Category: ICSE

ML Aggarwal Class 6 Solutions Chapter 2 Whole Numbers 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 2 Whole Numbers Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) A whole number is less than all those whole numbers that lie to its on the number line.
(ii) One more than a given whole is called its
(iii) There is atleast one whole number between two whole numbers.
(iv) 738 × 335 = 738 x (300 + 30 + ……..)
(v) If a is a non-zero whole number and a × a = a, then a = ……..
(vi) …….. is the only whole number which is not a natural number.
(vii) The additive identity in whole numbers is …….
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) The predecessor of a 3-digit number is always a 3-digit number.
(ii) The successor of a 3-digit number is always a 3-digit number.
(iii) If a is any whole number, then a + a = 1.
(iv) If a is any non-zero whole number, then 0 ÷ a = 0.
(v) On adding two different whole numbers, we always get a natural number.
(vi) Between two whole numbers there is a whole number.
(vii) There is a natural number which when added to a natural number, gives that number.
(viii) If the product of two whole numbers is zero, then atleast one of them is zero.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 16):
Question 3.
The whole number which does not have a predecessor in whole number system is
(a) 0
(b) 1
(c) 2
(d) none of these
Solution:

Question 4.
The predecessor of the smallest 4-digit number is
(a) 99
(b) 999
(c) 1000
(d) 1001
Solution:

Question 5.
The predecessor of 1 million is
(a) 9999
(b) 99999
(c) 999999
(d) 1000001
Solution:

Question 6.
The product of the predecessor and the successor of the greatest 2-digit number is
(a) 9900
(b) 9800
(c) 9700
(d) none of these
Solution:

Question 7.
The sum of the successor of the greatest 3-digit number and the predecessor of the smallest 3-digit number is
(a) 1000
(b) 1100
(c) 1101
(d) 1099
Solution:

Question 8.
The number of whole numbers between 22 and 54 is
(a) 30
(b) 31
(c) 32
(d) 42
Solution:

Question 9.
The number of whole numbers between the smallest whole number and the greatest 2-digit number is
(a) 100
(b) 99
(b) 98
(d) 88
Solution:

Question 10.
If a is a whole number such that a + a = a, then a is equal to
(a) 0
(b) 1
(c) 2
(d) none of these
Solution:

Question 11.
The value of (93 × 63 + 93 × 37) is
(a) 930
(b) 9300
(c) 93000
(d) none of these
Solution:

Question 12.
Which of the following is not equal to zero?
(a) 0 × 5
(b) 0 = 5
(c) (10 – 10) + 5
(d) (5 – 0) + 5
Solution:

Question 13.
Which of the following statement is true?
(a) 21 – (13 – 5) = (21 – 13) – 5
(b) 21 – 13 is not a whole number
(c) 21 × 1 = 21 × 0
(d) 13 – 21 is not a whole number
Solution:

Question 14.
Which of the following statement is not true?
(a) Zero is the identity for multiplication of whole numbers.
(b) Addition and multiplication both are commutative for whole numbers.
(c) Addition and multiplication both are associative for whole numbers.
(d) Multiplication is distributive over addition for whole numbers.
Solution:

Question 15.
On dividing a number by 9 we get 47 as quotient and 5 as remainder. The number is
(a) 418
(b) 428
(c) 429
(d) none of these
Solution:

Question 16.
By using dot (•) pattern, which of the following numbers can be arranged in two ways namely a triangle and a rectangle?
(a) 12
(b) 11
(c) 10
(d) 9
Solution:

Higher Order Thinking Skills (HOTS)
Question 1.
The height of a slippery pole is 10 m and an insect is trying to climb the pole. The insect climbs 5 m in one minute and then slips down by 4 m. In how much time will insect reach the top?
Solution:

Question 2.
Which is greater, the sum of first twenty whole numbers or the product of first twenty whole numbers?
Solution:

Question 3.
If a whole number is divisible by 2 and 4, is it divisible by 8 also?
Solution:

ML Aggarwal Class 7 Solutions for ICSE Maths Model Question Paper 3 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 3

(Based on Chapters 1 to 9)
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 comprises of 10 questions of 4 marks each and
• 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 are of 1 mark each.
Question 1.
The number of integers between -16 and 5 is
(a) 19
(b) 20
(c) 21
(d) 22
Solution:

Question 2.
50 m 5 cm is the same as
(a) 50.5 m
(b) 50.05 m
(c) 50.005 m
(d) 5.05 m
Solution:

Question 3.

Solution:

Question 4.
The number 5,540,000,000,000 in the scientific notation can be written as:
(a) 554 × 10¹⁰
(b) 55.4 × 10¹¹
(c) 5.54 × 10¹²
(d) 5.54 × 10¹¹
Solution:

Question 5.
The number of unlike terms in the expression 5x²y – 2xy² – 2yx² + 3y(xy + y²) + 7 is
(a) 3
(b) 4
(c) 5
(d) 6
Solution:

Question 6.
x = -2 is a solution of the equation
(a) 2x + 5 = 9
(b) 3x – 1 = 5
(c) 4x + 3 = 1
(d) 5x + 12 = 2
Solution:

Question 7.
The ratio of the number of girls to the number of boys in a class is 5 : 4. If there are 16 boys in the class, then the number of students in the class is
(a) 20
(b) 32
(c) 36
(d) 45
Solution:

Question 8.
If 12% of a number is 9, then the number is
(a) 36
(b) 48
(c) 60
(d) 75
Solution:

Section – B

Question numbers 9 to 14 are of 2 marks each.
Question 9.
Using suitable properties, evaluate:
238 × (-44) + (-238) × 56.
Solution:

Question 10.
State whether each of the following statement is true or false for the sets P and Q where P = {letters of TITLE} and Q = {letters of LITTLE}
(i) P ↔ Q
(ii) P = Q
Solution:

Question 11.
Evaluate: -3\(\frac { 3 }{ 8 }\) – (-2\(\frac { 1 }{ 6 }\))
Solution:

Question 12.
Simplify and express in the exponential form: (4³ × 3⁶) ÷ (16 × 9²).
Solution:

Question 13.
If I earn ₹ 75000 per month and spend ₹ 40000 per year for helping poor students then find the ratio of the money spent on helping poor students and the annual income.
Solution:

Question 14.
If ₹ 4000 amounts to ₹ 5000 in 2 years, find the rate of simple interest per annum.
Solution:

Section – C

Question numbers 15 to 24 are of 4 marks each.
Question 15.
Simplify:

Solution:

Question 16.
Vikram’s monthly salary is ₹ 12750. He spends \(\frac { 1 }{ 5 }\) of his salary on food and out of the remaining, he spends \(\frac { 1 }{ 4 }\) on rent and \(\frac { 1 }{ 6 }\) on the education of children. Find
(i) how much he spends on each item?
(ii) how much money is still left with him?
Solution:

Question 17.
Insert five rational numbers between \(\frac { -2 }{ 5 }\) and \(\frac { -1 }{ 3 }\)
Solution:

Question 18.
Afzal can walks 5\(\frac { 3 }{ 4 }\) km in one hour. How much distance will he cover in 2 hours 40 minutes? What are the health advantages of having a brisk walk?
Solution:

Question 19.
If a vehicle covers a distance of 57.72 km in 3.7 litres of petrol. How much distance will it cover in one litre of petrol?
Solution:

Question 20.
The perimeter of a triangle is 5 – 3x + 7x² and two of its sides are 2x² + 3x – 2 and 3x² – x + 3. Find the third side of the triangle.
Solution:

Question 21.

Solution:

Question 22.
Solve the equation: 3(2x – 1) – 2(2 – 5x) = 1
Solution:

Question 23.
If 74% of the population of a village is illiterate and the number of literate people is 2158, then find the population of the village.
Solution:

Question 24.
Simplify:

Solution:

Section – D

Question numbers 25 to 29 are of 6 marks each.
Question 25.
If we represent the distance above the ground by a positive rational number and that below the ground by a negative rational number, then answer the following question:
An elevator descends into a mine shaft at the rate of 4\(\frac { 3 }{ 4 }\) metre per minute. If it begins to descend from 7\(\frac { 1 }{ 2 }\) metre above the ground, what will be its position after 18 minutes from the ground?
Solution:

Question 26.
In a competition, the question paper consists of 25 questions. 4 marks are awarded for every correct answer, 2 marks are deducted for every incorrect answer and no marks for not attempting a question. If Vaishali scored 58 marks and got 17 correct answers, how many questions she attempted incorrectly? How many questions she did not attempt?
Solution:

Question 27.
Divide ₹ 216000 into two parts such that one-fourth of one part is equal to one-fifth of the other part. Find the two parts.
Solution:

Question 28.
If a table is sold for ₹ 437 at a loss of 8%, find its cost price. At what price must it be sold to gain 10%?
Solution:

Question 29.
Solve the inequality:
3 – 2x ≥ x – 10, x ∈ N.
Also, represent its solution set on the number line.
Solution:

ML Aggarwal Class 6 Solutions Chapter 2 Whole Numbers Ex 2.3 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 2 Whole Numbers Ex 2.3

Question 1.
Using shorter method, find
(i) 3246 + 9999
(ii) 7501 + 99999
(iii) 5377 – 999
(iv) 25718 – 9999
(v) 123 × 999
(vi) 203 × 9999
Solution:

Question 2.
Without using a diagram, find
(i) 9th square number
(ii) 7th triangular number
Solution:

Question 3.
(i) Can a rectangular number be a square number?
(ii) Can a triangular number be a square number?
Solution:

Question 4.
Observe the following pattern and fill in the blanks:
1 × 9 + 1 = 10
12 × 9 + 2= 110
123 × 9 + 3 = 1110
1234 × 9 + 4 = ……….
12345 × 9 + 5 = …………..
Solution:

Question 5.
Observe the following pattern and fill in the blanks:
9 × 9 + 7 = 88
98 × 9 + 6 = 888
987 × 9 + 5 = 8888
9876 x 9 + 4 = …………
98765 × 9 + 3 = ……….
Solution:

ML Aggarwal Class 6 Solutions Chapter 2 Whole Numbers Ex 2.2 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 2 Whole Numbers Ex 2.2

Question 1.
Fill in the blanks to make each of the following a true statement:
(i) 378 + 1024 = 1024 + …….
(ii) 337 + (528 + 1164) = (337 + ……..) + 1164
(iii) (21 + 18) + ……….. = (21 + 13) + 18
(iv) 3056 + 0 = ……….. = 0 + 3056
Solution:

Question 2.
Add the following numbers and check by reversing the order of addends :
(i) 3189 + 53885
(ii) 33789 + 50311.
Solution:

Question 3.
By suitable arrangements, find the sum of:
(i) 311,528,289
(ii) 723, 834, 66, 277
(iii) 78, 203, 435, 7197, 422.
Solution:

Question 4.
Fill in the blanks to make each of the following a true statement:
(i) 375 × 57 = 57 × ……….
(ii) (33 × 16) × 25 = 33 × (…….. × 25)
(iii) 37 × 24 = 37 × 18 + 37 × …………
(iv) 7205 × 1 = …………. = 1 × 7205
(v) 366 × 0 =
(vi) …………… × 579 = 0
(vii) 473 × 108 = 473 × 100 + 473 × ………….
(viii) 684 × 97 = 684 × 100 – …………… × 3
(ix) 0 ÷= 5 =
(x) (14 – 14) ÷ 7 = ………….
Solution:

Question 5.
Determine the following products by suitable arrangement:
(i) 4 × 528 × 25
(ii) 625 × 239 × 16
(iii) 125 × 40 × 8 × 25
Solution:

Question 6.
Find the value of the following:
(i) 54279 × 92 + 54279 × 8
(ii) 60678 × 262 – 60678 × 162
Solution:

Question 7.
Find the following products by using suitable properties:
(i) 739 × 102
(ii) 1938 × 99
(iii) 1005 × 188
Solution:

Question 8.
Divide 7750 by 17 and check the result by division algorithm.
Solution:

Question 9.
Find the number which when divided by 38 gives the quotient 23 and remainder 17.
Solution:

Question 10.
Which least number should be subtracted from 1000 so that the difference is exactly divisible by 35.
Solution:

Question 11.
Which least number should be added to 1000 so that 53 divides the sum exactly.
Solution:

Question 12.
Find the largest three-digit number which is exactly divisible by 47.
Solution:

Question 13.
Find the smallest five-digit number which is exactly divisible by 254.
Solution:

Question 14.
A vendor supplies 72 litres of milk to a student’s hostel in the morning and 28 litres of milk in the evening every day. If the milk costs?39 per litre, how much money is due to the vendor per day?
Solution:

Question 15.
State whether the following statements are true (T) or false (F):
(i) If the product of two whole numbers is zero, then atleast
one of them will be zero.
(ii) If the product of two whole numbers is 1, then each of
them must be equal to 1.
(iii) If a and b are whole numbers such that a ≠ 0 and b ≠ 0,
then ab may be zero.
Solution:

Question 16.
Replace each * by the correct digit in each of the following:

Solution:

ML Aggarwal Class 7 Solutions for ICSE Maths Model Question Paper 2 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 2

(Based on Chapters 4 to 7)
Time allowed: 1 Hour
Maximum Marks: 25

Instructions

• Questions 1-2 carry 1 mark each
• Questions 3-5 carry 2 marks each
• Questions 6-8 carry 3 marks each
• Questions 9-10 carry 4 marks each.

Choose the correct answer from the given four options (1-2):
Question 1.
The expression \(\left( \frac { 1 }{ 3 } \right) ^{ 9 }\) × (3⁴)² is equal to
(a) 3⁹
(b) 3
(c) \(\left( \frac { 1 }{ 3 } \right) ^{ 2 }\)
(d) \(\frac { 1 }{ 3 }\)
Solution:

Question 2.
On selling an article for ₹ 100, Renu gains ₹ 20. Her gain percentage is
(a) 25%
(b) 20%
(c) 16\(\frac { 2 }{ 3 }\) %
(d) 15%
Solution:

Question 3.
Ravi donated ₹ 3⁶ to a blind school and Rashmi donated ₹ 6³ to an orphanage. Who donated more money?
Solution:

Question 4.
Find the cardinal number of the set A where A = {x | x is a two-digit number, the sum of whose digits is 11}.
Solution:

Question 5.
Find the fourth proportional to 8, 24, 25.
Solution:

Question 6.

Solution:

Question 7.
18% of the apples in a basket go bad. If there are 123 good apples in the basket, find the total number of apples in the basket.
Solution:

Question 8.
A natural number has been divided into two parts in the ratio 8 : 5. If the difference of two parts is 24, find the number and the two parts.
Solution:

Question 9.
If 2.5 kg of apples cost ₹ 187.5, then how much quantity of apples can be bought for ₹ 330?
Solution:

Question 10.
What sum of money will amount to ₹ 2875 in 3 years at 5% per annum simple interest?
Solution:

ML Aggarwal Class 7 Solutions Chapter 13 Practical Geometry Ex 13 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 13 Practical Geometry Ex 13

Question 1.
Draw a line, say l, take a point P outside it. Through P, draw a line parallel to l using ruler and compasses only.
Solution:
Steps of Construction:

Question 2.
Draw a line l. Draw a perpendicular to l at any point on l. On this perpendicular choose a point A, 3.5 cm away from line l. Through A, draw a line m parallel to l.
Solution:

Question 3.
Let l be a line and P be a point not on l. Through P, draw a line m parallel to l. Now join P to any point Q on l. Choose any other point R on m. Through R, draw a line parallel to PQ. If this line meets l at S, then what shape do the two sets of parallel lines inclose?
Solution:

Question 4.
Construct a triangle ABC, given that
(i) AB = 5 cm, BC = 6 cm and AC = 7 cm
(ii) AB = 4.5 cm, BC = 5 cm and AC = 6 cm.
Solution:

(ii) Steps of Construction:

Question 5.
Construct a triangle PQR given that PQ = 5.4 cm, QR = PR = 4.7 cm. Name the triangle.
Solution:

Question 6.
Construct a triangle LMN such that the length of each side is 5.3 cm. Name the triangle.
Solution:

Question 7.
Construct a triangle ABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠ABC and name the triangle.
Solution:

Question 8.
Construct a triangle PQR, given that PQ = 3 cm, QR = 5.5 cm and ∠PQR = 60°.
Solution:

Question 9.
Construct ∆DEF such that DE = 5 cm, DF = 3 cm and m∠EDF = 90°.
Solution:

Question 10.
Construct an isosceles triangle in which the length of each of its equal sides is 6.5 cm and the angle between them is 110°. Measure base angles.
Solution:

Question 11.
Construct triangle XYZ if it is given that XY = 6 cm, ∠X = 30° and ∠Y = 100°.
Solution:

Question 12.
Construct a triangle PQR given that PQ = 4.9 cm, ∠P = 45° and ∠Q = 60°. Measure ∠R.
Solution:

Question 13.
Construct a triangle ABC such that AB = 4.1 cm, ∠B = 90° and hypotenuse AC = 5.2 cm.
Solution:

Question 14.
Construct a right-angled triangle whose hypotenuse is 6 cm long and one of the legs is 4 cm long.
Solution:

ML Aggarwal Class 7 Solutions Chapter 12 Congruence of Triangles 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 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress

Question 1.
State, giving reasons, whether the following pairs of triangles are congruent or not:

Solution:

Question 2.
Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not. In case of congruence, give reasons and write in symbolic form:

Solution:

Question 3.
In the given figure, ABC is an isosceles triangle with AB = AC and AD is one of its altitudes.
(i) State the three pairs of equal parts in ∆ADB and ∆ADC.
(zz) Is ∆ADB = ∆ADC? Give reasons.
(iii) Is ∠B = ∠C? Why?
(iv) Is BD = DC? Why?

Solution:

Question 4.
In the given figure, OA bisects ∠A and ∠ABO = ∠OCA. Prove that OB = OC.

Solution:

Question 5.
In the given figure , prove that
(i) AB = FC
(ii) AF = BC.

Solution:

ML Aggarwal Class 7 Solutions Chapter 12 Congruence of Triangles 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 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) Two line segments are congruent if ……….
(ii) Among two congruent angles, one has a measure of 63°; the measure of the other angle is ……….
(iii) When we write ∠A = ∠B, we actually mean ………
(iv) The side included between ∠M and ∠N of ∆MNP is ……….
(v) The side QR of ∆PQR is included between angles ……….
(vi) If two triangles ABC and PQR are congruent under the correspondence A ↔ R, B ↔ P and C ↔ Q, then in symbolic form it can be written as ∆ABC = ………
(vii) If ∆DEF = ∆SRT, then the correspondence between vertices is ……….
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) All circles are congruent.
(ii) Circles having equal radii are congruent.
(iii) Two congruent triangles have equal areas and equal perimeters.
(iv) Two triangles having equal areas are congruent.
(v) Two squares having equal areas are congruent.
(vi) Two rectangles having equal areas are congruent.
(vii) All acute angles are congruent.
(vii)All right angles are congruent.
(ix) Two figures are congruent if they have the same shape.
(x) A two rupee coin is congruent to a five rupee coin.
(xi) All equilateral triangles are congruent.
(xii) Two equilateral triangles having equal perimeters are congruent.
(xii) If two legs of one right triangle are equal to two legs of another right angle triangle, then the two triangles are congruent by SAS rule.
(xiv) If three angles of two triangles are equal, then triangles are congruent.
(xv) If two sides and one angle of one triangle are equal to two sides and one angle of another triangle, then the triangle are congruent.
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 14):
Question 3.
Which one of the following is not a standard criterion of congruency of two triangles?
(a) SSS
(b) SSA
(c) SAS
(d) ASA
Solution:

Question 4.
If ∆ABC = ∆PQR and ∠CAB = 65°, then ∠RPQ is
(a) 65°
(b) 75°
(c) 90°
(d) 115°
Solution:

Question 5.
If ∆ABC = ∆EFD, then the correct statement is
(a) ∠A = ∠D
(b) ∠A = ∠F
(c) ∠A = ∠E
(d) ∠B = ∠E
Solution:

Question 6.
If ∆ABC = ∆PQR, then the correct statement is
(a) AB = QR
(b) AB = PR
(c) BC = PR
(d) AC = PR
Solution:

Question 7.
If ∠D = ∠P, ∠E = ∠Q and DE = PQ, then ∆DEF = ∆PQR, by the congruence rule
(a) SAS
(b) ASA
(c) SSS
(d) RHS
Solution:

Question 8.
In ∆ABC and ∆PQR, BC = QR and ∠C = ∠R. To establish ∆ABC = ∆PQR by SAS congruence rule, the additional information required is
(a) AC = PR
(b) AB = PR
(c) CA = PQ
(d) AB = PQ
Solution:

Question 9.
In the given figure, the lengths of the sides of two triangles are given. The correct statement is
(a) ∆ABC = ∆PQR
(b) ∆ABC = ∆QRP
(c) ∆ABC = ∆QPR
(d) ∆ABC = ∆RPQ

Solution:

Question 10.
In the given figure, M is the mid-point of both AC and BD. Then
(a) ∠1 = ∠2
(b) ∠1 = ∠4
(c) ∠2 = ∠4
(d) ∠1 = ∠3

Solution:

Question 11.
In the given figure, ∆PQR = ∆STU. What is the length of TU?
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) cannot be determined

Solution:

Question 12.
In the given figure, ∆ABC and ∆DBC are on the same base BC. If AB = DC and AC = DB, then which of the following statement is correct?
(a) ∆ABC = ∆DBC
(b) ∆ABC = ∆CBD
(c) ∆ABC = ∆DCB
(d) ∆ABC = ∆BCD

Solution:

Question 13.
The two triangles shown in the given figure are:
(a) congruent by AAS rule
(b) congruent by ASA rule
(c) congruent by SAS rule
(d) not congruent.

Solution:

Question 14.
In .the given figure, ∆ABC = ∆PQR. The values of x and y are:
(a) x = 63, y = 35
(b) x = 77, y = 35
(c) x = 35, y = 77
(d) x = 63, y = 40

Solution:

Higher Order Thinking Skills (HOTS)

Question 1.
If all the three altitudes of a triangle are equal, then prove that it is an equilateral triangle.
Solution:

Question 2.
In the given fig., if BA || RP, QP || BC and AQ = CR, then prove that ∆ABC = ∆RPQ.

Solution:

ML Aggarwal Class 7 Solutions Chapter 17 Data Handling 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 7 Solutions for ICSE Maths Chapter 17 Data Handling Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) The number of times a particular observation occurs in a data is called ………. of that observation.
(ii) The frequency of 9 is written symbolically as ………. using tally marks.
(iii) In a bar graph, the height (or length) of a bar is equal to or proportional to the frequency of the ……….
(iv) Double bar graphs help us in comparing two ……….. at a glance.
(v) The most common representative value of a statistical data is the ……….. of the data.
(vi) Mode of a data is the observation which occurs …………. number of times in the given data.
(vii) The arithmetic mean of first 10 natural numbers is ……….
(viii) When a die is rolled, the probability of getting a number more than 5 is ………..
(ix) The probability of an ……….. event is 0.
(x) The probability of a ………… event is 1.
(xi) Median is one of the observations is the data if the number of observations is ………..
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) Mean is the value of observation that occurs most frequently.
(ii) The range of the data -3, 4, -5, 1, -2, 0 is -9.
(iii) Mode is always one of the numbers in a data.
(iv) There is only one mode for a given data.
(v) Mean is always one of the numbers in a data.
(vi) The data 6, 4, 3, 8,9, 12, 13, 9 has mean 9.
(vii) Median of the data may or may not be from given given data.
(viii) The measures of central tendency may not lie between the maximum and minimum value of data.
(ix) If the extreme observations on both ends of a data arranged in ascending order are removed, then the median gets affected.
(x) The probability of getting an ace out of a deck of playing cards can be greater than 1.
(xi) Median of 4, 5, 9, 2, 6, 8, 7 is 2.
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 18):
Question 3.
Which of the following is not a central tendency of a data?
(a) Mean
(b) Median
(c) Mode
(d) Range
Solution:

Question 4.
The difference between the highest and the lowest observations in a data is its
(a) frequency
(b) width
(c) range
(d) mode
Solution:

Question 5.
A cricketer scored 38, 79, 25, 52, 0, 8, 100 runs in seven innings. The range of the runs scored is
(a) 100
(b) 92
(c) 52
(d) 38
Solution:

Question 6.
If the mean of 3, 1, 5, x and 9 is 4, then the value of x is
(a) 6
(b) 4
(c) 2
(d) 0
Solution:

Question 7.
The number of goals scored by a football team in a series of matches are: 3, 5, 0, 1, 2, 0, 4, 1, 3. The median of this data is
(a) 3
(b) 2
(c) 2.5
(d) 1
Solution:

Question 8.
The median of the first 49 natural numbers is
(a) 24
(b) 25
(c) 25.5
(d) 26
Solution:

Question 9.
The mean of three different natural numbers is 40. If lowest is 19, what could be highest possible number of remaining two numbers?
(a) 40
(b) 71
(c) 81
(d) 100
Solution:

Question 10.
The mode of the data:
3, 5, 1, 2, 0, 2, 3, 5, 0, 2, 1, 6 is
(a) 6
(b) 3
(c) 2
(d) 1
Solution:

Question 11.
The probability of a sure event is
(a) 0
(b) \(\frac { 1 }{ 4 }\)
(c) \(\frac { 1 }{ 2 }\)
(d) 1
Solution:

Question 12.
The probability of an impossible event is
(a) -1
(b) 0
(c) \(\frac { 1 }{ 2 }\)
(d) 1
Solution:

Question 13.
The probability of a newly born baby to be a girl is
(a) 0
(b) \(\frac { 1 }{ 4 }\)
(c) \(\frac { 1 }{ 2 }\)
(d) 1
Solution:

Question 14.
The probability of selecting letter G from the word GIRL is
(a) 1
(b) \(\frac { 1 }{ 2 }\)
(c) \(\frac { 1 }{ 4 }\)
(d) \(\frac { 1 }{ 3 }\)
Solution:

Question 15.
The probability of selecting a vowel from the word ALPHABET is
(a) \(\frac { 1 }{ 2 }\)
(b) \(\frac { 1 }{ 7 }\)
(c) \(\frac { 2 }{ 7 }\)
(d) \(\frac { 3 }{ 8 }\)
Solution:

Question 16.
When a die is thrown, the probability of getting a composite number is
(a) \(\frac { 1 }{ 2 }\)
(b) \(\frac { 1 }{ 3 }\)
(c) \(\frac { 1 }{ 4 }\)
(d) \(\frac { 2 }{ 3 }\)
Solution:

Question 17.
A bag contains 5 white balls and 10 black balls. The probability of drawing a white ball from the bag is
(a) \(\frac { 5 }{ 10 }\)
(b) \(\frac { 5 }{ 15 }\)
(c) \(\frac { 10 }{ 15 }\)
(d) 1
Solution:

Question 18.
In a school, only 2 out of 5 students can participate in a quiz. What is the probability that a student picked at random makes it to the competition?
(a) 50%
(b) 40%
(b) 30%
(d) 20%
Solution:

Value Based Questions

Question 1.
The following table shows the time (in hours) spent by a student of class VII in a day:

Draw a bar graph to represent the above data. Is it correct to watch T.V. for 3 hours and studying just 2 hours daily?
Solution:

Question 2.
In a game, a fair coin is tossed. A person is paid ₹ 5 if he gets head and he pays ₹ 2 if he gets tail. Find the probability of winning ₹ 5. Is gambling a good way of earning money?
Solution:

Higher Order Thinking Skills (HOTS)

Question 1.
The mean of 6 observations is 17.5. If five of them are 14, 9, 23, 25 and 10, find the sixth observation.
Solution:

Question 2.
The mean height of 10 students is 151.8 cm. Two more students of heights 157.6 cm and 154.4 cm join the group. What is the new mean height?
Solution:

Question 3.
The following observations have been arranged in ascending order. If the median of the data is 13, find the value of x:
3, 6, 7, 10, x, x + 4, 19, 20, 25, 28
Solution:

Question 4.
If the mean of the data (given below) is 4.5, then find the median of the data:
5, 7, 7, 8, x, 3, 1, 5, 4, 2
Solution:

Question 5.
Find the probability of getting 53 Sunday’s in a leap year.
Solution:

ML Aggarwal Class 7 Solutions Chapter 16 Perimeter and Area Ex 16.1 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 16 Perimeter and Area Ex 16.1

Question 1.
ABCD is a square of side 24 cm. EF is parallel to BC and AE = 15 cm. By how much does
(i) the perimeter of AEFD exceed the perimeter of EBCF?
(ii) the area of AEFD exceed the area of EBCF?

Solution:

Question 2.
Nagma runs around a rectangular park 180 m long and 120 m wide at the rate of 7.5 km/ hour. In how much time will she complete five rounds?
Solution:

Question 3.
The area of a rectangular plot is 540 m². if its length is 27 m, find its breadth and perimeter.
Solution:

Question 4.
The perimeter of a rectangular field is 151 m. If its breadth is 32 m, find its length and area.
Solution:

Question 5.
The area of a rectangular plot is 340 m² and its breadth is 17 m. Find the cost of surrounding the plot with a fence at ₹ 5.70 per meter.
Solution:

Question 6.
The area of a square park is the same as that of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.
Solution:

Question 7.
A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side? Also, find which shape encloses more area and by how much?
Solution:

Question 8.
A door of breadth 1 m and height 2 m is fitted in a wall. The length of the wall is 4.5 m and the height is 3.6 m. Find the cost of whitewashing the wall, if the rate of whitewashing the wall is ₹ 20 per m².
Solution:

Question 9.
A rectangular park is 45 m long and 30 m wide. A path 2.5 m wide is constructed outside the park. Find the area of the path.
Solution:

Question 10.
A carpet of size 5 m × 2 m has 25 cm wide red border. The inner part of the carpet is blue in colour. Find the area of the blue portion. What is the ratio of the areas of red portion to blue portion?
Solution:

Question 11.
A verandah of width 2.25 m is constructed all along outside a room which is 5.5 m long and 4 m wide. Find:
(i) the area of the verandah.
(ii) the cost of cementing the floor of the verandah at the rate of ₹ 200 per m2.
Solution:

Question 12.
Two crossroads, each of width 5 m, run at right angles through the centre of a rectangular park of length 70 m and breadth 45 m and parallel to its sides. Find the area of the roads. Also, find the cost of constructing the roads at the rate of ₹ 105 per m2.
Solution:

Question 13.
A rectangular room is 10 m long and 7.5 m wide. Find the cost of covering the floor with carpet 1.25 m wide at ₹ 250 per metre.
Solution:

Question 14.
Find the cost of flooring a room 6.5 m by 5 m with square tiles of side 25 cm at the rate of ₹ 9.40 per tile.
Solution:

Question 15.
The floor of a room is in the shape of a square of side 4.8 m. The floor is to be covered with square tiles of perimeter 1.2 m. Find the cost of covering the floor if each tile costs ₹ 27.
Solution:

Question 16.
A rectangular plot of land is 50 m wide. The cost of fencing the plot at the rate of ₹ 18 per metre is ₹ 4680. Find:
(i) the length of the plot.
(ii) the cost of leveling the plot at the rate of ₹ 7.6 per m².
Solution:

ML Aggarwal Class 7 Solutions Chapter 15 Visualising Solid Shapes 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 7 Solutions for ICSE Maths Chapter 15 Visualising Solid Shapes Check Your Progress

Question 1.
Identify the nets which can be used to make a tetrahedron (cut out copies of the nets and try it):

Solution:

Question 2.
If four cubes each with 2 cm edge are placed side by side, what would the dimensions of the resultant cuboid be?
Solution:

Question 3.
Two dice are placed side by side as shown in the given figure. What would be the total on the face opposite to
(i) 5 + 6
(b) 4 + 3?

Solution:

Question 4.
For the structures given below sketch the front, side, and top view:

Solution: