REVIEW QUESTIONS AND EXERCISES

1. Write the algorithm and draw the flowchart to find the average of given 3 values.
   

Ans :

1. Read n1,n2 and n3 , where n repesent number.
2. avr = n1+n2+n3 / 3
3. print avr  

FLOWCHART :

flowchart TD
  A([Start]) --> B[Read n1,n2 and n3]
  B --> C[avr = n1+n2+n3 / 3]
  C --> D[Print avr]
  D --> E([Stop])

1. Write the algorithm and draw the flowchart to find the area and circumference of a circle of radius r.

[Hint: Area= πr²; Circumference = 2πr]

Ans :

1. Read r
2. Area = 22/7 \* r\*r , Circumference = 2\*22/7\*r
3. Print Area, Circumference

Flowchart :

flowchart TD
  A([Start]) --> B[Read r]
  B --> C[Area = 22/7\*r\*r, Circumference = 2\*22/7\*r]
  C --> D[Print Area, Circumference]
  D --> E([Stop])

1. Write the algorithm and draw the flowchart to convert the temperature given in °c to °f.

[Hint: Use the relation °f= 1.8°c +32]

Ans :

1. Read c
2. f = 1.8 * c + 32
3. Print f 

Flowchart :

flowchart TD
  A([Start]) --> B[Read c]
  B --> C[f = 1.8 \* c + 32]
  C --> D[Print f]
  D --> E([Stop])

1. Draw the flowchart to find the smallest of the given three numbers.
   Ans :

flowchart TD
  A(Start) --> B[Input A, B, C]
  B --> C{Is A < B?}
  C -- Yes --> D{Is A < C?}
  D -- Yes --> E[Smallest = A]
  D -- No --> F[Smallest = C]
  C -- No --> G{Is B < C?}
  G -- Yes --> H[Smallest = B]
  G -- No --> F
  E --> I[Print Smallest]
  F --> I
  H --> I
  I --> J(End)

1. Draw the flowchart to solve the following series which is the summation of cosine series
   $s = x - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots \infty$ neglecting the terms which are less that 10^-4 in magnitude.
   Ans :

flowchart TD
    A[Start] --> B[Input x]
    B --> C[Set term = x, sum = x, n = 1]
    C --> D{Is absolute value of term >= 0.0001?}
    D -- Yes --> E[Compute next term using: -1^n \* x^2n / 2n!]
    E --> F[Add term to sum]
    F --> G[Increment n]
    G --> D
    D -- No --> H[Print sum]
    H --> I[End]

[Hint: The method discussed in Example 8 can be used to solve this series with minor changes.]

1. Draw the flowchart to find the sum of natural numbers upto N.

[Hint: The method discussed in Example 10 can be used to solve the series, i.e. $s = 1 + 2+ 3 + 4 + … + N$.]
Ans :

flowchart TD
    A[Start] --> B[Read N and set S = 0]
    B --> C[Set i = 1]
    C --> D{Is i <= N?}
    D -- Yes --> E[S = S + i]
    E --> F[i = i + 1]
    F --> D
    D -- No --> G[Display S]
    G --> H[End]

1. Draw a flowchart to solve the following series:

\(s = 1 + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \cdots + \frac{1}{N!}\)

Ans :

flowchart TD
    A[Start] --> B[Read N, set S = 1 and i = 2]
    B --> C{Is i <= N?}
    C -- Yes --> D[Set fact = 1]
    D --> E[Set j = 1]
    E --> F{Is j <= i?}
    F -- Yes --> G[fact = fact \* j]
    G --> H[j = j + 1]
    H --> F
    F -- No --> I[S = S + 1 / fact]
    I --> J[i = i + 1]
    J --> C
    C -- No --> K[Display S]
    K --> L[End]

1. Draw a flowchart to solve the following series:
   \(e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \cdots\) ∞
   Neglect the terms which are less than 10 in magnitude.
   

Ans :

flowchart TD
    A[Start] --> B[Read x, set term = 1 and sum = 1, i = 1]
    B --> C{Is term >= 10?}
    C -- Yes --> D[term = term \* x / i]
    D --> E[sum = sum + term]
    E --> F[i = i + 1]
    F --> C
    C -- No --> G[Display sum]
    G --> H[End]

SHORT QUESTIONS

1. What is an algorithm?
   

Ans : An algorithm presents step-by-step instructions required to solve any problem.

1. What is a flowchart?
   

Ans : Flowchart is a symbolic or diagrammatic representation of an algorithm.

1. Procedural programming method is followed in C language.

2. Object-Oriented programming method is followed in C++.

3. Procedural programming method is commonly used for writing small programs which produce discrete results. (True/False) : True

4. Object-oriented programming method is commonly used to develop software packages to perform a task. (True/False) : True

5. Algorithms and flowcharts may be omitted after getting experience in writing program. (True/False) : False