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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.
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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
since remainder 0 we again apply the algorithm
since remainder 0 we again apply the algorithm
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
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
since remainder 0 we apply the algorithm again.
since 255 > 102
since remainder 0 we apply the algorithm again.
since 102 > 51
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 and
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
Since remainder 0 we again apply Euclid's Division Algorithm
Since 32 > 8
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 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 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.
Also Read | Real Numbers Class 10 Notes
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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.
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
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.
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.
Dear aspirant !
Hope you are doing well ! The class 10 Hindi mp board sample paper can be found on the given link below . Set your time and give your best in the sample paper it will lead to great results ,many students are already doing so .
Hope you get it !
Thanking you
Hello aspirant,
The dates of the CBSE Class 10th and Class 12 exams are February 15–March 13, 2024 and February 15–April 2, 2024, respectively. You may obtain the CBSE exam date sheet 2024 PDF from the official CBSE website, cbse.gov.in.
To get the complete datesheet, you can visit our website by clicking on the link given below.
https://school.careers360.com/boards/cbse/cbse-date-sheet
Thank you
Hope this information helps you.
Hello aspirant,
The paper of class 7th is not issued by respective boards so I can not find it on the board's website. You should definitely try to search for it from the website of your school and can also take advise of your seniors for the same.
You don't need to worry. The class 7th paper will be simple and made by your own school teachers.
Thank you
Hope it helps you.
The eligibility age criteria for class 10th CBSE is 14 years of age. Since your son will be 15 years of age in 2024, he will be eligible to give the exam.
That totally depends on what you are aiming for. The replacement of marks of additional subjects and the main subject is not like you will get the marks of IT on your Hindi section. It runs like when you calculate your total percentage you have got, you can replace your lowest marks of the main subjects from the marks of the additional subject since CBSE schools goes for the best five marks for the calculation of final percentage of the students.
However, for the admission procedures in different schools after 10th, it depends on the schools to consider the percentage of main five subjects or the best five subjects to admit the student in their schools.
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