The World of Algorithms — Class 9 MCQs with Answers
Class 9 CBSE Mathematics · Chapter 11
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 9 CBSE Mathematics questions from Chapter 11, "The World of Algorithms". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams and the JEE & NEET foundation years get right.
To score well in "The World of Algorithms", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on The World of Algorithms, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 9 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
The World of Algorithms — important questions & MCQs with answers (Class 9 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation.
- Q1Easy
In this chapter, what is an algorithm?
A.A table of answers learnt by heartB.A guess that is then checked by trialC.A step-by-step procedure to arrive at an answer✓ CorrectD.A single formula that gives the answer in one lineAnswer: C. A step-by-step procedure to arrive at an answer
Explanation: The chapter calls an algorithm a step-by-step procedure to arrive at an answer, written as precisely as possible. A formula or a memorised table is not a list of steps to follow.
- Q2Easy
The algorithm to find the divisors of n checks which numbers j?
A.Only the numbers from 2 to n − 1B.Only the numbers from 1 to 10C.Every j in 1, 2, 3, …, n✓ CorrectD.Only the prime numbers up to nAnswer: C. Every j in 1, 2, 3, …, n
Explanation: The algorithm checks each j from 1 to n and adds j to list-of-divisors if j divides n. Skipping 1 and n, or checking only primes, would miss divisors.
- Q3Easy
In this chapter, a list of numbers kept in ascending order is given as an example of a:
A.data structure✓ CorrectB.remainderC.prime factorisationD.basic stepAnswer: A. data structure
Explanation: A list is an example of a data structure: a way to organise information so that an algorithm can work well.
- Q4Easy
Euclid's subtraction algorithm is based on which fact, for m ≥ n?
A.gcd(m, n) = gcd(n, m + n)B.gcd(m, n) = gcd(n, m × n)C.gcd(m, n) = m − nD.gcd(m, n) = gcd(n, m − n)✓ CorrectAnswer: D. gcd(m, n) = gcd(n, m − n)
Explanation: Any common divisor of m and n also divides m − n, and the other way round, so the gcd does not change when m is replaced by m − n.
- Q5Easy
Here m mod n means the remainder when m is divided by n. What is 29 mod 6?
A.4B.5✓ CorrectC.1D.23Answer: B. 5
Explanation: 29 = 4 × 6 + 5, so the remainder is 5. The quotient 4 is not the answer, because m mod n means the remainder.
- Q6Easy
To write prime(n) using divisors(n), we can say n is prime exactly when divisors(n):
A.has an odd number of entriesB.has exactly two numbers in it✓ CorrectC.has exactly one number in itD.contains the number 2Answer: B. has exactly two numbers in it
Explanation: A prime p has exactly two distinct divisors, 1 and p, so its divisors list has two entries. The number 2 appears only in the lists of even numbers.
- Q7Medium
In Step 3 of the addition algorithm we add two digits and the carry. What is the largest sum one column can give?
A.19✓ CorrectB.27C.20D.18Answer: A. 19
Explanation: The biggest digits are 9 and 9 and the carry is at most 1, so 9 + 9 + 1 = 19. So the next carry is again at most 1. 18 forgets the carry.
- Q8Medium
Using the divisors algorithm, how many numbers are in divisors(36)?
A.8B.9✓ CorrectC.7D.10Answer: B. 9
Explanation: divisors(36) = [1, 2, 3, 4, 6, 9, 12, 18, 36], which has 9 entries. Pairing gives (1, 36), (2, 18), (3, 12), (4, 9), (6, 6), and 6 must be counted only once, not twice.
- Q9Medium
We combine the two scans into one and run j from 1 to max(m, n). For m = 96 and n = 150, how many values of j are checked?
A.246B.150✓ CorrectC.14400D.96Answer: B. 150
Explanation: One combined scan runs up to max(96, 150) = 150. 246 = 96 + 150 is the count for two separate scans.
- Q10Medium
Use Euclid's subtraction algorithm on gcd(91, 35). What is the gcd, and how many reduction steps (Step 3) are used?
A.gcd 7, after 6 reductions✓ CorrectB.gcd 5, after 6 reductionsC.gcd 7, after 4 reductionsD.gcd 1, after 6 reductionsAnswer: A. gcd 7, after 6 reductions
Explanation: The pairs go (91, 35) → (35, 56) → (56, 35) → (35, 21) → (21, 14) → (14, 7) → (7, 7) → (7, 0): six subtractions and one reversal, giving 7. Four steps is the count for the division method.
- Q11Medium
Use Āryabhaṭa's division algorithm on gcd(252, 105). What is the gcd, and how many reductions are used?
A.42, after 1 reductionB.21, after 3 reductions✓ CorrectC.7, after 3 reductionsD.21, after 2 reductionsAnswer: B. 21, after 3 reductions
Explanation: 252 mod 105 = 42, 105 mod 42 = 21, 42 mod 21 = 0, so we reach gcd(21, 0) after 3 reductions. The last step that gives remainder 0 is also a reduction.
- Q12Hard
Using the column-by-column addition method with carries, how many carries happen when you add 4,789 + 5,326?
A.3B.2C.4✓ CorrectD.5Answer: C. 4
Explanation: Units 9 + 6 = 15, tens 8 + 2 + 1 = 11, hundreds 7 + 3 + 1 = 11 and thousands 4 + 5 + 1 = 10, so every column carries: 4 carries, and the sum is 10,115. Counting 3 misses that a column sum of exactly 10 also carries; 5 wrongly counts the final leading 1 as another carry.
- Q13Hard
Run the first gcd algorithm on m = 144, n = 180. How many divisibility checks do Steps 1 and 2 make in all, and how many values of x does Step 4 go through?
A.180 checks; 15 values of xB.324 checks; 15 values of x✓ CorrectC.324 checks; 18 values of xD.144 checks; 18 values of xAnswer: B. 324 checks; 15 values of x
Explanation: Steps 1 and 2 check 1 to 144 and 1 to 180: 144 + 180 = 324. Step 4 goes through the divisors of m = 144, and 144 has 15 divisors (180 has 18).
- Q14Hard
For m = 48 and n = 36, we scan k = 36, 35, 34, … downwards and stop at the first k that divides both. How many values of k are checked, counting the one where we stop?
A.25✓ CorrectB.12C.36D.24Answer: A. 25
Explanation: gcd(48, 36) = 12 and no k between 13 and 36 divides both. So we check 36 down to 12, which is 36 − 12 + 1 = 25 values; 24 forgets to count the stopping value.
Key concepts: The World of Algorithms (Class 9 Mathematics)
An algorithm is a step-by-step procedure to get an answer. The chapter writes out column addition, builds a gcd algorithm from the definition and makes it faster, then meets Euclid's subtraction algorithm and Āryabhaṭa's quicker division algorithm, asking each time why a method is correct and how much work it needs.
- Algorithm
- A step-by-step procedure to arrive at an answer, built from basic steps we can already do, such as adding single digits or checking whether one number divides another. Some steps repeat, and some are done only if a condition holds.
- Digit-by-digit addition
- Write the numbers with digits lined up from the right, add each column from right to left with a carry, and at the end write a final carry of 1 if there is one (Step 5). Leaving out Step 5 turns 586 + 739 into 325.
- Carrying and why it works
- Ten units make a new ten, which is carried to the tens group, so adding units, tens, hundreds separately gives the right sum. A column sum is at most 9 + 9 + 1 = 19, so the carry is only 0 or 1, and a sum of exactly 10 must also give a carry.
- Efficiency: digits versus value
- Counting dots grows with the value (3 to 4 digits means 10 times the dots), but the column method needs only one more column. One dot per second makes 33 + 27 take a minute, while 15 s per column takes about half a minute.
- divisors(n) and lists
- Start with an empty list-of-divisors and, for each j = 1, 2, …, n, add j if it divides n. The list comes out in increasing order, e.g. divisors(18) = [1, 2, 3, 6, 9, 18].
- First gcd algorithm
- Find divisors(m) and divisors(n), put each divisor of m that is also in divisors(n) into common-divisors, and report the rightmost element. For 375 and 825 the list is [1, 3, 5, 15, 25, 75], so the gcd is 75.
- Data structure
- Names such as list-of-divisors and j let the steps refer to values kept along the way. A list kept in increasing order is an example of a data structure, a way to organise information so the algorithm works well.
- Improving the gcd scan
- Two separate scans check m + n numbers; one combined scan checks max(m, n); checking only for common divisors needs just 1 to min(m, n). The no-list version starts most-recent-common-divisor at 1 and updates it for each k from 2 to min(m, n) that divides both.
- Analysing the scan
- Each refinement saves work but computes the same value, so it stays correct. The work still grows with the value of min(m, n): going from 3 to 5 digits makes it about 100 times bigger.
- Euclid's subtraction algorithm
- For m ≥ n, gcd(m, n) = gcd(n, m − n): if m = ad and n = bd then m − n = (a − b)d, and the converse uses m = n + (m − n). Reverse the pair when m < n and stop at gcd(m, 0) = m (375 and 825 need 7 reductions).
- Subtraction can be slow
- gcd(2k + 1, 2) needs about k reductions, e.g. gcd(99, 2) goes 97, 95, 93, … down to gcd(1, 0). So the work grows with the value, not with the number of digits.
- Āryabhaṭa's division algorithm
- Āryabhaṭa's Āryabhaṭīya (499 CE) uses the long division method: replace gcd(m, n) by gcd(n, m mod n), where m mod n is the remainder. gcd(99, 2) now needs only 2 reductions, and the number of reductions grows with the number of digits.
- Al-Khwārizmī and the word 'algorithm'
- Al-Khwārizmī (780–850 CE), at the House of Wisdom in Baghdad, explained Indian numerals and the four operations around 820 CE. The Latin form of his name, Algoritmi, gave algorismus, then algorism and algorithm.
- Writing new algorithms
- prime(n) can check that divisors(n) has exactly two entries, and primedivisors(n) keeps only the primes in divisors(n). A prime factorisation such as 180 = 2² × 3² × 5¹ can be stored as pairs of prime and power.
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Start this chapter free →The World of Algorithms — FAQs
What are the key concepts in Class 9 Mathematics The World of Algorithms?+
An algorithm is a step-by-step procedure to get an answer. The chapter writes out column addition, builds a gcd algorithm from the definition and makes it faster, then meets Euclid's subtraction algorithm and Āryabhaṭa's quicker division algorithm, asking each time why a method is correct and how much work it needs. Key ideas include Algorithm, Digit-by-digit addition, Carrying and why it works, Efficiency: digits versus value, divisors(n) and lists, First gcd algorithm.
What does Class 9 Mathematics Chapter 11 (The World of Algorithms) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "The World of Algorithms": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.
Are these "The World of Algorithms" questions free to practise?+
Yes. Sign in with Google to practise "The World of Algorithms" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 9 till 31 March; on 1 April your account moves up to Class 10 and the rest of your year carries over. No chapter is charged separately.
How should I revise "The World of Algorithms" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "The World of Algorithms" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "The World of Algorithms" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from The World of Algorithms (Class 9 Mathematics)?+
The questions that matter most test Algorithm, Digit-by-digit addition, Carrying and why it works, Efficiency: digits versus value, divisors(n) and lists, First gcd algorithm. This page shows 14 solved important MCQs with answers and explanations. Sign in to practise all 90 questions on the chapter as timed quizzes.
Is there an online quiz for The World of Algorithms?+
Yes — Class 9 Mathematics The World of Algorithms has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.