Important Questions for Class 10 Maths Chapter 1 Real Numbers

Important Questions for Class 10 Maths Chapter 1 Real Numbers

Free PDF Download of CBSE Class 10 Maths Chapter 12 Areas Related to Circles Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Areas Related to Circles MCQs with Answers to know their preparation level.

Important Questions for Class 10 Maths Chapter 1 Real Numbers

Question 1.
The decimal expansion of the rational number will terminate after how many places of decimals? (2013)
Solution:

Question 2.
Write the decimal form of
Solution:
Non-terminating non-repeating.

Question 3.
Find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11, and 15 respectively.
Solution:
Algorithm
398 - 7 = 391, 436 - 11 = 425, 542 - 15 = 527
HCF of 391, 425, 527 = 17

Question 4.
Express 98 as a product of its primes.
Solution:
2 × 7²

Question 5.
If the HCF of 408 and 1032 is expressible in the form 1032 × 2 + 408 × p, then find the value of p.
Solution:
HCF of 408 and 1032 is 24.
1032 × 2 + 408 × (p) = 24
408p = 24 - 2064
p = -5

Real Numbers Class 10 Important Questions Short Answer-I (2 Marks)

Question 6.
HCF and LCM of two numbers is 9 and 459 respectively. If one of the numbers is 27, find the other number. (2012)
Solution:
We know,
1st number × 2nd number = HCF × LCM
⇒ 27 × 2nd number = 9 × 459
⇒ 2nd number = = 153

Question 7.
Find HCF and LCM of 13 and 17 by prime factorisation method. (2013)
Solution:
13 = 1 × 13; 17 = 1 × 17
HCF = 1 and LCM = 13 × 17 = 221

Question 8.
Find LCM of numbers whose prime factorisation are expressible as 3 × 5² and 3² × 7². (2014)
Solution:
LCM (3 × 5², 3² × 7²) = 3² × 5² × 7² = 9 × 25 × 49 = 11025

Question 11.
Find the largest number which divides 70 and 125 leaving remainder 5 and 8 respectively. (2015)
Solution:
It is given that on dividing 70 by the required number, there is a remainder 5.
This means that 70 - 5 = 65 is exactly divisible by the required number.
Similarly, 125 - 8 = 117 is also exactly divisible by the required number.
65 = 5 × 13
117 = 3² × 13
HCF = 13
Required number = 13

Question 16.
Explain why (17 × 5 × 11 × 3 × 2 + 2 × 11) is a composite number? (2015)
Solution:
17 × 5 × 11 × 3 × 2 + 2 × 11 …(i)
= 2 × 11 × (17 × 5 × 3 + 1)
= 2 × 11 × (255 + 1)
= 2 × 11 × 256
Number (i) is divisible by 2, 11 and 256, it has more than 2 prime factors.
Therefore (17 × 5 × 11 × 3 × 2 + 2 × 11) is a composite number.

Question 17.
Check whether 4n can end with the digit 0 for any natural number n. (2015)
Solution:
4ⁿ = (2²)ⁿ = 2²ⁿ
The only prime in the factorization of 4ⁿ is 2.
There is no other prime in the factorization of 4ⁿ = 2²ⁿ
(By uniqueness of the Fundamental Theorem of Arithmetic).
5 does not occur in the prime factorization of 4ⁿ for any n.
Therefore, 4ⁿ does not end with the digit zero for any natural number n.

Question 18.
Can two numbers have 15 as their HCF and 175 as their LCM? Give reasons. (2017 OD)
Solution:
No, LCM = Product of the highest power of each factor involved in the numbers.
HCF = Product of the smallest power of each common factor.
We can conclude that LCM is always a multiple of HCF, i.e., LCM = k × HCF
We are given that,
LCM = 175 and HCF = 15
175 = k × 15
⇒ 11.67 = k
But in this case, LCM ≠ k × HCF
Therefore, two numbers cannot have LCM as 175 and HCF as 15.

Real Numbers Class 10 Important Questions Short Answer-II (3 Marks)

Question 23.
The length, breadth, and height of a room are 8 m 50 cm, 6 m 25 cm and 4 m 75 cm respectively. Find the length of the longest rod that can measure the dimensions of the room exactly. (2015)
Solution:
To find the length of the longest rod that can measure the dimensions of the room exactly, we have to find HCF.
L, Length = 8 m 50 cm = 850 cm = 2¹ × 5² × 17
B, Breadth = 6 m 25 cm = 625 cm = 5⁴
H, Height = 4 m 75 cm = 475 cm = 5² × 19
HCF of L, B and H is 5² = 25 cm
Length of the longest rod = 25 cm

Question 26.
By using Euclid’s algorithm, find the largest number which divides 650 and 1170. (2017 OD)
Solution:
Given numbers are 650 and 1170.
1170 > 650
1170 = 650 × 1 + 520
650 = 520 × 1 + 130
520 = 130 × 4 + 0
HCF = 130
The required largest number is 130.

Question 34.
If two positive integers x and y are expressible in terms of primes as x = p²q³ and y = p³q, what can you say about their LCM and HCF. Is LCM a multiple of HCF? Explain. (2014)
Solution:
x = p²q³ and y = p³q
LCM = p³q³
HCF = p²q …..(i)
Now, LCM = p³q³
⇒ LCM = pq² (p²q)
⇒ LCM = pq² (HCF)
Yes, LCM is a multiple of HCF.
Explanation:
Let a = 12 = 2² × 3
b = 18 = 2 × 3²
HCF = 2 × 3 = 6 …(ii)
LCM = 2² × 3² = 36
LCM = 6 × 6
LCM = 6 (HCF) …[From (ii)]
Here LCM is 6 times HCF.

Question 35.
Show that one and only one out of n, (n + 1) and (n + 2) is divisible by 3, where n is any positive integer. (2015)
Solution:
Let n, n + 1, n + 2 be three consecutive positive integers.
We know that n is of the form 3q, 3q + 1, or 3q + 2.
Case I. When n = 3q,
In this case, n is divisible by 3,
but n + 1 and n + 2 are not divisible by 3.
Case II. When n = 3q + 1,
In this case n + 2 = (3q + 1) + 2
= 3q + 3
= 3(q + 1 ), (n + 2) is divisible by 3,
but n and n + 1 are not divisible by 3.
Case III.
When n = 3q + 2, in this case,
n + 1 = (3q + 2) + 1
= 3q + 3 = 3 (q + 1 ), (n + 1) is divisible by 3,
but n and n + 2 are not divisible by 3.
Hence, one and only one out of n, n + 1 and n + 2 is divisible by 3.

Question 36.
Find the HCF and LCM of 306 and 657 and verify that LCM × HCF = Product of the two numbers. (2016 D)
Solution:
306 = 2 × 3² × 17
657 = 32 × 73
HCF = 3² = 9
LCM = 2 × 3² × 17 × 73 = 22338
L.H.S. = LCM × HCF = 22338 × 9 = 201042
R.H.S. = Product of two numbers = 306 × 657 = 201042
L.H.S. = R.H.S.

Question 37.
Show that any positive odd integer is of the form 41 + 1 or 4q + 3 where q is a positive integer. (2016 OD)
Solution:
Let a be a positive odd integer
By Euclid’s Division algorithm:
a = 4q + r …[where q, r are positive integers and 0 ≤ r < 4]
a = 4q
or 4q + 1
or 4q + 2
or 4q + 3
But 4q and 4q + 2 are both even
a is of the form 4q + 1 or 4q + 3.

Post your comments

Your mobile number will not be published.

View Comments

• Jyoti
• 2024-September-10 06:14:39

Thanks

• A.Nikhil Goud
• 2024-February-10 02:44:01

Good wedsite nice

• Raj
• 2024-January-01 08:18:08

Good website

• Mdiqbal Mdiqbal
• 2023-September-01 03:08:35

Use full

• Bandapalli siva ganga Devi
• 2023-July-27 08:30:58

Super solutions

• D BALAJI
• 2023-May-22 03:18:23

Clear explanation

• M venkata bramha chowdhary
• 2023-May-16 12:21:53

Results

• Dumpa snehith
• 2023-May-01 05:12:48

Ncert to prepare for eamcet or eapcer

• Gauri
• 2023-January-05 08:05:07

Sabse khrab

• Gauri
• 2023-January-05 08:04:53

Sabse khrab

• Prajoal
• 2022-November-07 13:08:18

Verry good app

• Preethi kumarK
• 2022-April-04 08:42:37

I will very happy to sovle this mcqs

• PradeepGupta
• 2022-March-08 10:49:21

Super

• Ashwani kumar
• 2022-March-02 09:58:15

Nice

• Ashwani kumar
• 2022-March-02 09:58:04

Nice

• Zyan safi
• 2022-February-15 08:53:24

Nice

• Zyan safi
• 2022-February-15 08:53:12

Nice

• Priyanshi
• 2022-January-29 08:22:35

Thanks sir

• Naria
• 2022-January-24 09:11:38

Nice

• ningu
• 2022-January-08 08:56:50

good work sir

• hs
• 2021-December-06 08:44:35

good

• prabhakar
• 2021-November-05 13:29:34

How to download this

• Dharmen
• 2021-October-04 08:45:08

How to download

• Anubhav
• 2021-September-27 08:41:42

Math all chapter MCQ best

• NIL
• 2021-September-13 17:54:25

GOOD

• Anjali
• 2021-September-03 11:32:35

Ncert miscellaneous question pdf

• Manjeet manjhi
• 2021-September-02 08:25:59

Super

• Karanveer Kaur
• 2021-August-07 17:05:48

10 class workbook English answer

• P.Ashrafbaig
• 2021-August-06 17:34:20

My results How to check my 10th results

• Asish Kumar sahu
• 2021-July-30 15:35:38

Pls sir show my result my admit card is missing so I request you plz show my result

• Varsha
• 2021-July-29 14:58:13

This app is so..good it makes is understand better as we had seen many app with only answer we will not understand the method what they have done.....

• Anupam
• 2021-July-29 11:47:07

super

• Lavanya vishawas Sonavale
• 2021-July-28 08:23:33

Nice

• Sudha
• 2021-July-21 08:33:01

Super cute

• Matruprasad nath
• 2021-July-19 08:35:09

plese give me the answer for above question

• Abhiram
• 2021-July-17 10:49:18

8th class Telugu and maths social PDF text books

• Abhiram
• 2021-July-17 10:48:31

8th class Telugu and maths social PDF text books

• Abhiram
• 2021-July-17 10:48:21

8th class Telugu and maths social PDF text books

• Aman
• 2021-July-16 17:54:57

Nice

• Patil yasvitah
• 2021-July-15 08:48:58

S the practice question papers clasfrom foranothers districts of Karnataka 10th MCQ pattern 2021 exam 40 marks

• Ajay
• 2021-July-10 15:13:43

Basic questions

• Nikki
• 2021-July-03 16:36:13

How to download this pdf

• Murali
• 2021-June-29 17:38:23

How to get free download

• Murali
• 2021-June-29 17:38:23

How to get free download

• Murali
• 2021-June-29 17:38:13

How to get free download

• Kurmapu rohini
• 2021-June-26 17:51:15

How to download

• Yashvanth
• 2021-June-25 08:55:48

S PDF

• Bhoomi
• 2021-June-22 10:27:13

Nice this content is very helpful ....thnx a lot ..and pls expand the question there is only 58 which is less for class 10

• Omkar
• 2021-June-21 18:23:37

How to download

• tanya shukla
• 2021-June-14 09:27:07

hello thankyou so much it really helped me in my exam...........

• Ranjith
• 2021-June-11 09:43:25

Good

• R sudha
• 2021-June-05 18:16:47

Good

• Urvi
• 2021-April-08 13:34:59

Teacher

• Rohit
• 2021-April-06 08:36:53

Nice

• HARSH RAJPUT DEVSARIYA 🙏🙏🙏🙏
• 2021-March-04 14:03:46

Thanku for giving All chapter MCQ thanku you very much

• Rakesh
• 2021-February-18 08:58:15

I need 2019 10 Class Batch Results

• Daripalli ramu
• 2021-January-15 17:59:04

Super

• Subash Gond
• 2020-December-31 08:20:16

McQ question all chapter

• Vandna
• 2020-December-28 16:35:55

What,where and how lesson 1 class 6 pdf

• Yuvraj yadav
• 2020-December-19 09:45:44

Hi

• Manasa
• 2020-December-11 12:17:15

Good

• Gundi.sonia
• 2020-December-07 11:59:59

Hii

• Dhanam jay
• 2020-December-05 10:33:16

Very nice

• Tanveer
• 2020-December-02 14:50:15

Political Science question solution

• Trilok
• 2020-November-09 12:54:21

I like

• Anshu poonia
• 2020-October-24 15:03:52

Superb

• Ranjan Baruah
• 2020-October-22 09:02:59

Thank sir

• MATHURAM
• 2020-October-14 12:52:51

Need notes

• Yadnyesh ubhad
• 2020-October-12 08:42:03

So nice answer

• Anusha chettri
• 2020-October-09 13:21:16

Hello

• Anusha chettri
• 2020-October-09 13:20:28

Hello

• Jasmita Naik
• 2020-September-15 12:24:24

Thank you very much.... Sir we need more help from you.... From other subject also we need like this questions.. So please sir kindly help us through uploading questions from science... Please sir

• Jasmita Naik
• 2020-September-15 12:24:22

Thank you very much.... Sir we need more help from you.... From other subject also we need like this questions.. So please sir kindly help us through uploading questions from science... Please sir

• Mohini
• 2020-September-01 09:39:49

Kitne time se

• Rajudutta
• 2020-August-29 09:08:57

Excellent and reliable apps

• SALMAN
• 2020-August-28 09:54:17

I WANT 2019 ENGLISH CBSC CLASS 3RD COURSE BOOK SYLLABUS AND SOLUTIONS

• ULRICA
• 2020-August-20 18:23:29

It

• Rishabh Kumar
• 2020-August-20 12:06:16

Please give me

• Chandra shekar
• 2020-August-17 18:16:29

Mandasa

• p.harshavardhan
• 2020-August-17 09:41:40

Ok

• Charchit
• 2020-August-15 09:24:13

Yes they are all question are main

• Muthalagu
• 2020-August-10 13:04:53

10 A class

• Vadde madhu
• 2020-August-09 13:05:59

Hallo

• Veeranna
• 2020-August-04 18:04:29

1:1 2004

• Eslavath Kalyan
• 2020-July-29 13:13:11

Komatipalli kesamudram

• Gumma pavan kalyan
• 2020-July-27 19:15:47

Hall ticket

• Rajudutta
• 2020-July-21 14:09:35

Excellent solutions and easy to learn.

• VAGEESHA
• 2020-July-17 12:42:54

NICE JOB

• Syed sayeed saaqib
• 2020-July-17 09:17:31

10 th class marks

• P.fairoz khan
• 2020-July-17 09:17:26

My SSC result

• Gangavarapu Ashok Reddy
• 2020-July-16 18:48:26

10 the class 2020 markas

• Kusi Mani kumaR
• 2020-July-16 13:12:26

2008125010

• suhailhajam
• 2020-July-16 13:12:18

plz kindly MCQ question s

• suhailhajam
• 2020-July-16 09:23:15

plz kindly MCQ question s

• Koripalli. Bindu ramya
• 2020-July-16 09:23:07

Inter results second year

• Faizan
• 2020-July-15 19:05:41

Beautiful

• K. Umesh Chandra
• 2020-July-15 19:05:34

Please release 10th results

• Surra naidu
• 2020-July-15 18:11:06

S me result

• Lakpathi
• 2020-July-15 18:10:58

Cbse resuls

• S.sravani
• 2020-July-15 18:10:50

CBSE 10th class result

• Gundrathi Mohan
• 2020-July-15 18:10:35

S me results

• Gundrathi Mohan
• 2020-July-15 12:58:21

S me results

• suhailhajam
• 2020-July-15 12:02:02

plz kindly MCQ question s

• chandar
• 2020-July-15 12:01:55

chan

• suhailhajam
• 2020-July-15 09:56:17

plz kindly MCQ question s

• Kaustab Roy
• 2020-June-29 08:44:49

I want to explore everything

• Anup
• 2020-June-16 19:51:29

Workbook unit 1 exercise solution

• Khushdeep Kaur
• 2020-June-15 09:19:07

I want pdf of MCQ class 10th C.B.S.E

• Saddam
• 2020-June-09 15:24:13

Kindly s me 10 maths mcq question answer

• SADDAM
• 2020-June-08 14:24:07

SEND ME

• Bed prakash
• 2020-June-01 09:44:40

Mera result

• palla sivaram
• 2020-April-21 13:55:32

haiii

• Dany
• 2020-March-07 16:10:18

NCERT Solutions Very Good I Like It

• laxman
• 2020-February-17 15:31:16

good

• Bhanusam.manjula
• 2019-August-17 12:35:47

Ssc 2007batch regular halltichet number

• Ramu
• 2019-July-31 12:35:35

NCERT Solutions

• Kalamata gowriswari
• 2019-June-17 17:57:24

Open 10th result 2019ap

• Nagra rayal
• 2019-May-17 10:35:13

Yappudu 10th reselts

• Yanati nagarani
• 2019-May-17 10:20:31

10th result

• NAGESWARA
• 2019-May-11 18:30:50

How can see ssc ap 10th results

• m.kalyani
• 2019-May-11 18:30:36

10th result

• Naveen
• 2019-May-10 13:17:17

10th results

• Sri kesav
• 2019-May-10 09:58:50

Please tell me the correct date of AP ssc results

• K. Sudhakar
• 2019-May-10 09:58:43

Plz 10th result

• V pawan durga sriniva
• 2019-May-07 14:24:49

Please 10th cbsc results

• V pawan durga sriniva
• 2019-May-07 14:24:39

Please 10th cbsc results

• Charan
• 2019-May-07 14:24:21

Result ssc

• Ayesha
• 2019-May-07 14:24:17

At. What time did exam results will come?

• Vadithya suresh
• 2019-May-04 14:44:06

Results

• VANKUDOTH pavan kalyan
• 2018-May-30 10:16:07

Results

• C H VAISHAVI
• 2018-May-29 18:18:18

Cbse result by name

• varunsai sanne
• 2018-May-29 16:00:17

Xth results 2018

• varunsai sanne
• 2018-May-29 15:44:24

Xth results 2018

• Yalagala Srihari
• 2018-May-29 13:04:27

Exam results

• Alpesh Dhamale
• 2018-May-29 11:36:50

Nice article my baby wait for exam result i hope this year pass percentage may be increase

• m. mohan rao
• 2018-May-28 11:03:47

hi, s me cbse 10 class 2018 results

• akshaya
• 2018-May-26 10:22:07

at what time resilts are going to today

• Velupala Ashwarya
• 2018-May-15 11:01:52

My result

• Ramu
• 2018-May-12 16:09:34

good information