Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions

Fractions Exercise 14A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
For each expression, given below, write a fraction :
(i) 2 out of 7 = ………..
(ii) 5 out of 17 = ………..
(iii) three-fifths = ………
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14A 1

Question 2.
Fill in the blanks :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14A Q2
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14A Q2.1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14A 2

Question 3.
From the following fractions, separate :
(i) Proper fractions
(ii)Improper fractions :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14A Q3
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14A 3

Question 4.
Change the following mixed fractions to improper fractions :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14A Q4
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14A 4

Question 5.
Change the following improper fractions to mixed fractions :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14A Q5
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14A 5

Question 6.
Change the following groups of fractions to like fractions :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14A Q6
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14A 6
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14A 7
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14A 8

Fractions Exercise 14B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Reduce the given fractions to their lowest terms :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B Q1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B 9

Question 2.
State, whether true or false?
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B Q2
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B 10

Question 3.
Which fraction is greater?
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B Q3
Solution:
<Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B 11

Question 4.
Which fraction is smaller ?
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B Q4
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B 12

Question 5.
Arrange the given fractions in descending order of magnitude :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B Q5
Solution:
<Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B 13
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B 14

Question 6.
Arrange the given fractions in ascending order of magnitude :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B Q6
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B 15
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B 16
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B 17

Question 7.
I bought one dozen bananas and ate five of them. What fraction of the total number of bananas was left ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B 18

Question 8.
Insert the symbol ‘=’ or ‘>’ or ‘<’ between each of the pairs of fractions, given below :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B Q8
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B 19
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B 20

Question 9.
Out of 50 identical articles, 36 are broken. Find the fraction of :
(i) The total number of articles and the articles broken.
(ii) The remaining articles and total number of articles.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14B 21

Fractions Exercise 14C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Add the following fractions :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14C Q1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14C 22
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14C 23
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14C 24

Question 2.
Simplify :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14C Q2
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14C 25
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14C 26
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14C 27
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14C 28
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14C 29

Fractions Exercise 14D – Selina Concise Mathematics Class 6 ICSE Solutions

Point to Remember :
BODMAS :- While simplifying an expressions we can involve six operation in following orders.
B Stands for “BRACKET”
O Stands for “OF”
D Stands for “DIVISION”
M Stands for “MULTIPLICATION”
A Stands for “ADDITION”
S Stands for “SUBTRACTION”

Question 1.
Simplify :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D Q1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D 30
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D 31

Question 2.
Simplify :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D Q2
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D 32

Question 3.
Simplify :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D Q3
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D 33
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D 34

Question 4.
Simplify :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D Q4
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D Q4.1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D 35
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D 36
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D 37

Question 5.
Simplify :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D Q5
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D Q5.1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D 38
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D 39
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D 40
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D 41
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14D 42

Fractions Exercise 14E – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
From a rope of 10\(\frac { 1 }{ 2 }\) m long, 4\(\frac { 5 }{ 8 }\) m is cut off. Find the length of the remaining rope.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14E 43

Question 2.
A piece of cloth is 5 metre long. After washing, it shrinks by \(\frac { 1 }{ 25 }\) of its length. What is the length of the cloth after washing?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14E 44

Question 3.
I bought wheat worth Rs. 12\(\frac { 1 }{ 2 }\), rice worth Rs. 25\(\frac { 3 }{ 4 }\) and vegetables worth Rs. 10\(\frac { 1 }{ 4 }\). If I gave a hundred-rupee note to the shopkeeper ; how much did he return to me
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14E 45

Question 4.
Out of 500 oranges in a box, \(\frac { 3 }{ 25 }\) are rotten and \(\frac { 1 }{ 5 }\) are kept for some guests. How many oranges are left in the box?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14E 46

Question 5.
An ornament piece is made of gold and copper. Its total weight is 96g. If \(\frac { 1 }{ 12 }\) of the ornament hi copper, find the weight of gold in it.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14E 47

Question 6.
A girl did half of some work on Monday and one-third of it on Tuesday. How much will she have to do on Wednesday in order to complete the work?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14E 48

Question 7.
A man spends \(\frac { 3 }{ 8 }\) of his money and 8 still has Rs. 720 left with him. How much money did he have at first?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14E 49

Question 8.
In a school, \(\frac { 4 }{ 5 }\) of the students are boys, and the number of girls is 100. Find the number of boys.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14E 50

Question 9.
After finishing \(\frac { 3 }{ 4 }\) of my journey, I find that 12 km of my journey is covered. How much distance is still left to be covered?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14E 51

Question 10.
When Ajit travelled 15 km, he found that one-fourth of his journey was still left. What was the full length of the journey?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14E 52

Question 11.
In a particular month, a man earns Rs. 7,200. Out of this income, he spends \(\frac { 3 }{ 10 }\) on food, \(\frac { 1 }{ 4 }\) on house rent, \(\frac { 1 }{ 10 }\) on insurance and \(\frac { 2 }{ 25 }\) on holidays. How much did he save in that month ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Ex 14E 53

Fractions Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex Q1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex 54

Question 2.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex Q2
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex 55

Question 3.
Evaluate :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex Q3
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex 56
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex 57
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex 58
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex 59

Question 4.
Mr. Mehra gave one-third of his money to his son, one-fifth of his money to his daughter and the remaining amount to his wife. If his wife got Rs. 91,000, how much money did Mr. Mehra have originally?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex 60

Question 5.
A sum of Rs. 84,000 is divided among three persons A, B and C. If A gets one-fourth of it and B gets one-fifth of it; how much did C get?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex 61

Question 6.
In one hour Rohit walks 3\(\frac { 2 }{ 5 }\) km. How much distance will he cover in 2\(\frac { 1 }{ 2 }\) hours?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex 62

Question 7.
An 84 m long string is cut into pieces each of length 5\(\frac { 1 }{ 4 }\) m. How many pieces are obtained?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex 63

Question 8.
In buying a ready made shirt-two-fifths of my pocket money is spent If Rs. 540 is still left with me, find :
(i) The money I had before I bought the shirt.
(ii) The emit of the shirt
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex 64

Question 9.
Mohan leaves Rs. 1,20,000 to his wife and three children such that two-fifths of this money is given to his wife and the remaining is distributed equally among the children. Find, how much each child gets?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex 65

Question 10.
Simplify :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex Q10
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex 66
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions Revision Ex 67

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids

Recognition of Solids Exercise 31 – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Identify the nets which can be used to form cubes :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids Q1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids 1

Question 2.
Draw at least three different nets for making cube.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids 2

Question 3.
The dimensions of a cuboid are 6 cm, 4 cm and 3 cm. Draw two different types of oblique sketches for this cuboid.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids 3

Question 4.
Two cubes, each with 3 cm edge, are placed side by side to form a cuboid. For this cuboid, draw :
(i) an oblique sketch
(ii) an isometric sketch.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids 4

Question 5.
The figure, given below, shows shadows of some 3D objects, when seen under the lamp of an overhead projector :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids Q5
In each case, name the object.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids 5

Question 6.
Look at the solids, drawn below, and fill the given chart.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids Q6
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids Q6.1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids 6

P. Q. Using Euler’s formula, find the values of a, b, c and d.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids Q6.2
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids 7

P.Q. Using an isometric dot paper, draw :
(i) a cube with each edge 3 cm.
(ii) a cuboid measuring 5 cm x 4 cm x 3 cm.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids 8

Question 7.
Dice are cubes with dot or dots on each face. Opposite faces of a die always have a total of seven on them.
Below are given two nets to make dice (cube), the numbers inserted in each square indicate the number of dots in it.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids Q7
Insert suitable numbers in each blank so that numbers in opposite faces of the die have a total of seven dots.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids 9

Question 8.
The following figure represents mets of some solids. Name the solids.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids Q8
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 31 Recognition of Solids 10

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest

Simple Interest Exercise 10 – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the S.I. and amount on :
(i) Rs. 150 for 4 years at 5% per year.
(ii) Rs. 350 for 3\(\frac {1 }{ 2 }\) years at 8% p.a.
(iii) Rs. 620 for 4 months at 8 p. per rupee per month.
(iv) Rs. 3,380 for 30 months at 4 \(\frac { 1 }{ 2 }\) % p.a.
(v) 600 from July 12 to Dec. 5 at 10% p.a.
(vi) Rs. 850 from 10th March to 3rd August at 2 \(\frac { 1 }{ 2 }\) % p.a.
(vii) Rs. 225 for 3 years 9 months at 16% p.a.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 1
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 2
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 3
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 4
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 5

Question 2.
On what sum of money does the S.I. for 10 years at 5% become Rs. 1,600 ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 6

Question 3.
Find the time in which Rs. 2,000 will amount to Rs. 2,330 at 11% p.a. ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 7

Question 4.
In what time will a sum of money double it self at 8% p.a ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 8

Question 5.
In how many years will be ₹870 amount to ₹1,044, the rate of interest being 2\(\frac { 1 }{ 2 }\) % p.a ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 9

Question 6.
Find the rate percent if the S.I. on ₹275 is 2 years is ₹22.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 10

Question 7.
Find the sum which will amount to ₹700 in 5 years at 8% rate p.a.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 11

Question 8.
What is the rate of interest, if ₹3,750 amounts to ₹4,650 in 4 years ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 12

Question 9.
In 4 years, ₹6,000 amount to ₹8,000. In what time will ₹525 amount to ₹700 at the same rate ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 13

Question 10.
The interest on a sum of money at the end of 2\(\frac { 1 }{ 2 }\) years is \(\frac { 4 }{ 5 }\) of the sum. What is the rate percent ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 14

Question 11.
What sum of money lent out at 5% for 3 years will produce the same interest as Rs. 900 lent out at 4% for 5 years ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 15

Question 12.
A sum of Rs. 1,780 become Rs. 2,136 in 4 years,
Find :
(i) the rate of interest.
(ii) the sum that will become Rs. 810 in 7 years at the same rate of interest ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 16

Question 13.
A sum amounts to Rs. 2,652 in 6 years at 5% p.a. simple interest.
Find :
(i) the sum
(ii) the time in which the same sum will double itself at the same rate of interest.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 17

Question 14.
P and Q invest Rs. 36,000 and Rs. 25,000 respectively at the same rate of interest per year. If at the end of 4 years, P gets Rs. 3,080 more interest than Q; find the rate of interest.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 18

Question 15.
A sum of money is lent for 5 years at R% simple interest per annum. If the interest earned be one-fourth of the money lent, find the value of R.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 19

Question 16.
The simple interest earned on a certain sum in 5 years is 30% of the sum. Find the rate of interest.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 10 Simple Interest 20

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers

Rational Numbers Exercise 2A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Write down a rational number whose numerator is the largest number of two digits and denominator is the smallest number of four digits.

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 1

Question 2.
Write the numerator of each of the following rational numbers:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A Q2

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 1.1

Question 3.
Write the denominator of each of the following rational numbers:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A Q3

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 2

Question 4.
Write down a rational number numerator (-5) x (-4) and denominator (28 – 27) x (8 – 5).

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 3

Question 5.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A Q5

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 4

Question 6.
Separate positive and negative rational numbers from the following :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A Q6
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 5

Question 7.
Find three rational numbers equivalent to
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A Q7
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 6
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 7
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 8
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 9

Question 8.
Which of the following are not rational numbers :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A Q8

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 10

Question 9.
Express each of the following integers as a rational number with denominator 7 :
(i) 5
(ii) -8
(iii) 0
(iv) -16
(v) 7
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 11

Question 10.
Express \(\frac { 3 }{ 5 }\) as a rational number with denominator:
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 12
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 13

Question 11.
Express \(\frac { 4 }{ 7 }\) as a rational number with numerator :
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 14
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 15

Question 12.
Find x, such that:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A Q12
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 16
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 17
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 18
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 19
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 20

Question 13.
Express each of the following rational numbers to the lowest terms :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A Q13

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 21
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 22
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 23
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 24

Question 14.
Express each of the following rational numbers in the standard form.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A Q14

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2A 25

Rational Numbers Exercise 2B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Mark the following pairs of rational numbers on the separate number lines :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B Q1

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 26
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 27

Question 2.
Compare:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B Q2

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 28
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 29
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 30
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 31

Question 3.
Compare:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B Q3

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 32
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 33
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 34
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 35
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 36

Question 4.
Arrange the given rational numbers in ascending order :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B Q4

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 37
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 38
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 39

Question 5.
Arrange the given rational numbers in descending order:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B Q5

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 40
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 41
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 42

Question 6.
Fill in the blanks :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B Q6

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2B 43

Rational Numbers Exercise 2C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Add:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C Q1

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 44
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 45

Question 2.
Add:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C Q2

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 46
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 47
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 48
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 49
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 50

Question 3.
Evaluate:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C Q3

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 51
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 52
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 53

Question 4.
Evaluate:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C Q4

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 54
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 55
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 56
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 57
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 58

Question 5.
Subtract :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C Q5

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 59
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 60

Question 6.
Subtract :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C Q6

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 61
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 62
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 63
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 64

Question 7.
The sum of two rational numbers is \(\frac { 11 }{ 24 }\). If one of them is \(\frac { 3 }{ 8 }\), find the other.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 65

Question 8.
The sum of two rational numbers is \(\frac { -7 }{ 11 }\). If one of them is \(\frac { 13 }{ 24 }\), find the other.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 66

Question 9.
The sum of two rational numbers is -4. If one of them is \(-\frac { 13 }{ 12 }\) , find the other.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 67

Question 10.
What should be added to \(-\frac { 3 }{ 6 }\) to get \(-\frac { 11 }{ 24 }\) ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 68

Question 11.
What should be added to \(\frac { -3 }{ 5 }\) to get 2?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 69

Question 12.
What should be subtracted from \(\frac { -4 }{ 5 }\) to get 1?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 70

Question 13.
The sum of two numbers is \(-\frac { 6 }{ 5 }\). If one of them is -2, find the other.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 71

Question 14.
What should be added to \(\frac { -7 }{ 12 }\) to get \(\frac { 3 }{ 8 }\)?

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 72

Question 15.
What should be subtracted from \(\frac { 5 }{ 9 }\)to get \(\frac { 9 }{ 5 }\) ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2C 73

Rational Numbers Exercise 2D – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Evaluate:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D Q1
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 74
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 75
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 76

Question 2.
Multiply:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D Q2
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 77
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 78
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 79
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 80

Question 3.
Evaluate:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D Q3
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D Q3.1
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 81
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 82
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 83
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 84

Question 4.
Find the cost of 3 \(\frac { 1 }{ 2 }\) m cloth, if one metre cloth costs ₹325 \(\frac { 1 }{ 2 }\).
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 85

Question 5.
A bus is moving with a speed of 65 \(\frac { 1 }{ 2 }\) km per hour. How much distance will it cover in 1 \(\frac { 1 }{ 3 }\) hours.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 86

Question 6.
Divide:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D Q6
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 87
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 88
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 89

Question 7.
Evaluate:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D Q7
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 90
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 91

Question 8.
The product of two numbers is 14. If one of the numbers is \(\frac { -8 }{ 7 }\), find the other.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 92

Question 9.
The cost of 11 pens is ₹3 \(\frac { 2 }{ 3 }\). Find the cost of one pen.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 93

Question 10.
If 6 identical articles can be bought for ₹2 \(\frac { 6 }{ 17 }\). Find the cost of each article.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 94

Question 11.
By what number should \(\frac { -3 }{ 8 }\) be multiplied so that the product is \(\frac { -9 }{ 16 }\) ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 95

Question 12.
By what number should \(\frac { -5 }{ 7 }\) be divided so -15 that the result is\(\frac { -15 }{ 28 }\) ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 96

Question 13.
Evaluate :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 97
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D Q13

Question 14.
Seven equal piece are made out of a rope 5 of 21 \(\frac { 5 }{ 7 }\) m. Find the length of each piece.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2D 98

Rational Numbers Exercise 2E – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Evaluate:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E Q1
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 99
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 100
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 101
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 102
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 103
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 104
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 105

Question 2.
The sum of two rational numbers is \(\frac { -3 }{ 8 }\). If one of them is \(\frac { 3 }{ 16 }\), find the other,
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 106
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 107

Question 3.
The sum of two rational numbers is -5. If one of them is \(\frac { -52 }{ 25 }\) , find the other.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 108

Question 4.
What rational number should be added to \(-\frac { 3 }{ 16 }\) to get \(\frac { 11 }{ 24 }\)
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 109

Question 5.
What rational number should be added to \(-\frac { 3 }{ 5 }\) to get 2?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 110

Question 6.
What rational number should be subtracted from \(-\frac { 5 }{ 12 }\)to get \(\frac { 5 }{ 24 }\)
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 111

Question 7.
What rational number should be subtracted from \(\frac { 5 }{ 8 }\) to get \(\frac { 8 }{ 5 }\) ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 112

Question 8.
Evaluate:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E Q8
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 113
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 114
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 115
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 116
Question 9.
The product of two rational numbers is 24. If one of them is \(-\frac { 36}{ 11 }\), find the other.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 117

Question 10.
By what rational number should we multiply \(\frac { 20 }{ -9 }\) ,so that the product may be \(\frac { -5 }{ 9 }\) ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers Ex 2E 118

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry (Including Constructions on Symmetry)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry (Including Constructions on Symmetry)

Revision Exercise Symmetry Exercise 30 – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
State, whether true or false :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 12
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 1
Question 2.
Construct a triangle ABC, in which AB = AC = 5 cm and BC 6 cm. Draw all its lines of Symmetry.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 2

Question 3.
Examine each of the following figures carefully, draw line(s) of symmetry in which ever figure possible :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 13
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 3

Question 4.
Construct a triangle XYZ, in which XY = YZ = ZX = 4.5 cm. Draw all its lines of symmetry.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 4

Question 5.
Construct a triangle ABC, in which AB = BC = 4 cm and ∠ABC = 60°. Draw all its lines of symmetry.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 5

Question 6.
Draw the line(s) of symmetry for each figure drawn below :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 14
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 6

Question 7.
In each of the following case, construct a point that is symmetric to the given point P with respect to the given line AB.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 15
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 7

Question 8.
Mark two points A and B 5.5 cm apart. Draw a line PQ so that A and B are symmetric with respect to the line PQ. Give a special name to line PQ.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 8

Question 9.
For each letter of the English alphabet, draw the maximum possible number of lines of symmetry.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 9

Question 10.
Draw all the possible lines of symmetry for each figure given below :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 16>
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 10

Question 11.
For each shaded portion given below, draw all the possible lines of symmetry :
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 30 Revision Exercise Symmetry Ex 30A 11

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle

The Circle Exercise 29A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Use the figure given below to fill in the blanks :
(i) R is the …… of the circle.
(ii) Diameter of a circle is …… .
(iii) Tangent to a circle is … .
(iv) EF is a …… of the circle.
(v) …… is a chord of the circle.
(vi) Diameter = 2 x …..
(vii) ……. is a radius of the circle.
(viii) If the length of RS is 5 cm, the length of PQ = ……
(ix) If PQ is 8 cm long, the length of RS =…..
(x) AB is a ….. of the circle
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29A Q1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29A 1

Question 2.
Draw a circle of radius 4.2 cm. Mark its centre as O. Take a point A on the circumference of the circle. Join AO and extend it till it meets point B on the circumference of the circle,
(i) Measure the length of AB.
(ii) Assign a special name to AB.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29A 2

Question 3.
Draw circle with diameter :
(i) 6 cm
(ii) 8.4 cm.
In each case, measure the length of the radius of the circle drawn.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29A 3

Question 4.
Draw a circle of radius 6 cm. In the circle, draw a chord AB = 6 cm.
(i) If O is the centre of the circle, join OA and OB.
(ii) Assign a special name to ∆AOB
(iii) Write the measure of angle AOB.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29A 4

Question 5.
Draw a circle of radius 4.8 cm and mark its centre as P.
(i) Draw radii PA and PB such that ∠APB = 45°.
(ii) Shade the major sector of the circle
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29A 5

Question 6.
Draw a circle of radius 3.6 cm. In the circle, draw a chord AB = 5 cm. Now shade the minor segment of the circle.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29A 6

Question 7.
Mark two points A and B ,4cm a part, Draw a circle passing through B and with A as a center
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29A Q7
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29A 7

Question 8.
Draw a line AB = 8.4 cm. Now draw a circle with AB as diameter. Mark a point C on the circumference of the circle. Measure angle ACB.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29A 8
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29A 9

The Circle Exercise 29B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Construct a triangle ABC with AB = 4.2 cm, BC = 6 cm and AC = 5cm. Construct the circumcircle of the triangle drawn.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29B 10

Question 2.
Construct a triangle PQR with QR = 5.5 cm, ∠Q = 60° and angle R = 45°.
Construct the circumcircle cif the triangle PQR.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29B 11

Question 3.
Construct a triangle ABC with AB = 5 cm, ∠B = 60° and BC = 6. 4 cm.
Draw the incircle of the triangle ABC.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29B 12

Question 4.
Construct a triangle XYZ in which XY = YZ= 4.5 cm and ZX = 5.4 cm. Draw the circumcircle of the triangle and measure its circumradius.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29B 13

Question 5.
Construct a triangle PQR in which, PQ = QR = RP = 5.7 cm. Draw the incircle of the triangle and measure its radius.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Ex 29B 14

The Circle Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The centre of a circle is at point O and its radius is 8 cm. State the position of a point P (point P may lie inside the circle, on the circumference of the circle, or outside the circle), when :
(a) OP = 10.6 cm
(b) OP = 6.8 cm
(c) OP = 8 cm
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Revision Ex 15

Question 2.
The diameter of a circle is 12.6 cm. State, the length of its radius.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Revision Ex 16

Question 3.
Can the length of a chord of a circle be greater than its diameter ? Explain.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Revision Ex 17

Question 4.
Draw a circle of diameter 7 cm. Draw two radii of this circle such that the angle between these radii is 90°. Shade the minor sector obtained. Write a special name for this sector.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Revision Ex 18

Question 5.
State, which of following statements are true and which are false :
(i) If the end points A and B of the line segment lie on the circumference of a circle, AB is a diameter.
(ii) The longest chord of a circle is its diameter.
(iii) Every diameter bisects a circle and each part of the circle so obtained is a semi-circle.
(iv) The diameters of a circle always pass through the same point in the circle.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle Revision Ex 19

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons

Polygons Exercise 28A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
State, which of the following are polygons :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28A Q1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28A 1

Question 2.
Find the sum of interior angles of a polygon with :
(i) 9 sides
(ii) 13 sides
(iii) 16 sides
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28A 2

Question 3.
Find the number of sides of a polygon, if the sum of its interior angles is :
(i) 1440°
(ii) 1620°
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28A 3
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28A 4

Question 4.
Is it possible to have a polygon, whose sum of interior angles is 1030°.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28A 5

Question 5.
(i) If all the angles of a hexagon arc equal, find the measure of each angle.
(ii) If all the angles of an octagon are equal, find the measure of each angle,
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28A 6

Question 6.
One angle of a quadrilateral is 90° and all other angles are equal ; find each equal angle.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28A 7

Question 7.
If angles of quadrilateral are in the ratio 4 : 5 : 3 : 6 ; find each angle of the quadrilateral.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28A 8

Question 8.
If one angle of a pentagon is 120° and each of the remaining four angles is x°, find the magnitude of x.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28A 9

Question 9.
The angles of a pentagon are in the ratio 5 : 4 : 5 : 7 : 6 ; find each angle of the pentagon.
Solution:
<Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28A 10

Question 10.
Two angles of a hexagon are 90° and 110°. If the remaining four angles arc equal, find each equal angle.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28A 11

Polygons Exercise 28B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
In case of regular polygon, with
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28B Q1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28B 12
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28B 13

Question 2.
Find the number of sides in a regular polygon, if its each interior angle is :
(i) 160°
(ii) 150°
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28B 14

Question 3.
Find number of sides in a regular polygon, if its each exterior angle is :
(i) 30°
(ii) 36°
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28B 15

Question 4.
Is it possible to have a regular polygon whose each interior angle is :
(i) 135°
(ii) 155°
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28B 16
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28B 17

Question 5.
Is it possible to have a regular polygon whose each exterior angle is :
(i) 100°
(ii) 36°
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28B 18
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28B 19

Question 6.
The ratio between the interior angle and the exterior angle of a regular polygon is 2 : 1. Find :
(i) each exterior angle of this polygon.
(ii) number of sides in the polygon.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons Ex 28B 20

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral

Quadrilateral Exercise 27A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Two angles of a quadrilateral are 89° and 113°. If the other two angles are equal; find the equal angles.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 1

Question 2.
Two angles of a quadrilateral are 68° and 76°. If the other two angles are in the ratio 5 : 7; find the measure of each of them.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 2

Question 3.
Angles of a quadrilateral are (4x)°, 5(x+2)°, (7x-20)° and 6(x+3)°. Find
(i) the value of x.
(ii) each angle of the quadrilateral.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 3

Question 4.
Use the information given in the following figure to find :
(i) x
(ii) ∠B and ∠C
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A Q4
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 4

Question 5.
In quadrilateral ABCD, side AB is parallel to side DC. If ∠A : ∠D = 1 : 2 and ∠C : ∠B = 4:5
(i) Calculate each angle of the quadrilateral.
(ii) Assign a special name to quadrilateral ABCD.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 5

Question 6.
From the following figure find ;
(i) x,
(ii) ∠ABC,
(iii) ∠ACD.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 6

Question 7.
Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ;
∠A = 5(a+2)° and ∠B = 2(2a+7)°.
Calculate ∠A.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 7

Question 8.
In the given figure :
∠b = 2a + 15
and ∠c = 3a+5; find the values of b and c.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A Q8
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 8

Question 9.
Three angles of a quadrilateral are equal. If the fourth angle is 69°; find the measure of equal angles.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 9

Question 10.
In quadrilateral PQRS, ∠P : ∠Q : ∠R : ∠S = 3 : 4 : 6 : 7.
Calculate each angle of the quadrilateral and then prove that PQ and SR are parallel to each other. Is PS also parallel to QR ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 10

Question 11.
Use the information given in the following figure to find the value of x.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 11

Question 12.
The following figure shows a quadrilateral in which sides AB and DC are parallel.
If ∠A : ∠D = 4 : 5, ∠B = (3x – 15)° and ∠C = (4x + 20)°, find each angle of the quadrilateral ABCD.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A Q12
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 12

Quadrilateral Exercise 27B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In a trapezium ABCD, side AB is parallel to side DC. If ∠A = 78° and ∠C = 120°, find angles B and D.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 13

Question 2.
In a trapezium ABCD, side AB is parallel to side DC. If ∠A = x° and ∠D = (3x – 20)°; find the value of x.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 14

Question 3.
The angles A, B, C and D of a trapezium ABCD are in the ratio 3 : 4 : 5 : 6.
Le. ∠A : ∠B : ∠C : ∠D = 3:4: 5 : 6. Find all the angles of the trapezium. Also, name the two sides of this trapezium which are parallel to each other. Give reason for your answer
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 15

Question 4.
In an isosceles trapezium one pair of opposite sides are ….. to each Other and the other pair of opposite sides are ….. to each other.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 16

Question 5.
Two diagonals of an isosceles trapezium are x cm and (3x – 8) cm. Find the value of x.
Solution:
<Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 17

Question 6.
Angle A of an isosceles trapezium is 115° ; find the angles B, C and D.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 18

Question 7.
Two opposite angles of a parallelogram are 100° each. Find each of the other two opposite angles.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 19

Question 8.
Two adjacent angles of a parallelogram are 70° and 110° respectively. Find the other two angles of it.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 20

Question 9.
The angles A, B, C and D of a quadrilateral are in the ratio 2:3: 2 : 3. Show this quadrilateral is a parallelogram.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 21
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 22

Question 10.
In a parallelogram ABCD, its diagonals AC and BD intersect each other at point O.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B Q10
If AC = 12 cm and BD = 9 cm ; find; lengths of OA and OD.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 23

Question 11.
In parallelogram ABCD, its diagonals intersect at point O. If OA = 6 cm and OB = 7.5 cm, find the length of AC and BD.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B Q11
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 24

Question 12.
In parallelogram ABCD, ∠A = 90°
(i) What is the measure of angle B.
(ii) Write the special name of the paralleogram.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 25

Question 13.
One diagnol of a rectangle is 18 cm. What is the length of its other diagnol?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 26

Question 14.
Each angle of a quadrilateral is x + 5°. Find :
(i) the value of x
(ii) each angle of the quadrilateral.
Give the special name of the quadrilateral taken.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B Q14
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 27

Question 15.
If three angles of a quadrilateral are 90° each, show that the given quadrilateral is a rectangle.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 28

Question 16.
The diagnols of a rhombus are 6 .cm and 8 cm. State the angle at which these diagnols intersect.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 29

Question 17.
Write, giving reason, the name of the figure drawn alongside. Under what condition will this figure be a square.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B Q17
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 30

Question 18.
Write two conditions that will make the adjoining figure a square.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B Q18
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 31

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles (Including Types, Properties and Constructions)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles (Including Types, Properties and Constructions)

Triangles Exercise 26A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In each of the following, find the marked unknown angles :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A Q1
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A Q1.1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A 1

Question 2.
Can a triangle together have the following angles ?
(i) 55°, 55° and 80°
(ii) 33°, 74° and 73°
(iii) 85°, 95° and 22°.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A 2

Question 3.
Find x, if the angles of a triangle are:
(i) x°, x°, x°
(ii) x°, 2x°, 2x°
(iii) 2x°, 4x°, 6x°
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A 3

Question 4.
One angle of a right-angled triangle is 70°. Find the other acute angle.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A 4

Question 5.
In ∆ABC, ∠A = ∠B = 62° ; find ∠C.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A 5

Question 6.
In ∆ABC, C = 56°C = 56° ∠B = ∠C and ∠A = 100° ; find ∠B.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A 6

Question 7.
Find, giving reasons, the unknown marked angles, in each triangle drawn below:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A Q7
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A Q7.1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A 7

Question 8.
Classify the following triangles according to angle :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A Q8
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A Q8.1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A 8

Question 9.
Classify the following triangles according to sides :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A Q9
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26A 9

Triangles Exercise 26B – Selina Concise Mathematics Class 6 ICSE Solutions

Construct traingle ABC, when :
Question 1.
AB = 6 cm, BC = 8 cm and AC = 4 cm.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26B 10

Question 2.
AB = 3.5 cm, AC = 4.8 cm and BC = 5.2 cm.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26B 11

Question 3.
AB = BC = 5 cm and AC = 3 cm. Mea¬sure angles A and C. Is ∠A = ∠C?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26B 12

Question 4.
AB = BC = CA = 4.5 cm. Measure all the angles of the triangle. Are they equal ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26B 13

Question 5.
AB = 3 cm, BC = 7 cm and ∠B = 90°.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26B 14

Question 6.
AC = 4.5 cm, BC = 6 cm and ∠C = 60°.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26B 15

Question 7.
AC = 6 cm, ∠A = 60“ and ∠C = 45°. Measure AB and BC.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26B 16

Question 8.
AB = 5.4 cm, ∠A = 30° and ∠B = 90°. Measure ∠C and side BC.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26B 17

Question 9.
AB = 7 cm, ∠B = 120° and ∠A = 30°. Measure AC and BC.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26B 18

Question 10.
BC = 3 cm, AC = 4 cm and AB = 5 cm. Measure angle ACB. Give a special name to this triangle.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Ex 26B 19

Triangles Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
If each of the two equal angles of an isosceles triangle is 68°, find the third angle.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Revision Ex 20

Question 2.
One of the angles of a triangle is 110°, the two other angles are equal. Find their value.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Revision Ex 21

Question 3.
The angles of a triangle are in the ratio 3:5: 7. Find each angle.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Revision Ex 22

Question 4.
The angles of a triangle are (2x – 30°),(3x – 40°) and (\(\frac { 5 }{ 2 }\)x + 10°) Find the value of x .
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Revision Ex 23

Question 5.
In each of the following figures, triangle ABC is equilateral and triangle PBC is isosceles. If PBA = 20°; find in each case:
(a) angle PBC.
(b) angle BPC.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Revision Ex Q5
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Revision Ex 24
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Revision Ex 25

Question 6.
Construct a triangle ABC given AB = 6 cm, BC = 5 cm and CA = 5.6 cm. From vertex A draw a perpendicular on to side BC. Measure the length of this perpendicular.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Revision Ex 26

Question 7.
Construct a triangle PQR, given PQ = 6 cm, ∠P = 60° and ∠Q = 30°. Measure angle R and the length of PR.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Revision Ex 27

Question 8.
Construct a triangle ABC given BC = 5 cm, AC = 6 cm and ∠C = 75°. Draw the bisector of the interior angle at A. Let this bisector meet BC at P ; measure BP.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Revision Ex 28

Question 9.
Using ruler and a pair compass only, construct a triangle XYZ given YZ = 7 cm, ∠XYZ = 60° and ∠XZY = 45°. Draw the bisectors of angles X and Y.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Revision Ex 29

Question 10.
Using ruler and a pair compass only, construct a triangle PQR, given PQ = 5.5 cm, QR = 7.5 cm and RP = 6 cm. Draw the bisectors of the interior angles at P, Q and R. Do these bisectors meet at the same point ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Revision Ex 30

Question 11.
One angle of a triangle is 80° and the other two are in the ratio 3 : 2. Find the unknown angles of the triangle.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Revision Ex 31

Question 12.
Find the value of x if ∠A = 32°, ∠B = 55° and obtuse angle AED = 115°.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles Revision Ex 32

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount

Profit, Loss and Discount Exercise 9A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the gain or loss percent, if
(i) C.P. = Rs. 200 and S.P.: = Rs. 224
(ii) C.P. = Rs. 450 and S.P. = Rs. 400
(iii) C.P. = Rs. 550 and gain = Rs . 22
(iv) CP. = Rs. 216 and loss = Rs. 72
(v) S.P. = Rs. 500 and loss : = Rs. 100
(vi) S.P. = Rs. 12 and profit = Rs. 4
(vii) C.P. = Rs. 5 and gain = 60 P

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9A 1
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9A 2

Question 2.
Find the selling price, if:
(i) C.P. = Rs. 500 and gain = 25%
(ii) C.P. = Rs. 60 and loss = 12 1/2%
(iii) C.P. = Rs. 150 and loss = 20%
(iv) C.P. = Rs. 80 and gain = 2.5%
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9A 3
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9A 4

Question 3.
Rohit bought a tape-recorder for Rs. 1,500 and sold it for Rs. 1,800. Calculate his profit or loss percent.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9A 5

Question 4.
An article bought for Rs. 350 is sold at a profit of 20%. Find its selling price.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9A 6

Question 5.
An old machine is bought for Rs. 1,400 and is sold at a loss of 15%. Find its selling price.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9A 7

Question 6.
Oranges are bought at 5 for Rs. 10 and sold at 6 for Rs. 15. Find profit or loss as percent.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9A 8

Question 7.
A certain number of articles are bought at 3 for Rs. 150 and all of them are sold at 4 for Rs. 180. Find the loss or gain as percent.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9A 9

Question 8.
A vendor bought 120 sweets at 20 p each. In his house, 18 were consumed and he sold the remaining at 30 p each. Find his profit or loss as percent.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9A 10

Question 9.
The cost price of an article is Rs. 1,200 and selling price is \(\frac { 5 }{ 4 }\) times of its cost price. Find:
(i) selling price of the article
(ii) profit or loss as percent.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9A 11

Question 10.
The selling price of an article is Rs. 1,200 and cost price is \(\frac { 5 }{ 4 }\) times of its selling price,
find :
(i) cost price of the article ;
(ii) profit or loss as percent.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9A 12

Profit, Loss and Discount Exercise 9B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the cost price, if:
(i) S.P. = Rs. 21 and gain = 5%
(ii) S.P. = Rs. 22 and loss = 12%
(iii) S.P. = Rs. 340 and gain = Rs. 20
(iv) S.P. = Rs. 200 and loss = Rs. 50
(v) S.P. = Re. 1 and loss = 5 p.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 13

Question 2.
By selling an article for Rs. 810, a loss of 10 percent is suffered. Find its cost price.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 14

Question 3.
By selling a scooter for Rs. 9,200, a man gains 15%. Find the cost price of the scooter.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 15

Question 4.
On selling an article for Rs. 2,640, a profit of 10 percent is made. Find
(i) cost price of the article
(ii) new selling price of it, in order to gain 15%
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 16

Question 5.
A T.V. set is sold for Rs. 6800 at a loss of 15%. Find
(i)cost price of the T.V. set.
(ii)new selling price of it, in order to gain 12%
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 17

Question 6.
A fruit seller bought mangoes at Rs. 90 per dozen and sold them at a loss of 8 percent. How much will a customer pay for.
(i) one mango
(ii) 40 mangoes
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 18

Question 7.
By selling two transistors for Rs. 00 each, a shopkeeper gains 20 percent on one transistor and loses 20 percent on the other.
Find :
(i) C.P. of each transistor

(ii) total C.P. and total S.P. of both the transistors
(iii) profit or loss percent on the whole.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 19

Question 8.
Mangoes are bought at 20 for Rs. 60. If
they are sold at 33\(\frac { 1 }{ 3 }\) percent profit.
Find:

(i) selling price of each mango.
(ii) S.P. of 8 mangoes.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 20

Question 9.
Find the cost price of an article, which is sold for Rs. 4050 at a loss of 10%. Also, find the new selling price of the article which must give a profit of 8%.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 21

Question 10.
By selling an article for ₹825, a man loses \(\frac { 1 }{ 3 }\) equal to j of its selling price.
Find :

(i) the cost price of the article,
(ii) the profit percent or the loss percent made, if the same article is sold for ₹1265.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 22

Question 11.
Find the loss or gain as percent, if the C.P. of 10 articles, all of the same kind, is equal to S.P. of 8 articles.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 23

Question 12.
Find the loss or gain as percent, if the C.P. of 8 articles, all of the same kind, is equal to S.P. of 10 articles.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 24

Question 13.
The cost price of an article is 96% of its selling price. Find the loss or the gain as percent on the whole.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 25

Question 14.
The selling price of an article is 96% of its cost price. Find the loss or the gain as percent on the whole.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 26

Question 15.
Hundred oranges are bought for ₹350 and all of them are sold at the rate of ₹48 per dozen. Find the profit percent or loss percent made.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 27

Question 16.
Oranges are bought at 100 for ?80 and all of them are sold at ₹80 for ₹100. Find the loss or gain as percent in this transaction.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 28

Question 17.
An article is bought for ₹5,700 and ₹1,300 is spent on its repairing, transportion, etc. For how much should this article be sold in order to gain 20% on the whole.
Solution:
<Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9B 29

Profit, Loss and Discount Exercise 9C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
A machine is marked at ₹5000 and is sold at a discount of 10%. Find the selling price of the machine.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 30

Question 2.
shopkeeper marked a dinner set for ₹1000. He sold it at ₹900, what percent discount did he give ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 31

Question 3.
A pair of shoes marked at ₹320, are sold at a discount of 15 percent.
Find :
(i) discount
(ii) selling price of the shoes.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 32

Question 4.
The list price of an article is ₹450 and it is sold for ₹360.
Find :
(i) discount
(ii) discount percent
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 33

Question 5.
A shopkeeper buys an article for₹300. He increases its price by 20% and then gives 10% discount on the new price. Find:
(i) the new price (marked price) of the article.
(ii) the discount given by the shopkeeper.
(iii) the selling price.
(iv) profit percent made by the shopkeeper.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 34
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 35

Question 6.
A car is marked at Rs. 50,000. The dealer gives 5% discount on first Rs. 20,000 and 2% discount on the remaining Rs. 30,000.
Find :
(i) the total discount.
(ii) the price charged by the dealer.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 36

Question 7.
A dealer buys a T.V. set for Rs. 2500. He marks it at Rs. 3,200 and then gives a discount of 10% on it.
Find :
(i) the selling price of the T.V. set
(ii) the profit percent made by the dealer.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 37

Question 8.
A sells his goods at 15% discount. Find the price of an article which is sold for Rs. 680.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 38

Question 9.
A shopkeeper allows 20% discount on the marked price of his articles. Find the marked price of an article for which he charges Rs. 560.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 39

Question 10.
An article is bought for Rs. 1,200 and Rs. 100 is spent on its transportation, etc.
Find :
(i) the total C.P. of the article.
(ii) the selling price of it in order to gain 20% on the whole.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 40

Question 11.
40 pens are bought at 4 for Rs. 50 and all of them are sold at 5 for Rs. 80
Find :
(i) C.P. of one pen.
(ii) S/P. of one pen.
(iii) Profit made by selling one pen.
(iv) Profit percent made by selling one pen.
(v) C.P. of 40 pens
(vi) S.P. of 40 pens.
(vii) Profit made by selling 40 pens.
(viii) Profit percent made by selling 40 pens. Are the results of parts (iv) and (viii) same? What conclusion do you draw from the above result ?
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 41
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 42

Question 12.
The C.P. of 5 identical articles is equal to S.P. of 4 articles. Calculate the profit percent or loss percent made if all the articles bought are sold.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 43

Question 13.
The C.P. of 8 pens is same as S.P. of 10 pens. Calculate the profit or loss percent made, if all the pens bought are considered to be sold
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 44

Question 14.
A certain number of articles are bought at Rs. 450 per dozen and all of them are sold at a profit of 20%. Find the S.P. of:
(i) one article
(ii)seven articles.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 45

Question 15.
An article is marked 60% above the cost price and sold at 20% discount. Find the profit percent made.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount Ex 9C 46

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines (Including Parallel Lines)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines (Including Parallel Lines)

Properties of Angles and Lines Exercise 25A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Two straight lines AB and CD intersect each other at a point O and angle AOC = 50° ; find :
(i) angle BOD
(ii) ∠AOD
(iii) ∠BOC
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25A Q1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25A 1

Question 2.
The adjoining figure, shows two straight lines AB and CD intersecting at point P. If ∠BPC = 4x – 5° and ∠APD = 3x + 15° ; find :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25A Q2
(i) the value of x.
(ii) ∠APD
(iii) ∠BPD
(iv) ∠BPC
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25A 2

Question 3.
The given diagram, shows two adjacent angles AOB and AOC, whose exterior sides are along the same straight line. Find the value of x.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25A Q3
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25A 3

Question 4.
Each figure given below shows a pair of adjacent angles AOB and BOC. Find whether or not the exterior arms OA and OC are in the same straight line.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25A Q4
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25A Q4.1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25A 4

Question 5.
A line segment AP stands at point P of a straight line BC such that ∠APB = 5x – 40° and ∠APC = .x+ 10°; find the value of x and angle APB.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25A 5

Properties of Angles and Lines Exercise 25B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Identify the pair of angles in each of the figure given below :
adjacent angles, vertically opposite angles, interior alternate angles, corresponding angles or exterior alternate angles.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B Q1
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B Q1.1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B 6

Question 2.
Each figure given below shows a pair of parallel lines cut by a transversal For each case, find a and b, giving reasons.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B Q2
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B Q2.1
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B Q2.2
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B Q2.3
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B 7
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B 8

Question 3.
If ∠1 = 120°, find the measures of : ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8. Give reasons.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B Q3
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B 9

Question 4.
In the figure given below, find the measure of the angles denoted by x,y, z,p,q and r.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B Q4
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B 10

Question 5.
Using the given figure, fill in the blanks.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B Q5
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B 11

Question 6.
In the given figure, find the anlges shown by x,y, z and w. Give reasons.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B Q6
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B 12

Question 7.
Find a, b, c and d in the figure given below :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B Q7
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B 13

Question 8.
Find x, y and z in the figure given below :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B Q8
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25B 14

Properties of Angles and Lines Exercise 25C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In your note-book copy the following angles using ruler and a pair compass only.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C Q1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C 15
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C 16
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C 17

Question 2.
Construct the following angles, using ruler and a pair of compass only
(i) 60°
(ii) 90°
(iii) 45°
(iv) 30°
(v) 120°
(vi) 135°
(vii) 15°
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C 18
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C 19
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C 20
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C 21
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C 22
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C 23

Question 3.
Draw line AB = 6cm. Construct angle ABC = 60°. Then draw the bisector of angle ABC.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C 24

Question 4.
Draw a line segment PQ = 8cm. Construct the perpendicular bisector of the line segment PQ. Let the perpendicular bisector drawn meet PQ at point R. Measure the lengths of PR and QR. Is PR = QR ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C 25

Question 5.
Draw a line segment AB = 7cm. Mark a point Pon AB such that AP=3 cm. Draw perpendicular on to AB at point P.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C 26

Question 6.
Draw a line segment AB = 6.5 cm. Locate a point P that is 5 cm from A and 4.6 cm from B. Through the point P, draw a perpendicular on to the line segment AB.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C 27
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25C 28

Properties of Angles and Lines Exercise 25D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Draw a line segment OA = 5 cm. Use set-square to construct angle AOB = 60°, such that OB = 3 cm. Join A and B ; then measure the length ofAB.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25D 29

Question 2.
Draw a line segment OP = 8cm. Use set-square to construct ∠POQ = 90°; such that OQ = 6 cm. Join P and Q; then measure the length of PQ.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25D 30

Question 3.
Draw ∠ABC = 120°. Bisect the angle using ruler and compasses. Measure each angle so obtained and check whether or not the new angles obtained on bisecting ∠ABC are equal.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25D 31

Question 4.
Draw ∠PQR = 75° by using set- squares. On PQ mark a point M such that MQ = 3 cm. On QR mark a point N such that QN = 4 cm. Join M and N. Measure the length of MN.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Ex 25D 32

Properties of Angles and Lines Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In the following figures, AB is parallel to CD; find the values of angles x, y and z :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Revision Ex Q1
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rec Ex 33
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rec Ex 34

Question 2.
In each of the following figures, BA is parallel to CD. Find the angles a, b and c:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Revision Ex Q2
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 35
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 36

Question 3.
In each of the following figures, PQ is parallel to RS. Find the angles a, b and c:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Revision Ex Q3
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 37
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 38

Question 4.
Two straight lines are cut by a transversal. Are the corresponding angles always equal?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 39

Question 5.
Two straight lines are cut by a transversal so that the co-interior angles are supplementary. Are the straight lines parallel?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 40
Question 6.
Two straight lines are cut by a transversal so that the co-interior angles are equal. What must be the measure of each interior angle to make the straight lines parallel to each other ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 41

Question 7.
In each case given below, find the value of x so that POQ is straight line
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Revision Ex Q7
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Revision Ex Q7.1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 42
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 43
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 44

Question 8.
in each case, given below, draw perpendicular to AB from an exterior point P
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Revision Ex Q8
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 45
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 46

Question 9.
Draw a line segment BC = 8 cm. Using set-squares, draw ∠CBA = 60° and ∠BCA = 75°. Measure the angle BAC. Also measure the lengths of AB and AC.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 47

Question 10.
Draw a line AB = 9 cm. Mark a point P in AB such that AP=5 cm. Through P draw (using set-square) perpendicular PQ = 3 cm. Measure BQ.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 48

Question 11.
Draw a line segment AB = 6 cm. Without using set squares, draw angle OAB = 60° and angle OBA = 90°. Measure angle AOB and write this measurement.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 49

Question 12.
Without using set squares, construct angle ABC = 60° in which AB = BC = 5 cm. Join A and C and measure the length of AC.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines Rev Ex 50

Selina Concise Mathematics Class 6 ICSE Solutions