Important Questions for Class 9 Maths (Ganita Manjari II) Chapter 11 The World of Algorithms 2026-27

The Class 9 Maths Chapter 11 Important Questions PDF gives students an opportunity to practise important concepts and improve their understanding through solved examples. Work through each problem, compare your answers with the solutions and learn how to approach challenging questions more effectively.

Class 9 Maths Chapter 11 Important Questions – MCQs

Q1. Which of the following best describes an algorithm?

A) A method that works only for small numbers

B) A systematic, step-by-step procedure for solving a problem

C) A collection of numbers arranged randomly

D) A mathematical formula without any steps

Answer: B) A systematic, step-by-step procedure for solving a problem.

Explanation: An algorithm is a set of clearly defined steps used to solve a problem. Each step should be precise enough to carry out correctly.

Q2. While adding 786 and 459 using the digit-by-digit addition algorithm, what is the carry generated from the units column?

A) 0

B) 1

C) 2

D) 5

Answer: B) 1

Solution:

Units digits: 6 + 9 = 15

Write 5 in the units place and carry 1 to the tens column.

Therefore, the carry is 1.

Q3. An algorithm checks every positive integer from 1 to 36 and adds it to a list if it divides 36 exactly. Which of the following lists is correct?

A) [1, 2, 3, 4, 6, 9, 12, 18, 36]

B) [1, 2, 3, 6, 12, 36]

C) [2, 3, 4, 6, 9, 12, 18]

D) [1, 3, 6, 9, 18, 36]

Answer: A) [1, 2, 3, 4, 6, 9, 12, 18, 36]

Explanation: Each number in option A divides 36 without leaving a remainder. Since the algorithm checks numbers in increasing order, the list is also arranged in increasing order.

Q4. In Āryabhaṭa's division algorithm, what does the expression m mod n represent?

A) The product of m and n

B) The quotient when m is divided by n

C) The remainder when m is divided by n

D) The difference between m and n

Answer: C) The remainder when m is divided by n.

Explanation: The expression m mod n gives the remainder after dividing m by n.

For example:

29 ÷ 6 = 4 remainder 5

Therefore, 29 mod 6 = 5.

H3: Class 9 Maths Chapter 11 Very Short Answer Questions

Q5. What is meant by executing an algorithm?

Answer:

Executing an algorithm means following its instructions step by step to obtain the required result.

For example, checking the numbers from 1 to 12 to identify all divisors of 12 is an execution of a divisor-finding algorithm.

Q6. What is a data structure? Give one example from the chapter.

Answer:

A data structure is a way of organising and storing information so that an algorithm can use it.

For example, the list [1, 2, 4, 8, 16] stores the divisors of 16 in increasing order.

Q7. Find the value of gcd(48, 0).

Answer:

The GCD of a positive integer and 0 is the positive integer itself.

Therefore,

gcd(48, 0) = 48

This is also the stopping condition used in Euclid's algorithm.

H3: Class 9 Maths Chapter 11 Short Answer Questions

Q8. Write the steps of an algorithm to find the divisors of 24. Also, write the final list of divisors.

Solution:

Step 1: Start with an empty list.

List = [ ]

Step 2: Check every number from 1 to 24.

Step 3: If a number divides 24 exactly, add it to the list.

The numbers that divide 24 exactly are:

1, 2, 3, 4, 6, 8, 12 and 24.

Step 4: Write the completed list.

Answer:

divisors(24) = [1, 2, 3, 4, 6, 8, 12, 24]

The list is in increasing order because the algorithm checks the numbers from smallest to largest.

Q9. Find the GCD of 42 and 70 by comparing their lists of divisors.

Solution:

Step 1: 

Find the divisors of 42.

divisors(42) = [1, 2, 3, 6, 7, 14, 21, 42]

Step 2: 

Find the divisors of 70.

divisors(70) = [1, 2, 5, 7, 10, 14, 35, 70]

Step 3: 

Identify the common divisors.

Common divisors = [1, 2, 7, 14]

Step 4: 

Select the greatest common divisor.

The largest number in the common-divisors list is 14.

Answer: gcd(42, 70) = 14

Q10. An algorithm checks every number from 1 to the smaller of two given numbers to find their GCD. Explain how it can be improved without storing a list of common divisors.

Solution:

Instead of storing every common divisor, the algorithm can keep track of only the largest common divisor found so far.

Step 1: 

Set most-recent-common-divisor = 1.

Step 2: 

Check each number from 2 to the smaller of the two given numbers.

Step 3: 

Whenever a number divides both given numbers, update most-recent-common-divisor to that number.

Step 4: 

After checking all the numbers, report the final value.

Example: Find gcd(18, 30).

Initially, most-recent-common-divisor = 1.

Both numbers are divisible by 2, so update it to 2.

Both are divisible by 3, so update it to 3.

Both are divisible by 6, so update it to 6.

No larger number up to 18 divides both numbers.

Answer: gcd(18, 30) = 6

Why is this better?

The improved algorithm does not need to store a complete list of common divisors. It stores only one value, reducing the amount of information that must be maintained.

Class 9 Maths Chapter 11 Long Answer Questions

Q11. Use Euclid's subtraction algorithm to find the GCD of 84 and 36. Show every reduction step.

Solution:

Euclid's subtraction algorithm uses the property:

$$\gcd(m,n)=\gcd(n,m-n)$$, when $$m\geq n$$.

If the first number is smaller, interchange the numbers.

Step 1:

gcd(84, 36)

84 − 36 = 48

Therefore,

gcd(84, 36) = gcd(36, 48)

Step 2:

Interchange the numbers:

gcd(48, 36)

48 − 36 = 12

Therefore,

gcd(48, 36) = gcd(36, 12)

Step 3:

36 − 12 = 24

gcd(36, 12) = gcd(12, 24)

Step 4:

Interchange the numbers and subtract:

24 − 12 = 12

gcd(24, 12) = gcd(12, 12)

Step 5:

12 − 12 = 0

gcd(12, 12) = gcd(12, 0)

The algorithm stops when the second number becomes 0.

Answer: gcd(84, 36) = 12

Q12. Find the GCD of 252 and 198 using Āryabhaṭa's division algorithm. Explain why this method is more efficient than repeated subtraction.

Solution:

Āryabhaṭa's division algorithm uses:

$$\gcd(m,n)=\gcd(n,m\bmod n)$$

The process continues until the remainder becomes 0.

Step 1: 

Divide 252 by 198.

252 = 198 × 1 + 54

Therefore,

gcd(252, 198) = gcd(198, 54)

Step 2: 

Divide 198 by 54.

198 = 54 × 3 + 36

Therefore,

gcd(198, 54) = gcd(54, 36)

Step 3: 

Divide 54 by 36.

54 = 36 × 1 + 18

Therefore,

gcd(54, 36) = gcd(36, 18)

Step 4: 

Divide 36 by 18.

36 = 18 × 2 + 0

Therefore,

gcd(36, 18) = gcd(18, 0)

Answer: gcd(252, 198) = 18

Q13. A student wants to find the GCD of 96 and 64 using two algorithms.

(a) Find the GCD by listing the common divisors.

(b) Find the GCD using Āryabhaṭa's division algorithm.

Solution:

(a) Using lists of divisors

Step 1: 

Find the divisors of 96.

divisors(96) = [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96]

Step 2: 

Find the divisors of 64.

divisors(64) = [1, 2, 4, 8, 16, 32, 64]

Step 3: 

Identify the common divisors.

Common divisors = [1, 2, 4, 8, 16, 32]

The greatest common divisor is 32.

Therefore,

gcd(96, 64) = 32

(b) Using Āryabhaṭa's division algorithm

Step 1:

96 = 64 × 1 + 32

Therefore,

gcd(96, 64) = gcd(64, 32)

Step 2:

64 = 32 × 2 + 0

Therefore,

gcd(64, 32) = gcd(32, 0)

Hence,

gcd(96, 64) = 32

How to Solve Class 9 Maths Chapter 11 Algorithm-Based Questions Easily?

In The World of Algorithms, students learn to solve mathematical problems using logical steps and a clear sequence of instructions. Understanding how algorithms work helps students organise their thinking and avoid errors.

Follow these tips to solve algorithm-based questions:

• Understand the Problem: Identify the given information and what needs to be found.

• Follow the Sequence: Arrange the steps in the correct order to reach the answer.

• Use Simple Examples: Test an algorithm with small numbers to understand how it works.

• Check Each Step: Look for missing instructions or errors in the process.

• Verify the Result: Make sure the final answer follows the given conditions.

Why Choose Vedantu's Class 9 Maths Chapter 11 Important Questions PDF?

Vedantu's Class 9 Maths Chapter 11 Important Questions with Solutions help students practise The World of Algorithms through chapter-focused problems and clear explanations.

Here's how the PDF supports learning:

• Focused Practice: Work on important algorithm-based questions in one place.

• Clear Solutions: Understand the logical steps needed to solve each problem.

• Independent Learning: Attempt questions first and use the answers to check your approach.

• Easy PDF Access: Download and practise questions anytime, even offline.

• Exam Preparation: Build confidence in solving logical reasoning and algorithm-based problems.

The Class 9 Maths Chapter 11 Important Questions PDF helps students strengthen their understanding and prepare for the 2026-27 school exams.

Important Study Materials for Class 9 Maths (Manjari PART-II) Chapter 11 The World of Algorithms

CBSE Class 9 Maths Chapter-wise Important Questions

Other Important Related Links for CBSE Class 9 Maths