Category: ICSE

ML Aggarwal Class 6 Solutions Chapter 10 Basic Geometrical Concept Ex 10.4 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 10 Basic Geometrical Concept Ex 10.4

Question 1.
In the given figure, identify:
(i) the centre of the circle
(ii) three radii
(iii) a diameter
(iv) a chord
(v) two points in the interior
(vi) a point in the exterior
(vii) a sector
(viii) a segment

Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) Every diameter of a circle is also a chord.
(ii) Every chord of a circle is also a diameter.
(iii) Two diameters of a circle will necessarily intersect.
(iv) The centre of the circle is always in its interior.
Solution:

ML Aggarwal Class 6 Solutions Chapter 7 Decimals 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 7 Decimals Check Your Progress

Question 1.
Convert the following decimal numbers into fractions (in lowest terms).
(i) 6.015
(ii) 0.876
(iii) 23.375
Solution:

Question 2.
Write the following fractions as decimals numbers:

Solution:

Question 3.
Arrange the following decimal numbers in ascending order:
(i) 123.8, 74.205, 74.209, 7.4209
(ii) 85.01, 85.1, 85.001, 85.103
Solution:

Question 4.
Arrange the following decimal numbers in desending order:
(i) 6.45, 4.65, 6.405, 64.5, 6.54
(ii) 73.5, 35.7, 7.35, 7.53, 7.035
Solution:

Question 5.
If the school bags of Garima and Nakul weigh 5.2 kg and 4.832 kg respectively, find
(i) the total weight.
(ii) the difference in weight of the bags.
Solution:

Question 6.
Evaluate the following:
(i) 31.42 – 17.853 -6.43
(ii) 13.01 – 5.428 – 3.703 + 2.99.
Solution:

Question 7.
By how much does the sum of 15.453 and 31.647 exceed the sum of 18.47 and 19.506?
Solution:

Question 8.
Namita travels 20 km 50 m every day. Out of this she travels 10 km 200 m by bus and the rest by auto. How much distance does she travel by auto?
Solution:

Question 9.
Ravi purchased 5 kg 400 g rice, 2 kg 20 g sugar and 10 kg 850 g flour (aata). Find the total weight of his purchases.
Solution:

Question 10.
1 kg of pure milk contains 0.263 kg of fat. How much fat is there 15.5 kg of milk?
Solution:

Question 11.
The product of two numbers is 15.275. If one number is 4.7, find the other.
Solution:

ML Aggarwal Class 6 Solutions Chapter 10 Basic Geometrical Concept Ex 10.3 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 10 Basic Geometrical Concept Ex 10.3

Question 1.
Draw rough diagrams to illustrate the following:
(i) open simple curve
(ii) closed simple curve
(iii) open curve that is not simple
(iv) closed curve that is not simple.
Solution:

Question 2.
Consider the given figure and answer the following questions:
(i) Is it a curve?
(ii) Is it a closed curve?
(iii) Is it a polygon?

Solution:

Question 3.
Draw a rough sketch of a triangle ABC. Mark a point P in its interior and a point Q in its exterior. Is the point A in its exterior or in its interior?
Solution:

Question 4.
Draw a rough sketch of a quadrilateral PQRS. Draw its diagonals. Name them.
Solution:

Question 5.
In context of the given figure:
(i) Is it a simple closed curve?
(ii) Is it a quadrilateral?
(iii) Draw its diagonals and name them.
(iv) State which diagonal lies in the interior and which diagonal lies in the exterior of the quadrilateral.

Solution:

Question 6.
Draw a rough sketch of a quadrilateral KLMN. State,
(i) two pairs of opposite sides
(ii) two pairs of opposite angles
(iii) two pairs of adjacent sides
(iv) two pairs of adjacent angles.

Solution:

ML Aggarwal Class 6 Solutions Chapter 10 Basic Geometrical Concept Ex 10.2 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 10 Basic Geometrical Concept Ex 10.2

Question 1.
How many angles are shown in the following figure? Name them.

Solution:

Question 2.
In the given figure, name the point(s)
(i) In the interior of ∠DOE
(ii) In the exterior of ∠EOF
(iii) On ∠EOF

Solution:

Question 3.
Draw rough diagrams of two angles such that they have
(i) One point in common.
(ii) Two points in common.
(iii) One ray in common.
Solution:

ML Aggarwal Class 6 Solutions Chapter 7 Decimals 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 7 Decimals Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) The decimal point in a decimal number is placed between ones digit and ……….. digit.
(ii) The place value of the digit 3 in the decimal number 15.437 is ………
(iii) The decimal number 27.025 has ………. decimal places.
(iv) The decimal number 5.06 is read as five point
(v) If an object is divided into 1000 equal parts, then its 27 parts are represented by ………
(vi) Two decimal numbers having different number of …………. are called unlike decimal numbers.
(vii) 4 tens, 3 ones, 2 tenths, 0 hundredths and 5 thousandths in decimal form is written as ……
(viii)The smallest decimal number upto three decimal places is ……….
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) Every decimal number can be represented by a point on a number line.
(ii) Fractions with denominator 10, 100, 1000, are called decimal fractions.
(iii) A decimal number having 3 decimal places can be written as a fraction with denominator 1000.
(iv) The value of a decimal number remains the same if any number of extra zeros are written at the end of a decimal number.
(v) If a decimal number is multiplied by 10, then the decimal point moves by one place to the left.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 23):
Question 3.
Five and seven hundredths is equal to
(a) 5.7
(b) 5.07
(c) 5.70
(d) 0.57
Solution:

Question 4.
Sicty three thousandths is equal to
(a) 0.63
(b) 0.603
(c) 0.063
(d) 0.630
Solution:

Question 5.
\(3 \frac{7}{100}\) is equal to :
(a) 3.07
(b) 3.7
(c) 3.70
(d) 3.007
Solution:

Question 6.
\(5 \frac{3}{1000}\) is equal to
(a) 5.03
(b) 5.3
(c) 5.003
(d) 5.0003
Solution:

Question 7.
The place value of the digit 7 in the decimal number 5.0378 is

Solution:

Question 8.
The place value of the digit 0 in the decimal number 13.405 is

Solution:

Question 9.
The value of \(5+\frac{7}{10}+\frac{3}{1000}\) is
(a) 5.73
(b) 5.703
(c) 5.073
(d) 0.753
Solution:

Question 10.
The value of \(\frac{3}{25}\) is
(a) 1.2
(b) 0.012
(c) 0.12
(d) none of these
Solution:

Question 11.
The value of \(5 \frac{1}{25}\) is
(a) 5.4
(b) 5.25
(c) 5.04
(d) 5.004
Solution:

Question 12.
The decimal number not equivalent to 5.7 is
(a) 5.70
(b) 5.07
(c) 5.700
(d) 5.7000
Solution:

Question 13.
1 g is equal to
(a) 0.1 kg
(b) 0.01 kg
(c) 0.001 kg
(d) 0.0001 kg
Solution:

Question 14.
2 km 7 m is equal to
(a) 2.7 km
(b) 2.07 km
(c) 2.007 km
(d) 2.0007 km
Solution:

Question 15.
Among 2.34, 2 .43, 2.344 and 2.4, the greatest number is
(a) 2.34
(b) 2.43
(c) 2.344
(d) 2.4
Solution:

Question 16.
5.2 – 3.6 is equal to
(a) 0.16
(b) 2.6
(c) 0.26
(d) 1.6
Solution:

Question 17.
A decimal number lying between 2.2 and 2.22 is
(a) 2.12
(b) 2.23
(c) 2.219
(d) 2.3
Solution:

Question 18.
0.023 lies between
(a) 0.2 and 0.3
(b) 0.02 and 0.03
(c) 0.029 and 0.03
(d) 0.026 and 0.024
Solution:

Question 19.
0.7499 lies between
(a) 0.7 and 0.74
(b) 0.759 and 0.799
(c) 0.749 and 0.75
(d) 0.74992 and 0.75
Solution:

Question 20.
Which of the following decimal numbers is the greatest?
(a) 0.182
(b) 0.038
(c) 0.219
(d) 0.291
Solution:

Question 21.
Which of the following decimal numbers is the smallest?
(a) 0.108
(b) 1.08
(c) 0.801
(d) 0.81
Solution:

Question 22.
0.003 × 0.2 is equal to
(a) 0.6
(b) 0.06
(c) 0.006
(d) 0.0006
Solution:

Question 23.
0.45 + 0.9 is equal to
(a) 50
(b) 5
(c) 0.5
(d) 0.05
Solution:

Higher Order Thinking Skills(Hots)
Question 1.
On her birthday, Ayushi is taking her 5 friends to a movie and treats them with cold costs. The cost of a ticket is ₹150 and a cold drink cost ₹28.50. How much Ayushi has to spend?
Solution:

Question 2.
Write digits in the boxes of the number : \(3 \square 6 \square .8 \square \square\) to obtain
(i) greatest possible number
(ii) smallest possible number. Repetition of digits in a number is not allowed.
Solution:

ML Aggarwal Class 6 Solutions Chapter 10 Basic Geometrical Concept Ex 10.1 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 10 Basic Geometrical Concept Ex 10.1

Question 1.
How many lines can be drawn through a given point?
Solution:

Question 2.
How many lines can be drawn through two distinct given points?
Solution:

Question 3.
How many lines can be drawn through three collinear points?
Solution:

Question 4.
Mark three non-collinear points A, B and C in your note-book. Draw lines through these points taking two at a time and name these lines. How many such different lines can be drawn?
Solution:

Question 5.
Use the figure to name :
(i) Five point
(ii) Aline
(iii) Four rays
(iv) Five line segments

Solution:

Question 6.
Use the figure to name:

(i) Line containing point E.
(ii) Line passing through A.
(iii) Line on which point O lies.
(iv) Two pairs of intersecting lines.
Solution:

Question 7.
From the given figure, write

(i) collinear points
(ii) concurrent lines and their points of concurrence.
Solution:

Question 8.
In the given figure, write

(i) all pairs of parallel lines.
(ii) all pairs of intersecting lines,
(iii) concurrent lines.
(iv) collinear points.
Solution:

Question 9.
Count the number of line segments drawn in each of the following figures and name them:

Solution:

Question 10.
(i) Name all the rays shown in the following figure whose initial points are A, B and C respectively.

(ii) Is ray AB different from ray AD?
(iii) Is ray CA different from ray CE?
(iv) Is ray BA different from ray CA?
(v) Is ray ED different from ray DE?
Solution:

Question 11.
Consider the following figure of line \(\overleftrightarrow { MN } \). Says whether following statements are true or false in context of the given figure.

(i) Q, M, O, N and P are points on the line
\(\overleftrightarrow { MN } \).
(ii) M, O and N are points on a line segment
\(\overline{\mathrm{MN}}\).
(iii) M and N are end points of line segment
\(\overline{\mathrm{MN}}\) .
(iv) O and N are end points of line segment
\(\overline{\mathrm{OP}}\).
(v) M is a point on the ray \(\overline{\mathrm{OP}}\).
(vi) M is one of the end points of line segment
\(\overline{\mathrm{QO}}\).
(vii) Ray \(\overrightarrow { OP } \) is same as ray
\(\overrightarrow { OM } \).
(viii)Ray \(\overrightarrow { OM } \) is not opposite to ray
\(\overrightarrow { OP } \).
(ix) Ray \(\overrightarrow { OP } \) is different from ray
\(\overrightarrow { QP } \).
(x) O is not an initial point of ray \(\overrightarrow { OP } \).
(xi) N is the initial point of \(\overrightarrow { N } \) and
\(\overrightarrow { NM } \).
Solution:

ML Aggarwal Class 6 Solutions Chapter 7 Decimals Ex 7.5 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 7 Decimals Ex 7.5

Question 1.
Express as rupees using decimals:
(i) 75 paise
(ii) 1025 paise
(ii) 63 rupees 9 paise
Solution:

Question 2.
Express as cm using decimals:
(i) 8 mm
(ii) 263 mm
(iii) 13 cm 3 mm
Solution:

Question 3.
Express as metres using decimals:
(i) 6 cm
(ii) 528 cm
(iii) 7 m 55 cm
Solution:

Question 4.
Express as km using decimals:
(i) 5 m
(ii) 888 m
(iii) 15 km 88 m
Solution:

Question 5.
Express as kg using decimals:
(i) 37 g
(ii) 100 g
(iii) 5 kg 8 g
Solution:

Question 6.
Anita bought 2 m 70 cm cloth for her shirt and 2 m 85 cm cloth for her trouser. Find the total length of the cloth bought by her.
Solution:

Question 7.
Sunita travelled 15 km 268 m by bus, 7 km 7 m by car and 500 m on foot in order to reach her school. How far is her school from her residence?
Solution:

Question 8.
Rahul bought 4 kg 90 g apples, 2 kg 60 g grapes and 5 kg 300 g mangoes. Find the total weight of all the fruits he bought.
Solution:

Question 9.
Rani had ₹18.50. She bought one ice¬cream for ₹11.75. How much money does she have now?
Solution:

Question 10.
Tina had 20 m 5 cm long cloth. She cuts 4m 50 cm length of cloth from this for making a curtain. How much cloth is left with her?
Solution:

Question 11.
Ruby bought a watermelon weighing 5 kg 300 g. Out of which she gave 2 kg 680 g to her neighbour. What is the weight of the watermelon left with Ruby?
Solution:

Question 12.
The cost of 1 metre of cloth is ₹35.80. What will be cost of 9.8 metres of cloth?
Solution:

Question 13.
Farida bought some bags of cement, each weighing 49.8 kg. If the total weight of all the bags is 1792.8 kg, how many bags did she buy?
Solution:

ML Aggarwal Class 6 Solutions Chapter 12 Symmetry 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 12 Symmetry Check Your Progress

Question 1.
Draw the line (or lines) of symmetry, if any, of the following figures/shapes and count their number:

Solution:

Question 2.
Draw the line (or lines) of symmetry, if any, of the following pictures of playing cards and count their number:

Solution:

Question 3.
Write the letters of the word ‘ALGEBRA’ which have no line of symmetry.
Solution:
L, G, R

Question 4.
On a squared paper, sketch the following:
(i) A triangle with a horizontal line of symmetry but no vertical line of symmetry.
(ii) A quadrilateral with both horizontal and vertical lines of symmetry.
(iii) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.
(iv) A hexagon with exactly two lines of symmetry.
Solution:

Question 5.
Copy the following figures on a squared paper and complete each figure such that the resultant figure is symmetrical about the dotted line (or lines):

Solution:

Question 6.
State whether the following statement is true or false. Justify your answer:
“A straight line dividing a figure into two identical parts is necessarily a line of symmetry.”
Solution:

Question 7.
Find whether the figure on the left side is the reflection of the figure on right side. If not, draw the correct figure.

Solution:

ML Aggarwal Class 7 Solutions Chapter 14 Symmetry Ex 14.1 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 14 Symmetry Ex 14.1

Question 1.
Draw all lines of symmetry, if any, in each of the following figures:

Solution:

Question 2.
Copy the figures with a punched hole(s) and draw all the axes of symmetry in each of the following:

Solution:

Question 3.
In the following figure, mark the missing hole(s) in order to make them symmetrical about the dotted line:

Solution:

Question 4.
In the following figures, the mirror line (line of symmetry) is given as dotted line. Complete each figure by performing reflection in the mirror (dotted) line and name the figure you complete:

Solution:

Question 5.
Copy the adjoining figure.
Take any one diagonal as a line of symmetry and shade a few more squares to make the figure symmetric about a diagonal. Is there more than one way to do that? Will the figure be symmetric about both the diagonals?

Solution:

Question 6.
Draw the reflection of the following figures/letter in the given mirror line shown dotted:

Solution:

Question 7.
What other names can you give to the line of symmetry of
(i) an isosceles triangle
(ii) rhombus
(iii) circle?
Solution:

ML Aggarwal Class 6 Solutions Chapter 7 Decimals Ex 7.4 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 7 Decimals Ex 7.4

Question 1.
Evaluate the following:
(i) 3.7 × 4.5
(ii) 12.08 × 9.3
(iii) 238.06 × 7.5
(iv) 0.79 × 32.4
(v) 3.6 × 1.4 × 0.7
(vi) 9.01 × 2.5 × 1.6
Solution:

Question 2.
Work out the following:
(i) 70.756 ÷ 4
(ii) 2.46 ÷ 6
(iii) 3.016 ÷ 8
(iv) 8.64 ÷ 3.6
(v) 72.8 ÷ 0.04
(vi) 0.144 ÷ 0.02
Solution:

Question 3.
Multiply each of the following numbers by 10, 100 and 1000 orally ;
(i) 4.7
(ii) 3.45
(iii) 23.01
Solution:

Question 4.
Divide each of the following numbers by 10, 100 and 1000 (orally):
(i) 4.7
(ii) 3.45
(iii) 23.01
Solution:

ML Aggarwal Class 6 Solutions Chapter 9 Algebra 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 9 Algebra Check Your Progress

Question 1.
Look at the following matchstick pattern of polygons. Complete the table. Also write the general rule that gives the number of matchsticks.

Solution:

Question 2.
Write an algebraic expression for each of the following:
(i) If 1 metre cloth costs ₹ x, then what is cost of 6 metre cloth?
(ii) If the cost of a notebook is ₹ x and the cost of a book is ₹ y, then what is the cost of 5 notebooks and 2 books?
(iii) The score of Ragni in Mathematics is 23 more than two-third of her score in English. If she scores x marks in English, what is her score in Mathematics?
(iv) If the length of a side of a regular pentagon is x cm, then what is the perimeter of the pentagon?
Solution:

Question 3.
When x = 4 and y = 2, find the value of:
(i) x + y
(ii) x – y
(iii) x² + 2
(iv) x² – 2xy + y²
Solution:

Question 4.
When a = 3 and b = -1, find the value of 2a³ – b⁴ + 3a²b³.
Solution:

Question 5.
When a = 3, b = 0, c = -2, find the values of:
(i) ab + 2bc + 3ca + 4abc
(ii) a³ + b³ + c³ – 3abc
Solution:

Question 6.
Solve the following linear equations:
(i) 2x – \(1 \frac{1}{2}=4 \frac{1}{2}\)
(ii) 3(y – 1) = 2(y + 1)
(ii) n – 3 = 5n + 21
(iv) \(\frac{1}{3}(7 x-1)=\frac{1}{4}\)
Solution: