Prasanna

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability

Probability Exercise 23 – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
A die is thrown, find the probability of getting:
(i) a prime number
(ii) a number greater than 4
(iii) a number not greater than 4.
Solution:

Question 2.
A coin is tossed. What is the probability of getting:
(i) a tail? (ii) ahead?
Solution:

Question 3.
A coin is tossed twice. Find the probability of getting:
(i) exactly one head (ii) exactly one tail
(iii) two tails (iv) two heads
Solution:

Question 4.
A letter is chosen from the word ‘PENCIL’ what is the probability that the letter chosen is a consonant?
Solution:

Question 5.
A bag contains a black ball, a red ball and a green ball, all the balls are identical in shape and size. A ball is drawn from the bag without looking into it. What is the probability that the ball drawn is:
(i) a red ball
(ii) not a red ball
(iii) a white ball.
Solution:

Question 6.
6. In a single throw of a die, find the probability of getting a number
(i) greater than 2
(ii) less than or equal to 2
(iii) not greater than 2.
Solution:

Question 7.
A bag contains 3 white, 5 black and 2 red balls, all of the same shape and size.
A ball is drawn from the bag without looking into it, find the probability that the ball drawn is:
(i) a black ball.
(ii) a red ball.
(iii) a white ball.
(iv) not a red ball.
(v) not a black ball.
Solution:

Question 8.
In a single throw of a die, find the probability that the number:
(i) will be an even number.
(ii) will be an odd number.
(iii) will not be an even number.
Solution:

Question 9.
In a single throw of a die, find the probability of getting :
(i) 8
(ii) a number greater than 8
(iii) a number less than 8
Solution:

Question 10.
Which of the following can not be the probability of an event?

Solution:

Question 11.
A bag contains six identical black balls. A child withdraws one ball from the bag without looking into it. What is the probability that he takes out:
(i) a white ball,
(ii) a black ball
Solution:

Question 12.
Three identical coins are tossed together. What is the probability of obtaining:
all heads?
exactly two heads?
exactly one head?
no head?
Solution:

Question 13.
A book contains 92 pages. A page is chosen at random. What is the probability that the sum of the digits in the page number is 9?
Solution:

Question 14.
Two coins are tossed together. What is the probability of getting:
(i) at least one head
(ii) both heads or both tails.
Solution:

Question 15.
From 10 identical cards, numbered 1, 2, 3, …… , 10, one card is drawn at random. Find the probability that the number on the card drawn is a multiple of:
(i) 2 (ii) 3
(iii) 2 and 3 (iv) 2 or 3
Solution:

Question 16.
Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is:
(i) 0
(ii) 12
(iii) less than 12
(iv) less than or equal to 12
Solution:

Question 17.
A die is thrown once. Find the probability of getting:
(i) a prime number
(ii) a number greater than 3
(iii) a number other than 3 and 5
(iv) a number less than 6
(v) a number greater than 6.
Solution:

Question 18.
Two coins are tossed together. Find the probability of getting:
(i) exactly one tail
(ii) at least one head
(iii) no head
(iv) at most one head
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 13 Factorisation

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 13 Factorisation

Factorisation Exercise 13A – Selina Concise Mathematics Class 8 ICSE Solutions

Factorise :
Question 1.
15x + 5
Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Factorisation Exercise 13B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Factorise : a² + ax + ab + bx
Solution:

Question 2.
Factorise : a² – ab – ca + bc
Solution:

Question 3.
Factorise : ab – 2b + a² – 2a
Solution:

Question 4.
Factorise : a³ – a² + a – 1
Solution:

Question 5.
Factorise : 2a – 4b – xa + 2bx
Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Factorisation Exercise 13C – Selina Concise Mathematics Class 8 ICSE Solutions

Note : a² – b² = (a + b) (a – b)
Question 1.
Factorise : 16 – 9x²
Solution:

Question 2.
Factorise : 1 – 100a²
Solution:

Question 3.
Factorise : 4x² – 81y²
Solution:

Question 4.

Solution:

Question 5.
Factorise : (a+2b)² – a²
Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.
Evaluate :

Solution:

Question 15.
Evaluate :
(0.7)² – (0.3)²
Solution:

Question 16.
Evaluate :
(4.5)² – (1.5)²
Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Factorisation Exercise 13D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:
<

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Question 21.

Solution:

Question 22.

Solution:

Question 23.

Solution:

Question 24.

Solution:

Question 25.

Solution:

Factorisation Exercise 13E – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
In each case find whether the trinomial is a perfect square or not:

Solution:

Question 2.
Factorise completely 2 – 8x².
Solution:

Question 3.
Factorise completely : 8x²y – 18y³
Solution:

Question 4.
Factorise completely : ax² – ay²
Solution:

Question 5.
Factorise completely : 25x³ – x
Solution:

Question 6.
Factorise completely : a⁴ – b⁴
Solution:

Question 7.
Factorise completely : 16x⁴ – 81y⁴
Solution:

Question 8.
Factorise completely : 625 – x⁴
Solution:

Question 9.
Factorise completely : x² – y² – 3x – 3y
Solution:

Question 10.
Factorise completely : x² – y² – 2x + 2y
Solution:

Question 11.
Factorise completely : 3x² + 15x – 72
Solution:

Question 12.
Factorise completely : 2a² – 8a – 64
Solution:

Question 13.
Factorise completely : 5b² + 45b + 90
Solution:

Question 14.
Factorise completely : 3x²y + 11xy + 6y
Solution:

Question 15.
Factorise completely : 5ap² + 11ap + 2a
Solution:

Question 16.
Factorise completely : a² + 2ab + b² – c²
Solution:

Question 17.
Factorise completely : x² + 6xy + 9y² + x + 3y
Solution:

Question 18.
Factorise completely : 4a² – 12ab + 9b² + 4a – 6b
Solution:

Question 19.
Factorise completely : 2a²b² – 98b⁴
Solution:

Question 20.
Factorise completely : a² – 16b² – 2a – 8b
Solution:

Factorisation Exercise 13F – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Factorise :

Solution:

Question 2.
Factorise :

Solution:

Question 3.
Factorise :

Solution:

Question 4.
Factorise :

Solution:

Question 5.
Factorise :

Solution:

Question 6.
Factorise :


Solution:

Question 7.
Factorise xy² – xz², Hence, find the value of:

Solution:

Question 8.
Factorise :

Solution:

Question 9.
Factorise a²b – b³ Using this result, find the value of 101² × 100 – 100³.
Solution:

Question 10.
Evaluate (using factors): 301² × 300 – 300³.
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling

Data Handling Exercise 22A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Arrange the following data as an array (in ascending order):
(i) 7, 5, 15, 12, 10, 11, 16
(ii) 6.3, 5.9, 9.8, 12.3, 5.6, 4.7
Solution:

Question 2.
Arrange the following data as an array (descending order):
(i) 0 2, 0, 3, 4, 1, 2, 3, 5
(ii) 9.1, 3.7, 5.6, 8.3, 11.5, 10.6
Solution:

Question 3.
Construct a frequency table for the following data:
(i) 6, 7, 5, 6, 8, 9, 5, 5, 6, 7, 8, 9, 8, 10, 10, 9, 8, 10, 5, 7, 6, 8.
(ii) 3, 2, 1, 5, 4, 3, 2, 5, 5, 4, 2, 2, 2, 1, 4, 1, 5, 4.
Solution:

Question 4.
Following are the marks obtained by 30 students in an examinations.

Taking class intervals 0-10, 10-20, ……… 40-50 ; construct a frequency table.
Solution:

Question 5.
Construct a frequency distribution table for the following data ; taking class-intervals 4-6, 6-8, ……… 14-16.

Solution:

Question 6.
Fill in the blanks:
(i) Lower class limit of 15-18 is ………
(ii) Upper class limit of 24-30 is ……..
(iii) Upper limit of 5-12.5 is ………
(iv) If the upper and the lower limits of a class interval are 16 and 10 ; the class-interval is ……..
(v) If the lower and the upper limits of a class interval are 7.5 and 12.5 ; the class interval is ……..
Solution:

Data Handling Exercise 22B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Hundred students from a certain locality use different modes of travelling to school as given below. Draw a bar graph.

Solution:

Question 2.
Mr. Mirza’s monthly income is Rs. 7,200. He spends Rs. 1,800 on rent, Rs. 2,700 on food, Rs. 900 on education of his children ; Rs. 1,200 on Other things and saves the rest.
Draw a pie-chart to represent it.
Solution:

Question 3.
The percentage of marks obtained, in different subjects by Ashok Sharma (in an examination) are given below. Draw a bar graph to represent it.

Solution:

Question 4.
The following table shows the market position of different brand of tea-leaves.

Draw it-pie-chart to represent the above information.
Solution:

Question 5.
Students of a small school use different modes of travel to school as shown below:

Draw a suitable bar graph.
Solution:

Question 6.
For the following table, draw a bar-graph

Solution:

Question 7.
Manoj appeared for ICSE examination 2018 and secured percentage of marks as shown in the following table:

Represent the above data by drawing a suitable bar graph.
Solution:

Question 8.
For the data given above in question number 7, draw a suitable pie-graph.
Solution:

Question 9.
Mr. Kapoor compares the prices (in Rs.) of different items at two different shops A and B. Examine the following table carefully and represent the data by a double bar graph.

Solution:

Question 10.
The following tables shows the mode of transport used by boys and girls for going to the same school.

Draw a double bar graph representing the above data.
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder)

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder)

Surface Area, Volume and Capacity Exercise 21A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the volume and the total surface area of a cuboid, whose :
(i) length = 15 cm, breadth = 10 cm and height = 8 cm.
(ii) l = 3.5 m, b = 2.6 m and h = 90 cm,
Solution:

Question 2.
(i) The volume of a cuboid is 3456 cm³. If its length = 24 cm and breadth = 18 cm ; find its height.
(ii) The volume of a cuboid is 7.68 m³. If its length = 3.2 m and height = 1.0 m; find its breadth.
(iii) The breadth and height of a rectangular solid are 1.20 m and 80 cm respectively. If the volume of the cuboid is 1.92 m³; find its length.
Solution:

Question 3.
The length, breadth and height of a cuboid are in the ratio 5 : 3 : 2. If its volume is 240 cm³; find its dimensions. (Dimensions means : its length, breadth and height). Also find the total surface area of the cuboid.
Solution:

Question 4.
The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its total surface area is 504 cm2; find its dimensions. Also, find the volume of the cuboid.
Solution:

Question 5.
Find the volume and total surface area of a cube whose each edge is :
(i) 8 cm
(ii) 2 m 40 cm.
Solution:

Question 6.
Find the length of each edge of a cube, if its volume is :
(i) 216 cm³
(ii) 1.728 m³
Solution:

Question 7.
The total surface area of a cube is 216 cm2. Find its volume.
Solution:

Question 8.
A solid cuboid of metal has dimensions 24 cm, 18 cm and 4 cm. Find its volume.
Solution:

Question 9.
A wall 9 m long, 6 m high and 20 cm thick, is to be constructed using bricks of dimensions 30 cm, 15 cm and 10 cm. How many bricks will be required.
Solution:

Question 10.
A solid cube of edge 14 cm is melted down and recasted into smaller and equal cubes each of edge 2 cm; find the number of smaller cubes obtained.
Solution:

Question 11.
A closed box is cuboid in shape with length = 40 cm, breadth = 30 cm and height = 50 cm. It is made of thin metal sheet. Find the cost of metal sheet required to make 20 such boxes, if 1 m² of metal sheet costs Rs. 45.
Solution:

Question 12.
Four cubes, each of edge 9 cm, are joined as shown below :

Write the dimensions of the resulting cuboid obtained. Also, find the total surface area and the volume of the resulting cuboid.
Solution:

Surface Area, Volume and Capacity Exercise 21B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
How many persons can be accommodated in a big-hall of dimensions 40 m, 25 m and 15 m ; assuming that each person requires 5 m³ of air?
Solution:

Question 2.
The dimension of a class-room are; length = 15 m, breadth = 12 m and height = 7.5 m. Find, how many children can be accommodated in this class-room ; assuming 3.6 m³ of air is needed for each child.
Solution:

Question 3.
The length, breadth and height of a room are 6 m, 5.4 m and 4 m respectively. Find the area of :
(i) its four-walls
(ii) its roof.
Solution:

Question 4.
A room 5 m long, 4.5 m wide and 3.6 m high has one door 1.5 m by 2.4 m and two windows, each 1 m by 0.75 m. Find :
(i) the area of its walls, excluding door and windows ;
(ii) the cost of distempering its walls at the rate of Rs.4.50 per m².
(iii) the cost of painting its roof at the rate of Rs.9 per m².
Solution:

Question 5.
The dining-hall of a hotel is 75 m long ; 60 m broad and 16 m high. It has five – doors 4 m by 3 m each and four windows 3 m by 1.6 m each. Find the cost of :
(i) papering its walls at the rate of Rs.12 per m²;
(ii) carpetting its floor at the rate of Rs.25 per m².
Solution:

Question 6.
Find the volume of wood required to make a closed box of external dimensions 80 cm, 75 cm and 60 cm, the thickness of walls of the box being 2 cm throughout.
Solution:

Question 7.
A closed box measures 66 cm, 36 cm and 21 cm from outside. If its walls are made of metal-sheet, 0.5 cm thick ; find :
(i) the capacity of the box ;
(ii) volume of metal-sheet and
(iii) weight of the box, if 1 cm³ of metal weights 3.6 gm.
Solution:

Question 8.
The internal length, breadth and height of a closed box are 1 m, 80 cm and 25 cm. respectively. If its sides are made of 2.5 cm thick wood ; find :
(i) the capacity of the box
(ii) the volume of wood used to make the box.
Solution:

Question 9.
Find the area of metal-sheet required to make an open tank of length = 10 m, breadth = 7.5 m and depth = 3.8 m.
Solution:

Question 10.
A tank 30 m long, 24 m wide and 4.5 m deep is to be made. It is open from the top. Find the cost of iron-sheet required, at the rate of ₹ 65 per m², to make the tank.
Solution:

Surface Area, Volume and Capacity Exercise 21C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
The edges of three solid cubes are 6 cm, 8 cm and 10 cm. These cubes are melted and recast into a single cube. Find the edge of the resulting cube.
Solution:

Question 2.
Three solid cubes of edges 6 cm, 10 cm and x cm are melted to form a single cube of edge 12 cm, find the value of x.
Solution:

Question 3.
The length of the diagonals of a cube is 8√3 cm.
Find its:
(i) edge
(ii) total surface area
(iii) Volume
Solution:

Question 4.
A cube of edge 6 cm and a cuboid with dimensions 4 cm x x cm x 15 cm are equal in volume. Find:
(i) the value of x.
(ii) total surface area of the cuboid.
(iii) total surface area of the cube.
(iv) which of these two has greater surface and by how much?
Solution:

Question 5.
The capacity of a rectangular tank is 5.2 m³ and the area of its base is 2.6 x 104 cm²; find its height (depth).
Solution:

Question 6.
The height of a rectangular solid is 5 times its width and its length is 8 times its height. If the volume of the wall is 102.4 cm³, find its length.
Solution:

Question 7.
The ratio between the lengths of the edges of two cubes are in the ratio 3 : 2. Find the ratio between their:
(i) total surface area
(ii) volume.
Solution:

Question 8.
The length, breadth and height of a cuboid (rectangular solid) are 4 : 3 : 2.
(i) If its surface are is 2548 cm², find its volume.
(ii) If its volume is 3000 m³, find its surface area.
Solution:

Surface Area, Volume and Capacity Exercise 21D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
The height of a circular cylinder is 20 cm and the diameter of its base is 14 cm. Find:
(i) the volume
(ii) the total surface area.
Solution:

Question 2.
Find the curved surface area and the total surface area of a right circular cylinder whose height is 15 cm and the diameter of the cross-section is 14 cm.
Solution:

Question 3.
Find the height of the cylinder whose radius is 7 cm and the total surface area is 1100 cm².
Solution:

Question 4.
The curved surface area of a cylinder of height 14 cm is 88 cm². Find the diameter of the base of the cylinder.
Solution:

Question 5.
The ratio between the curved surface area and the total surface area of a cylinder is 1 : 2. Find the ratio between the height and the radius of the cylinder.
Solution:

Question 6.
Find the capacity of a cylindrical container with internal diameter 28 cm and height 20 cm.
Solution:

Question 7.
The total surface area of a cylinder is 6512 cm² and the circumference of its bases is 88 cm. Find:
(i) its radius
(ii) its volume
Solution:

Question 8.
The sum of the radius and the height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 cm². Find the height and the volume of the cylinder.
Solution:

Question 9.
A cylindrical pillar has radius 21 cm and height 4 m. Find :
(i) the curved surface area of the pillar
(ii) cost of polishing 36 such cylindrical pillars at the rate of ₹ 12 per m².
Solution:

Question 10.
If radii of two cylinders are in the ratio 4 : 3 and their heights are in the ratio 5 : 6, find the ratio of their curved surfaces.
Solution:

Surface Area, Volume and Capacity Exercise 21E – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
A cuboid is 8 m long, 12 m broad and 3.5 high, Find its
(i) total surface area
(ii) lateral surface area
Solution:

Question 2.
How many bricks will be required for constructing a wall which is 16 m long, 3 m high and 22.5 cm thick, if each brick measures 25 cm x 11.25 cm x 6 cm?
Solution:

Question 3.
The length, breadth and height of cuboid are in the ratio 6 : 5 : 3. If its total surface area is 504 cm², find its volume.
Solution:

Question 4.
The external dimensions of an open wooden box are 65 cm, 34 cm and 25 cm. If the box is made up of wood 2 cm thick, find the capacity of the box and the volume of wood used to make it.
Solution:

Question 5.
The curved surface area and the volume of a toy, cylindrical in shape, are 132 cm² and 462 cm³ respectively. Find, its diameter and its length.
Solution:

Question 6.
The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹ 10 per m² is ₹ 15,000, find the height of the hall.
Solution:

Question 7.
The length of a hall is double its breadth. Its height is 3 m. The area of its four walls (including doors and windows) is 108 m², find its volume.
Solution:

Question 8.
A solid cube of side 12 cm is cut into 8 identical cubes. What will be the side of the new cube? Also, find the ratio between the surface area of the original cube and the total surface area of all the small cubes formed.
Solution:

Question 9.
The diameter of a garden roller is 1.4 m and it 2 m long. Find the maximum area covered by it 50 revolutions?
Solution:

Question 10.
In a building, there are 24 cylindrical pillars. For each pillar, radius is 28 m and height is 4 m. Find the total cost of painting the curved surface area of the pillars at the rate of ₹ 8 per m².
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles (With their Types)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles (With their Types)

Angles Exercise 24A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
For each angle given below, write the name of the vertex, the names of the arms and the name of the angle.

Solution:

Question 2.
Name the points :
(i) in the interior of the angle PQR,
(ii) in the exterior of the angle PQR.

Solution:

Question 3.
In the given figure, figure out the number of angles formed within the arms OA and OE.

Solution:

Question 4.
Add :
(i) 29° 16′ 23″ and 8° 27′ 12″
(ii) 9° 45’56” and 73° 8′ 15″
(m) 56° 38′ and 27° 42’30”
(iv) 47° and 61° 17’4″
Solution:

Question 5.
In the figure, given below name :
(i) three pairs of adjacent angles.
(ii) two acute angles,
(iii) two obtuse angles
(iv) two reflex angles.

Solution:

Question 6.
In the given figure ; PQR is a straight line. If :
(i) ∠SQR = 75° ; find ∠PQS.
(ii) ∠PQS = 110°; find ∠RQS

Solution:

Question 7.
In the given figure ; AOC-is a straight line. If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of :
(i) angle BOC
(ii) angle EOD
(iii) obtuse angle BOD
(iv) reflex angle BOD
(v) reflex angle COE.

Solution:

Question 8.
In the given figure if :
(i) a = 130° ; find b.
(ii) b = 200 ; find a.
(iii) a = 5/3 right angle, find b

Solution:

Question 9.
In the given diagram, ABC is a straight line.
(i) If x = 53°, find y.
(ii) If y =1\(\frac { 1 }{ 2 }\) right angles ; find x.

Solution:

Question 10.
In the given figure, AOB is a straight line. Find the value ofx and also answer each of the following :
(i) ∠AOP = ……..
(ii) ∠BOP = ……..
(iii) which angle is obtuse ?
(iv) which angle is acute ?

Solution:

Question 11.
In the given figure, PQR is a straight line. Find x. Then complete the following:
(i) ∠AQB = ……..
(ii) ∠BQP = ……..
(iii) ∠AQR = …….

Solution:

Question 12.
In the given figure, lines AB and CD intersect at point O.
(i) Find the value of ∠a.
(ii) Name all the pairs of vertically opposite angles.
(iii) Name all the pairs of adjacent angles.
(iv) Name all the reflex angles formed and write the measure of each.

Solution:

Question 13.
In the given figure :
(i) If ∠AOB = 45°, ∠BOC = 30° and ∠AOD= 110°;
find : angles COD and BOD.
(ii) If ∠BOC = ∠DOC = 34° and ∠AOD = 120° ;
find : angle AOB and angle AOC.
(iii) If ∠AOB = ∠BOC = ∠COD = 38°
find : reflex angle AOC and reflex angle AOD.

Solution:

Angles Exercise 24B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write the complement angle of :
(i) 45°
(ii) x°
(iii) (x – 10)°
(iv) 20° + y°
Solution:

Question 2.
Write the supplement angle of :
(i) 49°
(ii) 111°
(iii) (x – 30)°
(iv) 20° + y°
Solution:

Question 3.
Write the complement angle of :


Solution:

Question 4.

Solution:

Question 5.
Find the angle :
(i) that is equal to its complement ?
(ii) that is equal to its supplement ?
Solution:

Question 6.
Two complementary angles are in the ratio 7 : 8. Find the angles.
Solution:

Question 7.
Two supplementary angles are in the ratio 7 : 11. Find the angles.
Solution:

Question 8.
The measures of two complementary angles are (2x – 7)° and (x + 4)°. Find x.
Solution:

Question 9.
The measures of two supplementary angles are (3x + 15)° and (2x + 5)°. Find x.
Solution:

Question 10.
For an angle x°, find :
(i) the complementary angle
(ii) the supplementary angle
(iii) the value of x° if its supplementary angle is three times its complementary angle.
Solution:

Angles Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Explain what do you understand by :
(i) Adjacent angles ?
(ii) Complementary angles ?
(iii) Supplementary angles ?
Solution:

Question 2.
Find the value of ‘x’ for each of the following figures :


Solution:

Question 3.
Find the number of degrees in an angle that is (i) \(\frac { 3 }{ 5 }\) of a right angle (ii) 0.2 times of a straight line angle.
Solution:

Question 4.
In the given figure; AB, CD and EF are straight lines. Name the pair of angles forming :
(i) straight line angles.
(ii) vertically opposite angles.

Solution:

Question 5.
Find the complement of :

Solution:

Question 6.
Find the supplement of :

Solution:

Question 7.
Two complementary angles are in the ratio 8 : 7. Find the angles.
Solution:

Question 8.
Two supplementary angles are in the ratio 7 : 5. Find the angles.
Solution:

Question 9.
Two supplementary angles are (5x – 82°) and (4x + 73°). Find the value of x.
Solution:

Question 10.
Find the angle formed by the arms of a clock at:
(i) 3 O’clock
(ii) 6 O’clock
(iii) 9 O’clock
(iv) 12 O’clock
Solution:

Question 11.
For an angle y°, find :
(i) its supplementary angle.
(ii) its complementary angle.
(iii) the value of y° if its supplement is four times its complement.
Solution:

Question 12.
Use the adjoining figure to find :
(i) ∠BOD
(ii) ∠AOC
Solution:

Question 13.
Two adjacent angles forming a linear pair are in the ratio 7:5, find the angles.
Solution:

Question 14.
Find the angle that is three times its complementary angle.
Solution:

Question 15.
An angle is one-thirds of a straight line angle ; find :
(i) the angle
(ii) the complement and the supplement of the angle obtained above.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 7 Unitary Method (Including Time and Work)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 7 Unitary Method (Including Time and Work)

Unitary Method Exercise 7A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Weight of 8 identical articles is 4.8 kg. What is the weight of 11 such articles ?
Answer:

Question 2.
6 books weigh 1 .260 kg. How many books will weigh 3.150 kg ?
Answer:

Question 3.
8 men complete a work in 6 hours. In how many hours will 12 men complete the same work ?
Answer:

Question 4.
If a 25 cm long candle burns for 45 minutes, how long will another candle of the same material and same thickness but 5 cm longer than the previous one, burn ?
Answer:

Question 5.
A typist takes 80 minutes to type 24 pages. How long will he take to type 87 pages ?
Answer:

Question 6.
Rs. 750 support a family for 15 days. For how many days will Rs. 2,500 support the same family ?
Answer:

Question 7.
400 men have provisions for 23 weeks. They are joined by 60 men. How long will the provisions last ?
Answer:

Question 8.
200 men have provisions for 30 days. If 50 men left, the same provisions would last for the remaining men, in how many days?
Answer:

Question 9.
8 men can finish a certain amount of provisions in 40 days. If 2 more men join with them, find for how many days the same amount of provisions be sufficient ?
Answer:

Question 10.
If interest on Rs. 200 be Rs. 25 in a certain time, what will be the interest on Rs 750 for the same time ?
Answer:

Question 11.
If 3 dozen eggs cost Rs. 90, find the cost of 3 scores of eggs. (1 score = 20)
Answer:

Question 12.
If the fare for 48 km is Rs. 288, what will be the fare for 36 km ?
Answer:

Question 13.
What will be the cost of 3.20 kg of an item, if 3 kg of it costs Rs. 360 ?
Answer:

Question 14.
If 9 lines of a print, in a column of a book contains 36 words. How many words will a column of 51 lines cqntain ?
Answer:

Question 15.
125 pupil have food sufficient for 18 days. If 25 more pupil join them, how long will the food last now ? What assumption have you made to come to your answer ?
Answer:

Question 16.
A carpenter prepares a new chair in 3 days, working 8 hours a day. Atleast how many hours per day must he work in order to make the same chair in 4 days ?
Answer:

Question 17.
A man earns ₹5,800 in 10 days. How much will he earn in the month of February of a leap year?
Answer:

Question 18.
A machine is used for making rubber balls and makes 500 balls in 30 minutes. How many balls will it make in 3\(\frac { 1 }{ 2 }\) hours?
Answer:

Question 19.
In a school’s hostel mess, 20 children consume a certain quantity of ration in 6 days. However, 5 children did not return to the hostel after holidays. How long will the same amount of ration last now?
Answer:

Unitary Method Exercise 7B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.

Answer:

Question 2.
3\(\frac { 1 }{ 2 }\)m of cloth costs Rs. 168 ; find the cost of 4\(\frac { 1 }{ 3 }\)m of the same cloth.
Answer:

Question 3.
A wrist watch loses 10 sec in every 8 hours; in how much time will it lose 15 sec. ?
Answer:

Question 4.
In 2 days and 20 hours, a watch gains 20 sec ; find how much time will the watch take to gain 35 sec. ?
Answer:

Question 5.
50 men mow 32 hectares of land in 3 days. How many days will 15 men take to mow it?
Answer:

Question 6.
The wages of 10 workers for a six days week are Rs, 1,200. What are the one day wages: (i) of one worker ? (ii) of 4 workers?
Answer:

Question 7.
If 32 apples weigh 2 kg 800 g. How many apples will there be in a box, containing 35 kg of apples ?
Answer:

Question 8.
A truck uses 20 litres of diesel for 240 km. How many litres will be needed for 1200 km?
Answer:

Question 9.
A garrison of 1200 men has provisions for 15 days. How long will the provisions last if the garrison be increased by 600 men ?
Answer:

Question 10.
A camp has provisions for 60 pupil for 18 days. In how many days, the same provisions will finish off if the strength of the camp is increased to 72 pupil ?
Answer:

EXERCISE 7 (C)

Question 1.
A can do a piece of work in 6 days and B can do it in 8 days. How long will they take to complete it together ?
Answer:

Question 2.
A and B working together can do a piece of work in 10 days B alone can do the same work in 15 days. How long will A alone take to do the same work ?
Answer:

Question 3.
A can do a piece of work in 4 days and B can do the same work in 5 days. Find, how much work can be done by them working together in : (i) one day (ii) 2 days.
What part of work will be left, after they have worked together for 2 days ?
Answer:

Question 4.
A and B take 6 hours and 9 hours respectively to complete a work. A works for 1 hour and then B works for two hours.
(i) How much work is done in these 3 hours ?
(ii) How much work is still left ?
Answer:

Question 5.
A, B and C can do a piece of work in 12, 15 and 20 days respectively. How long will they take to do it working together ?
Answer:

Question 6.
Two taps can fill a cistern in 10 hours and 8 hours respectively. A third tap can empty it in 15 hours. How long will it take to fill the empty cistern, if all of them are opened together ?
Answer:

Question 7.
Mohit can complete a work in 50 days, whereas Anuj can complete the same work in 40 days.
Find:
(i) work done by Mohit in 20 days.
(ii) work left after Mohit has worked on it for 20 days.
(iii) time taken by Anuj to complete the remaining work.
Answer:

Question 8.
Joseph and Peter can complete a work in 20 hours and 25 hours respectively.
Find :
(i) work done by both together in 4 hrs.
(ii) work left after both worked together for 4 hrs.
(iii) time taken by Peter to complete the remaining work.
Answer:

Question 9.
A is able to complete \(\frac { 1 }{ 3 }\) of a certain work in 10 hrs and B is able to complete\(\frac { 2 }{ 5 }\) of the same work in 12 hrs.
Find:
(i) how much work can A do in 1 hour ?
(ii) how much work can B do in 1 hour ?
(iii) in how much time will the work be completed, if both work together.
Answer:

Question 10.
Shaheed can prepare one wooden chair in 3 days and Shaif can prepare the same chair in 4 days. If they work together, in how many days will they prepare :
(i) one chair ?
(ii)14 chairs of the same kind?
Answer:

Question 11.
A, B and C together finish a work in 4 days. If A alone can finish the same work in 8 days and B in 12 days, find how long will C take to finish the work.
Answer:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 22 Simple (Linear) Equations (Including Word Problems)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 22 Simple (Linear) Equations (Including Word Problems)

Simple (Linear) Equations Exercise 22A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Solve:


Solution:

Question 2.
Solve:

Solution:

Question 3.
Solve:

Solution:

Question 4.
Solve:

Solution:

Question 5.
Solve:

Solution:

Simple (Linear) Equations Exercise 22B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Solve:


Solution:

Question 2.
Solve:

Solution:

Question 3.
Solve:

Solution:

Simple (Linear) Equations Exercise 22C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
5 – x = 3
Solution:

Question 2.
2 – y = 8
Solution:

Question 3.
8.4 – x = -2
Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.
1.6z = 8
Solution:

Question 8.
3a = – 2.1
Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.
– 5x = 10
Solution:

Question 12.
2.4z = -4.8
Solution:

Question 13.
2y – 5 = -11
Solution:

Question 14.
2x + 4.6 = 8
Solution:

Question 15.
5y – 3.5 = 10
Solution:

Question 16.
3x + 2 = -2.2
Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.
-3y – 2 = 10
Solution:

Question 21.
4z – 5 = 3 – z
Solution:

Question 22.
7x – 3x + 2 =22
Solution:

Question 23.
6y + 3 = 2y + 11
Solution:

Question 24.
3 (x + 5) = 18
Solution:

Question 25.
5 (x – 2) – 2 (x + 2) = 3
Solution:

Question 26.
(5x – 3) 4 = 3
Solution:

Question 27.
3(2x + 1) – 2(x – 5) -5 (5 – 2x) = 16
Solution:

Simple (Linear) Equations Exercise 22D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
A number increased by 17 becomes 54. Find the number.
Solution:

Question 2.
A number decreased by 8 equals 26, find the number.
Solution:

Question 3.
One-fourth of a number added to two- seventh of it gives 135; find the number.
Solution:

Question 4.
Two-fifths of a number subtracted from three-fourths of it gives 56, find the number.
Solution:

Question 5.
A number is increased by 12 and the new number obtained is multiplied by 5. If the resulting number is 95, find the original number.
Solution:

Question 6.
A number is increased by 26 and the new number obtained is divided by 3. If the resulting number is 18; find the original number.
Solution:

Question 7.
The age of a man is 27 years more than the age of his son. If the sum of their ages is 47 years, find the age of the son and his father.
Solution:

Question 8.
The difference between the ages of Gopal and his father is 26 years. If the sum of their ages is 56 years, find the ages of Gopal and his father.
Solution:

Question 9.
When two consecutive natural numbers are added, the sum is 31; find the numbers.
Solution:

Question 10.
When three consecutive natural numbers are added, the sum is 66, find the numbers.
Solution:

Question 11.
A natural number decreased by 7 is 12. Find the number.
Solution:

Question 12.
One fourth of a number added to one- sixth of itself is 15. Find the number.
Solution:

Question 13.
A whole number is increased by 7 and the new number so obtained is multiplied by 5; the result is 45. Find the number.
Solution:

Question 14.
The age of a man and the age of his daughter differ by 23 years and the sum of their ages is 41 years. Find the age of the man.
Solution:

Question 15.
The difference between the ages of a woman and her son is 19 years and the sum of their ages is 37 years; find the age of the son.
Solution:

Question 16.
Two natrual numbers differ by 6 and sum of them is 36. Find the larger number.
Solution:

Question 17.
The difference between two numbers is 15. Taking the smaller number as x; find:
(i) the expression for larger number.
(ii) the larger number, if the sum of these numbers is 71.
Solution:

Question 18.
The difference between two numbers is 23. Taking the larger number as x, find:
(i) the expression for smaller number.
(ii) the smaller number, if the sum of these two numbers is 91.
Solution:

Question 19.
Find three consecutive integers such that their sum is 78.
Solution:

Question 20.
The sum of three consecutive numbers is 54. Taking the middle number as x, find:
(i) expression for the smallest number and the largest number.
(ii) the three numbers.
Solution:

Simple (Linear) Equations Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Solve each of the following equations :
Question i.
2x + 3 = 7
Solution:

Question ii.
2x – 3 = 7
Solution:

Question iii.
2x ÷ 3 = 7
Solution:

Question iv.
3x – 8 = 13
Solution:

Question v.
3y + 8 = 13
Solution:

Question vi.
3y ÷ 8 = 13
Solution:

Question vii.

Solution:

Question viii.

Solution:

Question ix.

Solution:

Question x.
5x – 2.4 = 4.9
Solution:

Question xi.
5y + 4.9 = 2.4
Solution:

Question xii.
48 z + 3.6 = 1.2
Solution:

Question xiii.

Solution:

Question xiv.

Solution:

Question xv.

Solution:

Question xvi.
-3x + 4 = 10
Solution:

Question xvii.
5 = x – 3
Solution:

Question xviii.
8y = 3- 3y
Solution:

Question xix.
4x = 4.9 = 6.5
Solution:

Question xx.
3z + 2 = -4
Solution:

Question xxi.
7y – 18 = 17
Solution:

Question xxii.

Solution:

Question xxiii.

Solution:

Question xxiv.

Solution:

Question xxv.
7x – 2 = 4x + 7
Solution:

Question xxvi.
3y -(y + 2) = 4
Solution:
<

Question xxvii.
3z – 18 = z – (12 – 4z)
Solution:

Question xxiii.

Solution:

Question xxix.

Solution:

Question xxx.

Solution:

Question xxxi.
5x – 2x + 15 = 27
Solution:

Question xxxii.
5y – 15 = 27 -2y
Solution:

Question xxxiii.
7z + 15 = 3z – 13
Solution:

Question xxxiv.
2 (x -3) – 3 (x-4) =12
Solution:

Question xxxv.
(7y + 8) + 7 = 8
Solution:

Question xxxvi.
2(z – 5) +3 (z + 2) -(3 – 5z) = 10
Solution:

Question 2.
A natural number decreased by 7 is 12. Find the number.
Solution:

Question 3.
One-fourth of a number added to one-sixth of It is 15. Find the number.
Solution:

Question 4.
A whole number is increased by 7 and the number so obtained is multiplied by 5; the result is 45. Find the whole number.
Solution:

Question 5.
The age of a man and the age of his daughter differ by 23 years and the sum of their ages is 41 years. Find the age of the man.
Solution:

Question 6.
The difference between the ages of a woman and her son is 19 years and the sum of their ages is 37 years; find the age of the son.
Solution:

Question 7.
Two natural numbers differ by 6 and their sum is 36. Find the larger number.
Solution:

Question 8.
The difference between two numbers is 15. Taking the smaller number as x; find :
(i) the expression for the larger number.
(ii) the larger number, if the sum of these numbers is 71.
Solution:

Question 9.
The difference between two numbers is 23. Taking the larger number as x, find :
(i) the expression for smaller number.
(ii) the smaller number, if the sum of these two numbers is 91.
Solution:

Question 10.
Find the three consecutive integers whose sum is 78.
Solution:

Question 11.
The sum of three consecutive numbers is 54. Taking the middle number as x, find :
(i) the expressions for the smallest number and the largest number.
(ii) the three numbers.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 6 Ratio and Proportion (Including Sharing in a Ratio)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 6 Ratio and Proportion (Including Sharing in a Ratio)

Ratio and Proportion Exercise 6A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Express each of the given ratio in its simplest form :

Solution:

Question 2.
Divide 64 cm long string into two parts in the ratio 5 : 3.
Solution:

Question 3.
Rs. 720 is divided between x and y in the ratio 4:5. How many rupees will each get?
Solution:

Question 4.
The angles of a triangle are in the ratio 3 :2 : 7. Find each angle.
Solution:

Question 5.
A rectangular field is 100 m by 80 m. Find the ratio of
(i) length to its breadth
(ii) breadth to its perimeter.
Solution:

Question 6.
The sum of three numbers, whose ratios are 3 \(\frac { 1 }{ 3 }\) : 4 \(\frac { 1 }{ 5 }\) : 6 \(\frac { 1 }{ 8 }\) is 4917.Find the numbers.
Solution:

Question 7.
The ratio between two quantities is 3 : the first is Rs. 810, find the second.
Solution:

Question 8.
Two numbers are in the ratio 5 : 7. Their difference is 10. Find the numbers.
Solution:

Question 9.
Two numbers are in the ratio 10 : 11. Their sum is 168. Find the numbers.
Solution:

Question 10.
A line is divided in two parts in the ratio 2.5 : 1.3. If the smaller one is 35.1 cm, find the length of the line.
Solution:

Question 11.
In a class, the ratio of boys to the girls is 7:8. What part of the whole class are girls.
Solution:

Question 12.
The population of a town is ’ 50,000, out of which males are \(\frac { 1 }{ 3 }\) of the whole population. Find the number of females. Also, find the ratio of the number of females to the whole population.
Solution:

Question 13.
Ten gram of an alloy of metals A and B contains 7.5 gm of metal A and the rest is metal B. Find the ratio between :
(i) the weights of metals A and B in the alloy.
(ii) the weight of metal B and the weight of the alloy.
Solution:

Question 14.
The ages of two boys A and B are 6 years 8 months and 7 years 4 months respectively. Divide Rs. 3,150 in the ratio of their ages.
Solution:

Question 15.
Three persons start a business and spend Rs. 25,000; Rs. 15,000 atid Rs. 40,000 respectively. Find the share of each out of a profit of Rs. 14,400 in a year.
Solution:

Question 16.
A plot of land, 600 sq m in area, is divided between two persons such that the first person gets three-fifth of what the second gets. Find the share of each.
Solution:

Question 17.
Two poles of different heights are standing vertically on a horizontal field. At a particular time, the ratio between the lengths of their shadows is 2 :3. If the height of the smaller pole is 7.5 m, find the height of the other pole.
Solution:

Question 18.
Two numbers are in the ratio 4 : 7. If their L.C.M. is 168, find the numbers.
Solution:

Question 19.
is divided between A and B in such a way that A gets half of B. Find :
(i) the ratio between the shares of A and B.
(ii) the share of A and the share of B.
Solution:

Question 20.
The ratio between two numbers is 5 : 9. Find the numbers, if their H.C.F. is 16.
Solution:

Question 21.
A bag contains ₹ 1,600 in the form of ₹10 and ₹20 notes. If the ratio between the numbers of ₹10 and ₹20 notes is 2 : 3; find the total number of notes in all.
Solution:

Question 22.
The ratio between the prices of a scooter and a refrigerator is 4 : 1. If the scooter costs ₹45,000 more than the refrigerator, find the price of the refrigerator.
Solution:

Ratio and Proportion Exercise 6B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Check whether the following quantities form a proportion or not ?

Solution:

Question 2.
Find the fourth proportional of

Solution:

Question 3.
Find the third proportional of

Solution:

Question 4.
Find the mean proportional between

Solution:

Question 5.


Solution:

Question 6.
If x: y – 5 :4 and 2 : x = 3 :8, find the value of y.
Solution:

Question 7.
Find the value of x, when 2.5 : 4 = x : 7.5.
Solution:

Question 8.
Show that 2, 12 and 72 are in continued proportion.
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions (Including Evaluation)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions (Including Evaluation)

Framing Algebraic Expressions Exercise 21 – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write in the form of an algebraic expression :
(i) Perimeter (P) of a rectangle is two times the sum of its length (l) and its breadth (b).
(ii) Perimeter (P) of a square is four times its side.
(iii) Area of a square is square of its side.
(iv) Surface area of a cube is six times the square of its edge.
Solution:

Question 2.
Express each of the following as an algebraic expression :
(i) The sum of x and y minus m.
(ii) The product of x and y divided by m.
(iii) The subtraction of 5m from 3n and then adding 9p to it.
(iv) The product of 12, x, y and z minus the product of 5, m and n.
(v) Sum of p and 2r – s minus sum of a and 3n + 4x.
Solution:

Question 3.
Construct a formula for the following :
Total wages (₹ W) of a man whose basic wage is (₹ B) for t hours week plus (₹ R) per hour, if he Works a total of T hours.
Solution:

Question 4.
If x = 4, evaluate :
(i) 3x + 8
(ii) x² – 2x
(iii) \(\frac { { x }^{ 2 } }{ 2 }\)
Solution:

Question 5.
If m – 6, evaluate :
(i) 5m – 6
(ii) 2m² + 3m
(iii) (2m)²
Solution:

Question 6.
If x = 4, evaluate :
(i) 12x + 7
(ii) 5x² + 4x
(iii) \(\frac { { x }^{ 2 } }{ 8 }\)
Solution:

Question 7.
If m = 2, evaluate :
(i) 16m – 7
(ii) 15m² – 10m
(iii) \(\frac { 1 }{ 4 } \times { m }^{ 3 }\)
Solution:

Question 8.
If x = 10, evaluate :
(i) 100x + 225
(ii) 6x² – 25x
(iii) \(\frac { 1 }{ 50 } \times { x }^{ 3 }\)
Solution:

Question 9.
If a = – 10, evaluate :
(i) 5a
(ii) a²
(iii) a³
Solution:

Question 10.
If x = – 6, evaluate :
(i) 11x
(ii) 4x²
(iii) 2x³
Solution:

Question 11.
If m = – 7, evaluate :
(i) 12m
(ii) 2m²
(iii) 2m³
Solution:

Question 12.
Find the average (A) of four quantities p, q, r and s. If A = 6, p = 3, q = 5 and r = 7 ; find the value of s.
Solution:

Question 13.
If a = 5 and b = 6, evaluate :
(i) 3ab
(ii) 6a²b
(iii) 2b²
Solution:

Question 14.
If x = 8 and y = 2, evaluate :
(i) 9xy
(ii) 5x²y
(iii) (4y)²
Solution:

Question 15.
If x = 5 and y = 4, evaluate :
(i) 8xy
(ii) 3x²y
(iii) 3y²
Solution:

Question 16.
If y = 5 and z = 2, evaluate :
(i) 100yz
(ii) 9y²z
(iii) 5y²
(iv) (5z)³
Solution:

Question 17.
If x = 2 and y = 10, evaluate :
(i) 30xy
(ii) 50xy²
(iii) (10x)²
(iv) 5y²
Solution:

Question 18.
If m = 3 and n = 7, evaluate :
(i) 12mn
(ii) 5mn²
(iii) (10m)²
(iv) 4n²
Solution:

Question 19.
If a = -10, evaluate :
(i) 3a – 2
(ii) a² + 8a
(iii) \(\frac { 1 }{ 5 }\) x a²
Solution:

Question 20.
If x = -6, evaluate :
(i) 4x – 9
(ii) 3x² + 8x
(iii) \(\frac { { x }^{ 2 } }{ 2 }\)
Solution:

Question 21.
If m = -8, evaluate :
(i) 2m + 21
(ii) m² + 9m
(iii) \(\frac { { m }^{ 2 } }{ 4 }\)
Solution:

Question 22.
If p = -10, evaluate :
(i) 6p + 50
(ii) 3p² – 20p
(iii) \(\frac { { p }^{ 2 } }{ 50 }\)
Solution:

Question 23.
If y = -8, evaluate :
(i) 6y + 53
(ii) y² + 12y
(iii) \(\frac { { y }^{ 3 } }{ 4 }\)
Solution:

Question 24.
If x = 2 and 7 = -4, evaluate :
(i) 11xy
(ii) 5x²y
(iii) (5y)²
(iv) 8x²
Solution:

Question 25.
If m = 9 and n = -2, evaluate
(i) 4mn
(ii) 2m²n
(iii) (2n)³
Solution:

Question 26.
If m = -8 and n = -2, evaluate :
(i) 12mn
(ii) 3m²n
(iii) (4n)²
Solution:

Question 27.
If x = -5 and y = -8, evaluate :
(i) 4xy
(ii) 2xy²
(iii) 4x²
(iv) 3y²
Solution:

Question 28.
Find T, if T = 2a – b, a = 7 and b = 3.
Solution:

Question 29.
From the formula B = 2a² – b², calculate the value of B when a = 3 and b = -1.
Solution:

Question 30.
The wages ₹ W of a man earning ₹ x per hour for t hours are given by the formula W = xt. Find his wages for working 40 hours at a rate of ₹ 39.45 per hour.
Solution:

Question 31.
The temperature in Fahrenheit scale is represented by F and the tempera¬ture in Celsius scale is represented by C. If F = \(\frac { 9 }{ 5 }\) x C + 32, find F when C = 40.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots

Squares and Square Roots Exercise 3A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the square of :
(i) 59
(ii) 63
(iii) 15
Solution:

Question 2.
By splitting into prime factors, find the square root of :
(i) 11025
(ii) 396900
(iii) 194481
Solution:

Question 3.
(i) Find the smallest number by which 2592 be multiplied so that the product is a perfect square.
(ii) Find the smallest number by which 12748 be multiplied so that the product is a perfect square?
Solution:
</span

Question 4.
Find the smallest number by which 10368 be divided, so that the result is a perfect square. Also, find the square root of the resulting numbers.
Solution:

Question 5.
Find the square root of :
(i) 0.1764
(ii) \(96\frac { 1 }{ 25 }\)
(iii) 0.0169
Solution:

Question 6.
Evaluate

Solution:

Question 7.

Solution:

Question 8.
A man, after a tour, finds that he had spent every day as many rupees as the number of days he had been on tour. How long did his tour last, if he had spent in all ₹ 1,296
Solution:

Question 9.
Out of 745 students, maximum are to be arranged in the school field for a P.T. display, such that the number of rows is equal to the number of columns. Find the number of rows if 16 students were left out after the arrangement.
Solution:

Question 10.
13 and 31 is a strange pair of numbers such that their squares 169 and 961 are also mirror images of each other. Find two more such pairs.
Solution:

Question 11.
Find the smallest perfect square divisible by 3, 4, 5 and 6.
Solution:

Question 12.
If √784 = 28, find the value of:
(i) √7.84 + √78400
(ii) √0.0784 + √0.000784
Solution:

Squares and Square Roots Exercise 3B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the square root of:
(i) 4761
(ii) 7744
(iii) 15129
(iv) 0.2916
(v) 0.001225
(vi) 0.023104
(vii) 27.3529
Solution:

Question 2.
Find the square root of:
(i) 4.2025
(ii) 531.7636
(iii) 0.007225
Solution:

Question 3.
Find the square root of:
(i) 245 correct to two places of decimal.
(ii) 496 correct to three places of decimal.
(iii) 82.6 correct to two places of decimal.
(iv) 0.065 correct to three places of decimal.
(v) 5.2005 correct to two places of decimal.
(vi) 0.602 correct to two places of decimal
Solution:

Question 4.
Find the square root of each of the following correct to two decimal places:
(i) \(3\frac { 4 }{ 5 }\)
(ii) \(6\frac { 7 }{ 8 }\)
Solution:

Question 5.
For each of the following, find the least number that must be subtracted so that the resulting number is a perfect square.
(i) 796
(ii) 1886
(iii) 23497
Solution:

Question 6.
For each of the following, find the least number that must be added so that the resulting number is a perfect square.
(i) 511
(ii) 7172
(iii) 55078
Solution:

Question 7.
Find the square root of 7 correct to two decimal places; then use it to find the value of \(\sqrt { \frac { 4+\sqrt { 7 } }{ 4-\sqrt { 7 } } }\) correct to three significant digits.
Solution:

Question 8.
Find the value of √5 correct to 2 decimal places; then use it to find the square root of \(\sqrt { \frac { 3-\sqrt { 5 } }{ 3+\sqrt { 5 } } }\) correct to 2 significant digits.
Solution:

Question 9.
Find the square root of:
(i) \(\frac { 1764 }{ 2809 }\)
(ii) \(\frac { 507 }{ 4107 }\)
(iii) \(\sqrt { 108\times 2028 }\)
(iv) 0.01 + √0.0064
Solution:

Question 10.
Find the square root of 7.832 correct to :
(i) 2 decimal places
(ii) 2 significant digits.
Solution:

Question 11.
Find the least number which must be subtracted from 1205 so that the resulting number is a perfect square.
Solution:

Question 12.
Find the least number which must be added to 1205 so that the resulting number is a perfect square.
Solution:

Question 13.
Find the least number which must be subtracted from 2037 so that the resulting number is a perfect square.
Solution:

Question 14.
Find the least number which must be added to 5483 so that the resulting number is a perfect square.
Solution:

Squares and Square Roots Exercise 3C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Seeing the value of the digit at unit’s place, state which of the following can be square of a number :
(i) 3051
(ii) 2332
(iii) 5684
(iv) 6908
(v) 50699
Solution:

Question 2.
Squares of which of the following numbers will have 1 (one) at their unit’s place :
(i) 57
(ii) 81
(iii) 139
(iv) 73
(v) 64
Solution:

Question 3.
Which of the following numbers will not have 1 (one) at their unit’s place :
(i) 322
(ii) 572
(iii) 692
(iv) 3212
(v) 2652
Solution:

Question 4.
Square of which of the following numbers will not have 6 at their unit’s place :
(i) 35
(ii) 23
(iii) 64
(iv) 76
(v) 98
Solution:

Question 5.
Which of the following numbers will have 6 at their unit’s place :
(i) 262
(ii) 492
(iii) 342
(iv) 432
(v) 2442
Solution:

Question 6.
If a number ends with 3 zeroes, how many zeroes will its square have?
Solution:

Question 7.
If the square of a number ends with 10 zeroes, how many zeroes will the number have?
Solution:

Question 8.
Is it possible for the square of a number to end with 5 zeroes ? Give reason.
Solution:

Question 9.
Give reason to show that none of the numbers, given below, is a perfect square.
(i) 2162
(ii) 6843
(iii) 9637
(iv) 6598
Solution:

Question 10.
State, whether the square of the following numbers is even or odd?
(i) 23
(ii) 54
(iii) 76
(iv) 75
Solution:

Question 11.
Give reason to show that none of the numbers 640, 81000 and 3600000 is a perfect square.
Solution:

Question 12.
Evaluate:
(i) 37² – 36²
(ii) 85² – 84²
(iii) 101² – 100²
Solution:

Question 13.
Without doing the actual addition, find the sum of:
(i) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
(ii) 1 + 3 + 5 + 7 + 9 + ……………… + 39 + 41
(iii) 1 + 3 + 5 + 7 + 9 + ………………… + 51 + 53
Solution:

Question 14.
Write three sets of Pythagorean triplets such that each set has numbers less than 30.
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 12 Simple Linear Equations (Including Word Problems)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 12 Simple Linear Equations (Including Word Problems)

Simple Linear Equations Exercise 12A – Selina Concise Mathematics Class 7 ICSE Solutions

Solve the following equations :

Question 1.
x + 5 = 10
Solution:

Question 2.
2 + y = 7
Solution:

Question 3.
a – 2 = 6
Solution:

Question 4.
x – 5 = 8
Solution:

Question 5.
5 – d= 12
Solution:

Question 6.
3p = 12
Solution:

Question 7.
14 = 7m
Solution:

Question 8.
2x = 0
Solution:

Question 9.
\(\frac { x }{ 9 }\) = 2
Solution:

Question 10.
\(\frac { y }{ -12 }\) = -4
Solution:

Question 11.
8x-2 =38
Solution:

Question 12.
2x + 5 = 5
Solution:

Question 13.
5x – 1 = 74
Solution:

Question 14.
14 = 27-x
Solution:

Question 15.
10 + 6a = 40
Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.
12 = c – 2
Solution:

Question 19.
4 = x- 2.5
Solution:

Question 20.

Solution:

Question 21.

Solution:

Question 22.
p + 0.02 = 0.08

Solution:

Question 23.

Solution:

Question 24.

Solution:

Question 25.
1.3b = 39
Solution:

Question 26.

Solution:

Question 27.

Solution:

Question 28.
2a – 3 =5
Solution:

Question 29.
3p – 1 = 8
Solution:

Question 30.
9y -7 = 20
Solution:

Question 31.
2b – 14 = 8
Solution:

Question 32.

Solution:

Question 33.

Solution:

Simple Linear Equations Exercise 12B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
8y – 4y = 20
Solution:

Question 2.
9b – 4b + 3b = 16
Solution:

Question 3.
5y + 8 = 8y – 18
Solution:

Question 4.
6 = 7 + 2p -5
Solution:

Question 5.
8 – 7x = 13x + 8
Solution:

Question 6.
4x – 5x + 2x  = 28 + 3x
Solution:

Question 7.
9 + m = 6m + 8 – m
Solution:

Question 8.
24 = y + 2y + 3 + 4y
Solution:

Question 9.
19x -+ 13 -12x + 3 = 23
Solution:

Question 10.
6b + 40 = – 100 – b
Solution:

Question 11.
6 – 5m – 1 + 3m = 0
Solution:

Question 12.
0.4x – 1.2  = 0.3x + 0.6
Solution:

Question 13.
6(x+4) = 36
Solution:

Question 14.
9 ( a+ 5) + 2 = 11
Solution:

Question 15.
4 ( x- 2 ) = 12
Solution:

Question 16.
-3 (a- 6 ) = 24
Solution:

Question 17.
7 ( x-2) = 2 (2x -4)
Solution:

Question 18.
(x-4) (2x +3 ) = 2x²
Solution:

Question 19.
21 – 3 ( b-7 ) = b+ 20
Solution:

Question 20.
x (x +5 ) = x² +x + 32
Solution:

Simple Linear Equations Exercise 12C – Selina Concise Mathematics Class 7 ICSE Solutions

Solve
Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.
0.6a +0.2a = 0.4 a +8
Solution:

Question 13.
p + 1.4p= 48
Solution:

Question 14.
10% of x = 20
Solution:

Question 15.
y + 20% of y = 18
Solution:

Question 16.
x – 13% of x = 35
Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Question 21.

Solution:

Question 22.

Solution:

Question 23.
15 – 2 (5-3x ) = 4 ( x-3 ) + 13
Solution:

Question 24.

Solution:

Question 25.
21 – 3 (x – 7) = x + 20
Solution:

Question 26.

Solution:

Question 27.

Solution:

Question 28.

Solution:

Question 29.

Solution:

Question 30.
2x + 20% of x = 12.1
Solution:

Simple Linear Equations Exercise 12D – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
One-fifth of a number is 5, find the number.
Solution:

Question 2.
Six times a number is 72, find the number.
Solution:

Question 3.
If 15 is added to a number, the result is 69, find the number.
Solution:

Question 4.
The sum of twice a number and 4 is 80, find the number.
Solution:

Question 5.
The difference between a number and one- fourth of itself is 24, find the number.
Solution:

Question 6.
Find a number whose one-third part exceeds its one-fifth part by 20.
Solution:

Question 7.
A number is as much greater than 35 as is less than 53. Find the number.
Solution:

Question 8.
The sum of two numbers is 18. If one is twice the other, find the numbers.
Solution:

Question 9.
A number is 15 more than the other. The sum of of the two numbers is 195. Find the numbers.
Solution:

Question 10.
The sum of three consecutive even numbers is 54. Find the numbers.
Solution:

Question 11.
The sum of three consecutive odd numbers is 63. Find the numbers.
Solution:

Question 12.
A man has ₹ x from which he spends ₹6. If twice of the money left with him is ₹86, find x.
Solution:

Question 13.
A man is four times as old as his son. After 20 years, he will be twice as old as his son at that time. Find their present ages.
Solution:

Question 14.
If 5 is subtracted from three times a number, the result is 16. Find the number.
Solution:

Question 15.
Find three consecutive natural numbers such that the sum of the first and the second is 15 more than the third.
Solution:

Question 16.
The difference between two numbers is 7. Six times the smaller plus the larger is 77. Find the numbers.
Solution:

Question 17.
The length of a rectangular plot exceeds its breadth by 5 metre. If the perimeter of the plot is 142 metres, find the length and the breadth of the plot.
Solution:

Question 18.
The numerator of a fraction is four less than its denominator. If 1 is added to both, is numerator and denominator, the fraction becomes \(\frac { 1 }{ 2 }\) Find the fraction.
Solution:

Question 19.
A man is thrice as old as his son. After 12 years, he will be twice as old as his son at that time. Find their present ages.
Solution:

Question 20.
A sum of ₹ 500 is in the form of notes of denominations of ₹ 5 and₹ 10. If the total number of notes is 90, find the number of notes of each type.
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions