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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
Answer : D
Question. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is
Answer : B
Question. If two positive integers a and b are written as a = x3y2 and b = xy3; x, y are prime numbers, then HCF (a, b) is
Answer : B
Question. The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is
Answer : A
Question. If two positive integers p and q can be expressed as p = ab2 and q = a3b; a, b being prime numbers, then LCM (p, q) is
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 72
Question. HCF and LCM of two numbers is 9 and 459 respectively. If one of the numbers is 27, find the other number
Answer : 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 language
Answer : 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 method
Answer : 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 × 52 and 32 × 72.
Answer : 32 x 52 x 72
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 number
Answer : 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 : 25 × 54 × 72 × 136 and 23 × 56 × 7 × 173.
Answer : LCM=25 x 56 x 72 x 136 x 173 ; HCF = 23 x 54 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 = 𝑥𝑦2 and b = 𝑥3𝑦, where x, y are prime numbers, then find LCM (a, b).
Answer : X3Y2
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 1st kind, 8 of 2nd 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 ,162
Answer : 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 numbers
Answer : 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.
(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.
(d) none of these
Answer : 21
Question. Find the LCM of 60, 84 and 108.
Answer : 3780
Question. Based on the above conditions, find the minimum number of rooms required for all the participants and officials.
(d) none of these
Answer : 22
Question. Find the HCF of 60, 84 and 108.
Answer : 12
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CBSE Class 10 Mathematics Chapter 1 Real Numbers VBQs
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VBQs for Mathematics CBSE Class 10 Chapter 1 Real Numbers
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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
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CBSE VBQs Mathematics Class 10 Chapter 1 Real Numbers
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