Class 10 Maths Chapter 1 Real Numbers MCQ (Multiple Choice Objective Questions) with answers and complete explanation case study type questions for the first term examination 2024-25. The answers of 10th Maths Chapter 1 MCQ are given with explanation, so that students can understand easily. This page of Class 10 Maths MCQ contains the questions released by CBSE as well as extra questions for practice.
Class 10 Maths Chapter 1 MCQ – Case Study
Case Study – 1
To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.
Q1
What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B?
[A]. 144
[B]. 128
[C]. 288
[D]. 272
Answer: Option C
Explanation:
Factors of 32 = 2 х 2 х 2 х 2 х 2 = 2⁵
Factors of 36 = 2 х 2 х 3 х 3 = 2² х 3²
LCM of 32 and 36 = 2⁵ х 3² = 32 х 9 = 288
Hence, the correct option is (C).
If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32, 36) is
[A]. 2
[B]. 4
[C]. 6
[D]. 8
Answer: Option B
Explanation:
Factors of 32 = 2 х 2 х 2 х 2 х 2 = 2⁵
Factors of 36 = 2 х 2 х 3 х 3 = 2² х 3²
LCM of 32 and 36 = 2⁵ х 3² = 32 х 9 = 288
HCF (32, 36) = (32 х 36) / LCM = (32 х 36) / 288 = 4
Hence, the correct option is (B).
7 х 11 х 13 х 15 + 15 = 15 х (7 х 11 х 13 + 1) = 15 х (Integer)
It has more than two factor.
So, it is a composite number.
Hence, the correct option is (B).
A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English, and Mathematics are 60, 84, and 108 respectively.
Q6
In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are
[A]. 14
[B]. 12
[C]. 16
[D]. 18
Answer: Option B
Explanation:
Factors of 60 = 2 х 2 х 3 х 5 = 2² х 3 х 5
Factors of 84 = 2 х 2 х 3 х 7 = 2² х 3 х 7
Factors of 108 = 2 х 2 х 3 х 3 х 3 = 2² х 3³
HCF of 60, 84, and 108 = 2² х 3 = 12
Hence, the correct option is (B).
What is the minimum number of rooms required during the event?
[A]. 11
[B]. 31
[C]. 41
[D]. 21
Answer: Option D
Explanation:
Factors of 60 = 2 х 2 х 3 х 5 = 2² х 3 х 5
Factors of 84 = 2 х 2 х 3 х 7 = 2² х 3 х 7
Factors of 108 = 2 х 2 х 3 х 3 х 3 = 2² х 3³
HCF of 60, 84, and 108 = 2² х 3 = 12
Number of room required for Hindi participants = 60/12 = 5
Number of room required for English participants = 84/12 = 7
Number of room required for Mathematics participants = 108/12 = 9
Total number of room required = 5 + 7 + 9 = 21
Hence, the correct option is (D).
Factors of 60 = 2 х 2 х 3 х 5 = 2² х 3 х 5
Factors of 84 = 2 х 2 х 3 х 7 = 2² х 3 х 7
Factors of 108 = 2 х 2 х 3 х 3 х 3 = 2² х 3³
LCM of 60, 84, and 108 = 2² х 3³ х 5 х 7 = 4 х 27 х 5 х 7 = 3780
Hence, the correct option is (A).
Factors of 60 = 2 х 2 х 3 х 5 = 2² х 3 х 5
Factors of 84 = 2 х 2 х 3 х 7 = 2² х 3 х 7
Factors of 108 = 2 х 2 х 3 х 3 х 3 = 2² х 3³
HCF of 60, 84, and 108 = 2² х 3 = 12
LCM of 60, 84, and 108 = 2² х 3³ х 5 х 7 = 4 х 27 х 5 х 7 = 3780
Product of HCF and LCM of 60, 84, and 108 = 12 х 3780 = 45360
Hence, the correct option is (D).
Rohit Singh is a worker in a petrol pump. He along with the other co-workers, use to transfer petrol from tanker to storage. On Monday, there were two tankers containing 850 litres and 680 litres of petrol respectively.
Q11
What is the maximum capacity of a container which can measure the petrol of either tanker in exact number of time?
[A]. 150 litres
[B]. 160 litres
[C]. 170 litres
[D]. 180 litres
Answer: Option C
Explanation:
The maximum capacity of the container is the HCF of 850 and 680.
Factors of 850 = 2 х 5 х 5 х 17 = 2 х 5² х 17
Factors of 680 = 2 х 2 х 2 х 5 х 17 = 2³ х 5 х 17
HCF of 850 and 680 = 2 х 5 х 17 = 170
Hence, the correct option is (C).
If the product of two positive integers is equal to the product of their HCF and LCM is true then, the LCM (850, 680) is
[A]. 3100
[B]. 3200
[C]. 3300
[D]. 3400
Answer: Option D
Explanation:
Factors of 850 = 2 х 5 х 5 х 17 = 2 х 5² х 17
Factors of 680 = 2 х 2 х 2 х 5 х 17 = 2³ х 5 х 17
HCF of 850 and 680 = 2 х 5 х 17 = 170
LCM (850, 680) = (850 х 680) / HCF = (850 х 680) / 170 = 3400
Hence, the correct option is (D).
2 х 3 х 5 х 11 х 17 + 11 = 11 х (2 х 3 х 5 х 17 + 1) = 11 х (Integer)
It has more than two factor.
So, it is a composite number.
Hence, the correct option is (B).
A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.
Observe the following factor tree and answer the following:
Q16
What will be the value of x?
[A]. 15005
[B]. 13915
[C]. 56920
[D]. 17429
Answer: Option B
Explanation:
X = 5 х 2783 = 13915
Hence, the correct option is (B).
We all know that morning walk is good for health. In a morning walk, three friends Anjali, Sofia, and Angelina step of together. There steps measure 80 cm, 85 cm, and 90 cm. respectively.
Q21
What is the minimum distance each should walk so that they can cover the distance in complete steps?
[A]. 120 m 40 cm
[B]. 122 m 40 cm
[C]. 12 m 4 cm
[D]. None of these
Answer: Option B
Explanation:
The minimum distance covered by each in complete steps must be the LCM of 80 cm, 85 cm, and 90 cm.
Factors of 80 = 2 х 2 х 2 х 2 х 5 = 2⁴ х 5
Factors of 85 = 5 х 17
Factors of 90 = 2 х 3 х 3 х 5 = 2 х 3² х 5
LCM of 80, 85, and 90 = 2² х 3² х 5 х 17 = 12240
Now, 12240 cm = 122 m 40 cm
Hence, the correct option is (B).
What is the minimum number of steps taken by any of the three friends, when they meet again?
[A]. 120
[B]. 125
[C]. 130
[D]. 136
Answer: Option D
Explanation:
Factors of 80 = 2 х 2 х 2 х 2 х 5 = 2⁴ х 5
Factors of 85 = 5 х 17
Factors of 90 = 2 х 3 х 3 х 5 = 2 х 3² х 5
LCM of 80, 85, and 90 = 2² х 3² х 5 х 17 = 12240
The step size of Angelina is maximum among these three. So, she will take minimum number of steps to cover the same distance.
Number of steps = 12240/90 = 136
Hence, the correct option is (D).
Factors of 80 = 2 х 2 х 2 х 2 х 5 = 2⁴ х 5
Factors of 85 = 5 х 17
Factors of 90 = 2 х 3 х 3 х 5 = 2 х 3² х 5
HCF of 80, 85, and 90 = 5
Hence, the correct option is (A).
Factors of 80 = 2 х 2 х 2 х 2 х 5 = 2⁴ х 5
Factors of 85 = 5 х 17
Factors of 90 = 2 х 3 х 3 х 5 = 2 х 3² х 5
HCF of 80, 85, and 90 = 5
LCM of 80, 85, and 90 = 2² х 3² х 5 х 17 = 12240
Therefore, the product of HCF and LCM of 80, 85, and 90 = 12240 х 5 = 61200
Hence, the correct option is (C).
Class 10 Maths Chapter 1 MCQ are given below. There are total of 5 questions with four choices. Only one option is correct and the explanation of correct answer is given below the questions. Every time the students will get a new set of five questions with different levels of questions. For any further discussion, please join the Discussion Forum.
Q26
The decimal form of 120 /(2^2 × 5^7 × 7^5 )is
[A]. Terminating
[B]. Non terminating
[C]. Non terminating non repeating
[D]. None of the above
Answer: Option C
Explanation:
Because the denominator contains the factors of 7.
Largest number which divides 60 and 75, leaving remainders 8 and 10 respectively, is
[A]. 260
[B]. 75
[C]. 55
[D]. 13
Answer: Option D
Explanation:
This means 60 – 8 = 52 and 75 – 10 = 65, are completely divided by a integer.
Therefore, we have to find the HCF of 52 and 65..
According to Euclid’s Division Lemma,
65 = 52 × 1 +13
and
52 = 13 × 4 + 0,
Hence 13 is HCF.
The decimal expansion of the rational number 14587/250 will terminate after
[A]. One decimal place
[B]. Two decimal places
[C]. Three decimal places
[D]. Four decimal places
Answer: Option C
Explanation:
The factors of denominator 250 = 2 × 5 × 5 × 5.
There are three factors of 5, that is why it will terminate after three decimal places.
[Always more number of factors will be considered, whether it is 5 or 2, does not matter.]
By dividing actually 14587 by 250 we get the quotient as 58.348.
What are the important topics in Class 10 Maths Chapter 1 MCQ?
Euclid’ division lemma and the Fundamental Theorem of Arithmetic are the two main topics in 10th Maths chapter 1 Real Numbers. Now questions are designed on the basis of case study. So practice MCQ questions based on daily life events which will be more helpful in CBSE exams.
In which of the four exercise of 10th Maths Chapter 1, are Case Study MCQ asked?
There are questions from each exercise of Chapter 1 of 10th Maths, but most of the MCQs can be formed from Exercise 1.4. Now CBSE introduces the questions based on CASE STUDY which may be asked from any section of class 10 Maths chapter 1.
How many MCQ are required to be perfect in Chapter 1 of Class 10 Maths?
If your concepts are clear, the MCQs provide more confidence in that section. More practice means more to retain and better understanding with the concepts of topics.
How many questions from Chapter 1 of Class 10 Maths asked in CBSE Board?
There is no classification of number of questions from the different chapters. There may be one, more than one or none from Chapter 1 Real Numbers of Class 10 Maths.
We are adding more questions frequently, so that students can have a good practice of Class 10 Maths Chapters. If you have suggestion or feedback about this page or website improvement, you are welcome. Important questions with solutions and answers will be added very soon for each chapter of class 10 Maths.
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