Category: ICSE

ML Aggarwal Class 6 Solutions Chapter 11 Understanding Symmetrical Shapes Ex 11.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 11 Understanding Symmetrical Shapes Ex 11.3

Question 1.
Which of the following are models for perpendicular lines?
(i) The adjacent edges of a postcard.
(ii) the lines of a railway track.
(iii) The line segment forming the letter ‘L’.
(iv) The adjacent edges of your Math book.
(v) The line segments forming the letter ‘V’.
Solution:

Question 2.
In the figure given below, line l is perpendicular to line m.

(a) Is CE = EG?
(b) Does \(\overleftrightarrow { PE } \) bisect segment \(\overline{\mathrm{BH}}\) ?
(c) Identify any two line segments for which \(\overleftrightarrow { PE } \) is the perpendicular bisector.
(d) Are these true?
(i) AC > FG
(ii) CD = GH
(iii) BC < EG.
Solution:

ML Aggarwal Class 6 Solutions Chapter 11 Understanding Symmetrical Shapes Ex 11.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 11 Understanding Symmetrical Shapes Ex 11.2

Question 1.
What fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from:
(i) 4 to 10
(ii) 2 to 5
(iii) 7 to 10
(iv) 8 to 5
(v) 11 to 5
(vi) 6 to 3
Also find the number of right angles turned in each case.
Solution:

Question 2.
Where will the hand of a clock stop if it
(i) starts at 10 and makes \(\frac{1}{2}\) of a revolution, clockwise?
(ii) starts at 4 and makes \(\frac{1}{4}\) of a revolution, clockwise?
(iii) starts at 4 and makes \(\frac{3}{4}\) of a revolution, clockwise?
Solution:

Question 3.
Where will the hand of a clock stop if it starts from
(i) 6 and turns through 1 right angle?
(ii) 8 and turns through 2 right angles?
(iii) 10 and turns through 3 right angles?
(iv) 7 and turns through 2 straight angles?
Solution:

Question 4.
What fraction of a revolution have you turned through if you stand facing
(i) north and turn clockwise to face west?
(ii)south and turn anti-clockwise to face east?
(iii) east and turn clockwise (or anti-clockwise) to face west?
Also find the number of right angles turned in each case.
Solution:

Question 5.
Match the following

Solution:

Question 6.
Classify the angles whose magnitudes are given below:
(i) 56°
(ii) 125°
(iii) 90°
(iv) 180°
(v) 215°
(vi) 328°
(vii) 89°
(viii) 178°
Solution:

Question 7.
State which of the following angles with a small letter in the following diagrams are acute, which obtuse and which are reflex:


Solution:

Question 8.
Use your protector to measure each of the angles marked in the following figures:

Solution:

Question 9.
Use your protector to measure the reflex angles marked in the following figures:

Solution:

Question 10.
Find the measure of the angle between the hands of the clock in each figure:

Solution:

Question 11.
Write the measure of the smaller angle formed by the hour and the minutes hands of a clock at 7 O’clock. Also write the measure of the other angle and also state what types of angles these are.
Solution:

Question 12.
There are two set-squares in your geometry box. What are measures of the angles formed at their corners? Do they have any angle measure that is common?
Solution:

ML Aggarwal Class 6 Solutions Chapter 8 Ratio and Proportion Ex 8.5 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 8 Ratio and Proportion Ex 8.5

Question 1.
The speed of a car is \(105 \frac{1}{5}\) km/h, find the distance covered by it in \(3 \frac{3}{5}\) hours.
Solution:

Question 2.
If the speed of a car is 50.4 km/h, find the distance covered in 3.6 hours.
Solution:

Question 3.
If a car covers a distance of 201.25 km in 3.5 hours, find the speed of the car.
Solution:

ML Aggarwal Class 6 Solutions Chapter 8 Ratio and Proportion Ex 8.4 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 8 Ratio and Proportion Ex 8.4

Question 1.
Find the value of:

Solution:

Question 2.
In a class of 60 student, 45% are girls. Find the number of boys in the class.
Solution:

Question 3.
Mr. Malkani saves 22% of his salary every month. If his salary is ₹ 12750 per month, what is his expenditure?
Solution:

Question 4.
On a rainy day, 94% of the students were present in a school, if the number of students absent on that day was 174, find the total strength of the school.
Solution:

ML Aggarwal Class 6 Solutions Chapter 11 Understanding Symmetrical Shapes Ex 11.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 11 Understanding Symmetrical Shapes Ex 11.1

Question 1.
Why is it better to use a divider and a ruler than a ruler only, while measuring the length of a line segment?
Solution:

Question 2.
In the given figure, compare the line segments with the help of a divider and fill in the blanks by using the symbol >, = or <:
(i) AB ………. CD
(ii) BC ………. AB
(iii) AC ………. BD
(iv) CD ………. BD

Solution:

Question 3.
If A, B and C are collinear points such that AB = 6 cm, BC = 4 cm and AC = 10 cm, which one of them lies between the other two?
Solution:

Question 4.
In the given figure, verify the following by measurement:
(i) AB + BC = AC
(ii) AC – BC = AB

Solution:

Question 5.
In the given figure, verify by measurement that:
(i) AC + BD = AD + BC
(ii) AB + CD = AD – BC

Solution:

Question 6.
In the given figure, measure the lengths of the sides of the triangle ABC and verify:
(i) AB + BC > AC
(ii) BC + AC > AB
(iii) AC + AB > BC

Solution:

ML Aggarwal Class 6 Solutions Chapter 10 Basic Geometrical Concept Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 10 Basic Geometrical Concept Check Your Progress

Question 1.
(i) Name all the rays shown in the given figure whose initial point is A.
(ii) Is ray \(\overrightarrow{\mathrm{AB}}\) different from ray \(\overrightarrow{\mathrm{AD}}\) ?
(iii) Is ray \(\overrightarrow{\mathrm{CA}}\) different from ray \(\overrightarrow{\mathrm{CE}}\) ?
(iv) Is ray \(\overrightarrow{\mathrm{BA}}\) different from ray \(\overrightarrow{\mathrm{CA}}\) ?
(v) Is ray \(\overrightarrow{\mathrm{ED}}\) different from ray \(\overrightarrow{\mathrm{DE}}\) ?

Solution:

Question 2.
From the given figure, write

(i) all pairs of parallel lines.
(ii) all pairs of intersecting lines.
(iii) lines whose point of intersecting is E.
(iv) collinear points.
Solution:

Question 3.
In the given figure :

(a) Name;
(i) Parallel lines.
(ii) All pairs of intersecting lines.
(iii) concurrent lines.
(b) State wheather true or false:
(i) points A, B and D are collinear.
(ii) lines AB and ED interesect at C.
Solution:

Question 4.
In context of the given figure, state whether the following statements are true (T) or false (F):

(i) Point A is in the interior of ∠AOD.
(ii) Point B is in the interior of ∠AOC.
(iii) Point C is in the exterior of ∠AOB.
(iv) Point D is in the exterior of ∠AOC.
Solution:

Question 5.
How many angles are marked in the given figure? Name them?

Solution:

Question 6.
In context of the given figure, name
(i) all triangles
(ii) all triangles having point E as common vertex.

Solution:

Question 7.
In context of the given figure, answer the following questions:

(i) Is ABCDEFG a polygon?
(ii) How many sides does it have?
(iii) How many vertices does it have?
(iv) Are \(\overline{\mathrm{AB}}\)
and \(\overline{\mathrm{FE}}\) adjacent sides?
(v) Is \(\overline{\mathrm{GF}}\)
a diagonal of the polygon?
(vi) Are \(\overline{\mathrm{AC}}, \overline{\mathrm{AD}} \text { and } \overline{\mathrm{AE}}\) diagonals of the polygon?
(vii) Is point P in the interior of the polygon?
(viii)Is point A in the exterior of the polygon?
Solution:

ML Aggarwal Class 7 Solutions Chapter 15 Visualising Solid Shapes Ex 15.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 15 Visualising Solid Shapes Ex 15.1

Question 1.
Match the following shapes with their names:


Solution:

Question 2.
Identify the nets which can be folded to form a cube (cut out copies of the nets and try it):

Solution:

Question 3.
Dice are cubes with dots on each face. Opposite faces of a die always have a total of sevend dots on them.

Here are two nets to make dice (cubes); the numbers inserted in each square indicate the number of dots in that box.

Insert suitable numbers in the blanks, remembering that the number on the opposite faces should total to 7.
Solution:

Question 4.
Can any of the following be a net for a die? If no, explain your answer:

Solution:

Question 5.
Here is an incomplete net for making a cube. Complete it in at least two different ways. Remember that a cube has six faces. How many are there in the net here? (You may use a squared paper for easy manipulation.)

Solution:

ML Aggarwal Class 6 Solutions Chapter 10 Basic Geometrical Concept Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 10 Basic Geometrical Concept Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) There is exactly one line passing through ……….. distinct points in a plane.
(ii) Two different lines in a plane either ……….. at exactly one point or are parallel.
(iii) The curves which have different beginning and end points are called ……….. curves.
(iv) A curve which does not cross itself at any point is called a ……….. curve.
(v) A simple closed curve made up entirely of line segments is called a ………..
(vi) A line segment formed by joining two non- adjacent vertices of a polygon is called its ………..
(vii) A quadrilateral has ……….. diagonals.
(viii) A lines segment has a ……….. length.
Solution:

Question 2.
Fill in the blanks with correct word(s) to make the statement true.
(i) Radius of a circle is one-half of its ………..
(ii) A radius of a circle is a line segment with one end point
at ……….. and the other end-point on
(iii) A chord of a circle is a line segment with its end points ………..
(iv) A diameter of a circle is a chord that ……….. the centre of the circle.
(v) All radii of a circle are ………..
Solution:

Question 3.
State whether the following statements are true (T) or false (F):
(i) The line segment AB is the shortest route from A to B.
(ii) A line cannot be drawn wholly on a sheet of paper..
(iii) A line segment is made of infinite (uncountable) number of points.
(iv) Two lines in a plane always intersect.
(v) Through a given point only one line can be drawn.
(vi) Two different lines can be drawn passing through two distinct points.
(vii) Every simple closed curve is a polygon.
(viii)Every polygon has atleast three sides.
(ix) A vertex of a quadrilateral lies in its interior.
(x) A line segment with its end-points lying on a circle is called a diameter of the circle.
(xi) Diameter is the longest chord of the circle.
(xii) The end-points of a diameter of a circle divide the circle into two points, each part is called a semi-circle.
(xiii) A diameter of a circle divides the circular region into two parts, each part is called a semi-circular region.
(xiv) The diameter’s of a circle are concurrent the centre of the circle is the point common to all diameters.
(xv) Every circle has unique centre and it lies inside the circle.
(xvi) Every circle has unique diameter.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (4 to 20):
Question 4.
Which of the following has no end points?
(a) a line
(b) a ray
(c) a line segment
(d) none of these
Solution:

Question 5.
Which of the following has definite length?
(a) a line
(b) a ray
(c) a line segment
(d) none of these
Solution:

Question 6.
The number of points required to name a line if
(a) 1
(b) 2
(c) 3
(d) 4
Solution:

Question 7.
The number of lines that can be drawn through a given point is
(a) 1
(b) 2
(c) 3
(d) infinitely many
Solution:

Question 8.
The number of lines that can be drawn passing through two distinct points is
(a) 1
(b) 2
(c) 3
(d) inifinitely many
Solution:

Question 9.
The maximum number of points of intersection of three lines drawn in a plane is
(a) 1
(b) 2
(c) 3
(d) 6
Solution:

Question 10.
The minimum number of points of intersection of three lines drawn in a plane is
(a) 0
(b) 1
(c) 2
(d) 3
Solution:

Question 11.
In the given figure, the number of line segment is
(a) 5
(b) 10
(c) 12
(d) 15
Solution:

Question 12.
In a polygon with 5 sides, the number of diagonals is
(a) 3
(b) 4
(c) 5
(d) 10
Solution:

Question 13.
The number of lines passing through 5 points such that no three of them are collinear are
(a) 10
(b) 5
(c) 8
(d) 20
Solution:

Question 14.
In context of the given figure, which of the following statement is correct ?
(a) B is not a point on segment \(\overline{\mathrm{AC}}\)
(b) B is the initial point of the ray \(\overrightarrow{\mathrm{AD}}\)
(c) D is a point on the ray \(\overrightarrow{\mathrm{CA}}\)
(d) C is a point on the ray \(\overrightarrow{\mathrm{BD}}\)

Solution:

Question 15.
The figure formed by two rays with same initial point is known as
(a) a line
(b) a line segment
(c) a ray
(d) an angle
Solution:

Question 16.
In the given figure, the number of angles is
(a) 3
(b) 4
(c) 5
(d) 6

Solution:

Question 17.
Which of the following statements is false?
(a) A triangle has three sides
(b) A triangle has three vertices
(c) A triangle has three angles
(d) A triangle has two diagonals
Solution:

Question 18.
Which of the following statements is false?
(a) A quadrilateral has four sides and four vertices
(b) A quadrilateral has four angles
(c) A quadrilateral has four diagonals
(d) A quadrilateral has two diagonals
Solution:

Question 19.
By joining any two points of a circle, we obtain its
(a) radius
(b) chord
(c) diameter
(d) circumference
Solution:

Question 20.
If the radius of a circle is 4 cm, then the length of its diameter is
(a) 2 cm
(b) 4 cm
(c) 8 cm
(d) 16 cm
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
Can a sector and segment of a circle coincide? If so, name it.
Solution:

Question 2.
In the given figure, find:
(i) the number of triangles pointing up.
(ii) the total number of triangles.

Solution:

Question 3.
In the given figure, find the total number of squares.

Solution:

ML Aggarwal Class 6 Solutions Chapter 8 Ratio and Proportion Ex 8.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 8 Ratio and Proportion Ex 8.3

Question 1.
If the cost of 9 m cloth is ₹378, find the cost of 4 m cloth.
Solution:

Question 2.
The weight of 36 books is 12 kg. What is weight of 75 such books?
Solution:

Question 3.
Five pens cost ₹115. How many pens can you buy in ₹207?
Solution:

Question 4.
A car consumes 8 litres of petrol in covering a distance of 100 km. How many kilometres will it travel in 26 litres of petrol?
Solution:

Question 5.
A truck requires 108 litres of diesel for covering a distance of 594 km. How much diesel will be required by the truck to cover a distance of 1650 km?
Solution:

Question 6.
A transport company charges ₹5400 to carry 80 quintals of weight. What will it charge to carry 126 quintals of weight (same distance)?
Solution:

Question 7.
42 metres of cloth is required to make 20 shirts of the same size. How much cloth will be required to make 36 shirts of that size?
Solution:

Question 8.
Cost of 5 kg of rice is ₹107.50.
(i) What will be the cost of 8 kg of rice?
(ii) What quantity of rice can be purchased in ₹64.5?
Solution:

Question 9.
Cost of 4 dozen bananas is ₹ 180. How many bananas can be purchased for ₹37.50?
Solution:

Question 10.
Aman purchases 12 pens for ₹156 and Payush buys 9 pens for ₹1108. Can you say who got the pens cheaper?
Solution:

Question 11.
Rohit made 42 runs in 6 overs and Virat made 63 runs in 7 overs. Who made more runs per over?
Solution:

Question 12.
A bus travels 160 km in 4 hours and a train travels 320 km in 5 hours at uniform speeds, then find the ratio of the distance travelled by them in one hour.
Solution:

ML Aggarwal Class 6 Solutions Chapter 8 Ratio and Proportion Ex 8.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 8 Ratio and Proportion Ex 8.2

Question 1.
Check whether the given two ratios form a proportion or not:
(i) 4 : 6 and 12 : 18
(ii) 15:45 and 40 :120
(iii) 14 : 4 and 18 : 6
(iv) 12 : 18 and 28 : 12
Solution:

Question 2.
Write true (T) or false (F) against each of the following statements:
(i) 16 : 24 = 20 : 30
(ii) 16 : 24 = 30 : 20
(iii) 21 : 6 :: 35 : 10
(iv) 5.2 : 3.9 :: 3 :4
Solution:

Question 3.
Find which of the following are in proportion:
(i) 12, 16, 6, 8
(ii) 2, 3, 4, 5
(iii) 18, 10, 9, 5
(iv) 18, 9, 10, 5
Solution:

Question 4.
Are the following statements true?
(i) 39 kg : 36 kg = 26 men : 24 men
(ii) 45 km : 60 km = 12 hours : 15 hours
(iii) 40 people : 200 people = ₹1000 : ₹5000
(iv) 7.5 litres: 15 litres = 15 children: 30 children
Solution:

Question 5.
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms when the ratios form a proportion. .
(i) 25 cm : 1 m and ₹40 : ₹ 160
(ii) 39 litres : 65 litres and 6 bottles : 10 bottles
(iii) 2 kg : 80 kg and 30 sec : 5 minutes
(iv) 200 g : 2.5 kg and ₹4 : ₹50
Solution:

ML Aggarwal Class 6 Solution Chapter 8 Ratio and Proportion Ex 8.2

ML Aggarwal Class 6 Solutions Chapter 8 Ratio and Proportion Ex 8.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 8 Ratio and Proportion Ex 8.1

Question 1.
Express the following ratios in simplest form:
(i) 20 : 40
(ii) 40 : 20
(iii) 81 : 108
(iv) 98 : 63
Solution:

Question 2.
Fill in the missing numbers in the following equivalent ratios:

Solution:

Question 3.
Find the ratio of each of the following in simplest form :
(i) 2.1 m to 1.2 m
(ii) 91 cm to 1.04m
(iii) 3.5 kg to 250gm
(iv) 60 paise to 4 rupees
(v) 1 minute to 15 seconds
(vi) 15 mm to 2 cm
Solution:

Question 4.
The length and the breadth of a rectangular park are 125 m and 60 m respectively. What is the ratio of the length to the breadth of the park?
Solution:

Question 5.
The population of village is 4800. If the numbers of females is 2160, find the ratio of males to that of females.
Solution:

Question 6.
In a class, there are 30 boys and 25 girls. Find the ratio of the numbers of
(i) boys to that of girls.
(ii) girls to that of total number of students.
(iii) boys to that of total numbers of students.
Solution:

Question 7.
In a year, Reena earns ₹ 1,50,000 and saves ₹ 50,000. Find the ratio of
(i) money she earns to the money she saves.
(ii) money that she saves to the money she spends.
Solution:

Question 8.
The monthly expenses of a student have increased from ₹350 to ₹500. Find the ratio of
(i) increase in expenses and original expenses.
(ii) original expenses to increased expenses.
(iii) increased expenses to increased in expenses.
Solution:

Question 9.
Mr Mahajan and his wife are both school teachers and earn ₹20900 and ₹ 18700 per month respectively. Find the ratio of
(i) Mr Mahajan’s income to his wife’s income.
(ii) Mrs Mahajan’s income to the total income of both.
Solution:

Question 10.
Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find the ratio of
(a) Number of students liking football to number of students liking tennis.
(b) Number of students liking cricket to total number of students.
Solution:

Question 11.
Divide ₹ 560 between Ramu and Munni in the ratio 3 : 2.
Solution:

Question 12.
Two people invested ₹ 15000 and ₹25000 respectively to start a business. They decided to share the profits in the ratio of their investments. If their profit is ₹ 12000, how much does each get?
Solution:

Question 13.
The ratio of Ankur’s money to Roma’s money is 9 : 11. if Ankur has ₹540, how much money does Roma have?
Solution:

Question 14.
The ratio of weights of tin and zinc in on alloy is 2 : 5. How much zinc is there in 31.5g of alloy?
Solution: