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NCERT solutions for class 10 maths chapter 1 exercise 1.1 are discussed here. These NCERT Solutions are created by expert team at Careers360 considering the latest syllabus and pattern of CBSE, NCERT, and State Board exams. These are designed comprehensively covering all the concepts, detailed and step by step solutions so that students get deeper understanding and score well during the competitive exams. NCERT Solutions for Class 10 Maths chapter 1 exercise 1.1 includes complete solutions of each and every problem that can be studied using PDF which is downloaded freely using the link given below.
The 10th class maths exercise 1.1 answers, teaches you about how to figure out if one number can be divided by another using Euclid's Division Algorithm. It provides clear, step-by-step answers to the questions in the Class 10 NCERT math book. These answers are made to follow the NCERT guidelines, which means they help you cover everything you need to know for your exams and do well in them.
Q1 (1) Use Euclid’s division algorithm to find the HCF of 135 and 225
Answer:
225 > 135. Applying Euclid's Division algorithm we get
$225=135\times 1+90$
since remainder $\neq$ 0 we again apply the algorithm
$135=90\times 1+45$
since remainder $\neq$ 0 we again apply the algorithm
$90=45\times 2$
since remainder = 0 we conclude the HCF of 135 and 225 is 45.
Q1 (2) Use Euclid’s division algorithm to find the HCF of 196 and 38220
Answer:
38220 > 196. Applying Euclid's Division algorithm we get
$38220=196\times 195+0$
since remainder = 0 we conclude the HCF of 38220 and 196 is 196.
Q1 (3) Use Euclid’s division algorithm to find the HCF of 867 and 255
Answer:
867 > 225. Applying Euclid's Division algorithm we get
$867=255\times 3+102$
since remainder $\neq$ 0 we apply the algorithm again.
since 255 > 102
$255=102\times 2+51$
since remainder $\neq$ 0 we apply the algorithm again.
since 102 > 51
$102=51\times 2+0$
since remainder = 0 we conclude the HCF of 867 and 255 is 51.
Answer:
Let p be any positive integer. It can be expressed as
p = 6q + r
where $q\geq 0$ and $0\leq r< 6$
but for r = 0, 2 or 4 p will be an even number therefore all odd positive integers can be written in the form 6q + 1, 6q + 3 or 6q + 5.
Answer:
The maximum number of columns in which they can march = HCF (32, 616)
Since 616 > 32, applying Euclid's Division Algorithm we have
$616=32\times 19+8$
Since remainder $\neq$ 0 we again apply Euclid's Division Algorithm
Since 32 > 8
$32=8\times 4+0$
Since remainder = 0 we conclude, 8 is the HCF of 616 and 32.
The maximum number of columns in which they can march is 8.
[Hint : Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1]
Answer:
Let x be any positive integer.
It can be written in the form 3q + r where $q\geq 0$ and r = 0, 1 or 2
Case 1:
For r = 0 we have
x2 = (3q)2
x2 = 9q2
x2 = 3(3q2 )
x2 = 3m
Case 2:
For r = 1 we have
x2 = (3q+1)2
x2 = 9q2 + 6q +1
x2 = 3(3q2 + 2q) + 1
x2 = 3m + 1
Case 3:
For r = 2 we have
x2 = (3q+2)2
x2 = 9q2 + 12q +4
x2 = 3(3q2 + 4q + 1) + 1
x2 = 3m + 1
Hence proved.
Answer:
Let x be any positive integer.
It can be written in the form 3q + r where $q\geq 0$ and r = 0, 1 or 2
Case 1:
For r = 0 we have
x3 = (3q)3
x3 = 27q3
x3 = 9(3q3 )
x3 = 9m
Case 2:
For r = 1 we have
x3 = (3q+1) 3
x3 = 27q 3 + 27q2 + 9q + 1
x3 = 9(3q3 + 3q2 +q) + 1
x3 = 3m + 1
Case 3:
For r = 2 we have
x3 = (3q + 2)3
x3 = 27q3 + 54q2 + 36q + 8
x3 = 9(3q3 + 6q2 +4q) + 8
x3 = 3m + 8
Hence proved.
The set of real numbers in 10th class maths exercise 1.1 answers are of various categories, like natural and whole numbers, integers, rational and irrational numbers. Real Numbers obey commutative and associative property along with identity and distributive properties. NCERT solutions for Class 10 Maths exercise 1.1 mainly focus on the application of Euclid's division Lemma and algorithm. Five important questions related to Euclid's division Lemma and algorithm are given in class 10 maths ex 1.1.
Also get access of all important formulae and eBook for class 10 maths which is helpful to solve problems given in NCERT class 10 maths exercise. Practice all exercise at one place listed below.
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Also Read | Real Numbers Class 10 Notes
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Frequently Asked Questions (FAQs)
There are 5 questions covered in Class 10 Maths exercise 1.1, in which the first questions have 3 sub-questions. Students should practice these problem to command the concepts.
NCERT questions are designed to get more clarity of the concepts covered in the chapter. These questions are also helpful from an exam point of view. students can find extra problems in class 10 ex 1.1.
For Class 10 CBSE board exams students can expect two or three questions from real numbers. One question may be related to the concepts covered in exercise 1.1
Yes, the real numbers include both rational and irrational numbers. For example, pi is an irrational number and also pi is a real number.
The Class 10 NCERT Mathematics Book has 15 chapters in total. Class 10 Mathematics covers topics from algebra, geometry, trigonometry, statistics and probability.
Yes, you can expect similar types of questions discussed in exercise 1.1 Class 10 Maths for board exam, but may not be the same questions.
You may expect either 2 or 3 marks questions from exercise 1.1. Sometimes there may not be any questions. But still the probability of getting questions from this exercise is very high.
On Question asked by student community
Hello,
If you want to get your 10th marksheet online, you just need to visit an official website like https://www.cbse.gov.in/ or https://results.cbse.nic.in/ for the CBSE board, and for the state board, you can check their website and provide your roll number, security PIN provided by the school, and school code to download the result.
I hope it will clear your query!!
Hello
You asked about Class 10 sample paper board exam and most important questions. Practicing sample papers and previous year questions is one of the best ways to prepare for the board exam because it gives a clear idea of the exam pattern and types of questions asked. Schools and teachers usually recommend students to solve at least the last five years question papers along with model papers released by the board.
For Class 10 board exams, the most important areas are Mathematics, Science, Social Science, English, and Hindi or regional language. In Mathematics, questions from Algebra, Linear Equations, Geometry, Trigonometry, Statistics, and Probability are repeatedly seen. For Science, the key chapters are Chemical Reactions, Acids Bases and Salts, Metals and Non metals, Life Processes, Heredity, Light and Electricity. In Social Science, priority should be given to Nationalism, Resources and Development, Agriculture, Power Sharing, Democratic Politics, and Economics related topics. In English, focus on unseen passages, grammar exercises, and important writing tasks like letter writing and essays.
Follow these steps to access the SQPs and marking schemes:
Step 1: Visit https://cbseacademic.nic.in/
Step 2: Click on the link titled “CBSE Sample Papers 2026”
Step 3: A PDF will open with links to Class 10 and 12 sample papers
Step 4: Select your class (Class 10 or Class 12)
Step 5: Choose your subject
Step 6: Download both the sample paper and its marking scheme
Hello,
Yes, you can give the CBSE board exam in 2027.
If your date of birth is 25.05.2013, then in 2027 you will be around 14 years old, which is the right age for Class 10 as per CBSE rules. So, there is no problem.
Hope it helps !
Here are some strategies so u can do best in your board exams and get god score
1. Make a good and smart schedule
2. If u r from cbse board go through ncert books by heart
3. Solve pyqs of each subject
4. Do revision on daily basis
5. Practice on presentation and writing the answer .
6. Do your best and give exam with the best way possible all the best blud .
Hello! If you selected “None” while creating your APAAR ID and forgot to mention CBSE as your institution, it may cause issues later when linking your academic records or applying for exams and scholarships that require school details. It’s important that your APAAR ID correctly reflects your institution to avoid verification problems. You should log in to the portal and update your profile to select CBSE as your school. If the system doesn’t allow editing, contact your school’s administration or the APAAR support team immediately so they can correct it for you.
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