promoting modularity and reusability.

Formula:
$$\text{Attendance \%} = \frac{\text{Days Present}}{\text{Total Working Days}} \times 100$$

• If Attendance % $< 78\%$ → return 1 (short attendance / defaulter)
• If Attendance % $\geq 78\%$ → return 0 (attendance is not short)

# Function to check short attendance

def check_attendance(total_working_days):
    """
    Function to check if a student has short attendance.
    Parameter: total_working_days - total number of working days in a month
    Returns: 1 if attendance < 78% (short attendance / defaulter)
             0 if attendance >= 78% (attendance is fine)
    """
    days_present = int(input(f"Enter number of days present (out of {total_working_days}): "))

    # Validate input
    if days_present < 0 or days_present > total_working_days:
        print("Invalid input: days present cannot be negative or exceed working days.")
        return -1

    # Calculate attendance percentage
    attendance_percent = (days_present / total_working_days) * 100

    print(f"\nDays Present    : {days_present}")
    print(f"Working Days    : {total_working_days}")
    print(f"Attendance      : {attendance_percent:.2f}%")

    if attendance_percent < 78:
        print("Status: SHORT ATTENDANCE (Defaulter)")
        return 1
    else:
        print("Status: Attendance is satisfactory.")
        return 0

# Integration into SMIS main menu
total_days = int(input("Enter total working days in the month: "))
result = check_attendance(total_days)

if result == 1:
    print("\nAlert: Student is marked as DEFAULTER due to short attendance.")
elif result == 0:
    print("\nStudent attendance is within acceptable limits.")

Sample Output 1 (Short Attendance):

Enter total working days in the month: 25
Enter number of days present (out of 25): 18

Days Present    : 18
Working Days    : 25
Attendance      : 72.00%
Status: SHORT ATTENDANCE (Defaulter)

Alert: Student is marked as DEFAULTER due to short attendance.

Sample Output 2 (Attendance OK):

Enter total working days in the month: 25
Enter number of days present (out of 25): 22

Days Present    : 22
Working Days    : 25
Attendance      : 88.00%
Status: Attendance is satisfactory.

Student attendance is within acceptable limits.