ICSE

ML Aggarwal Class 7 Solutions Chapter 6 Ratio and Proportion Ex 6.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 6 Ratio and Proportion Ex 6.1

Question 1.
Express the following ratios in simplest form:

Solution:

Question 2.
Find the ratio of each of the following in simplest form:
(i) ₹ 5 to 50 paise
(ii) 3 km to 300 m
(iii) 9 m to 27 cm
(iv) 15 kg to 210 g
(v) 25 minutes to 1.5 hours
(vi) 30 days to 36 hours
Solution:

Question 3.
If A : B = 3 : 4 and B : C = 8 : 9, then find A : C.
Solution:

Question 4.
If A : B = 5 : 8 and B : C = 18 : 25, then find A : B : C.
Solution:

Question 5.
If 3A = 2B = 5C, then find A : B : C.
Solution:

Question 6.
Out of daily income of ₹ 120, a labourer spends ₹ 90 on food and shelter and saves the rest. Find the ratio of his
(i) spending to income
(ii) saving to income
(iii) saving to spending.
Solution:

Question 7.
5 grams of an alloy contains 3\(\frac { 3 }{ 4 }\) grams copper and the rest is nickel. Find the ratio by weight of nickel to copper.
Solution:

Question 8.
A pole of height 3 meters is struck by a speeding car and breaks into two pieces such that the first piece is \(\frac { 1 }{ 2 }\) of the second. Find the length of both pieces.
Solution:

Question 9.
Heights of Anshul and Dhruv are 1.04 m and 78 cm respectively. Divide 35 sweets between them in the ratio of their heights.
Solution:

Question 10.
₹ 180 are to be divided among three children in the ratio \(\frac { 1 }{ 3 } :\frac { 1 }{ 4 } :\frac { 1 }{ 6 }\) Find the share of each child.
Solution:

Question 11.
A natural number has been divided into two parts in the ratio 7 : 11. If the difference between the two parts is 20, find the number and the two parts.
Solution:

Question 12.
A certain sum of money has been divided into two parts in the ratio 9 : 13. If the second part is ₹ 260, find the total amount.
Solution:

Question 13.
The ratio of the present ages of Anjali and Ashu is 2 : 3. Five years hence, the ratio of their ages will be 3 : 4. Find their present ages.
Solution:

Question 14.
The present ages of A and B are in the ratio 5 : 6. Three years ago, their ages were in the ratio 4 : 5. find their present ages.
Solution:

Question 15.
Two numbers are in the ratio 5 : 6. When 2 is added to first and 3 is added to second, they are in the ratio 4 : 5. Find the numbers.
Solution:

Question 16.
The ratio of number of boys to the number of girls in a school of 1430 students is 7 : 6. If 26 new girls are admitted in the school, find how many new boys may be admitted so that the ratio of number of boys to the number of girls may change to 8 : 7.
Solution:

Question 17.
Which ratio is greater?
(i) 5 : 6 or 6 : 7
(ii) 13 : 24 or 17 : 32
Solution:

ML Aggarwal Class 7 Solutions Chapter 5 Sets 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 7 Solutions for ICSE Maths Chapter 5 Sets Check Your Progress

Question 1.
Write the following sets in tabular form and also in set builder form:
(i) The set of even integers which lie between -6 and 10.
(ii) The set of two digit numbers which are perfect square.
(iii) {factors of 42}
Solution:

Question 2.
Write the following sets in roster form:
(i) {x : x = 5n, n ∈ I and -3 < n ≤ 13}
(ii) {x : x = n², n ∈ W and n < 5}
(iii) {x : x = n² – 2, n ∈ W and n < 4}
Solution:

Question 3.
Write the following sets in set builder form:
(i) {-14, -7, 0, 7, 14, 21, 28}
(ii) {1, 2, 3, 6, 9, 18}
Solution:

Question 4.
Classify the following sets into the finite set, infinite set the empty set. In the case of a (non-empty) finite set, mention the cardinal number.
(i) The set of even prime numbers.
(ii) {multiples of 9}
(iii) {x : x is a prime factor of 84}
(iv) {x : 2x + 5 = 1, x ∈ N}
(v) {x : x is a month of a year having less than 30 days}
(vi) {x | x is a month of a leap year having 28 days}
Solution:

Question 5.
In the following, determine whether A and B are equivalent sets and if so, whether A = B.
(i) A = {1, 3, 5}, B = {Red, Blue, Green}
(ii) A = {prime factors of 70}, B = {prime factors of 60}
(iii) A = {even natural numbers less than 10}, B = {odd natural numbers less than 10}
Solution:

Question 6.
Let P = {letters of SCHOOL} and Q = {letters of FALSE}, then State whether each of the following statement is true or false for the above sets:
(i) P ⊂ Q
(ii) Q ⊂ P
(iii) P ↔ Q
Solution:

Question 7.
State whether each of the following statement is true or false for the sets A, B and C where
A = {x | x ∈ N, x < 40 and x is a multiple of 6}
B = {x | x ∈ W, x ≤ 40 and x is a multiple of 8}
C = {x | x is a factor of 28}.
(i) A ↔ B
(ii) B ↔ C
(iii) A ↔ C
Solution:

ML Aggarwal Class 7 Solutions Chapter 5 Sets 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 7 Solutions for ICSE Maths Chapter 5 Sets Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) If x is not a member of the set A, then symbolically we write it as ……..
(ii) Each element of a set is listed once and only ……….. repetitions are removed.
(iii) A set that contains a limited number of different elements is called a ……… set.
(iv) Two finite sets are called equivalent if and only if they have ………. a number of elements.
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) A collection of books is a set.
(ii) If X = {letters of the word PRINCIPAL}, then the cardinal number of set X is 9.
(iii) If P = {letters of the word AHMEDABAD}, then n(P) = 6.
(iv) If A is any set, then A ⊂ A.
(v) An empty set is a subset of every set.
(vi) If set A = {0}, then n{A} = 0.
(vii) If A and B are two sets such that A ⇔ B, then A = B.
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 9):

Question 3.
Which of the following collection forms a set?
(a) Collection of 5 odd prime numbers
(b) Collection of 3 most intelligent students of your class
(c) Collection of 4 vowels of the English alphabet
(d) Collection of first 6 months of a year.
Solution:

Question 4.
The tabular form for the statement ‘Days of the week starting with the letter T’ will be
(a) {Days of week starting with letter T}
(b) {Tuesday, Thursday}
(c) {x | x is a day of the week starting with letter T}
(d) none of these
Solution:

Question 5.
A set with a limited number of distinct elements is called
(a) a finite set
(b) an infinite set
(c) both finite as well as an infinite set
(d) none of these
Solution:

Question 6.
The symbol ↔ stands for
(a) belongs to
(b) is a subset of
(c) is equivalent to
(d) none of these
Solution:

Question 7.
The empty set is denoted as
(a) {Φ}
(b) { }
(c) {0}
(d) 0
Solution:

Question 8.
The cardinal number n(A) = for A = {x : x is an odd prime number less than 20} is
(a) 8
(b) 7
(c) 9
(d) 10
Solution:

Question 9.
If A = {x | x is a positive mutliple of 3 less than 20} and B = {x | x is a prime number less than 20}, then n(A) + n(B) is
(a) 6
(b) 8
(c) 13
(d) 14
Solution:

ML Aggarwal Class 7 Solutions Chapter 5 Sets Ex 5.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 5 Sets Ex 5.2

Question 1.
Classify the following sets into empty set, finite set and infinite set. In case of (non-empty) finite sets, mention the cardinal number.
(i) {all colours of a rainbow}
(ii) {x | x is a prime number between 7 and 11}
(iii) {multiples of 5}
(iv) {all straight lines drawn in a plane}
(v) {x | x is a digit in the numeral 550131527}
(vi) {x | x is a letter in word SUFFICIENT}
(vii) {x | x = 4n, n ∈ I and x < 10}
(viii) {x | x ∈ N, x is a prime factor of 180}
(ix) {x : x is a vowel in the word WHY}
(x) {x : x = 5n, n ∈ W and x < 60}
Solution:

Question 2.
Which of the following describe the same sets:
(i) {vowels of English alphabet} and {e, a, u, i, o}
(ii) {a, b, d} and {d, a, b, b}
(iii) {letters of PUPPET} and {E, T, P, U}
(iv) {1, 2, 3} and {2, 3, 4}
(v) {1, 2, 3, 4, 5} and {x | x ∈ N, x ≤ 5}
Solution:

Question 3.
Find pairs/groups of equal sets from the following sets:
A = {0, 1, 2, 3}
B = {x : x² < 10, x ∈ W}
C = {letters of word FOLLOW}
D = {days of a week}
E = {x | x ∈ W, x < 4}
F = {letters of word FLOW}
G = {Monday, Tuesday, ……… , Sunday}
H = {letters of word WOLF}
Solution:

Question 4.
Find pairs/groups of equivalent sets from the following sets.
A = {colours of a rainbow}
B = {letters of word GOOD}
C = {x : x is a digit in the numeral 371011489}
D = {letters of word TOM}
E = {x : x ∈ I, x² < 10}
F = {months of a year}
G = {days of a week}
H = {x | x = 3n, n ∈ W and n < 12}
I = {all even numbers between 1 and 53}
J = {all letters of English alphabets}
Solution:

Question 5.
In the following, find whether A ⊂ B or B ⊂ A or none of these:
(i) A = { 1, 2, 3}, B = {2, 3, 3, 3, 1, 3}
(ii) A = {2, 4, 6,….}, B = {all natural numbers}
(iii) A = {x | x ∈ I, x² < 20}, B = {0, 1, 2, 3, 4}
(iv) A = {letters of KING},
B = {letters of QUEEN}
Solution:

Question 6.
State whether each of the following statement is true or false for the sets A and B where
A = {letters of CLOUD} and B = {letters of KOLKATA}
(i) A ⊂ B
(ii) B ⊂ A
(iii) A ↔ B
Solution:

Question 7.
Write all the subsets of the following sets:
(i) Φ
(ii) {3, 5}
(iii) {2, 4, 6}
Solution:

Question 8.
If A = {x : x = 2n, n < 5}, then find A when
(i) ξ = N
(ii) ξ = W
(iii) ξ = I
Solution:

ML Aggarwal Class 7 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 7 Solutions for ICSE Maths Chapter 5 Sets Ex 5.1

Question 1.
State which of the following collections are set:
(i) All states of India.
(ii) Four cities of India having more than one lac population.
(iii) All tall students of your school.
(iv) Four colours of a rainbow.
(v) All the beautiful flowers.
(vi) All clever people of Lucknow.
(vii) Last three days of a week.
(viii)All months of a year having at least 30 days.
Solution:

Question 2.
Let A = {vowels of English alphabet}, then which of the following statements are true. In case a statement is incorrect, mention why.
(i) c ∈ A
(ii) {a} ∈ A
(iii) a, i, u, ∈A
(iv) {a, u} ∉ A
(v) {a, i, u } ∈ A
(vi) a, b, ∈ A
Solution:

Question 3.
Describe the following sets:
(i) {a, b, c, d, e, f}
(ii) {2, 3, 5, 7, 11, 13, 17, 19}
(iii) {Friday, Saturday, Sunday}
(iv) {April, August, October}
Solution:

Question 4.
Write the following sets in tabular form and also in set builder form:
(i) The set of even whole numbers which lie between 10 and 50.
(ii) {months of a year having more than 30 days}
(iii) The set of single-digit whole numbers which are a perfect square.
(iv) The set of factors of 36.
Solution:

Question 5.
Write the following sets in roster form and also in description form:
(i) {x | x = 4n, n ∈ W and n < 5}
(ii) {x : x = n², n ∈ N and n < 8}
(iii) y : y = 2x – 1, x ∈ W and x < 5}
(iv) {x : x is a letter in word ULTIMATUM}
Solution:

Question 6.
Write the following sets in roster form:
(i) {x | x ∈ N, 5 ≤ x < 10 }
(ii) {x | x = 6 p, p ∈ I and – 2 ≤ p ≤ 2}
(iii) {x | x = n² – 1, n ∈ N and n < 5}
(iv) {x | x – 1 = 0}
(v) {x | x is a consonant in word NOTATION}
(vi) {x | x is a digit in the numeral 11056771}
Solution:

Question 7.
Write the following sets in set builder form:
(i) (1, 3, 5, 7, …….. 29}
(ii) {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
(iii) {1, 4, 9, 16, 25, ………}
(iv) {\(\frac { 1 }{ 5 }\), \(\frac { 1 }{ 6 }\), \(\frac { 1 }{ 7 }\), …… \(\frac { 1 }{ 20 }\)}
(v) {-16, -8, 0, 8, 16, 24, 32, 40}
(vi) {January, June, July}
Solution:

Question 8.
If V is the set of vowels in the word COMPETITION, write the given set in
(i) description form
(ii) set builder form
(iii) roster form
Solution: