Ch 01 Real numbers Assignment
Q1. What is the H.C.F of the smallest composite number and the smallest prime number? (CBSE 2018)
Q2. If 'p' is a prime number then what is the L.C.M of p, p2, p3 ?
Q3. The product of a non-zero rational and an irrational number is always .
Q.4 Three sets of English, Hindi and Mathematics books have to be stacked in such a way that all the books
are stored topic wise and the height of each stack is the same. The number of English books is 96, the number of Hindi books is 240 and the number of Mathematics books is 336. Assuming that the books are of same thickness, determine the number of stacks of English, Hindi and Mathematics books.
Q5. 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?
Q6. Can two numbers have 18 as their HCF and 380 as their LCM? Give reason.
7. Can we have any n ∈ N, where 4^n ends with the digit zero?
8. 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.
9. Find the largest number that divides 2053 and 967 and leaves a remainder of 5 and 7
respectively.
10. Two numbers are in the ratio 21 : 17. If their HCF is 5, find the numbers.
11. The HCF of two numbers is 29 and other two factors of their LCM are 16 and 19. Find
the larger of the two numbers.
12. Given that √2 is irrational, prove that (5 + 3√2) is an irrational number.
13. Given that √3 is irrational, prove that
(2 + √3) is an irrational number.
14. Find the HCF and LCM of 288, 360 and 384 by prime factorisation method.
15. Find the largest number which divides 615 and 963 leaving remainder 6 in each case.
16. Given that √3 is irrational, prove that (2 + 5√3) is an irrational number.
17. Prove that √5 is and irrational number.
18. Prove that √2 is and irrational number.
19. Prove that √3 is and irrational number.
20. Prove that √7 -√3 is and irrational number.
21. 4 Bells toll together at 10 .00 am. They toll after 7, 8, 11 and 12 seconds respectively.How many times will they toll together again in the next 3 hours?
22. There are 576 boys and 448 girls in a school that are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed.
23. Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds if they first beep together at 12 noon, at what time will they beep again for the first
time?
24. Three sets of physics, chemistry and mathematics books have to be stacked in such a way that all the books are stored topic wise and the number of books in each stack is the same. The number of physics books is 192, the number of chemistry books is 240 and the number of mathematics books is 168. Determine the number of stacks of physics, chemistry and mathematics books.
25. 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). Find the number of minimum rows
required.
26. In a seminar the number of participants in Mathematics, Physics and Biology are 336,240 and 96. Find the minimum number of rooms required if in each room same
number of participants is to be seated and all of them being in the same subject.
27. The length, breadth and height of a room are 8 m 25 cm, 6 m 75 cm and 4 m 50 cmrespectively. Determine the length of the longest rod which can measure the three
dimensions of the room exactly.
28. On a morning walk three persons step off together and their steps measure 40 cm,
42 cm, 45cm, what is the minimum distance each should walk so that each can cover
the same distance incomplete steps?
29. Find the largest number that divides 1251.9377 and 13628 leaving reminders 1, 2 and 3 respectively.
30.Two alarm clocks ring their alarms at regular intervals of 50 sec and 48 sec. If they first beep together at 12 noon.at what time willbeep again for the first time?
31. Show the reciprocal of 3+2√2 is an irrational number.
32. Three bells toll at intervals of 12 min, 15 min and 18 min respectively. If they start tolling together, after what time will they next toll together?
33. Find the LCM and HCF of 336 and 54 and verify that HCF ×LCM= product of two
numbers.
34. Can 12^ n end with the digit 0, for any natural number n? Justify your answer.
35. If the HCF of 65 and 117 is expressible in the form of 65m-117,then find the value of m .
36. Find HCF of 612 and 1314 using prime factorization.
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MCQ
1. What is the HCF of 24 and 36?
a) 6
b) 12
c) 18
d) 24
2. The LCM of 8 and 12 is:
a) 24
b) 32
c) 48
d) 96
3. If the HCF of two numbers is 5 and their LCM is 60, what are the numbers?
a) 10 and 15
b) 15 and 20
c) 20 and 25
d) 25 and 30
4. The LCM of two numbers is 72 and their HCF is 8. If one number is 24, what is the other number?
a) 32
b) 36
c) 40
d) 48
5. If the HCF of two numbers is 9 and their LCM is 63, what are the numbers?
a) 18 and 27
b) 27 and 36
c) 36 and 45
d) 45 and 54
6. What is the HCF of two prime numbers?
a) Always 1
b) Always the smaller prime number
c) Always the larger prime number
d) Depends on the specific prime numbers
7. The LCM of two co-prime numbers is:
a) Always equal to the product of the two numbers
b) Always equal to the sum of the two numbers
c) Always equal to the difference of the two numbers
d) None of the above
8. If the HCF of two numbers is 1, what can we say about those numbers?
a) They are prime to each other
b) They are composite to each other
c) They are even numbers
d) They are odd numbers
9. The HCF of two numbers is always a factor of their:
a) Sum
b) Product
c) Difference
d) Quotient
10. If the LCM of two numbers is equal to one of the numbers, what can we conclude about those numbers?
a) They are both prime numbers
b) They are both composite numbers
c) They are co-prime numbers
d) They are consecutive numbers
11. The HCF of two numbers is 9 and their LCM is 72. If one number is 27, what is the other number?
a) 18
b) 24
c) 36
d) 45
12. The LCM of two numbers is 120 and their HCF is 5. If one number is 20, what is the other number?
a) 24
b) 30
c) 40
d) 60
13. If the HCF of two numbers is 7 and their LCM is 105, what are the numbers?
a) 14 and 21
b) 21 and 28
c) 28 and 35
d) 35 and 42
14. The LCM of two numbers is 84 and their HCF is 6. If one number is 18, what is the other number?
a) 24
b) 30
c) 36
d) 42
15. If the HCF of two numbers is 4 and their LCM is 48, what are the numbers?
a) 8 and 16
b) 12 and 24
c) 16 and 32
d) 20 and 40
16. What is the HCF of two consecutive numbers?
a) Always 1
b) Always the smaller number
c) Always the larger number
d) Depends on the specific numbers
17. The LCM of two consecutive numbers is:
a) Always equal to the product of the two numbers
b) Always equal to the sum of the two numbers
c) Always equal to the difference of the two numbers
d) None of the above
18. If the HCF of two numbers is a prime number, what can we conclude about those numbers?
a) They are both prime numbers
b) They are both composite numbers
c) They are co-prime numbers
d) They are consecutive numbers
19. The HCF of two numbers is always a multiple of their:
a) Sum
b) Product
c) Difference
d) Quotient
20. If the LCM of two numbers is equal to the product of the two numbers, what can we conclude about those numbers?
a) They are both prime numbers
b) They are both composite numbers
c) They are co-prime numbers
d) They are consecutive numbers
21. What is the relationship between the HCF and LCM of two numbers?
a) The HCF is always greater than the LCM
b) The LCM is always greater than the HCF
c) The HCF and LCM are always equal
d) There is no fixed relationship between the HCF and LCM
22. Can the HCF of two numbers be negative?
a) Yes
b) No
23. Can the LCM of two numbers be zero?
a) Yes
b) No
24. If the HCF of two numbers is 1, what can we say about those numbers?
a) They are both prime numbers
b) They are both composite numbers
c) They are co-prime numbers
d) They are consecutive numbers
25. What is the HCF of two prime numbers?
a) Always 1
b) Always a prime number
c) Always a composite number
d) Depends on the specific prime numbers
26. If the LCM of two numbers is 1, what can we conclude about those numbers?
a) They are both prime numbers
b) They are both composite numbers
c) They are co-prime numbers
d) They are consecutive numbers
27. Can the HCF and LCM of two numbers be the same?
a) Yes
b) No
28. What is the HCF of any two multiples of a number?
a) Always the number itself
b) Always a multiple of the number
c) Always 1
d) Depends on the specific multiples
29. What is the LCM of any two multiples of a number?
a) Always the number itself
b) Always a multiple of the number
c) Always 1
d) Depends on the specific multiples
30. If the HCF of two numbers is 0, what can we conclude about those numbers?
a) They are both positive
b) They are both negative
c) They are zero and a positive number
d) They are zero and a negative number
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