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ML Aggarwal Class 6 Solutions Chapter 1 Knowing Our Numbers Ex 1.4 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 1 Knowing Our Numbers Ex 1.4

Question 1.
Round off each of the following numbers to their nearest tens:
(i) 77
(ii) 903
(iii) 70 1205
(iv) 999
Solution:

Question 2.
Estimate each of the following numbers to their nearest hundreds:
(i) 1246
(ii) 32057
(iii) 53961
(iv) 555555
Solution:

Question 3.
Estimate each of the following numbers to their nearest thousands:
(i) 5706
(ii) 378
(iii) 47,599
(iv) 1,09,736
Solution:

Question 4.
Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens):
(i) 439 + 334 + 4317
(ii) 8325 – 491
(iii) 1,08,734-47,599
(iv) 4,89,348 – 48,365
Solution:

Question 5.
Estimate each of the following by rounding off each number nearest to its greatest place:
(i) 730 + 998
(ii) 5,290 + 17,986
(iii) 796-314
(iv) 28,292 – 21,496
Solution:

Question 6.
Estimate the following products by rounding off each of its factors nearest to its greatest place:
(i) 578 × 161
(ii) 9650 × 27
Solution:

Question 7.
Estimate the following products by rounding off each of its factors nearest to its hundreds place:
(i) 5281 × 3491
(ii) 1387 × 888
Solution:

ML Aggarwal Class 6 Solutions Chapter 1 Knowing Our Numbers Ex 1.1 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 1 Knowing Our Numbers Ex 1.3

Question 1.
In a particular year, a company manufactured 8570435 bicycles and next year it manufactured 8756430 bicycles. In which year more bicycles were manufactured and by how many?
Solution:

Question 2.
What number must be subtracted from 1,02,59,756 to get 77,63,835?
Solution:

Question 3.
The sale receipt of a company during a year was ₹ 30587850. Next year it increased by ₹ 6375490. What was the total sale receipt of the company during these two years?
Solution:

Question 4.
A machine manufactures 23875 screws per day. How many screws did it produce iff the year 2012? Assume that the machine worked on all the days of the year.
Solution:

Question 5.
A merchant had ₹ 78,592 with him. He placed an order for puchasing 54 bicycles at ₹ 970 each. How much money will remain with him after the purchase?
Solution:

Question 6.
Amitabh is 1 m 82 cm tall and his wife is 35 cm shorter than him. What is his wife’s height?
Solution:

Question 7.
The mass of each gas cylinder is 21 kg 270g. What is total mass of 28 such cylinders?
Solution:

Question 8.
In order to make a shirt, 2 m 25 cm cloth is needed. What length of cloth is required to make 18 such shirts?
Solution:

Question 9.
The total mass of 12 packets of sweets, each of the same size, is 15 kg 600 g. What is the mass of each such packet?
Solution:

Question 10.
A vessel has 4 litres 500 millilitres of orange juice. In how many glasses, each of 25 mL capacity, can it be filled?
Solution:

Question 11.
To stitch a trouser, 1 m 30 cm cloth is needed. Out of 25 m cloth, how many trousers can be stitched and how much cloth will remain?
Solution:

ML Aggarwal Class 6 Solutions Chapter 1 Knowing Our Numbers Ex 1.2 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 1 Knowing Our Numbers Ex 1.2

Question 1.
Use the appropriate symbol < or > to fill in the blanks:
(i) 173 … 189
(ii) 1058 … 1074
(iii) 8315 … 8037
Solution:

Question 2.
In each of the following pairs of numbers, state which number is smaller:
(i) 553,503
(ii) 41338,1139
(iii) 25431,24531
Solution:

Question 3.
Find the greatest and the smallest numbers in each row:
(i) 71834, 75284, 571, 2333, 594
(ii) 9853, 7691, 9999, 12002.
Solution:

Question 4.
Arrange the following numbers in ascending order:
304, 340, 34, 43, 430
Solution:

Question 5.
Arrange the following numbers in descending order:
53, 7333, 553, 7529, 335.
Solution:

Question 6.
Write all possible 2-digits numbers that can be formed by using the digits 2, 3 and 4. Repetition of digits is not allowed. Also find their sum.
Solution:

Question 7.
Write all possible 3-digits numbers using the digits 3, 1 and 5. Repetition of digits is not allowed.
Solution:

Question 8.
Write all possible 3-digits numbers using the digits 7, 0 and 6. Repetition of digits is not allowed. Also, find their sum.
Solution:

Question 9.
Write all possible 2-digit numbers using the digits 4, 0 and 9. Repetition of digits is not allowed. Also find their sum.
Solution:

Question 10.
Write all possible 2-digit numbers that can be formed by using the digit 3, 7 and 9. Repetition of digits is allowed.
Solution:

Question 11.
Write all possible numbers using the digits 3,1 and 5. Repetition of digits is not allowed.
Solution:

Question 12.
How many 6-digit numbers are there in all ?
Solution:

Question 13.
Write down the greatest number and the smallest number of 4-digits that can be formed by the digits 7, 5,0 and 4 using each digit only once.
Solution:

Question 14.
Rearrange the digits of the number 5701024 to get the largest number and the smallest number of 7 digits.
Solution:

Question 15.
Keeping the place value of digit 3 in the number 730265 same, rearrange
the digits of the given number to get the largest number and smallest number of 6 digits.
Solution:

Question 16.
Form the smallest and greatest 4-digit numbers by using any one digit twice from the digits:
(i) 5, 2, 3, 9
(ii) 6, 0, 1, 4
(iii) 4, 6, 1, 5, 8.
Solution:

Question 17.
Write
(i) the greatest number of 6 digits
(ii) the smallest number of 7 digits. Also find their difference.
Solution:

Question 18.
Write the greatest 4-digit number of distinct digits.
Solution:

Question 19.
Write the smallest 4-digit number of distinct digits.
Solution:

Question 20.
Write the greatest 6-digit number using three different digits.
Solution:

Question 21.
Write the smallest 7-digit number using four different digits.
Solution:

Question 22.
Write the greatest and the smallest 4-digit numbers using four different digits with the conditions as given:
(i) Digit 7 is always at units place.
(ii) Digit 4 is always at tens place.
(iii) Digit 9 is always at hundreds place.
(iv) Digit 2 is always at thousands place.
Solution:

ML Aggarwal Class 6 Solutions Chapter 1 Knowing Our Numbers Ex 1.1 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 1 Knowing Our Numbers Ex 1.1

Question 1.
Write the smallest natural number. Can you write the largest natural number?
Solution:

Question 2.
Fill in the blanks:
(i) 1 lakh = … ten thousand
(ii) 1 million = … hundred thousand
(iii) 1 crore = … ten lakh
(iv) 1 billion =… hundred million.
Solution:

Question 3.
Insert commas suitably and write each of the following numbers in words in the Indian system and the International system of numeration.
(i) 506723
(ii) 180018018
Solution:

Question 4.
Write the following numbers in expanded form:
(i) 750687
(ii) 5032109
Solution:

Question 5.
Write the following number in figures:
(i) Seven lakh three thousand four hundred twenty.
(ii) Eighty crore twenty three thousand ninety three.
Also write the above numbers in the place value chart.
Solution:

Question 6.
Write each of the following numbers in numeral form and place commas correctly:
(i) Seventy three lakh seventy thousand four hundred seven.
(ii) Nine crore five lakh forty one.
(iii) Fifty eight million four hundred twenty three thousand two hundred two.
Solution:

Question 7.
Write the face value and place value of the digit 6 in the number 756032.
Solution:

Question 8.
Find the difference between the place value and the face value of the digit 9 in the number 229301.
Solution:

Question 9.
Determine the difference of the place value of two 7’s in 37014472 and write it in words in International system.
Solution:

Question 10.
Determine the product of place value and the face value of the digit 4 in the number 5437.
Solution:

Question 11.
Find the difference between the number 895 and that obtained on reversing its digits.
Solution:

ML Aggarwal Class 7 Solutions for ICSE Maths Model Question Paper 6 acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 ICSE Maths Model Question Paper 6

(Based on Chapters 10 to 17)
Time allowed: 2\(\frac { 1 }{ 2 }\) Hours
Maximum Marks: 90

General Instructions

• All questions are compulsory.
• The question paper consists of 29 questions divided into four sections A, B, C, and D.
• Section A comprises of 8 questions of 1 mark each.
• Section B comprises of 6 questions of 2 marks each.
• Section C comparises of 10 questions of 4 marks each.
• Section D comprises of 5 questions of 6 marks each.
• Question numbers 1 to 8 in Section A is multiple choice questions where you are to select one correct option out of the given four.

Section – A

Question numbers 1 to 8 is of 1 mark each.
Question 1.
In the given figure, if ∠AOC and ∠COB form a linear pair, then the value of x
(a) 60
(b) 55
(c) 50
(d) 45

Solution:

Question 2.
An exterior angle of a triangle is 118°. If one of the two interior opposite angle is 54°, then the other interior opposite angle is
(a) 62°
(b) 54°
(c) 64°
(d) 59°
Solution:

Question 3.
In a right-angled triangle, the lengths of two legs are 8 cm and 15 cm. The length of the hypotenuse is
(a) 23 cm
(b) 20 cm
(c) 17 cm
(d) 17 m
Solution:

Question 4.
If ΔABC = ΔPRQ, the the correct statement is
(a) AB = PQ
(b) ∠B = ∠Q
(c) ∠C = ∠R
(d) AC = PQ
Solution:

Question 5.
The number of lines that can be drawn parallel to a given line l through a point outside the line l is
(a) 0
(b) 1
(c) 2
(d) infinitely many
Solution:

Question 6.
If the area of a circle is numerically equal to its circumference, then the diameter of the circle is
(a) 2 units
(b) 4 units
(c) 6 units
(d) 8 units
Solution:

Question 7.
A quadrilateral having exactly two lines of symmetry and rotational symmetry of order 2 is a
(a) square
(b) parallelogram
(c) rhombus
(d) kite
Solution:

Question 8.
A mode is the observation of the data
(a) whose position is in the middle
(b) having maximum value
(c) occurring a maximum number of times
(d) occurring a minimum number of times
Solution:

Section – B

Question numbers 9 to 14 are of 2 marks each.
Question 9.
An angle is 30° more than one-half of its complement. Find the angle.
Solution:

Question 10.
In the given figure, find the value of x.

Solution:

Question 11.
A die is thrown once. Find the probability of getting
(i) a prime number
(ii) a composite number
Solution:

Question 12.
You want to show that ΔDEF = ΔPQR by SAS congruence rule.
It is given that ∠E = ∠Q, you need to have
(i) EF = …….
(ii) PQ = ………

Solution:

Question 13.
In the given figure, two adjacent sides of a parallelogram are 15 cm and 10 cm. If the distance between the longer sides is 8 cm, find the
(i) area of parallelogram
(ii) the distance between the shorter sides.

Solution:

Question 14.
Find the mean age of six students whose ages (in years) are:
15, 13, 16, 13, 14, 16.
Solution:

Section – C

Question numbers 15 to 24 are of 4 marks each.
Question 15.
In the given figure, lines l and m are parallel. Find the values of x, y, and z.

Solution:

Question 16.
In the given figure, BC = AC. Find the value of x.

Solution:

Question 17.
If the lengths of the two sides of a triangle are 6 cm and 8.5 cm, then what can be the length of the third side?
Solution:

Question 18.
In the given figure, AD is perpendicular bisector of \(\bar { BC }\).
(i) State three pairs of equal parts in ∆ABD and ∆ACD.
(ii) Is ∆ABD = ∆ACD? Give reasons.
(iii) Is ABC an isosceles triangle? Give reasons.

Solution:

Question 19.
Draw a line, say AB, take a point P outside line AB. Through P, draw a line parallel to line AB using ruler and compasses only.
Solution:

Question 20.
In the given figure, ABCD is a rectangle with AB = 20 cm and BC = 14 cm. Two semicircles are cut from each of two breadths as diameters. Find
(i) the area of the shaded region
(ii) the perimeter of the shaded region.
Take π = \(\frac { 22 }{ 7 }\).

Solution:

Question 21.
Draw the reflection of the letter E in the given mirror line shown dotted.

Solution:

Question 22.
Three cubes each with edge 2 units are placed side by side to form a cuboid. Find the dimensions of the cuboid so formed and draw an isometric sketch of this cuboid.
Solution:

Question 23.
Draw two nets of a regular tetrahedron.
Solution:

Question 24.
A boy scored the following marks in various class tests during a year, each test is marked out of 20:
15, 17, 16, 7, 9, 12, 14, 16, 3, 19, 12, 16
(i) Arrange the marks in ascending order.
(ii) What are his modal marks?
(iii) What are his median marks?
(iv) What are his mean marks?
Solution:

Section – D

Question numbers 25 to 29 are of 6 marks each.
Question 25.
In the given figure, all measurements are in centimeters. If AD is perpendicular to BC, find the length of B.

Solution:

Question 26.
In the adjoining figure, show that ΔABC = ΔDBC. Hence, find the values of x and y.

Solution:

Question 27.
By using ruler and compasses only, construct a triangle ABC with BC = 7.5 cm, ∠B = 60° and ∠A = 90°.
Solution:

Question 28.
Anjali took a wire of length 88 cm and bent it into the shape of a circle. Find the area enclosed by that circle. If the same wire is bent in the shape of a square, then find the area enclosed by that square. Which shape encloses more area and by how much?
Take π = \(\frac { 22 }{ 7 }\)
Solution:

Question 29.
Given below is the data of school going students (boys and girls):

Draw a double bar graph to represent the above data and hence answer the following questions:
(i) Which mode of transport is used by more students?
(ii) Which mode of transport is used by more number of girls that the number of boys?
What values are being promoted by using a bicycle as a mode of transport?
Solution: