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ML Aggarwal Class 6 Solutions Chapter 5 Sets Ex 5.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 5 Sets Ex 5.1

Question 1.
State which of the following collections are sets:
(i) collection of odd natural numbers less than 50
(ii) collection of four colours of a rainbow
(iii) collection of first three days of a week
(iv) collection of all tall students of your class
(v) collection of all clever students of your school
(vi) collection of all rich people of Bangalore
(vii) collection of some multiples of 5 (viii) collection of all prime numbers
(ix) collection of all even integers which lie between -5 and 15
(x) collection of all good cricket players of India
(xi) collection of three youngest students of your class
(xii) collection of three healthy students of your class
Solution:

Question 2.
Let E = {even integers}. Insert the appropriate symbol ϵ or ∉ in the blanks:
(i) 10 …. E
(ii) -8 …. E
(iii) 13 … E
(iv) {6} …. E
(v) a …. E (vi) -4, 12, …. E
Solution:

Question 3.
Let V = {vowels in English alphabet}. Write which of the following statements are true and which are false :
(i) c ϵ V
(ii) {a} ϵ V
(iii) a, e, i ϵ V
(iv) a, b ϵ V
(v) {a, u} ∉ V
(vi) {a, o, u} ϵ V
Solution:

Question 4.
Write the following sets in roster form:
(i) the set of first five odd counting numbers
(ii) the set of all even natural numbers less than 101
(iii) {months of year whose names begin with a vowel}
(iv) {one digit natural numbers which are perfect squares}
(v) the set of multiples of 7 which lie between -20 and 25
(vi) {factors of 36}
(vii) {prime factors of 360}
(viii) the set of whole numbers which are multiples of 5
(ix) the set of all letters in the word ‘CHENNAI’
(x) The set of all vowels in the word ‘MUSSOORIE’
(xi) the set of all consonants in the word ‘MATHEMATICS’
Solution:

Question 5.
Write the following sets in tabular form:
(i) {x : is a natural number and x < 7}
(ii) {x : x e W and x ≤ 5}
(iii) {x : x is a month.of a year having less than 31 days}
(iv) {x | x is a letter in the word ‘CIRCUMFERENCE’}
(v) {x | x is a vowel in the word ‘NOTATION’}
(vi) (x : x is a digit in the numeral 110526715}
(vii) {x : x is a factor of 48}
(viii) (x : x is a multiple of 11 and 0 ≤ x < 80}
(ix) [y : y is a two digit natural number divisible by 10}
Solution:

Question 6.
Write the following sets in roster form and also in set builder form:
(i) the set of integers which lie between -2 and 3 (both inclusive)
(ii) the set of letters in the word ‘ULTIMATUM’
(iii) {months of a year whose names begin with J}
(iv) the set of single digit whole numbers which are perfect squares
Solution:

Question 7.
Write the following sets in tabular form and also in descriptive form :
(i) {x : x is a prime number less than 30}
(ii) the set of whole numbers which are multiples of 8 and less than 50
(iii) {x | x is a consonant in the word ‘QUESTION PAPER’}
Solution:

Question 8.
Write the following sets in the set builder form:
(i) A= {0, 1, 2, …, 11}
(ii) B = {7, 14, 21, 28, …}
(iii) C = {1, 4, 9, 16, 25, 36, 49}
(iv) D = {-12, -9, -b, -3, 0, 3, 6, 9, 12, 15, 18}
Solution:

ML Aggarwal Class 6 Solutions Chapter 4 Playing with Numbers Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 4 Playing with Numbers Check Your Progress

Question 1.
Write all factors of:
(i) 88
(ii) 105
(iii) 96
Solution:

Question 2.
Find the common mutliples of 8 and 12.
Solution:

Question 3.
Which of the following pairs of numbers are co-prime?
(i) 25 and 105
(ii) 59 and 97
(iii) 161 and 192
Solution:

Question 4.
Using divisibility tests, determine which of the following numbers are divisible by 4, 6, 8, 9 or 11:
(i) 197244
(ii) 613440
(iii) 4100448
Solution:

Question 5.
In 92 * 389, replace * by a digit so that the number formed is divisible by 11.
Solution:

Question 6.
Find the prime factorisation of the following numbers:
(i) 168
(ii) 2304
Solution:

Question 7.
Find the G.C.D. of the given numbers by prime factorisation method :
(i) 24,45
(ii) 180, 252, 324
Solution:

Question 8.
Find the H.C.F of the given numbers by division method.
(i) 54, 82
(ii) 84, 120, 156
Solution:

Question 9.
Find the L.C.M of the given numbers by prime factorisation method.
(i) 27, 90
(ii) 36, 48, 210
Solution:

Question 10.
Find the L.C.M of the given numbers by division method:
(i) 48, 60
(ii) 112, 168, 266
Solution:

Question 11.
Find the greatest number which divides 2706, 7041 and 8250 leaving remainder 6, 21 and 42 respectively.
Solution:

Question 12.
Find the least number which on decreasing by 20 is exactly divisible by 18, 21, 28 and 30.
Solution:

Question 13.
There are three heaps of rice weighing 120 kg, 144 kg and 204 kg. Find the maximum capacity of a bag so that the rice of each heap can be packed in exact number of bags.
Solution:

Question 14.
Three bells are ringing continuously at intervals of 30, 36 and 45 minutes respectively. At what time will they ring together again if they ring simultaneously at 8 a.m.
Solution:

Question 15.
Two numbers are co-prime and their L.C.M. is 4940. If one of the numbers is 65, find the other number.
Solution:

ML Aggarwal Class 6 Solutions Chapter 4 Playing with Numbers Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 4 Playing with Numbers Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) The only natural number which has exactly one factor is ……….
(ii) The only prime number which is even is ……….
(iii) The HCF of two co-prime numbers is ……….
(iv) Two perfect numbers are ………. and ……….
(v) The only prime-triplet is ……….
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) Every natural number has a finite number of factors.
(ii) Every natural number has an infinite number of its multiples.
(iii) There are infinitely many prime numbers.
(iv) If two numbers are separately divisible by a number, then their difference is also divisible by that number.
(v) LCM of two prime numbers equals their product.
(vi) LCM of two co-prime numbers equals their product.
Solution:

Question 3.
State whether the following statements are true or false. If a statement is false, justify your answer.
(i) The sum of two prime numbers is always an even number.
(ii) The sum of two prime numbers is always a prime number.
(iii) The sum of two prime numbers can never be a prime number
(iv) No odd number can be written as the sum of two prime numbers.
(v) If two numbers are co-prime, then atleast one of them must be prime.
(vi) If a number is divisible by 18, it must be divisible by 3 and 6 both.
(vii) If a number is divisible by 2 and 4 both, it must be divisible by 8.
(viii) If a number is divisible by 3 and 6 both, it must be divisible by 18.
(ix) HCF of an even number and an odd number is always 1.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (4 to 28):
Question 4.
All factors of 6 are
(a) 1, 6
(b) 2, 3
(c) 1, 2, 3
(d) 1, 2, 3, 6
Solution:

Question 5.
Which of the following is an odd composite number?
(a) 7
(b) 9
(c) 11
(d) 12
Solution:

Question 6.
The number of even numbers between 68 and 90 is
(a) 10
(b) 11
(c) 12
(d) 31
Solution:

Question 7.
Which of the following is a prime number?
(a) 69
(b) 87
(c) 91
(d) 97
Solution:

Question 8.
Which of the following is a pair of twin- prime number?
(a) 19, 21
(b) 43, 47
(c) 59, 61
(d) 73, 79
Solution:

Question 9.
The number of distinct prime factors of the largest 4-digit number is
(a) 2
(b) 3
(c) 5
(d) none of these
Solution:

Question 10.
The number of distinct prime factors of the smallest 5-digit number is
(a) 2
(b) 4
(c) 6
(d) 8
Solution:

Question 11.
The sum of the prime factors of 1729 is
(a) 13
(b) 19
(c) 32
(d) 39
Solution:

Question 12.
Which of the following is a pair of co-prime numbers?
(a) 8, 45
(b) 3, 18
(c) 5, 35
(d) 6, 39
Solution:

Question 13.
Every natural number has an infinite number of
(a) prime factors
(b) factors
(c) multiples
(d) none of these
Solution:

Question 14.
Which of the following numbers is divisible by 4?
(a) 308594
(b) 506784
(c) 732106
(d) 9301538
Solution:

Question 15.
Which of the following numbers is divisible by 8?
(a) 503786
(b) 505268
(c) 305678
(d) 703568
Solution:

Question 16.
Which of the following numbers is divisible by 3?
(a) 50762
(b) 42063
(c) 52871
(d) 37036
Solution:

Question 17.
Which of the following numbers is divisible by 9?
(a) 972063
(b) 730542
(c) 785423
(d) 5612844
Solution:

Question 18.
Which of the following numbers is divisible by 6?
(a) 560324
(b) 650374
(c) 798653
(d) 750972
Solution:

Question 19.
The digit by which ‘*’ should be replaced in 54 * 281 so that the number formed is divisible by 9 is
(a) 6
(b) 7
(c) 8
(d) 9
Solution:

Question 20.
The digit by which should be replaced in 7254 * 98 so that the number formed is divisible by 22 is
(a) 0
(b) 1
(c) 2
(d) 6
Solution:

Question 21.
If a number is divisible by 5 and 6 both, then it may not be divisible by
(a) 10
(b) 15
(c) 30
(d) 60
Solution:

Question 22.
The number of common prime factors of 60, 75 and 105 is
(a) 2
(b) 3
(c) 4
(d) 5
Solution:

Question 23.
The H.C.F. of 144 and 198 is
(a) 6
(b) 9
(c) 12
(d) 18
Solution:

Question 24.
The L.C.M. of 30 and 45 is
(a) 15
(b) 30
(c) 45
(d) 90
Solution:

Question 25.
The L.C.M. of 4 and 44 is
(a) 4
(b) 11
(c) 44
(d) 176
Solution:

Question 26.
The LCM of 7 and 13 is 1
(a) 1
(b) 7
(c) 13
(d) 91
Solution:

Question 27.
If H.C.F. of two numbers is 15 and their product is 1575, then their L.C.M. is
(a) 15
(b) 105
(c) 525
(d) 1575
Solution:

Question 28.
If the LCM of two natural numbers is 180, then which of the following is not the HCF of the numbers?
(a) 45
(b) 60
(c) 75
(d) 90
Solution:

Value Based Questions
Question 1.
To teach the value of gratitude and appreciation to the students, a school organised a ‘Card Making’ activity in which the students were asked to make “THANK YOU CARDS” for the people who helped them in some way. Assorted cards were made with different titles. Their numbers are given below:
T cards for teachers = 120
F cards for friends = 540
S cards for servants = 90
P cards for parents = 240 and
G cards for grandparents = 150
(i) Find the HCF and LCM of all the different number of cards.
(ii) Find HCF and LCM of maximum and minimum number of cards.
(iii) Is the number of T-cards is a factor of number of P-cards?
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
Write 2-digit odd numbers whose sum of digits is 8.
Solution:

Question 2.
Write all pairs of 2-digit twin primes such that on changing the places of their digits, they still remain prime numbers.
Solution:

Question 3.
There are just four natural numbers less than 100, which have exactly three factors. One of them is 25, what are the other three? What can be said about these numbers?
Solution:

ML Aggarwal Class 6 Solutions Chapter 4 Playing with Numbers Ex 4.5 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 4 Playing with Numbers Ex 4.5

Question 1.
Find the L.C.M. of the given numbers by prime factorisation method :
(i) 28, 98
(ii) 36, 40, 126
(iii) 108, 135, 162
(iv) 24, 28, 196.
Solution:

Question 2.
Find the L.C.M. of the given numbers by division method :
(i) 480, 672
(ii) 6, 8, 45
(iii) 24, 40, 84
(iv) 20, 36, 63, 67
Solution:

Question 3.
Find the least number which when increased by 15 is exactly divisible by 15, 35 and 48.
Solution:

Question 4.
Find the least number which when divided by 6, 15 and 18 leaves remainder 5 in each case.
Solution:

Question 5.
Find the least number which when divided by 24, 36, 45 and 54 leaves a remainder of 3 in each case.
Solution:

Question 6.
Find the greatest 3-digit number which is exactly divisible by 8, 20 and 24.
Solution:

Question 7.
Find the smallest 4-digit number which is exactly divisible by 32, 36 and 48.
Solution:

Question 8.
Find the greatest 4-digit number which is exactly divisible by each of 8, 12 and 20.
Solution:

Question 9.
Find the least number of five digits which is exactly divisible by 32, 36 and 45.
Solution:

Question 10.
Three boys step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. What is the minimum distance each should cover so that all can cover the same distance in complete steps?
Solution:

Question 11.
Traffic lights at three different road crossing change after 48 seconds, 72 seconds and 108 seconds respectively. At what time will they change together again if they change simultaneously at 7 A.M.?
Solution:

Question 12.
If the product of two numbers is 4032 and their HCF is 12, find their LCM.
Solution:

Question 13.
The HCF and LCM of two numbers are 9 and 270 respectively. If one of the numbers is 45, find the other number.
Solution:

Question 14.
Find the HCF of 180 and 336. Hence, find their LCM.
Solution:

Question 15.
Can two numbers have 15 as their HCF and 110 as their LCM? Give reason to justify your answer.
Solution:

ML Aggarwal Class 6 Solutions Chapter 4 Playing with Numbers Ex 4.4 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 4 Playing with Numbers Ex 4.4

Question 1.
Find the H.C.F. of the given numbers by prime factorisation method :
(i) 28, 36
(ii) 54, 72, 90
(iii) 105, 140, 175.
Solution:

Question 2.
Find the H.C.F. of the given numbers by division method:
(ii) 198, 429
(ii) 20, 64, 104
(iii) 120, 144, 204
Solution:

Question 3.
Fill in the blanks:
(i) HCF of two consecutive natural numbers is ……
(ii) HCF of two consecutive odd numbers is …..
(iii) HCF of two consecutive even numbers is ……
Solution:

Question 4.
Find the greatest number which can divide 257 and 329 so as to leave a remainder 5 in each case. .
Solution:

Question 5.
Find the largest number that will divide 623, 729 and 841 leaving remainder 3, 9 and 1 respectively.
Solution:

Question 6.
Meenu purchases two bags of rice of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the rice exact number of times.
Solution:

Question 7.
Three tankers contain 403 litres, 434 litres and 465 litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of three containers exact number of times.
Solution: