CBSE Class 10 Mathematics Real Numbers VBQs read and download in pdf. Value Based Questions come in exams for Mathematics in Class 10 and are easy to learn and helpful in scoring good marks. You can refer to more chapter wise VBQs for Class 10 Mathematics and also get latest topic wise very useful study material as per latest NCERT book for Class 10 Mathematics and all other subjects for free on Studiestoday designed as per latest Class 10 CBSE, NCERT and KVS syllabus and examination pattern

## VBQ for Class 10 Mathematics Chapter 1 Real Numbers

Class 10 Mathematics students should refer to the following value based questions with answers for Chapter 1 Real Numbers in Class 10. These VBQ questions with answers for Class 10 Mathematics will come in exams and help you to score good marks

### Chapter 1 Real Numbers VBQ Questions Class 10 Mathematics with Answers

**Question. A forester wants to plant 66 apple trees, 88 banana trees and 110 mango trees in equal rows (in terms of number of trees). Also he wants to make distinct rows of trees (i.e., only one type of trees in one row). The number of minimum rows required are**

(a) 2

(b) 3

(c) 10

(d) 12**Answer : D**

**Question. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is**

(a) 4

(b) 2

(c) 1

(d) 3**Answer : B**

**Question. If two positive integers a and b are written as a = x ^{3}y^{2} and b = xy^{3}; x, y are prime numbers, then HCF (a, b) is**

(a) xy

(b) xy

^{2}

(c) x

^{3}y

^{3}

(d) x

^{2}y

^{2}

**Answer : B**

**Question. The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is**

(a) 13

(b) 65

(c) 875

(d) 1750**Answer : A**

**Question. If two positive integers p and q can be expressed as p = ab ^{2} and q = a3b; a, b being prime numbers, then LCM (p, q) is**

(a) ab

(b) a

^{2}b

^{2}

(c) a

^{3}b

^{2}

(d) a

^{3}b

^{3}

**Answer : C**

**Direction: In the following questions, short answer of 2 marks each**

**Question. Express 98 as a product of its primes.Answer : **2 X 7

^{2}

**Question. HCF and LCM of two numbers is 9 and 459 respectively. If one of the numbers is 27, find the other numberAnswer : **153

**Question. In a seminar, the number of participants in German, English and French are 130, 130 and 286 respectively. Find the numbers of rooms required to house them if in each room, the same number of participants are to be accommodated and all of them must belong to the same languageAnswer : **26

**Question. Zoe and Sam are racing on a circular track. If Zoe takes 48 minutes and Sam takes 80 minutes to complete the round. If they both start at the same point at the same time and go in same direction, after how many minutes will they meet again at the start point?Answer : **240 mins

**Question. Find HCF and LCM of 13 and 17 by prime factorisation methodAnswer : **HCF=1 ; LCM= 221

**Question. Mitchell and Courtney are racing on a circular track. If Mitchell takes 36 minutes and Courtney takes 24 minutes to complete the round. If they both start at the same point at the same time and go in same direction, then they will meet again at the start point after how many minutes.Answer : **72 mins

**Question. Find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11, and 15 respectively.Answer : **17

**Question. If the HCF of 408 and 1032 is expressible in the form 1032 × 2 + 408 × p, then find the value of p.Answer : **-5

**Question. Find the LCM of 96 and 360 by using fundamental theorem of arithmetic.Answer : **1440

**Question. Find LCM of numbers whose prime factorisation are expressible as 3 × 5 ^{2} and 3^{2} × 7^{2}.**3

Answer :

^{2}x 5

^{2}x 7

^{2}

**Question. Karan has 180 blue marbles and 150 red marbles. He wants to pack them into packets containing equal number of marbles of the same colour. What is the maximum number of marbles that each packet can hold?Answer : **30

**Question. Three bells toll at intervals of 12 minutes, 15 minutes and 18 minutes respectively. If they start tolling together, after what time will they next toll together?Answer : **90 mins

**Question. Prove that 2-3√5 is an irrational numberAnswer : **Irrational

**Question. What is the largest number that divides 967 and 1767 leaving remainders of 71 and 103 respectively?Answer : **128

**Question. What is the largest number that divides 170, 220, and 420 leaving remainder 8, 4 and 15 respectively?Answer : **27

**Question. Find the largest number that will divide 382 and 710 and leaves a remainder 13 in each case.Answer : **41

**Question. The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then find the other number.Answer : **320

**Question. What is the largest number that divides 437, 732, and 1263 leaving remainder of 24 in each case?Answer : **59

**Question. Find the LCM and HCF of the following : 2 ^{5} × 5^{4} × 7^{2} × 13^{6} and 2^{3} × 5^{6} × 7 × 17^{3}.**LCM=2

Answer :

^{5}x 5

^{6}x 7

^{2}x 13

^{6}x 17

^{3}; HCF = 2

^{3}x 5

^{4}x 7

**Question. An army contingent of 1000 members is to march behind an army band of 56 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? Answer : **8

**Question. Anish goes fishing every 5th day and Balaji goes fishing every 7th day. If Anish and Balaji both went fishing today, how many days until they will go fishing on the same day again?Answer : **35

**Question. Find HCF of 378,180 and 420 by prime factorisation method. Is HCF x LCM of three numbers equal to the product of the three numbers?Answer : **6 ; YES

**Question. Katya has 49 paintings and 35 medals. She wants to display them in groups throughout her house, each with the same combination of paintings and medals, with none left over. What is the greatest number of groups Katya can display?Answer : **7

**Question. The Muscle Gym has bought 63 treadmills and 108 elliptical machines. The gym divides them into several identical sets of treadmills and elliptical machines for its branches located throughout the city, with no exercise equipment left over. What is the greatest number of branches the gym can have in the city?Answer : **9

**Question. Tamanna is arranging black marbles in groups of 13 and purple marbles in groups of 25. If she has the same number of black and purple marbles, what is the smallest number of marbles of each colour that she could have?Answer : **325

**Question. The product of two numbers is 228096 and their LCM is 66. Find their HCF.Answer : **36

**Question. If two positive integers a, b are written as a = 𝑥𝑦 ^{2} and b = 𝑥^{3}𝑦, where x, y are prime numbers, then find LCM (a, b).**X

Answer :

^{3}Y

^{2}

**Question. The difference of the irrational numbers 5 + √2 and 5 - √2?Answer : **2√2

**Short Answer type Questions**

**Question. Two brands of chocolates are available in packs of 24 and 15 respectively. If I need to buy an equal number of chocolates of both kinds, what is the least number of boxes of each kind I would need to buy?Answer : **5 of 1

^{st}kind, 8 of 2

^{nd}kind

**Question. Find the LCM and HCF of the following pairs of positive integers by applying the prime factorization method.****a) 225, 240 b) 52 ,63 ,162Answer : **a) HCF (225, 240 ) = 15 LCM (225, 240) = 600

b) HCF (52, 6, 162) = 1 LCM (52, 63, 162) = 29484

**Question. The LCM of two numbers is 64699, their HCF is 97 and one of the numbers is 2231.Find the other.Answer : **2813

**Question. If the sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF then, find the product of two numbers.Answer : **194400

**Question. Find HCF and LCM of 135 and 225 and verify the that HCF x LCM = Product of the two given numbers.Answer : **LCM (135, 225) = 675, HCF (135, 225) = 45. Verification by showing LHS = RHS i.e., 135 x 225 = 675 x 45

**Question. Find HCF and LCM of 867 and 255 and verify the that HCF x LCM = Product of the two given numbersAnswer : **LCM (867, 255) = 4335, HCF (867, 255) = 51. Verification by showing LHS = RHS i.e., 867 x 255 = 4335 x 51

**Question. What is the LCM of smallest prime number and smallest composite number?Answer : **4

**Question. Is (√2 + √3 ) ^{2} and (2- √2) (2 + √2) irrational? Justify your answer.Answer : **(√2 + √3 )

^{2}is irrational as the result is 5 + √6 , which is irrational.

(2- √2 ) (2 + √2 ) is rational as the result is 2, which is rational.

**CASE STUDY QUESTION**

The department of Computer Science and Technology is conducting an International Seminar. In the seminar, the number of participants in Mathematics, Science and Computer Science are 60, 84 and 108 respectively. The coordinator has made the arrangement such that in each room, the same number of participants are to be seated and all of them being in the same subject. Also, they allotted the separate room for all theofficial other than participants.

**Question. Find the total number of participants.**

(a) 60

(b) 84

(c) 108

(d) none of these**Answer : **252

**Question. Find the minimum number of rooms required, if in each room, the same number of participants are to be seated and all of them being in the same subject.**

(a) 12

(b) 20

(c) 21

(d) none of these**Answer : **21

**Question. Find the LCM of 60, 84 and 108.**

(a) 12

(b) 504

(c) 544320

(d) 3780**Answer : **3780

**Question. Based on the above conditions, find the minimum number of rooms required for all the participants and officials.**

(a) 12

(b) 20

(c) 21

(d) none of these**Answer : **22

**Question. Find the HCF of 60, 84 and 108.Answer : **12

CBSE Class 10 Mathematics Real Numbers VBQs |

CBSE Class 10 Mathematics Polynomials VBQs |

CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables VBQs |

CBSE Class 10 Mathematics Quadratic Equations VBQs |

CBSE Class 10 Mathematics Arithmetic Progressions VBQs |

CBSE Class 10 Mathematics Triangles VBQs |

CBSE Class 10 Mathematics Coordinate Geometry VBQs |

CBSE Class 10 Mathematics Coordinate Geometry VBQs Set A |

CBSE Class 10 Mathematics Heights And Distances VBQs |

CBSE Class 10 Mathematics VBQs Applications Of Trigonometry |

CBSE Class 10 Mathematics VBQs Heights And Distances |

CBSE Class 10 Mathematics Circles VBQs |

CBSE Class 10 Mathematics Circles VBQs Set A |

CBSE Class 10 Mathematics Constructions VBQs |

CBSE Class 10 Mathematics Area Related To Circles VBQs |

CBSE Class 10 Mathematics Areas Related to Circles VBQs |

CBSE Class 10 Mathematics Surface Areas And Volume VBQs |

CBSE Class 10 Mathematics Statistics VBQs |

CBSE Class 10 Mathematics Probability VBQs |

CBSE Class 10 Mathematics Probability VBQs Set A |

CBSE Class 10 Mathematics Introduction to Trigonometry VBQs |

## More Study Material

### CBSE Class 10 Mathematics Chapter 1 Real Numbers VBQs

We hope students liked the above VBQs for Chapter 1 Real Numbers designed as per the latest syllabus for Class 10 Mathematics released by CBSE. Students of Class 10 should download the Value Based Questions and Answers in Pdf format and practice the questions and solutions given in above Class 10 Mathematics VBQs Questions on daily basis. All latest VBQs with answers have been developed for Mathematics by referring to the most important and regularly asked topics which the students should learn and practice to get better score in school tests and examinations. Studiestoday is the best portal for Class 10 students to get all latest study material free of cost.

### VBQs for Mathematics CBSE Class 10 Chapter 1 Real Numbers

Expert teachers of studiestoday have referred to NCERT book for Class 10 Mathematics to develop the Mathematics Class 10 VBQs. If you download VBQs with answers for the above chapter daily, you will get higher and better marks in Class 10 test and exams in the current year as you will be able to have stronger understanding of all concepts. Daily Value Based Questions practice of Mathematics and its study material will help students to have stronger understanding of all concepts and also make them expert on all critical topics. You can easily download and save all VBQs for Class 10 Mathematics also from www.studiestoday.com without paying anything in Pdf format. After solving the questions given in the VBQs which have been developed as per latest course books also refer to the NCERT solutions for Class 10 Mathematics designed by our teachers

**Chapter 1 Real Numbers VBQs Mathematics CBSE Class 10**

All VBQs given above for Class 10 Mathematics have been made as per the latest syllabus and books issued for the current academic year. The students of Class 10 can refer to the answers which have been also provided by our teachers for all VBQs of Mathematics so that you are able to solve the questions and then compare your answers with the solutions provided by us. We have also provided lot of MCQ questions for Class 10 Mathematics so that you can solve questions relating to all topics given in each chapter. All study material for Class 10 Mathematics students have been given on studiestoday.

**Chapter 1 Real Numbers CBSE Class 10 VBQs Mathematics**

Regular VBQs practice helps to gain more practice in solving questions to obtain a more comprehensive understanding of Chapter 1 Real Numbers concepts. VBQs play an important role in developing understanding of Chapter 1 Real Numbers in CBSE Class 10. Students can download and save or print all the VBQs, printable assignments, practice sheets of the above chapter in Class 10 Mathematics in Pdf format from studiestoday. You can print or read them online on your computer or mobile or any other device. After solving these you should also refer to Class 10 Mathematics MCQ Test for the same chapter

**CBSE VBQs Mathematics Class 10 Chapter 1 Real Numbers**

CBSE Class 10 Mathematics best textbooks have been used for writing the problems given in the above VBQs. If you have tests coming up then you should revise all concepts relating to Chapter 1 Real Numbers and then take out print of the above VBQs and attempt all problems. We have also provided a lot of other VBQs for Class 10 Mathematics which you can use to further make yourself better in Mathematics

You can download the CBSE VBQs for Class 10 Mathematics Chapter 1 Real Numbers for latest session from StudiesToday.com

Yes, you can click on the links above and download topicwise VBQs Questions PDFs for Class 10 for Mathematics Chapter 1 Real Numbers

Yes, the VBQs issued by CBSE for Chapter 1 Real Numbers Class 10 Mathematics have been made available here for latest academic session

You can easily access the links above and download the Chapter 1 Real Numbers Class 10 VBQs Mathematics for each chapter and topic

There is no charge for the VBQs and their answers for Class 10 CBSE Mathematics Chapter 1 Real Numbers you can download everything free

Regular revision of VBQs given on studiestoday for Class 10 subject Mathematics Chapter 1 Real Numbers can help you to score better marks in exams

Value Based Questions (VBQs) for Class 10 Mathematics Chapter 1 Real Numbers help to test the ability of students to apply learnings to various situations in life.