ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 6 Operation on sets Venn Diagrams Ex 6.1

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 6 Operation on sets Venn Diagrams Ex 6.1

Question 1.
If A = {0, 1, 2, 3, …….., 8}, B = {3, 5, 7, 9, 11} and C = {0, 5, 10, 20}, find
(i) A ∪ B
(ii) A ∪ C
(iii) B ∪ C
(iv) A ∩ B
(v) A ∩ C
(vi) B ∩ C
Also find the cardinal number of the sets B ∪ C, A ∪ B, A ∩ C and B ∩ C.
Solution:
APC Maths Class 8 Solutions Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q1

Question 2.
Find A’ when
(i) A= {0, 1, 4, 7} and E, = {x | x ϵ W, x ≤ 10}
(ii) A = {consonants} and ξ = {alphabets of English}
(iii) A = boys in class VIII of all schools in Bengaluru} and ξ = {students in class VIII of all schools in Bengaluru}
(iv) A = {letters of KALKA} and ξ = {letters of KOLKATA}
(v) A = {odd natural numbers} and ξ = {whole numbers}.
Solution:
ICSE Understanding Mathematics Class 8 Solutions Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q2
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q2.1

Question 3.
If A {x : x ϵ N and 3 < x < 1} and B = {x : x ϵ Wand x ≤ 4}, find
(i) A ∪ B
(ii) A ∩ B
(iii) A – B
(iv) B – A
Solution:
Maths Questions for Class 8 ICSE With Answers Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q3

Question 4.
If P = {x : x ϵ W and x < 6} and Q = {x : x ϵ N and 4 ≤ x ≤ 9}, find
(i) P ∪ Q
(ii) P ∩ Q
(iii) P – Q
(iv) Q – P
Is P ∪ Q a proper superset of P ∩ Q ?
Solution:
ICSE Mathematics Class 8 Solutions Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q4

Question 5.
If A = (letters of word INTEGRITY) and B = (letters of word RECKONING), find
(i) A ∪ B
(ii) A ∩ B
(iii) A – B
(iv) B – A
Also verify that:
(a) n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
(b) n(A – B) = n(A ∪ B) – n(B)
= n(A) – n(A ∪ B)
(c) n(B – A) = n(A ∪ B) – n(A)
= n(B) – n(A ∩ B)
(d) n(A ∪ B) = n(A – B) + n(B – A) + n(A ∩ B).
Solution:
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q5
ML Aggarwal Class 8 Solutions Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q5.1

Question 6.
If ξ = {natural numbers between 10 and 40}
A = {multiples of 5} and
B = {multiples of 6}, then
(i) find A ∪ B and A ∩ B
(ii) verify that
n(A ∪ B) = B (A) + n(B) – n(A ∩ B).
Solution:
APC Maths Class 8 Solutions Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q6

Question 7.
If ξ ={1,2, 3, …. 9}, A = {1, 2, 3, 4, 6, 7, 8} and B = {4, 6, 8}, then find.
(i) A’
(ii) B’
(iii) A ∪ B
(iv) A ∩ B
(v) A – B
(vi) B – A
(vii) (A ∩ B)’
(viii) A’ ∪ B’
Also verify that:
(a) (A ∩ B)’ = A’ ∪ B’
(b) n(A) + n(A’) = n(ξ)
(c) n(A ∩ B) + n((A ∩ B)’) = n(ξ)
(d) n(A – B) + n(B – A) + n(A ∩ B)
= n(A ∪ B).
Solution:
ICSE Understanding Mathematics Class 8 Solutions Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q7
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q7.1
Maths Questions for Class 8 ICSE With Answers Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q7.2

Question 8.
If 4 = {x : x ϵ W, x ≤ 10}, A. = {x : x ≥ 5} and B = {x : 3 ≤ x < 8}, then verify that:
(i) (A ∪ B)’ = A’ ∩ B’
(ii) (A ∩ B)’= A’ ∪ B’
(iii) A – B = A ∩ B’
(iv) B – A = B ∩ A’
Solution:
ICSE Mathematics Class 8 Solutions Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q8
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q8.1
ML Aggarwal Class 8 Solutions Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q8.2

Question 9.
If n(A) = 20, n(B) = 16 and n(A ∪ B) = 30, find n(A ∩ B).
Solution:
APC Maths Class 8 Solutions Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q9

Question 10.
If n ξ = 20 and n(A’) = 7, then find n(A).
Solution:
ICSE Understanding Mathematics Class 8 Solutions Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q10

Question 11.
If n(ξ) = 40, n(A) = 20, n(B’) = 16 and n(A ∪ B) = 32, then find n(B) and n(A ∩ B).
Solution:
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q11

Question 12.
If n(ξ) = 32, n(A) = 20, n(B) = 16 and n((A ∪ B)’) = 4, find :
(i) n(A ∪ B)
(ii) n(A ∩ B)
(iii) n(A – B)
Solution:
Maths Questions for Class 8 ICSE With Answers Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q12

Question 13.
If n(ξ) = 40, n(A’) = 15, n(B) = 12 and n((A ∩ B)’) = 32, find :
(i) n(A)
(ii) n(B’)
(iii) n(A ∩ B)
(iv) n(A ∪ B)
(v) n(A – B)
(vi) n(B – A)
Solution:
ICSE Mathematics Class 8 Solutions Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q13

Question 14.
If n(A – B) = 12, n(B – A) = 16 and n(A ∩ B) = 5, find:
(i) n(A)
(ii) n(B)
(iii) n(A ∪ B)
Solution:
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 6 Operation on sets Venn Diagrams Ex 6.1 Q14

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 5 Playing with Numbers Check Your Progress

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 5 Playing with Numbers Check Your Progress

Question 1.
In a 2-digit number, sum of digits is 7. If the difference of 2 digit number and number obtained by reversing the digits is 9, then find the number.
Solution:
APC Maths Class 8 Solutions Chapter 5 Playing with Numbers Check Your Progress Q1

Question 2.
In a 3 digit number, the difference of hundred’s digit and unit’s digit is 5. Find the quotient when the difference of 3-digit number and number obtained by reversing the digits is divided by 9.
Solution:
ICSE Understanding Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Check Your Progress Q2

Question 3.
Without actual calculation, write the quotient when sum of 3 digit numbers 567, 675 and 756 is divided by
(i) 111
(ii) 18
(iii) 37
(iv) 3
Solution:
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 5 Playing with Numbers Check Your Progress Q3

Question 4.
Find the values of the letters in each of the following and give reasons for the steps involved:
Maths Questions for Class 8 ICSE With Answers Chapter 5 Playing with Numbers Check Your Progress Q4
Solution:
ICSE Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Check Your Progress Q4.1

Question 5.
If 923×783 is divisible by 11, what is the value of digit x?
Solution:
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 5 Playing with Numbers Check Your Progress Q5

Question 6.
Check the divisibility of following numbers by 2, 3, 9 and 11:
(i) 76543
(ii) 65432
(iii) 98765436
(iv) 234567
Solution:
ML Aggarwal Class 8 Solutions Chapter 5 Playing with Numbers Check Your Progress Q6
APC Maths Class 8 Solutions Chapter 5 Playing with Numbers Check Your Progress Q6.1

Question 7.
Check the divisibility of the following numbers by 5 or 10:
(i) 23565
(ii) 45270
Solution:
ICSE Understanding Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Check Your Progress Q7

Question 8.
Check the divisibility of the following numbers by 4 or 8:
(i) 47596
(ii) 593024
Solution:
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 5 Playing with Numbers Check Your Progress Q8

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 5 Playing with Numbers Objective Type Questions

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 5 Playing with Numbers Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) The sum of a 2-digit number and number obtained by reversing the digits is always divisible by 11 and ……….
(ii) The difference of a 2-digit number and number obtained by reversing the digits is always divisible by ………. and ……….
(iii) The difference of a 3=digit number a b c (a > c) and the number obtained by reversing the digits is always divisible by ………. and ……….
(iv) The next number of the series 0, 1, 1, 2, 3, 5, 8, 13, ………. is ……….
(v) General form of a 2 digit number 57 is ……….
(vi) Usual form of number 100 × 7 + 10 × 4 + 1 is ……….
(vii) If the division N ÷ 5 leaves remainder 4 and the division N ÷ 2 leaves remainder 1, then unit’s digit of N must be ……….
(viii)If 213×52 is divisible by 9, then digit x is ……….
Solution:
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 5 Playing with Numbers Objective Type Questions Q1

Question 2.
State whether the following statements are true (T) or false (F):
(i) If the division N ÷ 5 leaves a remainder 4, then unit’s digit of N may be 1 or 6.
(ii) If the division N ÷ 2 leaves a remainder 1, then unit’s digit of N may be 1, 3, 5, 7 or 9.
(iii) If a number is divisible by any number m, then it will also be divisible by each of the factors of m.
(iv) If a number is divisible by sum of two numbers then it will also be divisible by each of the two numbers separately.
(v) If 3651x is divisble by 9, then value of digit x is 3.
(vi) If 42×7 is divisible by 3, then value of digit x is 4.
(vii) The number 152875 is divisible by 9.
(viii)The number 389072 is divisible by 8.
(ix) The number 27402 is divisible by 6.
(x) The number 359249 is not divisible by 11.
Solution:
ML Aggarwal Class 8 Solutions Chapter 5 Playing with Numbers Objective Type Questions Q2
APC Maths Class 8 Solutions Chapter 5 Playing with Numbers Objective Type Questions Q2.1

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 13):
Question 3.
When the sum of a 2-digit number ab and number obtained by reversing the digits is divided by (a + b), the quotient is
(a) a – b
(b) 9
(c) 11
(d) None of these
Solution:
ICSE Understanding Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Objective Type Questions Q3

Question 4.
When the sum of a 3-digit number abc and numbers obtained by changing the order of the digits cyclically is divided by 111, then the quotient is
(a) 37
(b) a – b + c
(c) a + b + c
(d) 3
Solution:
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 5 Playing with Numbers Objective Type Questions Q4

Question 5.
If A + A + A = BI, where A and B are different digits, then
(a) A = 1, B = 5
(b) A = 5, B = 2
(c) A = 5, B = 1
(d) A = 7, B = 2
Solution:
Maths Questions for Class 8 ICSE With Answers Chapter 5 Playing with Numbers Objective Type Questions Q5

Question 6.
Which of the following numbers is not divisible by 2?
(a) 437218
(b) 437821
(c) 437812
(d) 437182
Solution:
ICSE Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Objective Type Questions Q6

Question 7.
Which of the following numbers is not divisible by 10?
(a) 32570
(b) 32750
(c) 32500
(d) 32075
Solution:
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 5 Playing with Numbers Objective Type Questions Q7

Question 8.
Which of the following numbers is divisible by 4?
(a) 98764
(b) 98746
(c) 98674
(d) 98647
Solution:
ML Aggarwal Class 8 Solutions Chapter 5 Playing with Numbers Objective Type Questions Q8

Question 9.
Which of the following numbers is divisible by 8?
(a) 32466
(b) 32476
(c) 32486
(d) 32456
Solution:
APC Maths Class 8 Solutions Chapter 5 Playing with Numbers Objective Type Questions Q9

Question 10.
Which of the following numbers is divisible by 11?
(a) 725824
(b) 752824
(c) 725842
(d) 725482
Solution:
ICSE Understanding Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Objective Type Questions Q10

Question 11.
Which of the following numbers is not divisible by 9?
(a) 24354
(b) 24453
(c) 24534
(d) 24564
Solution:
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 5 Playing with Numbers Objective Type Questions Q11

Question 12.
If 467×8 is divisible by 3, then the value of x
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
Maths Questions for Class 8 ICSE With Answers Chapter 5 Playing with Numbers Objective Type Questions Q12

Question 13.
If 36x52y8 is divisible by 9, then x + y is
(a) 2
(b) 3
(c) 4
(d) 5
Solution:
ICSE Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Objective Type Questions Q13

Value Based Question
Question 1.
Rishabh plays a game with two dice in a fete. He draws three columns on a chart paper. In the left-most column, he writes the digits less than 7 and in the rightmost column he writes the numbers greater than 7. In the middle column, he writes digit 7 only. He offers people to keep money on any one of the columns. He throws two dice together if the sum of the digits on the two dice is less than 7, he doubles the money kept on the left-most column and collect the money kept on the remaining two columns. Similarly, he doubles the money on a rightmost column if the sum of digits is greater than 7 and triples on the middle column if the sum of the digits is 7. What digits should he write on leftmost and rightmost columns?
Is this game a sort of gambling? Is gambling a good way of earning money?
Solution:
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 5 Playing with Numbers Objective Type Questions VBQ 1

Higher Order Thinking Skills (Hots)
Question 1.
If the difference of two-digit number and number obtained by reversing the digits is 45, then write all possible 2-digit numbers.
Solution:
ML Aggarwal Class 8 Solutions Chapter 5 Playing with Numbers Objective Type Questions HOTS 1

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 5 Playing with Numbers Ex 5.3

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 5 Playing with Numbers Ex 5.3

Question 1.
Which of the following numbers are divisible by 5 or by 10:
(i) 87035
(ii) 75060
(iii) 9685
(iv) 10730
Solution:
ICSE Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.3 Q1

Question 2.
Which of the following numbers are divisible by 2, 4 or 8:
(i) 67894
(ii) 5673244
(iii) 9685048
(iv) 6533142
(v) 75379
Solution:
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 5 Playing with Numbers Ex 5.3 Q2

Question 3.
Which of the following numbers are divisible by 3 or 9:
(i) 45639
(ii) 301248
(iii) 567081
(iv) 345903
(v) 345046
Solution:
ML Aggarwal Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.3 Q3

Question 4.
Which of the following numbers are divisible by 11:
(i) 10835
(ii) 380237
(iii) 504670
(iv) 28248
Solution:
APC Maths Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.3 Q4

Question 5.
Which of the following numbers are divisible by 6:
(i)15414
(ii) 213888
(iii) 469876
Solution:
ICSE Understanding Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.3 Q5

Question 6.
Which of the following numbers are divisible by 7:
(i) 46f8894875
(ii) 3794856
(iii) 39823
Solution:
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 5 Playing with Numbers Ex 5.3 Q6

Question 7.
(i) If 34x is a multiple of 3, where x is a digit, what is the value of x?
(ii) If 74×5284 is a multiple of 3, where x is a digit, find the value(s) of x.
Solution:
Maths Questions for Class 8 ICSE With Answers Chapter 5 Playing with Numbers Ex 5.3 Q7

Question 8.
If 42z3 is a multiple of 9, where z is a digit, what is the value of z?
Solution:
ICSE Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.3 Q8

Question 9.
In each of the following replace * by a digit so that the number formed is divisible by 9:
(i) 49 * 2207
(ii) 5938 * 623
Solution:
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 5 Playing with Numbers Ex 5.3 Q9

Question 10.
In each of the following replace * by a digit so that the number formed is divisible by 6:
(i) 97 * 542
(ii) 709 * 94
Solution:
ML Aggarwal Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.3 Q10

Question 11.
In each of the following replace * by a digit so that the number formed is divisible by 11:
(i) 64*2456
(ii) 86*6194
Solution:
APC Maths Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.3 Q11

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 5 Playing with Numbers Ex 5.2

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 5 Playing with Numbers Ex 5.2

Find the values of the letters in each of the following and give reasons for the steps involved (1 to 11):
Question 1.
ML Aggarwal Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q1
Solution:
APC Maths Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q1.1

Question 2.
ICSE Understanding Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q2
Solution:
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 5 Playing with Numbers Ex 5.2 Q2.1

Question 3.
Maths Questions for Class 8 ICSE With Answers Chapter 5 Playing with Numbers Ex 5.2 Q3
Solution:
ICSE Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q3.1

Question 4.
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 5 Playing with Numbers Ex 5.2 Q4
Solution:
ML Aggarwal Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q4.1

Question 5.
APC Maths Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q5
Solution:
ICSE Understanding Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q5.1

Question 6.
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 5 Playing with Numbers Ex 5.2 Q6
Solution:
Maths Questions for Class 8 ICSE With Answers Chapter 5 Playing with Numbers Ex 5.2 Q6.1

Question 7.
ICSE Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q7
Solution:
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 5 Playing with Numbers Ex 5.2 Q7.1

Question 8.
ML Aggarwal Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q8
Solution:
APC Maths Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q8.1

Question 9.
ICSE Understanding Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q9
Solution:
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 5 Playing with Numbers Ex 5.2 Q9.1

Question 10.
Maths Questions for Class 8 ICSE With Answers Chapter 5 Playing with Numbers Ex 5.2 Q10
Solution:
ICSE Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q10.1

Question 11.
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 5 Playing with Numbers Ex 5.2 Q11
Solution:
ML Aggarwal Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q11.1

Question 12.
Fill in the numbers from 1 to 6 (without repetition) so that each side of the magic triangle adds up to 12.
APC Maths Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q12
Solution:
ICSE Understanding Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q12.1

Question 13.
Complete the magic square given alongside using number 0, 1, 2, 3, ……., 15 (only once), so that sum along each row, column and diagonal is 30.
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 5 Playing with Numbers Ex 5.2 Q13
Solution:
Maths Questions for Class 8 ICSE With Answers Chapter 5 Playing with Numbers Ex 5.2 Q13.1

Question 14.
Fill in the blanks to complete the following number triangle:
ICSE Mathematics Class 8 Solutions Chapter 5 Playing with Numbers Ex 5.2 Q14
Solution:
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 5 Playing with Numbers Ex 5.2 Q14.1

ML Aggarwal Class 8 Solutions for ICSE Maths