Category: ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling

ICSE SolutionsSelina ICSE SolutionsML Aggarwal Solutions

APlusTopper.com provides step by step solutions for Selina Concise ICSE Solutions for Class 7 Mathematics. You can download the Selina Concise Mathematics ICSE Solutions for Class 7 with Free PDF download option. Selina Publishers Concise Mathematics for Class 7 ICSE Solutions all questions are solved and explained by expert mathematic teachers as per ICSE board guidelines.

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Data Handling Exercise 21A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Consider the following numbers :
68, 76, 63, 75, 93, 83, 70, 115, 82, 105, 90, 103, 92, 52, 99, 73, 75, 63, 77 and 71.
(i) Arrange these numbers in ascending order.
(ii) What the range of these numbers?
Solution:
(i) When the above data are written in ascending order. We get,
52, 63, 63, 68, 70, 71, 73, 75, 75, 76, 77, 82, 83, 90, 92, 93, 99, 103, 105, 115
(ii) Range of given numbers = Largest number – Smallest number
= 115-52 = 48

Question 2.
Represent the following data in the form of a frequency distribution table :
16, 17, 21, 20, 16, 20, 16, 18, 17, 21, 17, 18, 19, 17, 15, 15, 19, 19, 18, 17, 17, 15, 15, 16, 17, 17, 19, 18, 17, 16, 15, 20, 16, 17, 19, 18, 19, 16, 21 and 17.
Solution:
The frequency distribution for these data will be as shown below :

Question 3.
A die was thrown 20 times and following scores were recorded.
2, 1, 5, 2, 4, 3, 6, 1, 4, 2, 5, 1, 6, 2, 6, 3, 5, 4, 1 and 3.
Prepare a frequency table for the scores.
Solution:
The frequency table for the scores will be as shown below :

Question 4.
Following data shows the weekly wages (in ₹) of 10 workers in a factory.
3500, 4250, 4000, 4250, 4000, 3750, 4750, 4000, 4250 and 4000
(i) Prepare a frequency distribution table.
(ii) What is the range of wages (in ₹)?
(iii) How many workers are getting the maximum wages?
Solution:
(i) The frequency table for the wages of 10 workers will be as shown below :

(ii) Range of wages (₹) = ₹4750 – ₹3500 = ₹1250
(iii) One

Question 5.
The marks obtained by 40 students of a class are given below :
80, 10, 30, 70, 60, 50, 50, 40, 40, 20, 40, 90, 50, 30, 70, 10, 60, 50, 20, 70, 70, 30, 80, 40,20, 80, 90, 50, 80, 60, 70, 40, 50, 60, 90, 60, 40, 40, 60 and 60
(i) Construct a frequency distribution table.
(ii) Find how many students have marks equal to or more than 70?
(iii) How many students obtained marks below 40?
Solution:
(i) The frequency distribution table will be shown as below :

(ii)Students have marks equal to or more than 70 = 5 + 4 + 3 = 12
(iii) Students obtained marks below 40 = 2 + 3 + 3 = 8 students

Question 6.
Arrange the following data in descending order:
3.3, 3.2, 3.1, 3.7, 3.6, 4.0, 3.5, 3.9, 3.8, 4.1, 3.5, 3.8, 3.7, 3.9 and 3.4.
(i) Determine the range.
(ii) How many numbers are less than 3.5?
(iii) How many numbers are 3.8 or above?
Solution:
Descending order : 4.1, 4.0, 3.9, 3.9, 3.8, 3.8, 3.7, 3.7, 3.6, 3.5, 3.5, 3.4, 3.3, 3.2, 3.1
(i) Range = 4.1 – 3.1 = 1
(ii) Number less than 3.5 = 4
i.e., 3.4, 3.3, 3.2, 3.1
(iii) Number are 3-8 or above = 6
i.e., 3.8, 3.8, 3.9, 3.9, 4.0, 4.1

Data Handling Exercise 21B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the mean of 53, 61, 60, 67 and 64.
Solution:
Mean of 53, 6i, 60, 67 and 64

Question 2.
Find the mean of first six natural numbers.
Solution:
First six natural numbers are : 1, 2, 3, 4, 5, 6

Question 3.
Find the mean of first ten odd natural numbers.
Solution:
First ten odd natural numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

Question 4.
Find the mean of all factors of 10.
Solution:
The factor of 10 are 2 and 5

Question 5.
Find the mean of x + 3, x + 5, x + 7, x + 9 and x + 11.
Solution:
Mean of x + 3, x + 5, x + 7, x + 9 and x + 11

Question 6.
If different values of variable x are 19.8,15.4,13.7,11.71,11.8, 12.6,12.8,18.6,20.5 and 2.1, find the mean.
Solution:
19. +15.4 +13.7 +11.71 +11.8 +12.6 + 12.8 +18.6 + 20.5 +21.1

Question 7.
The mean of a certain number of observations is 32. Find the resulting mean, if each observation is,
(i) increased by 3
(ii) decreased by 7
(iii) multiplied by 2
(iv) divided by 0.5
(v) increased by 60%
(vi) decreased by 20%
Solution:

Question 8.
The pocket expenses (per day) of Anuj, during a certain week, from monday to Saturday were ₹85.40, ₹88.00, ₹86.50, ₹84.75, ₹82.60 and ₹87.25. Find the mean pocket expenses per day.
Solution:
The pocket expenses (per day) during a certain week are : ₹85.40, ₹88.00, ₹86.50, ₹84.75, ₹82.60 and ₹87.25

∴Anuj expenses per day = ₹85.75

Question 9.
If the mean of 8, 10, 7, x + 2 and 6 is 9, find the value of x.
Solution:
The mean 8, 10, 7, x + 2 and 6 is 9

Question 10.
Find the mean of first six multiples of 3.
Solution:
The six multiples of 3 are 3, 6, 9, 12, 15, 18

Question 11.
Find the mean of first five prime numbers.
Solution:
The first five prime numbers are 2, 3, 5, 7, 11

Question 12.
The mean of six numbers :x-5,x- 1, x, x + 2, x + 4 and x + 12 is 15. Find the mean of first four numbers.
Solution:
The mean of six numbers are x – 5, x – 1,x,x + 2,x + 4 and x + 12 is 15

Question 13.
Find the mean of squares of first five whole numbers.
Solution:
First five whole numbers are 0, 1, 2, 3, 4
Then square the whole prime numbers

Question 14.
If the mean of 6, 4, 7, p and 10 is 8, find the value of p.
Solution:
The mean of 6, 4, 7, p and 10 is 8

Question 15.
Find the mean of first six multiples of 5.
Solution:
Six multiples of 5 are :
5, 10, 15, 20, 25 and 30

Question 16.
The rainfall (in mm) in a city on 7 days of a certain week is recorded as follows

Find the total and average (mean) rainfall for the week.
Solution:
The rainfall in a city on 7 days are 0.5, 2.7, 2.6, 0.5, 2, 5.8, 1.5

Question 17.
The mean of marks scored by 100 students was found to be 40, later on it was discovered that a score of 53 was misread as 83. Find the correct mean.
Solution:
Mean of 40 observations = 100
Total sum of 40 observations = 100 × 40 = 4000
Incorrect total of 40 observation is = 4000
Correct total of 40 observations = 4000 – 83 + 53 = 3970
∴ Correct mean = \(\frac { 3970 }{ 100 }\) = 39.70

Question 18.
The mean of five numbers is 27. If one number is excluded, the mean of remaining numbers is 25. Find the excluded number.
Solution:
Mean of 5 observations = 27
Total sum of 5 observations = 27 × 5 = 135
On excluding an observation, the mean of remaining 6 observations = 25
⇒ Total of remaining 4 observations = 25 x 4 = 100
⇒ Included observation = Total mean of 5 observations – Total mean of 4 observations
= 135- 100 = 35

Question 19.
The mean of 5 numbers is 27. If one new number is included, the new mean is 25. Find the included number.
Solution:
Mean of 5 observations = 27
Total sum of 5 observations = 27 x 5 = 135
On including an observation the mean of 6 observation = 25 x 6 = 150
⇒ Included observations = Total Mean of 6 observations – Total mean of 5 observations = 150- 135 = 15

Question 20.
Mean of 5 numbers is 20 and mean of other 5 numbers is 30. Find the mean of all the 10 numbers taken together.
Solution:
The mean of 5 number = 20
Then, mean of other 5 number = 30

Question 21.
Find the median of:
(i) 5,7, 9, 11, 15, 17,2, 23 and 19
(ii) 9, 3, 20, 13, 0, 7 and 10
(iii) 18, 19, 20, 23, 22, 20, 17, 19, 25 and 21
(iv) 3.6, 9.4, 3.8, 5.6, 6.5, 8.9, 2.7, 10.8, 15.6, 1.9 and 7.6.
Solution:

Question 22.
Find the mean and the mode for the following data :

Solution:
We prepare the table given below :

Question 23.
Find the mode of:
(i) 5, 6, 9, 13, 6, 5, 6, 7, 6, 6, 3
(ii) 7, 7, 8, 10, 10, 11, 10, 13, 14
Solution:
(i) Arranging the Numbers in ascending order : 3, 5, 5, 6, 6, 6, 6, 6, 7, 9, 13
Mostly repeated term = 6
∴ Mode = 6
(ii) Arranging the Numbers in ascending order = 7, 7, 8, 10, 10, 10, 11, 13, 14
Mostly repeated term =10
∴ Mode = 10

Question 24.
Find the mode of :

Solution:
(i) Since, the frequency of number 18 is maximum
∴Mode = 18
(ii) Since, the frequency of number 41 is maximum
∴ Mode = 41

Question 25.
The heights (in cm) of 8 girls of a class are 140,142,135,133,137,150,148 and 138 respectively. Find the mean height of these girls and their median height.
Solution:
Arranging in ascending order : 133, 135, 137, 138, 140, 142, 148, 150
Here, number of girls = 8 which is even

Question 26.
Find the mean, the median and the mode of:
(i) 12, 24, 24, 12, 30 and 12
(ii) 21, 24, 21, 6, 15, 18, 21, 45, 9, 6, 27 and 15.
Solution:

Question 27.
The following table shows the market positions of some brands of soap.
Draw a suitable bar graph :

Solution:

Question 28.
The birth rate per thousand of different countries over a particular period of time is shown below.

Solution:

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles (Including Construction of angles)

Selina Publishers Concise Maths Class 7 ICSE Solutions Chapter 14 Lines and Angles (Including Construction of angles)

ICSE SolutionsSelina ICSE SolutionsML Aggarwal Solutions

APlusTopper.com provides step by step solutions for Selina Concise ICSE Solutions for Class 7 Mathematics. You can download the Selina Concise Mathematics ICSE Solutions for Class 7 with Free PDF download option. Selina Publishers Concise Mathematics for Class 7 ICSE Solutions all questions are solved and explained by expert mathematic teachers as per ICSE board guidelines.

Selina Class 7 Maths ICSE SolutionsPhysicsChemistryBiologyGeographyHistory & Civics

POINTS TO REMEMBER

1. POINT : A point: is a mark of position; which has no length, no breadth and no thickness. It, in general, is represented by a capital letter as shown alongside.

2. LINE : A line has length, but no breadth or thickness.

“The given figure shows a line AB in which two arrow-heads in opposite directions show that can be extended infinitely in both the directions.
A line may be straight or curved but when we say a line’ it means a straight line only.

3. RAY : It is a straight line which stats from a fixed point and moves in the same direction.

The given figure shows a ray\(\xrightarrow { AB }\) with fixed initial point A ‘and moving in the direction AB.

4. LINE SEGMENT : It is a straight line with its both ends fixed. The given figure shows a line segment, whose both the ends A and B are fixed.

(i) The adjoining figure shows a line AB which can be extended upto infinitey on both the sides of it.

(ii) The adjoining figure shows a ray AB with fixed end as point A and which can be extended upto infinity through point B. It is clear from the figure, that a ray is a part of a line.

(iii) The adjoining figure shows a line-segment AB with fixed ends A and B. It is clear from the figure, that a line-segment is a part of a ray as well as of a line. Also, a line segment is the shortest distance between two fixed points.

5. ANGLE : An angle is formed when two line segments or two rays have a common end-point.
The two line segments, forming an angle, are called the arms of the angle whereas their common end-point is called the vertex of the angle.

The adjacent figure represents an angle ABC or ∠ABC or simply ∠B. AB and BC are the arms of the angle and their common point B is the vertex.

6. MEASUREMENT OF AN ANGLE : The unit of measuring an angle is degree. The symbol for degree is °.
Thus : 60 degree = 60°, 87 degree = 87’ and so on.
If one degree is divided into 60 equal parts, each part is called a minute ( ‘) and if one minute is further divided into 60 equal parts, each part is called a second ( ” ).
Thus, (i) r = 60′ and l’ = 60″
(ii) 9 minutes 45 seconds = 9′ 45″
(iii) 85 degrees 30 minutes 15 seconds = 85° 30′ 15″ and so on.

7. TYPES OF ANGLES :
1. Acute angle :
measures less than 90°

2. Right angle:
measures 90°

3. Obtuse angle :
measures between 90° and 180°

4. Straight angle : 
measures 180°

5. Reflex angle :
measures between 180° and 360°

8. MORE ABOUT ANGLES :
(A) Angles about a point: If a number of angles are formed about a point, their sum is always 360°.

In the adjoining figure :
∠AOB + ∠BOC + ∠COD +∠DOE + ∠EOA = 360°
(B) Adjacent angles : Two angles are said to be adjacent angles, if:
(i) they have a common vertex,
(ii) they have a common arm and
(iii) the other arms of the two angles lie on opposite sides of the common arm.
The adjoining figure shows a pair of adjacent angles :
(i) they have a common vertex (O),
(ii) they have a common ann (OB) and

(iii) the other arms OA and OC of the two angles are on opposite sides of the common arm OB.
(C) Vertically opposite angles : When two straight lines intersect each other four angles are formed.
The pair of angles which lie on the opposite sides of the point of intersection are called vertically opposite angles.

In the adjoining figure, two straight lines AB and CD intersect each other at point 0. Angles AOD and BOC form one pair of vertically opposite angles; whereas angles AOC and BOD form another pair of vertically opposite angles.
Vertically opposite angles are always equal.

i. e. ∠AOD = ∠BOC and ∠AOC = ∠BOD.
Important: In the adjoining figure, rays OX and OY meet a O to form ∠XOY (i.e. ∠a) and reflex ∠XOY (i. e. ∠b). It must be noted that ∠XOY means the smaller angle only unless it is mentioned to take otherwise.

9. COMPLEMENTARY AND SUPPLEMENTARY ANGLES
1. Two angles are called complementary angles, if their sum is one’right angle i.e. 90° Each angle is called the complement of the other.
e.g., 20″ and 70″ are complementary angles, because 20° + 70° = 90°.
Clearly, 20″ is the complement of 70° and 70° is the complement of 20°.
Thus, the complement of angle 53° = 90° – 53° = 37°.
2. Two angles are called supplementary angles, if their sum is two right angles i.e. 180″. Each angle is called the supplement of the other.
e.g., 30″ and 150° are supplementary angles because 30° + 150° = 180°.
Clearly, 30″ is the supplement of 150° and vice-versa.
Thus, the supplement of 105° = 180° – 105° = 75°.

10. Transversal : It is a straight line which cuts two or more given straight lines.

In the adjoining figure, PQ cuts straight lines AB and CD, and so it is a transversal.
When a transversal cuts two given straight lines (refer the adjoining figure), the following pairs of angles are formed.
1. Two pairs of interior alternate angles : Angles marked 1 and 2 form one pair of interior alternate angles, while angles marked 3 and 4 form another pair of interior alternate angles.
2. Two pairs of exterior alternate angles : Angles marked 5 and 8 form one pair, while angles marked 6 and 7 form the other pair of exterior alternate angles.
3. Four pairs of corresponding angles : Angles marked 3 and 6; 1 and 5; 8 and 2; 7 and 4 form the four pairs of corresponding angles.
4. Two pairs of allied or co-interior or conjoined angles : Angles marked 3 and 2 form one pair and angles marked 1 and 4 form another pair of allied angles.

11. PARALLEL LINES : Two straight lines are said to be parallel, if , they do not meet anywhere; no matter how long are they produced in any direction.

The adjacent figure shows two parallel straight lines AB and CD.
When two parallel lines AB and CD are cut by a transversal PQ :
(i) Interior and exterior alternate angles are equal:
i.e. ∠3 = ∠6 and ∠4 = ∠5 [Interior alternate angles]
∠1 = ∠8 and ∠2 = ∠7 [Exterior alternate angles]
(ii) Corresponding angles are equal:
i.e. ∠1 = ∠5;∠2 = ∠6;∠3 = ∠7 and ∠4 = ∠8
(iii) Co-interior or allied angles are supplementary :
i. e. ∠3 + ∠5 = 180° and ∠4 +∠6 = 180°

12. CONDITIONS OF PARALLELISM : If two straight lines are cut by a transversal such that:
(i) a pair of alternate angles are equal, or
(ii) a pair of corresponding angles are equal, or
(iii) the sum of the interior angles on the same side of the transversal is 180°, then the two straight lines are parallel to each other.
Therefore, in order to prove that the given lines are parallel, show either alternate angles are equal or, corresponding angles are equal or, the co-interior angles are supplementary.

Lines and Angles Exercise 14A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
State, true or false :
(i) A line segment 4 cm long can have only 2000 points in it.
(ii) A ray has one end point and a line segment has two end-points.
(iii) A line segment is the shortest distance between any two given points.
(iv) An infinite number of straight lines can be drawn through a given point.
(v) Write the number of end points in
(a) a line segment AB (b) arayAB
(c) alineAB
(vi) Out of \(\overleftrightarrow { AB }\) , \(\overrightarrow { AB }\) , \(\overleftarrow { AB }\) and \(\overline { AB }\) , which one has a fixed length?
(vii) How many rays can be drawn through a fixed point O?
(viii) How many lines can be drawn through three
(a) collinear points?
(b) non-collinear points?
(ix) Is 40° the complement of 60°?
(x) Is 45° the supplement of 45°?
Solution:
(i) False : It has infinite number of points.
(ii) True
(iii) True
(iv) True
(v) (a) 2 (b) 1 (c) 0
(vi) AB
(vii) Infinite
(viii) (a) 1 (b) 3
(ix) False : 40° is the complement of 50° as 40° + 50° = 90°
(x) False : 45° is the supplement of 135° not 45°.

Question 2.
In which of the following figures, are ∠AOB and ∠AOC adjacent angles? Give, in each case, reason for your answer.


Solution:
If ∠AOB and ∠AOC are adjacent angle if they have OA their common arm.
(i) In the figure, OB is their common arm
∴∠AOB and ∠AOC are not adjacent angles.
(ii) In the figure, OC is their common arm
∴∠AOB and ∠AOC also not adjacent angles.
(iii) In this figure, OA is their common arm
∴ ∠AOB and ∠AOC are adjacent angles.
(iv) In this figure, OB is their common arm
∴ ∠AOB and ∠AOC are not adjacent angles.

Question 3.
In the given figure, B AC is a straight line.
Find : (i) x (ii) ∠AOB (iii) ∠BOC

Solution:

Question 4.
Find yin the given figure.

Solution:

Question 5.
In the given figure, find ∠PQR.

Solution:
SQR is a straight line
∴∠SQT + ∠TQP + ∠PQR = 180°
⇒ x + 70° + 20° – x + ∠PQR = 180°
⇒ 90″ + ∠PQR = 180°
⇒ ∠PQR = 180°-90° = 90°
Hence ∠PQR = 90°

Question 6.
In the given figure. p° = q° = r°, find each.

Solution:

Question 7.
In the given figure, if x = 2y, find x and y

Solution:

Question 8.
In the adjoining figure, if b° = a° + c°, find b.

Solution:

Question 9.
In the given figure, AB is perpendicular to BC at B.
Find : (i) the value of x.
(ii) the complement of angle x.

Solution:

Question 10.
Write the complement of:


Solution:

Question 11.
Write the supplement of:
(i) 100°
(ii) 0°
(iii) x°
(iv) (x + 35)°
(v) (90 +a + b)° f
(vi) (110 – x – 2y)°
(vii) \(\frac { 1 }{ 5 }\) of a right angle
(viii) 80° 49′ 25″
Solution:

Question 12.
Are the following pairs of angles complementary ?
(i) 10° and 80°
(ii) 37° 28′ and 52° 33′
(iii) (x+ 16)°and(74-x)°
(iv) 54° and \(\frac { 2 }{ 5 }\) of a right angle.
Solution:

Question 13.
Are the following pairs of angles supplementary?

Solution:

Question 14.
If 3x + 18° and 2x + 25° are supplementary, find the value of x.
Solution:

Question 15.
If two complementary angles are in the ratio 1:5, find them.
Solution:

Question 16.
If two supplementary’ angles are in the ratio 2 : 7, find them.
Solution:

Question 17.
Three angles which add upto 180° are in the ratio 2:3:7. Find them.
Solution:

Question 18.
20% of an angle is the supplement of 60°. Find the angle.
Solution:

Question 19.
10% of x° is the complement of 40% of 2x°. Find x
Solution:

Question 20.
Use the adjacent figure, to find angle x and its supplement.

Solution:

Question 21.
Find k in each of the given figures.

Solution:

Question 22.
In the given figure, lines PQ, MN and RS intersect at O. If x : y = 1 : 2 and z = 90°, find ∠ROM and ∠POR.

Solution:

Question 23.
In the given figure, find ∠AOB and ∠BOC.

Solution:

Question 24.
Find each angle shown in the diagram.

Solution:

Question 25.
AB, CD and EF are three lines intersecting at the same point.
(i) Find x, if y = 45° and z = 90°.
(ii) Find a, if x = 3a, y = 5x and r = 6x.

Solution:

Lines and Angles Exercise 14B – Selina Concise Mathematics Class 7 ICSE Solutions

In questions 1 and 2, given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles :
Question 1.
(i) ∠3 and ∠6
(ii) ∠2 and ∠4
(iii) ∠3 and ∠7
(iv) ∠2 and ∠7
(v) ∠4 and∠6
(vi) ∠1 and ∠8
(vii) ∠1 and ∠5
(viii) ∠1 and ∠4
(ix) ∠5 and ∠7

Solution:
(i) ∠3 and ∠6 are interior alternate angles.
(ii) ∠2 and ∠4 are adjacent angles.
(iii) ∠3 and ∠7 are corresponding angles.
(iv) ∠2 and ∠7 are exterior alternate angles,
(v) ∠4 and ∠6 are allied or co-interior angles,
(vi) ∠1 and ∠8 are exterior alternate angles.
(vii) ∠1 and ∠5 are corresponding angles.
(viii) ∠1 and ∠4 are vertically opposite angles.
(ix) ∠5 and ∠7 are adjacent angles.

Question 2.
(i) ∠1 and ∠4
(ii) ∠4 and ∠7
(iii) ∠10 and ∠12
(iv) ∠7 and ∠13
(v) ∠6 and ∠8
(vi) ∠11 and ∠8
(vii) ∠7 and ∠9
(viii) ∠4 and ∠5
(ix) ∠4 and ∠6
(x) ∠6 and ∠7
(xi) ∠2 and ∠13

Solution:
(i) ∠1 and ∠4 are vertically opposite angles.
(ii) ∠4 and ∠7 are alternate angles.
(iii) ∠10 and ∠12 are vertically opposite angles.
(iv) ∠7 and ∠13 are corresponding angles.
(v) ∠6 and ∠8 are vertically opposite angles.
(vi) ∠11 and ∠8 are allied or co-interior angles.
(vii) ∠7 and ∠9 are vertically opposite angles.
(viii) ∠4 and ∠5 are adjacent angles.
(ix) ∠4 and ∠6 are allied or co-interior angles.
(x) ∠6 and ∠7 are adjacent angles.
(xi) ∠2 and ∠13 are allied or co-interior angles.

Question 3.
In the given figures, the arrows indicate parallel lines. State which angles are equal. Give reasons.

Solution:
In the figure (i),
a = b (corresponding angles)
b = c (vertically opposite angles)
a = c (alternate angles)
∴ a = b = c
(ii) In the figure (ii),
x =y (vertically opposite angles)
y=l (alternate angles)
x = I (corresponding angles)
1 = n (vertically opposite angles)
n = r (corresponding angles)
∴ x = y = l = n = r
Again m = k (vertically opposite angles)
k = q (corresponding angles)
∴ m = k = q

Question 4.
In the given figure, find the measure of the unknown angles :

Solution:
a = d (vertically opposite angles)
d=f (corresponding angles)
f= 110° (vertically opposite angles)
∴ a = d = f = 110°
e + 110° = 180° (co-interior angles)
∴ e = 180°- 110° = 70°
b = c (vertically opposite angles)
b = e (corresponding angles)
e = g (vertically opposite angles)
∴ b = c = e = g = 70° ”
Hence a = 110°, b = 70°, e = 70°, d = 110°, e = 70°,f= 110° and g = 70°

Question 5.
Which pair of the dotted line, segments, in the following figures, are parallel. Give reason:


Solution:
(i) In figure (i), If lines are parallel, then 120°+ 50° =180°
But there are co-interior angles
⇒170° = 180°. But it not true Hence, there are not parallel lines
(ii) In figure (ii),
∠1 = 45° (vertically opposite angles)
Lines are parallel if
∠1 + 135° = 180° (co-interior angles)
⇒45°+ 135°= 180°
⇒ 180° = 180° which is true.
Hence, the lines are parallel.
(iiii) In figure (iii),
Lines are parallel if corresponding angles are equal
If 120° =130° which is not correct
∴ Lines are not parallel.
(iv) ∠1 = 110° (vertically opposite angles)
If lines are parallel then
∠1 + 70° = 180° (co-interior angles)
⇒110° + 70°= 180°
⇒180° =180°
Which is correct.
∴ Lines are parallel.
(v) ∠1 + 100°= 180°
⇒∠1 = 180°- 100°= 80 (linear pair)
Lines l1 and l2 will be parallel If ∠1 = 70°
⇒ 80° = 70° which is not true
∴ l1 and 12 are not parallel Again, A, l3and l5 will be parallel
If 80° = 70° (corresponding angle)
Which is not true.
∴l3 and l5 are not parallel
But ∠1 = 80° (alternate angles)
⇒ 80° = 80°
Which is true
∴ l2 and l4 are parallel
(vi) Lines are parallel
If alternate angles are equal
⇒ 50° = 40°
Wliich is not ture lines are not parallel.

Question 6.
In the given figures, the directed lines are parallel to each other. Find the unknown angles.



Solution:

Question 7.
Find x. y and p is the given figures

Solution:

Question 8.
Find x in the following cases :

Lines and Angles Exercise 14C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Using ruler and compasses, construct the following angles :
(i)30°
(ii)15°
(iii) 75°
(iv) 180°
(v) 165°
(vi) 22.5°
(vii) 37.5°
(viii) 67.5°
Solution:
(i) 30°
Steps of Construction :
(i) Draw a line segment BC.
(ii) With centre B and a suitable radius draw an arc meeting BC at P.
(iii) With centre P and with same radius cut off the arc at Q.
(iv) Now with centre P and Q draw two arcs intersecting each other at R.
(v) Join BR and produce it to A, forming ZABC
= 30°

(ii) (15°)
Steps of Construction:
(i) Draw a line segment BC.
(ii) With centre B and a suitable radius draw an arc meeting BC at P.
(iii) With centre P and with same radius cut off the arc at Q.
(iv) Taking P and Q as curves, draw two arcs intersecting each other at D nnd join BD.
(v) With centre P and R, draw two more arcs intersecting each other at S.
(vi) Join BS and produce it to A.
Then ∠ABC = 15°.

(iii) 75°
Steps of Construction :
(i) Draw a line segment BC.
(ii) With centre B and a suitable radius draw an arc and cut off PQ, then QR of the same radius.
(iii) With centre Q and R, draw two arcs intersecting each other at S.
(iv) Join SB.
(v) With centre Q and D draw two arcs intersecting each other at T.
(vi) Join BT and produce it to A.
Then ∠ABC = 75°.

(iv) 180°
Steps of Construction :
(i) Draw a line segment BC.
(ii) With centre B and some suitable radius draw arc meeting BC at P.
(iii) With centre P and with same radius cut of arcs PQ, QR and then RS.
(iv) Join BS and produce it to A.
Then ∠ABC = 180°.

(v) 165°
Steps of Construction :
(i) Draw a line segment BC.
(ii) With centre B and some suitable radius draw an arc meeting BC at P.
(iii) With centre P and same radius cut off arcs PQ, QR and then RS.

(iv) Join SB.
(v) With centres R and S, draw two arcs intersecting each other at M.
(vi) With centre T and S draw two arcs intersecting each other at L.
(vi) Join BL and produce it to A. Then ∠ABC = 165°

(vi) 22.5°
Steps of Construction :
(i) Draw a line segment BC.
(ii) With centre B and some suitable radius, draw an arc meeting BC at P.

(iii) With centre P and some radius, cut off arcs PQ.
(iv) Bisect arc PQ at R and join BR.
(v) Bisect arc QR at S and join BS.
(vii) Now bisect arc PR at T.
(viii) Join BT and produce it to A.
Then ∠ABC = 22 \(\frac { 1 }{ 2 }\) ° or 22.5°.

(vii) 37.5°
Steps of Construction :
(i) Draw a line segment BC.
(ii) With centre B and some suitable radius, draw an arc meeting BC at P.
(iii) With centre P and same radius cut off arcs PQ and QR.
(iv) Now bisect arc QR at S and again bisect arc QS at T.
(v) Bisect arc PT at K.
(vi) Join BK and produce it to A.
Then, ∠ABC – 37 \(\frac { 1 }{ 2 }\) °or 37-5.

(viii) 67.5°
Steps of Construction :
(i) Draw a line segment BC.
(ii) With centre B and some suitable radius, draw an arc meeting BC at P.
(iii) With centre P and with same radius, cut arcs PQ and then QR.
(iv) Bisect arc QR at K and again bisect arc QK at S.
(v) Bisect again arc SQ at T.
(vi) Join BT and produce it to A.
Then ∠ABC = 67\(\frac { 1 }{ 2 }\) ° or 67.5°

Question 2.
Draw ∠ABC = 120°. Bisect the angle using ruler and compasses only. Measure each 1 angle so obtained and check whether the angles obtained on bisecting ∠ABC are equal or not.
Solution:
Steps of Construction :
(i) Draw a line segment BC.
(ii) With centre B and some suitable radius, draw an arc meeting BC at P.

(iii) With centre P and with same radius, cut arcs PQ and QR.
(iv) Join BR and produce it to A.
Then ∠ABC = 120°
(v) With centres P and R, draw two arcs intersecting each other at S.
(vi) Join BS and produce it to D. BD is the bisector of ∠ABC.
On measuring each angle, it is of 60° each. Yes, both angles are equal in measure.

Question 3.
Draw a line segment PQ = 6 cm. Mark a point A in PQ so that AP = 2 cm. At point A, construct angle QAR = 60°.
Solution:
Steps of Construction :
(i) Draw a line segment PQ = 6 cm.

(ii) Mark a point A on PQ so that AP = 2 cm.
(iii) With centre A and some suitable radius draw an arc meeting AQ at C.
(iv) With centre C and with same radius, cut arc CB.
(v) Join AB and produce it to R.
Then ∠QAR = 60°

Question 4.
Draw a line segment AB = 8 cm. Mark a point P in AB so that AP = 5 cm. At P, construct angle APQ = 30°.
Solution:
Steps of Construction :
(i) Draw a line segment AB = 8 cm.
(ii) Mark a point P in AB such that AP = 5 cm.
(iii) With centre P and some suitable radius, draw an arc meeting AB in L.
(iv) With centre L and same radius cut arc LM.
(v) Bisect arc LM at N.
(vi) Join PN and produce it to Q.
Then ∠APQ = 30°

Question 5.
Construct an angle of 75° and then bisect it.
Solution:
Steps of Construction :
(i) Draw a line segment BC.
(ii) At B, draw an angle ABC equal to 75°.

(iii) With centres P and T, draw arcs intersecting each other at L.
(iv) Join BL and produce it to D. Then BD bisects ∠ABC.

Question 6.
Draw a line segment of length 6 .4 cm. Draw its perpendicular bisector.
Solution:
Steps of Construction :
(i) Draw a line segment AB = 6.4 cm.
(ii) With centres A and B and with some suitable radius, draw arcs intersecting each other at S and R.
(iii) Join SR intersecting AB at Q. Then PQR is the perpendicular bisector of line segment AB

Question 7.
Draw a line segment AB = 5.8 cm. Mark a point P in AB such that PB = 3.6 cm. At P, draw perpendicular to AB.
Solution:
Steps of Construction :
(i) Draw a line segment AB = 5.8 cm.
(ii) Mark a point P in AB such that PB = 3.6 cm.
(iii) With centre P and some suitable radius draw an arc meeting AB in L.
(iv) With centre L and same radius cut arcs LM and then as N.
(v) Bisect arc MN at S.
(vi) Join PS and produce it to Q. Then PQ is perpendicular to AB at P.

Question 8.
In each case, given below, draw a line through point P and parallel to AB :

Solution:
Steps of construction :
(i) From P. draw a line segment meeting AB at
(ii) With centre Q and some suitable radius draw an arc CD.
(iii) With centre P and same radius draw another arc meeting PQ at E.

(iv) With centre E and radius equal to CD, cut this arc at F

(v) Join PF and produce it to both sides to L and M. Then line LM is parallel to given line AB.

 

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration

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Mensuration Exercise 20A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
The length and the breadth of a rectangular plot are 135 m and 65 m. Find, its perimeter and the cost of fencing it at the rate of ₹60 per m.
Solution:
Given :
Length (l) = 135 m
Breadth (b) = 65 m

Perimeter = 2 (l + b)
= 2(135 + 65)
= 2(200) = 400 m
∴Perimeter of rectangular plot is = 400 m
Cost of fencing per m = ₹60
∴Cost of fencing 400 m = ₹60 x 400 m = ₹24000

Question 2.
The length and breadth of a rectangular field are in the ratio 7 : 4. If its perimeter is 440 m, find its length and breadth. Also, find the cost of fencing it @ ₹150 per m.
Solution:
Given : Perimeter = 440 m
Let the length of rectangular field = lx and breadth = 4x
2(l + b) = Perimeter
2(7x + 4x) = 440 m
2(11x) = 440 m
22x = 440 m
x = \(\frac { 440 }{ 22 }\)
x = 11 m
∴Length = 7x = 7 x 11 = 77 m
Breadth = Ax = 4 x 11 = 44 m
Cost of fencing per m = ₹150
Cost of fencing 440 m = ₹150 x 440 = ₹66,000

Question 3.
The length of a rectangular field is 30 m and its diagonal is 34 m. Find the breadth of the field and its perimeter.
Solution:

Question 4.
The diagonal of a square is 12\(\sqrt { 2 } \) cm. Find its perimeter.
Solution:
Diagonal of square = Its side x \(\sqrt { 2 } \)
Side \(\sqrt { 2 } \) = \(\sqrt { 2 } \) \(\sqrt { 2 } \)
i.e. side = 12 cm
Perimeter of a square = 4 x Side
= 4 x 12 = 48 cm

Question 5.
Find the perimeter of a rectangle whose length = 22.5 m and breadth = 16 dm.
Solution:
Length = 22.5 m
Breadth = 16 dm = 1.6 m
Perimeter of rectangle = 2(l + b)
– 2(22.5 + 1.6)
– 2(24.1) = 48.2 m

Question 6.
Find the perimeter of a rectangle with length = 24 cm and diagonal = 25 cm
Solution:
Length of a rectangle (l) = 24 cm Diagonal = 25 cm

Let breadth of the rectangle = b m
Applying Pythagoras Theorem in triangle ABC,
We get, (AC)² = (AB)² + (BC)²
(25)² = (24)² + (b)²
625 = 576 + (b)²
625 – 576 = b²
49 = A2
\(\sqrt { 7 x 7 } \) =b
∴b = 7 cm
Now, perimeter of the rectangle
= 2(1 + b)
= 2(24 + 7)
= 2(31)
= 62 cm

Question 7.
The length and breadth of rectangular piece of land are in the ratio of 5 : 3. If the total cost of fencing it at the rate of ₹48 per metre is ₹19,200, find its length and breadth.
Solution:
Ratio in length and breadth of a rectangular piece of land = 5:3
Cost of fencing =₹ 19,200
and rate = ₹48 per m
∴Perimeter = \(\frac { 19200 }{ 48 }\)= 400 m 48
Let length = 5x.
Then breadth = 3x
∴Perimeter = 2(l + b)
400 = 2(5x + 3x)
400 = 2 x 8x= 16x
∴16x = 400
⇒ x = \(\frac { 400 }{ 16 }\) = 25
∴Length of the land = 5x= 5 x 25 = 125 m and breadth = 3x = 3 x 25 = 75 m

Question 8.
A wire is in the shape of square of side 20 cm. If the wire is bent into a rectangle of length 24 cm, find its breadth.
Solution:
Side of square = 20 cm
Perimeter of square = 4 x 20 = 80 cm
Or perimeter of rectangle = 80 cm
Length of a rectangle = 24 cm
∴ Perimeter of a rectangle = 2(l + b)
b = \(\frac { 80 }{ 2 }\) – 24
b = 40 – 24 = 16 m

Question 9.
If P = perimeter of a rectangle, l= its length and b = its breadth find :
(i) P, if l = 38 cm and b = 27 cm
(ii) b, if P = 88 cm and l = 24 cm
(iii) l, if P = 96 m and b = 28 m
Solution:

Question 10.
The cost of fencing a square field at the rate of
Cost of fencing 440 m = ₹150 x 440 = ₹75 per meter is
Cost of fencing 440 m = ₹150 x 440 = ₹67,500. Find the perimeter and the side of the square field.
Solution:

Question 11.
The length and the breadth of a rectangle are 36 cm and 28 cm. If its perimeter is equal to the perimeter of a square, find the side of the square.
Solution:

Question 12.
The radius of a circle is 21 cm. Find the circumference (Take π = 3 \(\frac { 1 }{ 7 }\) ).
Solution:

Question 13.
The circumference of a circle is 440 cm. Find its radius and diameter. (Take π = \(\frac { 22 }{ 7 }\)
Solution:

Question 14.
The diameter of a circular field is 56 m. Find its circumference and cost of fencing it at the rate of ₹80 per m. (Take n = \(\frac { 22 }{ 7 }\))
Solution:

Question 15.
The radii of two circles are 20 cm and 13 cm. Find the difference between their circumferences. (Take π = \(\frac { 22 }{ 7 }\))
Solution:

Question 16.
The diameter of a circle is 42 cm, find its perimeter. If the perimeter of the circle is doubled, what will be the radius of the new circle. (Take π = \(\frac { 22 }{ 7 }\) )
Solution:

Question 17.
The perimeter of a square and the circumference of a circle are equal. If the length of each side of the square is 22 cm, find:
(i) perimeter of the square.
(ii) circumference of the circle.
(iii) radius of the circle.
Solution:

Question 18.
Find the radius of the circle whose circumference is equal to the sum of the circumferences of the circles having radii 15 cm and 8 cm.
Solution:

Question 19.
Find the diameter of a circle whose circumference is equal to the sum of circumference of circles with radii 10 cm, 12 cm and 18 cm.
Solution:

Question 20.
The circumference of a circle is eigth time the circumference of the circle with radius 12 cm. Find its diameter.
Solution:

Question 21.
The radii of two circles are in the ratio 3 : 5, find the ratio between their circumferences.
Solution:

Question 22.
The circumferences of two circles are in the ratio 5 : 7, find the ratio between their radii.
Solution:

Question 23.
The perimeters of two squares are in the ratio 8:15, find the ratio between the lengths of their sides.
Solution:

Question 24.
The lengths of the sides of two squares are in the ratio 8:15, find the ratio between their perimeters.
Solution:
Let the side of first square = 8x
∴Perimeter of first square = 4 x Side = 4 x 8x = 32 x
and the side of second squares = 15x
∴Perimeter of second square = 4 x Side = 4 x 15s = 60s
Now, the ratio between their perimeter = 32x: 60x= 8: 15

Question 25.
Each side of a square is 44 cm. Find its perimeter. If this perimeter is equal to the circumference of a circle, find the radius of the circle.
Solution:

Mensuration Exercise 20B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the area of a rectangle whose length and breadth are 25 cm and 16 cm.
Solution:

Question 2.
The diagonal of a rectangular board is 1 m and its length is 96 cm. Find the area of the board.
Solution:

Question 3.
The sides of a rectangular park are in the ratio 4 : 3. If its area is 1728 m², find
(i) its perimeter
(ii) cost of fencing it at the rate of ₹40 per meter.
Solution:

Question 4.
A floor is 40 m long and 15 m broad. It is covered with tiles, each measuring 60 cm by 50 cm. Find the number of tiles required to cover the floor.
Solution:

Question 5.
The length and breadth of a rectangular piece of land are in the ratio 5 : 3. If the total cost of fencing it at the rate of ₹24 per meter is ₹9600, find its :
(i) length and breadth
(ii) area
(iii) cost of levelling at the rate of ₹60 per m².
Solution:

Question 6.
Find the area of the square whose perimeter is 56 cm.
Solution:

Question 7.
A square lawn is surrounded by a path 2.5 m wide. If the area of the path is 165 m² find the area of the lawn.
Solution:

Question 8.
For each figure, given below, find the area of shaded region : (All measurements are in cm)

Solution:

Question 9.
One side of a parallelogram is 20 cm and its distance from the opposite side is 16 cm. Find the area of the parallelogram.
Solution:

Question 10.
The base of a parallelogram is thrice it height. If its area is 768 cm², find the base and the height of the parallelogram.
Solution:

Question 11.
Find the area of the rhombus, if its diagonals are 30 cm and 24 cm.
Solution:

Question 12.
If the area of a rhombus is 112 cm² and one of its diagonals is 14 cm, find its other diagonal.
Solution:

Question 13.
One side of a parallelogram is 18 cm and its area is 153 cm². Find the distance of the given side from its opposite side.
Solution:

Question 14.
The adjacent sides of a parallelogram are 15 cm and 10 cm. If the distance between the longer sides is 6 cm, find the distance between the shorter sides.
Solution:

Question 15.
The area of a rhombus is 84 cm2 and its perimeter is 56 cm. Find its height.
Solution:

Question 16.
Find the area of a triangle whose base is 30 cm and height is 18 cm.
Solution:

Question 17.
Find the height of a triangle whose base is 18 cm and area is 270 cm².
Solution:

Question 18.
The area of a right-angled triangle is 160 cm². If its one leg is 16 cm long, find the length of the other leg.
Solution:

Question 19.
Find the area of a right-angled triangle whose hypotenuse is 13 cm long and one of its legs is 12 cm long.
Solution:

Question 20.
Find the area of an equilateral triangle whose each side is 16 cm. (Take \(\sqrt { 3 } \)= 1.73)
Solution:

Question 21.
The sides of a triangle are 21 cm, 17 cm and 10 cm. Find its area.
Solution:

Question 22.
Find the area of an isosceles triangle whose base is 16 cm and length of each of the equal sides is 10 cm.
Solution:

Question 23.
Find the base of a triangle whose area is 360 cm²and height is 24 cm.
Solution:

Question 24.
The legs of a right-angled triangle are in the ratio 4 :3 and its area is 4056 cm². Find the length of its legs.
Solution:

Question 25.
The area of an equilateral triangle is (64 x \(\sqrt { 3 } \) ) cm²– Find the length of each side of the triangle.
Solution:

Question 26.
The sides of a triangle are in the ratio 15 : 13 : 14 and its perimeter is 168 cm. Find the area of the triangle.
Solution:

Question 27.
The diameter of a circle is 20 cm. Taking π = 3.14, find the circumference and its area.
Solution:

Question 28.
The circumference of a circle exceeds its diameter by 18 cm. Find the radius of the circle.
Solution:

Question 29.
The ratio between the radii of two circles is 5 : 7. Find the ratio between their :
(i) circumference
(ii) areas
Solution:

Question 30.
The ratio between the areas of two circles is 16 : 9. Find the ratio between their :
(i) radii
(ii) diameters
(iii) circumference
Solution:

Question 31.
A circular racing track has inner circumference 528 m and outer circumference 616 m. Find the width of the track.
Solution:

Question 32.
The inner circumference of a circular track is 264 m and the width of the track is 7 m. Find:
(i) the radius of the inner track.
(ii) the radius of the outer circumference.
(iii) the length of the outer circumference.
(iv) the cost of fencing the outer circumference at the rate of ₹50 per m.
Solution:

Question 33.
The diameter of every wheel of a car is 63 cm. How much distance will the car move during 2000 revolutions of its wheel.
Solution:

Question 34.
The diameter of the wheel of a car is 70 cm. How many revolutions will it make to travel one kilometre?
Solution:

Question 35.
A metal wire, when bent in the form of a square of largest area, encloses an area of 484 cm². Find the length of the wire. If the same wire is bent to a largest circle, find:
(i) radius of the circle formed.
(ii) area of the circle.
Solution:

Question 36.
A wire is along the boundary of a circle with radius 28 cm. If the same wire is bent in the form of a square, find the area of the square formed.
Solution:

Question 37.
The length and the breadth of a rectangular paper are 35 cm and 22 cm. Find the area of the largest circle which can be cut out of this paper.
Solution:

Question 38.
From each comer of a rectangular paper (30 cm x 20 cm) a quadrant of a circle of radius 7 cm is cut. Find the area of the remaining paper i.e., shaded portion.

Solution:

Selina Concise Mathematics class 7 ICSE Solutions – Simple Interest

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POINTS TO REMEMBER

Question 1.
Find the S.I. and amount on :
(i) Rs. 150 for 4 years at 5% per year.
(ii) Rs. 350 for 3\(\frac {1 }{ 2 }\) years at 8% p.a.
(iii) Rs. 620 for 4 months at 8 p. per rupee per month.
(iv) Rs. 3,380 for 30 months at 4 \(\frac { 1 }{ 2 }\) % p.a.
(v) 600 from July 12 to Dec. 5 at 10% p.a.
(vi) Rs. 850 from 10th March to 3rd August at 2 \(\frac { 1 }{ 2 }\) % p.a.
(vii) Rs. 225 for 3 years 9 months at 16% p.a.

Solution:

Question 2.
On what sum of money does the S.I. for 10 years at 5% become Rs. 1,600 ?

Solution:

Question 3.
Find the time in which Rs. 2,000 will amount to Rs. 2,330 at 11% p.a. ?

Solution:

Question 4.
In what time will a sum of money double it self at 8% p.a ?

Solution:

Question 5.
In how many years will be ₹870 amount to ₹1,044, the rate of interest being 2\(\frac { 1 }{ 2 }\) % p.a ?

Solution:

Question 6.
Find the rate percent if the S.I. on ₹275 is 2 years is ₹22.

Solution:

Question 7.
Find the sum which will amount to ₹700 in 5 years at 8% rate p.a.

Solution:

Question 8.
What is the rate of interest, if ₹3,750 amounts to ₹4,650 in 4 years ?

Solution:

Question 9.
In 4 years, ₹6,000 amount to ₹8,000. In what time will ₹525 amount to ₹700 at the same rate ?

Solution:

Question 10.
The interest on a sum of money at the end of 2\(\frac { 1 }{ 2 }\) years is \(\frac { 4 }{ 5 }\) of the sum. What is the rate percent ?

Solution:

Question 11.
What sum of money lent out at 5% for 3 years will produce the same interest as Rs. 900 lent out at 4% for 5 years ?

Solution:

Question 12.
A sum of Rs. 1,780 become Rs. 2,136 in 4 years,
Find :
(i) the rate of interest.
(ii) the sum that will become Rs. 810 in 7 years at the same rate of interest ?

Solution:

Question 13.
A sum amounts to Rs. 2,652 in 6 years at 5% p.a. simple interest.
Find :
(i) the sum
(ii) the time in which the same sum will double itself at the same rate of interest.

Solution:

Question 14.
P and Q invest Rs. 36,000 and Rs. 25,000 respectively at the same rate of interest per year. If at the end of 4 years, P gets Rs. 3,080 more interest than Q; find the rate of interest.

Solution:

Question 15.
A sum of money is lent for 5 years at R% simple interest per annum. If the interest earned be one-fourth of the money lent, find the value of R.

Solution:

Question 16.
The simple interest earned on a certain sum in 5 years is 30% of the sum. Find the rate of interest.

Solution:

Selina Concise Mathematics class 7 ICSE Solutions – Exponents (Including Laws of Exponents)

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EXERCISE 5 (A)

Question 1.
Find the value of:
(i) 6² 
(ii) 7³
(iii) 4⁴
(iv) 5⁵
(v) 8³
(vi) 7⁵

Solution:
(i) 6² = 6 x 6 = 36
(ii) 7³ = 7 x 7 x 7 = 343
(iii) 4⁴ = 4 x 4 x 4 x 4 = 256
(iv) 5⁵= 5 x 5 x 5 x 5 x 5 = 3125
(v) 8³ = 8 x 8 x 8 = 512
(vi) 7⁵ = 7 x 7 x 7 x 7 x 7 =16807

Question 2.
Evaluate:
(i) 2³ x 4²
(ii) 2³ x 5²
(iii) 3³ x 5²
(iv) 2² x 3³
(v) 3² x 5²
(vi) 5³ x 2⁴
(vii) 3² x 4²
(ix) (5 x 4)²

Solution:
(i) 2³ x 4²
= 2 x 2 x 2 x 4 x 4
= 8 x 16
= 128
(ii) 2³ x 5²
= 2 x 2 x 2 x 5 x 5
= 8 x 25
= 200
(iii) 3³ x 5²
=3 x 3 x 3 x 5 x 5
= 27 x 25
= 675
(iv) 2² x 3³
= 2 x 2 x 3 x 3 x 3
= 4 x 27
= 108
(v) 3² x 5³
=3 x3 x 5 x 5 x 5
= 9 x 125
= 1125
(vi) 5³ x 2⁴
= 5 x 5 x 5 x 2 x 2 x 2 x 2
= 125 x 16
= 2000
(vii) 3² x 4²
=3 x 3 x 4 x 4
= 9 x 16
=144
(viii) (4 x 3)³
=4 x 4 x 4 x 3 x 3 x 3
= 64 x 27
= 1728
(ix) (5 x 4)²
=5 x 5 x 4 x 4
= 25 x 16
= 400

Question 3.
Evaluate:

Solution:

Question 4.
Evaluate :

Solution:

Question 5.
Which is greater :
(i) 2³ or 3²
(ii) 2⁵ or 5²
(iii) 4³ or 3⁴
(iv) 5⁴ or 4⁵

Solution:
(i) 2³ or 3³
Since, 2³ = 2 x 2 x 2 = 8
and, 3² = 3 x 3 = 9
∵9 is greater than 8 ⇒ 3² > 2³
(ii) 2⁵ or 5²
Since, 2⁵ = 2 x 2 x 2 x 2 x 2 = 32
and, 5² = 5 x 5 = 25
∵32 is greater than 25 ⇒ 2³⁵ > 5³²
(iii) 4³ or 3⁴
Since, 4³ = 4 x 4 x 4 = 64
and, 3⁴ = 3 x 3 x 3 x 3 = 81
∵ 81 is greater than 64 ⇒ 3⁴ > 4³
(iv) 5⁴ or 4⁵
Since, 5⁴ = 5 x 5 x 5 x 5 = 625
and, 4⁵ = 4 x 4 x 4 x 4 x 4= 1024
∵ 1024 is greater than 625 ⇒ 4⁵ > 5⁴

Question 6.
Express each of the following in exponential form :
(i) 512
(ii) 1250
(iii) 1458
(iv) 3600
(v) 1350
(vi) 1176

Solution:
(i) 512

(ii) 1250

(iii) 1458

(iv) 3600

(v) 1350

(vi) 1176

Question 7.
If a = 2 and b = 3, find the value of:
(i) (a + b)²
(ii) (b – a)³
(iii) (a x b)a (iv) (a x b)b

Solution:
(i) (a + b)²
= (2 + 3)² = (5)² = 5 x 5 = 25

(ii) (b – a)²
= (3 – 2)²= (1)³
= 1 x 1 x 1 = 1

(iii) (a x b)^a
= (2 x 3)² – (6)²
= 6 x 6 = 36

(iv) (a x b)^b
= (2 x 3)³ = (6)³ = 6 x 6 x 6 = 216

Question 8.
Express:
(i) 1024 as a power of 2.
(ii) 343 as a power of 7.
(iii) 729 as a power of 3.
Solution:
(i) 1024 as a power of 2.

(ii) 343 as a power of 7.

(iii) 729 as a power of 3.

Question 9.
If 27 x 32 = 3^x x 2^y; find the values of x and y.

Solution:

Question 10.
If 64 x 625 = 2^a x 5^b; find :
(i) the values of a and b.
(ii) 2^b x 5^a

Solution:
(i) the values of a and b.

(ii) 2^b x 5^a

EXERCISE 5 (B)

Question 1.
Fill in the blanks:
In 5² = 25, base = ……… and index = ……….
If index = 3x and base = 2y, the number = ………

Solution:
(i) In 5² = 25, base = 5 and index = 2
(ii) If index = 3x and base = 2y, the number = 2y^3x

Question 2.
Evaluate:
(i) 2⁸ ÷ 2³
(ii) 2^3÷ 2⁸
(iii) (2⁶)⁰
(iv) (3^o)⁶
(v) 8³ x 8^-5 x 8⁴
(vi) 5⁴  x 5³ + 5⁵
(vii) 5⁴ ÷ 5³ x 5⁵
(viii) 4⁴ ÷ 4³ x 4⁰
(ix) (3⁵ x 4⁷ x 5⁸)⁰

Solution:

Question 3.
Simplify, giving Solutions with positive index:

Solution:

Question 4.
Simplify and express the Solution in the positive exponent form :

Solution:

Question 5.
Evaluate

Solution:

Question 6.
If m² = -2 and n = 2; find the values of:
(i) m + r² – 2mn
(ii) mⁿ + n^m
(iii) 6m^-3 + 4n²
(iv) 2n³ – 3m

Solution:

 

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency: Congruent Triangles

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency: Congruent Triangles

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POINTS TO REMEMBER

1. Meaning of Congruency : If two geometrical figures coincide exactly, by placing one over the other, the figures are said to be congruent to each other.
1. Two lines AB and CD are said to be congruent if, on placing AB on CD, or CD on AB ; the two AB and CD exactly coincide.
It is possible only when AB and CD are equal in length.Two figures ABCD and PQRS are said to be

congruent if, on placing ABCD on PQRS or PQRS on ABCD the two figures exactly coincide i.e. A and P coincide. B and Q coincide, C and R coincide and D and S coincide.
It is possible only when :
AB = PQ, BC = QR, CD = RS and AD = PS
Also, ∠A = ∠P, ∠B = ∠Q, ∠C = ∠R and ∠D = ∠S.

2. Congruency in Triangles : Let triangle ABC is placed over triangle DEF ; such that, vertex A falls on vertex D and side AB falls on side DE ; then if the two triangles coincide with each other in such a way that B falls on E ; C falls on F ; side BC coincides with side EF and side AC coincides with side DF, then the two triangles are congruent to each other.
The symbol used for congruency is “ ≡ ” or “ ≅ ”
∴∆ ABC is congruent to ∆ DEF is written as :
∆ ABC = ∆ DEF or ∆ABC = ∆DEF.

3. Corresponding Sides and Corresponding Angles : In case of congruent triangles ABC and DEF, drawn above ; when A ABC is placed over A DEF to cover it exactly; then the sides of the two triangles, which coincide with each other, are called corresponding sides. ‘ Thus, the side AB and DE are corresponding sides; sides BC and EF are corresponding sides and sides AC and DF are also corresponding sides.
In the same way. the angles of the two triangles which coincide with each other, are called corresponding angles. Thus, three pairs of corresponding angles are ∠A and ∠D ; ∠B and ∠E and also ∠C and ∠F.
Note : The corresponding parts of congruent triangles are always equal (congruent).
∴(i) AB = DE, BC = EF and AC = DF. i.e. corresponding sides are equal.
Also (ii) ∠A = ∠D, ZB = ∠E and ∠C = ∠F
i.e. corresponding angles are equal.
4. Conditions of Congruency:
1. If three sides of one triangle are equal to three sides of the other triangle, each to each, then the two triangles are congruent.
The test is known as : side, side, side and is abbreviated as S.S.S.
In triangle ABC and PQR, given alongside:
AB = PQ ; BC = QR and AC = PR
And, so A ABC is congruent to ∆ PQR e. ∆ ABC = ∆ PQR by S.S.S.
Because in congruent triangles, corresponding sides and corresponding angles are equal.
∴ ∠A = ∠P : ∠B = ∠Q and ∠C =∠R

2. If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, each to each, then the triangles are congruent.
This test is known as : side, angle, side and is abbreviated as S.A.S. In the given triangles, AB = XZ ; BC = XY and ∠ABC = ∠ZXY
∴ ∆ ABC ≅ ∆ ZXY
Note : Triangles will be congruent by S.A.S., only when the angles included by the corresponding equal sides are equal.
The pairs of corresponding sides of these two congruent triangles are : AB and ZX ; BC and XY ; AC and ZY
The pairs of corresponding angles are :
∠B and ∠X ; ∠A and ∠Z : ∠C and ∠Y.

3. If two angles and the included side of one triangle are equal to the two angles and the included side of the other triangle ; then the triangles are congruent.
This test is known as : angle, side, angle and is abbreviated as A.S.A.
In the given figure :
BC = QR;
∠B = ∠Q and ∠C = ∠R
∴ ∆ABC = ∆ PQR.. (by A.S.A.)

4. If the hypotenuse and one side of a right angled triangle are equal to the hypotenuse and one side of another right angled triangle, then the two triangles are congruent.
This test is known as : right angle, hypotenuse, side and is abbreviated as R.H.S.
In the given figure :
∠B = ∠E = 90° ; AB = FE
and hypotenuse AC = hypotenuse FD
∴ ∆ ABC = ∆ FED (byRH.S.)
The corresponding angles in this case are :
∠A and ∠F ; ∠B and ∠E ; ∠C and ∠D and the corresponding sides are :
AB and EF ; AC and FD ; BC and ED.
Since the triangles are congruent, therefore all its corresponding sides are equal and corresponding angles are also equal.
∴ BC = ED ; ∠A = ∠F and ∠C = ∠D
Note : If three angles of a triangle are equal to the three angles of the other triangle, then the triangle are not necessarily congruent.
For congruency at least one pair of corresponding sides must be equal.
∴A.A.A. is not a test of congruency.

Congruency: Congruent Triangles Exercise 19 – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
State, whether the pairs of triangles given in the following figures are congruent or not:

Solution:
(i) In these triangles, corresponding sides are not equal. Hence these are not congruent triangles.
(ii) In the first A, third angle
= 180°-(40°+ 30°)
= 180° – 70°
= 110°
Now in these two triangles the sides and included angle of the one are equal to the corresponding sides and included angle.
Hence these are congruent triangles
(S.A.S. axiom)
(iii) In these triangles, corresponding two sides are equal but included angles are not-equal. Hence these are not congruent triangles.
(iv) In these triangles, corresponding three sides are equal.
Hence these are congruent triangles.
(S.S.S. Axiom)
(v) In these right triangles, one side and diagonal of the one, are equal to the corresponding side and diagonal are equal. Hence these are congruent triangles. –
(R.H.S. Axiom)
(vi) In these triangles two sides and one angle of the one are equal to the corresponding sides and one angle of the other are equal.
Hence these are congruent triangles.
(S.S. A. Axiom).
(vii) In A ABC. AB = 2 cm, BC = 3.5 cm and ∠C = 80° and in ∆ DEF,
DE = 2 cm, DF = 3.5 cm and ∠D = 80°

From the figure  we see that two corresponding sides  are equal but their included angles are not equal.
Hence, these are not congruent triangles

Question 2.
In the given figure, prove that:
∆ABD ≅ ∆ ACD

Solution:

Question 3.
Prove that:
(i) ∆ABC ≡∆ADC
(ii) ∠B = ∠D
(iii) AC bisects angle DCB

Solution:

Question 4.
Prove that:
(i) ∆ABD  ≡ ∆ACD
(ii) ∠B = ∠C
(iii) ∠ADB = ∠ADC
(iv) ∠ADB = 90°

Solution:

Question 5.
In the given figure, prove that:
(i) ∆ACB ≅ ∆ECD
(ii) AB = ED

Solution:

Question 6.
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D

Solution:

Question 7.
In the given figure, prove that: BD = BC.

Solution:

Question 8.
In the given figure ;
∠1 = ∠2 and AB = AC. Prove that:
(i) ∠B = ∠C
(ii) BD = DC
(iii) AD is perpendicular to BC.

Solution:

Question 9.
In the given figure prove tlyat:
(i) PQ = RS
(ii) PS = QR

Solution:

Question 10.
(i) ∆ XYZ ≅ ∆ XPZ
(ii) YZ = PZ
(iii) ∠YXZ = ∠PXZ

Solution:

Question 11.
In the given figure, prove that:
(i) ∆ABC ≅ ∆ DCB
(ii) AC=DB

Solution:

Question 12.
In the given figure, prove that:
(i) ∆ AOD ≅ ∆ BOC
(ii) AD = BC
(iii) ∠ADB = ∠ACB
(iv) ∆ADB ≅ ∆BCA

Solution:

Question 13.
ABC is an equilateral triangle, AD and BE are perpendiculars to BC and AC respectively. Prove that:
(i) AD = BE
(ii)BD = CE

Solution:

Question 14.
Use the informations given in the following figure to prove triangles ABD and CBD are congruent.
Also, find the values of x and y.

Solution:

Question 15.
The given figure shows a triangle ABC in which AD is perpendicular to side BC and BD = CD. Prove that:
(i) ∆ABD ≅ ∆ACD
(ii) AB=AC
(iii) ∠B = ∠C

Solution:

Selina Concise Chemistry Class 7 ICSE Solutions – Matter and Its Composition

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Selina Concise ICSE Solutions for Class 7 Chemistry Chapter 1 Matter and Its Composition

Points to Remember :

1. Matter has mass and occupies space.
2. Matter is made up of atoms and molecules.
3. Atoms are the smallest particles of matter which may or may not have independent existence.
4. Molecules are capable of independent existence. They are made up of atoms of same kind or different kinds.
5. The atoms and molecules are in random motion.
6. There are gaps between the molecules of matter called as intermolecular space.
7. There exists a force of attraction between the molecules known as intermolecular force of attraction.
8. Matter exists in three states : solids, liquid and gas.
9. Matter can change from one state to another on changing temperature and pressure.
10. The change of state of a matter from one form into another is called interconversion of states of matter.

EXERCISE

Question 1.
Define matter.
Answer:
Anything that has mass and occupies space is called matter.

Question 2.
What is the difference between mass and weight.
Answer:
Mass is the “quantity of matter” and weight is “the force with which the earth pulls a body towards itself’. The mass of a body does not change but its weight changes from place to place.

Question 3.
If an object weighs 6 N on earth what will be its weight on moon. What will be the change in its mass?
Answer:
Weight of body on moon = \(\frac { 1 }{ 6 }\)th of its weight on earth.
∴ Body will weigh \(\frac { 1 }{ 6 }\) of 6 = \(\frac { 1 }{ 6 }\) x 6 = 1 N on moon
Mass of a body does not change with change in gravity. So mass of a body will remain the same on moon.

Question 4.
Write your observation and conclusion for the following:
(a) When few marbles are put in a glass half filled with water.
(b) Ice is kept at room temperature.
Answer:
(a) Take some marbles and put them into the water of glass tumbler one by one. After some time you will notice that water level crosses the mark and rises. This is because the marbles occupy space. Again weigh the glass with the marbles. You will find that the second mass is greater than the first one. This proves that, marbles have mass.

This proves that, matter has mass and occupies space.
(b) Ice when kept at room temperature again changes back into liquid water.

Question 5.
State three main characteristics of the particles of matter.
Answer:
Characteristics of Matter

1. It can neither be created nor destroyed.
2. It is composed of a particular material which can either be Homogeneous or Heterogeneous.
3. Matter has, volume, mass and weight as per their state.

Question 6.
Differentiate between an atom and a molecule.
Answer:

Atom	Molecule
It is the smallest part of an element. It does not have independent existence.	It is the smallest part of a compound. It has an independent existence.

 Question 7.
Define :
(a) Solid
(b) Liquid
(c) Gas

Answer:
Giving two examples of each type.
(a) Solid : A solid is that state of matter which has a fixed shape, mass and volume. It suffers very small changes in volume by changing the temperature. It can not be compressed,
e.g. – Sand, Wood, Copper, Ice, etc.
(b) Liquid : It has a definite mass and volume but lacks a shape of its own. It takes up the shape of the containing vessels. It can be compressed to an extents,
e.g. – Milk, water, ink, etc.
(c) Gas : It is a state of matter which has only definite mass but no definite shape and volume. It takes up the shape of the container
e.g. – Carbon dioxide, oxygen, etc.

Question 8.
Why are liquids and gases called as fluids.
Answer:
The particles are free to move in any direction i.e. they can
flow because all substances that can flow are called fluids.
Liquids and gases are fluids.

Question 9.
(a) Define interconversion of states of matter.
(b) Why do solids, liquids and gases differ in their physical state?
(c) Under what conditions do solids, liquids and gases change their state.
Answer:
(a) The process by which matter changes from one state to another and back to original state, without any change in its chemical composition.
(b)Intermolecular force of attraction.
Intermolecular spaces are two important properties of matter that account for the different states of matter.
(c) Matter can change from one state to another on changing temperature and pressure.

Question 10.
Give reasons :
(a) When a stone is dipped in a glass containning some water the level of water rises but when a spoon of sugar is added to it and stired, the water level does not rise?
(b) A drop of ink added to water in a glass turns whole water blue.
Answer:
(a) Take half a glass of water. Dip a spoon in it. What do you observe? The water level rises, indicating that spoon occupies space.

Now remove the spoon, water comes down to its original level. Now add a spoon of sugar to it and stir well. The sugar disappears but the level of water in the glass does not rise, that means the volume of water has not increased. But where did the sugar particles disappear?
The sugar particles being smaller get adjusted between the water molecules. This shows that there are intermolecular space in water.
(b) This is because tfie water as well as ink particles (molecules) are in continuous random motion. Due to motion, the blue coloured particles of the ink spreads all over and give blue colour to the water.

Question 11.
Fill in the blanks :

(a) Air is a matter because it has weight, mass and space and it can be compressed.
(b) The molecules are made up of atoms.
(c) The quantity of matter in an object is called its mass.
(d) The state of matter with definite volume and definite shape is called solid.
(e) The substances which can flow are called fluids.

Question 12.
Name the terms for the following :
(a) The change of a solid into liquid.
(b) The force of attraction between the molecules of matter.
(c) The particles of matter which may or may not have independent existence.
(d) The process due to which a solid directly changes into its vapours.
(e) The change of vapour into a liquid.
Answer:
(a) Melting.
(b) Intermolecular force of attraction.
(c) Solid.
(d) Sublimation.
(e) Condensation.

Question 13.
Classify the following into solid, liquid and gas :
Coal, kerosene, wood, oxygen, sugar, blood, water vapour, milk, wax.
Answer:

 

Selina Concise Biology Class 6 ICSE Solutions – Habitat and Adaptation

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Selina Concise ICSE Solutions for Class 6 Biology Chapter 8 Health and Hygiene

Multiple Choice questions:
1. Put a tick mark (✓ ) against the correct alternative in the following statements:

(a) In cactus plant found in desert regions, the photosynthesis occur in:
(i) leaves
(ii) spines
(iii) modified roots
(iv) modified stem

(b) The animals such as birds have:
(i) light pneumatic bones
(ii) solid heavy bones
(iii) heavy pointed bones
(iv) no bones

(c) The biotic components of environment includes:
(i) greeen plants
(ii) animals
(iii) decomposer
(iv) all of these

(d) The presence of hollow plant stems is the characterstics of:
(i) desert plants
(ii) aquatic plants
(iii) mountaineous trees
(iv) none of these

(e) Slow breathing is the characterstics of:
(i) desert animals
(ii) aquatic animals
(iii) aerial animals
(iv) mesophytic animals

(f) Diversity of organisms are found in the different habitats because of different for
(i) average temperature
(ii) soil type
(iii) annual precipitation
(iv) all the these

Short Answer Questions:

Question 1.
List any four abiotic factors which affect different living beings.
Answer:
The various non-living things, such as soil, rocks, air, water, temperature, etc. are its abiotic components.

Question 2.
How is a whale similar to a fish in adaption to life in water ? Explain any two features.
Answer:
Whale are marine mammals. Its huge body is also spindle — shaped (streamlined). It front legs are modified into paddles or flippers for kicking water, hind limbs are absent. Whales have to periodically come up to the surface of water to breathe-inthe atmospheric air into their lungs.

Question 3.
Describe any two adaptations seen in desert plants.
Answer:
The adaptations seen in desert plants are :

1. Well-developed root systems.
2. Leaves either very small or converted to spines.
3. Stem is green and fleshy in some plants.

Question 4.
Describe the aerial adaptations in birds.
Answer:
The bird’s body is perfectly adapted for aerial life. Various aerial adaptations found in birds are:

1. Body shape: The body of birds is streamlined. Necks stretched forward with the head pointed in front and a narrowed tail at the end provide them a sleek shape. The body surface is smooth to minimize resistance against air.
2. Wings: The forelimbs are modified into wings.The fingers are very much reduced. The whole length of the forelimb carries long flight feathers.         .
3. Steering and brakes: The feathers on the tail help to slow down the speed and also help in steering (changing direction).
4. Wing muscles: These are the much strong, active and enlarged breast muscles.
5. Cutting down the body weight: Except for the most necessary bulky heavy wing muscles, the rest of the bird’s body tends to be light to facilitate flight.

• Bones have air cavities.
• Much less water is required in the body. The birds excrete solid urine (formed of uric acid instead of urea which otherwise requires much water to be excreted out).
• Right ovaiy and oviduct are greatly reduced.

Question 5.
Briefly explain the term “Habitat”.
Answer:
The place where animals survive, flourish and reproduce is known as habitat. A suitable habitat should be safe and food should be available in plenty. The climate of the habitat should be favourable for the animals living there.

Question 6.
Give two adaptations in animals found in mountain habitat by which they protect themselves from the cold climate.
Answer:
Animals living in the mountain regions are also adapted. Such adaptations are basically to protect them from cold and snow. For example, yak has thick skin covered with fur to protect it from cold. Mountain goat has thick fur on its body including feet and toes. These animals have strong hooves for running up rocky slopes of the mountains.

• The oxygen content in the mountain air is thin. So the blood of most of these animals contains more red blood cells. This helps them to breathe in sufficient oxygen even when air pressure is low.
• Some animals hibernate or go for a long winter sleep when the temperatures are very low. In this way they conserve their energy and survive the winter without food. Frogs, and hedgehogs are some animals which hibernate.

Question 7.
Define the following: habitat, adaptation.
Answer:
Habitat — The place where a biotic community lives is called a habitat. It includes plants, animals along with their physical environment.

Question 8.
List the environmental factors that influence a habitat.
Answer:
Environment in which that organism generally lives. The special feature of habitat is that this environment includes all the physical characteristics around (air, water, temperature, etc.), along with the effective plants and animals. Forexample, a pond is the habitat of a fish where it lives with other organisms and also interacts with water, air, temperature, etc. The natural home of an organism (niche) and its immediate surroundings is called its habitat. The habitat of any living creature should be a place where it can find shelter, food, water and suitable conditions for breeding.

Question 9.
Differentiate between an aquatic habitat and a terrestrial habitat.
Answer:
Habitats of plants and animals that live in water are called aquatic habitat.The plants and animals that live on land are said to live in terrestrial habitats

Question 10.
Name any three types of terestrial habitat.
Answer:
The plants and animals that live on land are said to live in terrestrial habitats: For example, forests, grasslands, deserts, coastal and mountain region.
The three types of terrestrial habitat are:

• Desert habitat — Vast regions of sand, high daytime temperatures and low night time temperatures, very little water are the main environmental factors of this habitat.
• Mountain habitat — Rocky land, snow and ice laden regions are the main features of this habitat. Temperatures in the mountains change with altitude. The lower regions are cooler whereas at higher altitudes it gets extremely icy and cold.
• Polar habitat—is extremely cold and covered with snow throughout the year. Polar bears, reindeer, penguins and very scanty plant growth survive in the cold regions.

Question 11.
Name two types of terrestrial habitats with low temperature.
Answer:
Desert habitat — Vast regions of sand, high daytime temperatures and low night time temperatures, very little water are the main environmental factors of this habitat.

Mountain habitat — Rocky land, snow and ice laden regions are the main features of this habitat. Temperatures in the mountains change with altitude. The lower regions are cooler whereas at higher altitudes it gets extremely icy and cold.

Question 12.
Complete the table given below. Write down two points in each given column.

Answer:

ICSE Solutions for Class 6 Geography Voyage – North America : Location, Area, Political and Physical Features

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POINTS TO REMEMBER

• North America has been named after Amerigo Vespucci, an Italian explorer. However, Christopher Columbus is credited with the discovery of this continent.
• The continent lies in the northern and the western hemispheres surrounded by the Arctic, the Atlantic and the Pacific oceans. The Isthmus of Panama joins North America to South America.
• The United States of America and Canada occupy three fourths of North america.
• NorthAmerica can be divided into four major physical divisions— the Canadian or Laurentian Shield, the Western Mountain System or Western Cordilleras, the Eastern Highlands or Appalachian Mountains and the Central Lowlands or Great Central Plains.
• The Canadian Shield is composed of some of the oldest known hard rocks of the world. The surface of the Shield consists of many deep depressions formed by scraping and scouring out by moving ice. These depressions have been filled up with meltwater to form many freshwater lakes such as the five Great Lakes.
• The Western Cordilleras are a series of young fold mountain ranges which have many active and extinct volcanoes, earthquake-prone regions and hot springs. The Cordilleras consist of several parallel ranges such as the Alaska Range and the Brooks Range. The highest point in North America, Mt McKinley, lies here. .
• The Appalachians are lower than the Western Cordilleras. The eastern slopes of these highlands are very steep.
• The edge of the Piedmont Plateau (located at the foot of the Appalachians or the Eastern Highlands) has many waterfalls along its length. It is referred to as the Fall Line.
• The Great Central Plains have the largest river system in North America—the Mississippi-Missouri river system.
• North America has several large rivers such as the Mississippi, Missouri, Mackenzie, Nelson, St Lawrence, Hudson, Yukon, Columbia and Rio Grande.
• Lumbering is an important activity in the coniferous or taiga forests of Canada, carried out by lumbermen or lumberjacks.
• Lumbering involves several stages of work such as cutting, skidding and hauling.

IMPORTANT TERMS

Gorge : A deep narrow valley with near vertical sides. Intermontane plateau: a plateau surrounded by mountains on all sides.
Lumbering : The cutting down of trees and the processes leading to the manufacture of products like paper, newsprint, synthetic fibres, etc.
Lumberjacks : Workers engaged in lumbering.
Meltwater : Water derived from the melting of glacier ice and/or snow.

VALUES AND LIFE SKILLS

All occupations are important. Every job has dignity and deserves our respect.
How do you treat the people who work in your home and help you in your daily life ?
Answer:
We treat them with respect and dignity.

EXERCISES

A. Fill in the blanks

1. A narrow stretch of land that joins North America to South America and separates the Atlantic Ocean from the Pacific Ocean : The Isthmus of Panama.
2. The tropical islands, called the West Indies, are located in this sea : Caribbean Sea.
3. Aphysical division of North America around the Hudson Bay which has the oldest known hard rocks of the world : The Canadian Shield.
4. A river that flows northwards and drains into the Hudson Bay : River Meckenzie and River Nelson.

B. Identify who I am.

1. I am a city in North America which is a symbol of unity, history, and democracy : Washington DG.
2. I am an island at the entrance of river Hudson where the famous Statue of Liberty is situated : Liberty Island.
3. I am the city which is world famous for its film industry : Los Angeles.
4. I am the city which has the Ridean Canal : Ottawa
5. I am the city of Canada which was once the world’s leading grain port : Montreal

C. Give geographical reasons why 

Question 1.
The 49° N latitude and the 100°W longitude are important for North America.
Answer:
The 49° N latitude marks the boundary between Canada and United States whereas 100°W longitude passes through the centre of North America. So both are important.

Question 2.
The Western Cordilleras form part of the ‘Pacific Ring of Fire’.
Answer:
The Western Cordilleras i.e. the western part of North America from Alaska to the Isthmus of Panama consists of young fold mountain ranges which contain very active volcanoes and lie close to the pacific ocean thus forming a part of the ‘ Pacific Ring of Fire’.

Question 3.
The Appalachians appear as low hills today.
Answer:
The Appalachians are old fold mountains and the glaciers and rivers have eroded them over millions of years. So they appear as low hills today.

Question 4.
Lumbering is traditionally done in the winter season.
Answer:
In winters the sap in trees is frozen,making it easier to cut and drag the logs on frozen river grounds. The winter air is clean, refreshing and free from perts.

D. Answer the following questions in brief
Question 1.
Name the Italian explorer who reached North America in 1507 CE.
Answer:
Amerigo Vespucci.

Question 2.
Name some of the islands that are collectively called the West Indies.
Answer:
The tropical islands of the Caribbean sea are collectively called the West Indies. They include Cuba, Jamaica, Puerto Rico, Dominican Republic, Haiti, etc. form West Indies.

Question 3.
Why is New York an important city in the USA ?
Answer:
Hudson River is the famous Statue of Liberty on Liberty Island.

Question 4.
Where are the Great Lakes situated ? Which river drains these lakes into the Atlantic Ocean ?
Answer:
The Great Rivers are located in the Canadian or Laurentian shield. The St. Lawrence River connects and drains the Great Lakes.

Question 5.
Write about the largest river system of North America.
Answer:
The largest river system of America includes River Mackenzie falling into the Arctic Ocean. St. Lawrence, Hudson connecting all the Great Lakes draining into the North Atlantic Ocean, Yukon, Columbia falling into Pacific Ocean and Mississippi and Missouri rivers falling into Gulf of Mexico.

Question 6.
Where is the Grand Canyon situated ? Why is it so famous?
Answer:
The Grand Canyon of the Colorado River is 2000 m deep and 400 km long and so it is famous for its majesty and beauty.

D. Answer the following questions in one or two paragraphs

Question 1.
List the four major physical divisions of North America. Describe any one of them briefly.
Answer:
The four major physical divisions of North America are the Canadian or Laurentian shield, the Western Mountain System or Western Cordilleras, the eastern highlands or Appalachians Mountains and the central lowlands or Great Central Plains. The Central lowlands extend from Hindsom Bay in the north to
the Gulf of Mexico in the South covering distance of more than 6000 km and about 2000 km in width. They are also called the Great Central Plains. The plains are higher in West and slope northward in Canada. The main rivers which flow in these plains include Mackenzie, Mississippi—Missouri.

Question 2.
Why is the Canadian Shield region full of lakes ? Name any three lakes other than the five Great Lakes.
Answer:
The Canadian Shield is composed of oldest known hard rocks and the surface of land consists of many deep hollows of depression. When Ice Age ended, these depressions were filled by meltwater from glaciers and ice-sheets. Apart from the Great Lakes, Lake Winnipeg, Great Bear Lake, Great Slave Lake and Lake Athabasca are important lakes present in this region.

Question 3.
What are the various categories of lumberjacks ? What kind of work do they do ?
Answer:
The various categories of Lumberjacks include the high riggers, sawers or buckers. Skidders and haulers or transporters. The high riggers are people who climb the tall coniferous trees to cut off its branches first and then trunk.
The sawers use saw and axes to cut the trunk into lengths measuring 1 to 5 m.
The skidders mainly collect the logs and stack them along a frozen river bank, road or railway line.
The haulers ensure the transfer of logs down a river till they reach, a sawnill or factory. This include clearing ‘ log-jams’ with long poles or use sticks of dynamites to move logs which cause jams.

Question 4.
Describe how the lives and work of lumberjacks have changed in modern times.
Answer:
Lumberjacks used to have a very hard life in earlier days as their work of falling trees begins early followed by cutting off branches of fallen trees, skidding and hauling. They had to live in camps and start their days quiet early. But now settled communities of forest workers have developed. The forests are more accessible and they use power driven saws, powered cranes and automobiles.

E. Read books and encyclopaedias to find more information about Christopher Columbus, Amerigo Vespucci and other great explorers. Record your findings and stick some pictures alongside, if possible. Then share this information with other classmates and have a classroom discussion.
Answer:
Do it yourself.

F. Picture study


This is a photograph of the Grand Canyon in Arizona.

Question 1.
Why do you think this canyon is called ‘Grand’ ?
Answer:
This Canyon is about 2000 m deep and 400 km long because it is world famous for its majesty and beauty, so it is called the Grand Canyon.

Question 2.
Name the river that has carved out the Grand Canyon.
Answer:
Its carved out of Colorado River.

ICSE Solutions for Class 6 History and Civics – History – An Introduction

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APlusTopper.com provides step by step solutions for ICSE Solutions for Class 6 History and Civics Chapter 1 History – An Introduction. You can download the History and Civics ICSE Solutions for Class 6 with Free PDF download option. History and Civics for Class 6 ICSE Solutions all questions are solved and explained by expert teachers as per ICSE board guidelines.

ICSE Solutions Class 6 History & Civics Geography Biology Chemistry Physics Maths

Exercise

I. Fill in the blanks:

1. People who write history are known as Historians.
2. By Archaeology we mean the study of the remains of the ancient past.
3. The two Great epics tells us about the life and society in ancient past, besides being religious books.
4. Old buildings which are important historically are known as Monuments.
   
5. Meghadoot was written by Kalidasa.

II. Match Column A with Column B:


Answer:

III. Answer the following questions briefly :

Question 1.
What is history? What is the origin of the word‘history’?
Answer:
History is the study of our past, a record of the events that happened long ago. It tells us about the life of people during a particular period. The word ‘History’ comes from the Greek word ‘Histo’ which means ‘know this’.

Question 2.
Why do we study history? Give two reasons.
Answer:

1. History helps us to understand our society and culture.
2. History helps us to leam from our past mistakes so that we don’t repeat them.

Question 3.
Which period in history is called prehistoric?
Answer:
‘Pre-history’ means ‘before history’. This period refers to the era when man had not developed the art of writing. Hence, there are no written records of this period. The life of people during this period is constructed through tools, weapons, bones, etc.

Question 4.
Name two sources of history. What do literary sources include?
Answer:
Two sources of history are literary sources and archaeological sources. Literary sources include secular literature and religious literature. Writings related to a religion are called religious literature, for example, the Jatakas, the Ramayana. Secular literature is not related to a religion. It includes poems, plays, accounts by travelers, for example, the Indika of Megasthenes.

Question 5.
Give one example each of religious and secular literature.
Answer:
Example of religious literature — the Mahabharata. Example of secular literature —Abhigyan Shakuntalam.

Question 6.
What do we mean by culture?
Answer:
Culture is the sum total of knowledge, beliefs, morals, art, customs and laws and other capabilities and habits acquired by man as a member of society.

Question 7.
Explain the term archaeology.
Answer:
Archaeology means the study of the remains of the past such as inscriptions, monuments, tools, coins, potteiy, etc.

IV. Distinguish between

1. Archaeological sources and literary sources.
2. Monuments and inscriptions.
3. Religious and secular literature.

Answer:

1. Archaeological sources include inscriptions, coins, tools, weapons, pottery, bones, etc. Literary sources include books related to a religion and poems, plays, travelogues, etc.
2. Monuments are old buildings such as caves, stupas, temples, forts and palaces. Inscriptions are writings engraved on rocks, pillars, buildings, metal plates, etc.
3. Religious literature is related to a religion, for example, the Puranas (Hindus), the Jatakas (Buddhists), the Angas (Jains). Secular literature has nothing to do with a religion, for example, the Arthashastra of Kautilya, the Indika of Megasthenes.

V. Given below are some drawings. Circle those which you think below to prehistory.
VI. Picture study — This picture shows a valuable source of history.

1.Identify the source
Ans. The source is coin.

2.How do you think these are useful ?
Ans. Coins give us information about use of a metal during a particular period and the economic conditions of the people.

3.What do you understand by the term ‘numismatics’ ?
Ans. Numismatics is the study of coins.

Textbook Keywords

1. History is a record of people, places and events of the past arranged in chronological order.
2. Prehistory is the history of the period before writing was invented.
3. Archaeology  is the study of material remains of the distant past.
4. Parchment  is the dried skin of goats and sheep used for writing.
5. Sources Sources are clues from archaeology’ or literature which help historians to put together a period of history.
6. Monuments Monuments are ancient buildings such as temples, palaces and forts, which are valuable sources of information of the life and times of people in the distant past. Numismatics It is a study of coins.
7. Inscriptions are the engraving on solid objects such as metal surfaces, stone tablets, rocks, pillars, cave walls, etc. Epigraphy Epigraphy is the study of old inscriptions. Edicts Edicts are royal commands issued by the rulers. Manuscripts Manuscripts are the handwritten records of the past in the form of books.
8. Religious literature It refers to literacy writing dealing with religion.
9. Secular literature is non-religious literature such as plays, poems, accounts of foreign travelers and other works on politics, science, etc.

Additional Questions

A. Fill in the blanks.

1. History is record of people, places and events of the past, arranged in chronological order.
2. Prehistory is the history of the period before writings was invented.
3. The sources of history can be broadly classified into archaeological sources and literary
4. The study of coins is known as numismatics
5. Edicts are royal commands issued by kings.
6. Inscriptions are engravings on solid objects.
7. Handwritten records of the past are known as Manuscripts
8. Literary source material can be divided into religious literature and secular literature
9. The Greek ambassador in Chandragupta Maurya’s court was Magasthenes
10. The Chinese travelers who came to India were Fa Hien and Hiuen Tsang

B. Match the following.


Answer:


C. Answer the following questions.

Question 1.
What is history? Why do we study history?
Answer:
History is a record of people, places and events of the past, arranged in chronological order.We study history because it tells us about the problems of our ancestors, their aspirations as well as their achievements.

Question 2.
What is the difference between prehistory and history?
Answer:
The main difference between prehistory and history is that we have written records in history and have no written records in prehistory.

Question 3.
How many groups can the sources of history be broadly divided into? Name them.
Answer:
The sources of history can be broadly divided into two groups.

1. Archaeological Sources.
2. Literary Sources

Question 4.
What is archaeology? Why is it so important for the study of prehistory?
Answer:
Archaeology is the study of material remains of distant past. Archaeology is so important for the study of prehistory because we have no written records, only the materials like stones, metal tools, pottery, images, coins, monuments, jewelry and figures are very helpful in the study of past.

Question 5.
What are monuments?
Answer:
Monuments are ancient buildings such as temples, palaces and forts, which are valuable sources of information of the life and time of people in the distant past.

Question 6.
Name five archaeological objects that provide important clues to the history of humans in the Ancient Period.
Answer:
Stones, metal tools, pottery, monuments, coins and figures are archaeological objects, that provide important clues to the history of humans in the Ancient Period.

Question 7.
Why is the study of coins considered an important source of ancient history?
Answer:
The coins are an important source of information about the reign of kings the extent of their empires, economic conditions, trade, art and religion of that era. So the coins are considered an important source of ancient history.

Question 8.
What information do we get from inscriptions?
Answer:
The Inscriptions provide us the information about rulers, the extent of their empires, important events and also about the religious and cultural life of people in a particular period.

Question 9.
Why are inscriptions a reliable source of information?
Answer:
Inscriptions are reliable source of information because they were written during the reign of great king., and are still intact in their original form.

Question 10.
What are manuscripts? On what surfaces were they ; written?
Answer:
Manuscripts are the handwritten records of the past in the form of books. These records were written on a variety of surfaces such as dried sheep or goat skin, dried palm leaf, the bark of birch trees and much later, on paper.

Question 11.
How many categories can you divide literary sources into? Name them.
Answer:
Literary source can be divided into two categories

1. religious literature
2. secular literature

Question 12.
What do you understand by secular literature? Give two examples.
Answer:
Non-religious literature is known as secular literature, it includes biographies of important historical characters. For example Harshacharita by Banabhatta, dramas and poems by famous writers Kalidasa, folk tales such as Panchatantra.

D. State whether the following are true or false.

1. History is only a record of great kings and queens.
   False
2. The study of old inscriptions is known as epigraphy.
   True
3. Banabhatta wrote Harshacharita.
   True
4. Panchatantra is a part of religious literature.
   False
5. The Angas are the religious literature of the Buddhists.
   False

E. Picture study.

The picture below is a painting from a manuscript of the Rig Veda showing the various gods and goddesses worshiped.

1. What kind of source of history is this?
Ans. It is a Literary source of history.

2.Is this religious or secular in nature?
Ans. This is religious in nature.

3. What kind of information does this source of history reveal?
Ans. This sources of history have helped historians to reconstruct the distant past and give a fairly accurate picture of ancient India.

Selina Concise Biology Class 7 ICSE Solutions – Nervous System

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ICSESolutions.com provides step by step solutions for Selina Concise ICSE Solutions for Class 7 Biology. You can download the Selina Concise Biology ICSE Solutions for Class 7 with Free PDF download option. Selina Publishers Concise Biology for Class 7 ICSE Solutions all questions are solved and explained by expert teachers as per ICSE board guidelines.

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Selina Concise ICSE Solutions for Class 7 Biology Chapter 6 Nervous System

Synopsis —

• The interaction of these activities of a living being as per the needs of the body internally or externally is called coordination.
• Nervous coordination is brought about by the nervous system which is made up of the brain, spinal cord, nerves and the sense organs.
• Chemical coordination is brought about through chemical messengers called hormones.
• The nervous system is made up of special cells called nerve cells or neurons.
• The end of the axon terminates in a number of branches called terminal branches.
• The terminal branches of the axon of one neuron lie very close to the dendrites of another neuron. This point of contact is called a synapse.
• A nerve is formed of a bundle of axons (nerve fibres) enclosed in a tubular medullary sheath. There are three kind of nerves as describe
  1. sensory nerve
  2. motor nerve
  3. mixed nerve.
• The nervous sytem of human beings consists of the following three systems:
  1. The central nervous system
  2. The peripheral nervous system
  3. The autonomic nervous system
• The brain has three main parts:
  1. The cerebrum
  2. The cerebellum, and
  3. The medulla oblongata
• The main functions of the spinal cord are:
  1. To control reflexes below the neck.
  2. To conduct messages from the skin and muscles to the brain.
  3. To conduct commands from the brain to muscles of the trunk and limbs.
• The autonomic nervous system consists of a pair of chain of nerves and ganglia found on either side of the backbone.  This system controls the involuntary activities of the internal organs.
• Stimulus: Any change in the environment that usually results in change in the activity of the body.
• Response: The activity of the body in response to a received stimulus.
• Impulse: A wave of electrical disturbance that runs through the nerves.
• Receptors : These are sense organs which receives the stimulus.
• Effector: Any muscle or gland where the response occurs.

Review Questions

Multiple Choice Questions:

1. Put a tick mark (✓) against the correct alternative in the following statements:

(a) Medulla oblongata controls
(i) Smelling
(ii) Beating of heart and respiratory movement
(iii) Intelligence and will power
(iv) Balancing the body

(b) Spinal cord is an extention of:
(i) Cerebellum
(ii) Cerebrum
(iii) Vertebral column
(iv) Medulla oblongata

(c) Body posture is mantained by:
(i) Cerebellum
(ii) Cerebrum
(iii) Medulla oblongata
(iv) Spinal cord

Short Answer Questions:

1. Write one word in the space provided to complete the second pair of the related words pertaining to nervous system.
Memory: cerebrum:: breathing:
Balance: cerebellum:: reasoning:
Answer:
Memory: cerebrum: beathing: medulla oblongata
Balance: cerebellum:: reasoning: cerebrum

2. (a) Name three major divisions of the human nervous system.
Answer:

1. The central nervous system (brain and spinal cord)
2. The peripheral nervous system
3. The autonomic nervous system

(b) Name the three main parts of human brain.
Answer:

1. Cerebrum
2. Cerebellum
3. Medulla oblongata

3. Given here is the diagram of a neuron. Name the parts numbered 1-6.

Answer:

1. dendrite
2. dendrite (Terminal Arborization)
3. nucleus
4. axon (Nerve fibre)
5. cell Body (cyton)
6. node of ranvier
7. sheath

Long answer questions

Question 1.
With the help of a suitable diagram describe the structure of a neuron.
Answer:

Nervous system consists of special cells called nerve cells or neurons. It has a main cell body called cyton. It gives out many processes called dendrites. From it a very long process is given out. It is called axon or nerve fibre.

The cell body has a nucleus. The dendrites get the message from the organs and send this message to the axon through the cell body. Then the axon sends the message to muscles to contrast or to the gland for secretion.

The neurons make contact with one another through their processes. The axon at its end branches and meets the dendrites of another neuron. The meeting point is called synapse. The message is passed on from one axon to the dendrites of another neuron. How the message goes ? It is like this:
Organ → Message goes to dendrites →Cell body → Axon → Muscles or  glands

Question 2.
Briefly describe the structure of the cerebrum in human brain, and mention its functions.
Answer:
Brain consists of main three parts and lies in the cranial cavity of skull.

1. The cerebrum
2. The cerebellum
3. The medulla oblongata

Cerebrum — It is very large and form two third of the whole brain. The two hemispheres are separated from each other by a deep longitudinal groove, the median fissure. The outer surface is folded with ridges and grooves. The hemispheres are hollow from inside and their walls have outer and inner portions. The outer portion has cell bodies of the neurons and it is called grey matter.
The wavery edges of the folded layer has large number of neurons to the extent of nine billion. The inner portion of the cerebrum has axons and it is called white matter.
Functions:

1. It controls all the voluntary activities.
2. It is the seat of intelligence, consciousness and will power.

Question 3.
Mention the three functions of spinal cord.
Answer:
Spinal cord has the following functions.

1. It is the centre of reflex actions below the neck.
2. It carries messages from the skin and muscles to the brain.
3. All the stimuli and responses are passed from and to the brain through the spinal cord.

Question 4.
Describe three kinds of nerves, giving example of each.
Answer:
A nerve is formed by a group of nerve fibres (axons) encased
by tubular medullary sheath. The medullary sheath acts as insulation and do not allow mixing up of impulses of the neighbouring axons (nerve fibres) We have three kinds of nerves:

1. Sensory nerve — It brings impulses from sense organs as these have sensory fibres. These nerve carry the impulses from the sense organs to the brain or to the spinal cord as optic nerve of the eye.
2. Motor nerves—These carry impulses to muscles or glands from the brain or spinal cord. These nerves have only motor fibres as nerves to the muscles of the eye ball.
3. Mixed nerve — It has both sensory and motors fibres as nerve going to the tongue.

Question 5.
What are voluntary and involuntary actions ? Which part of the nervous system controls them ?
Answer:
Voluntary action: When an action is produced with the involvement of thoughts, they are called the voluntary action. For example, writing an article jumping from heights. These actions are produced consciously by our body.
Involuntary action: Actions which take place without consciousness or willingness of an individual are called the involuntary action. Digestion, heart beating, sneezing, etc are few examples of involuntary actions.

1. The cerebral cortex controls our voluntary actions like running and walking etc.
2. Medulla helps in involuntary actions like hearbeat, breathing etc.

Additional Questions

I. Multiple choice questions. Tick (✓) the correct choice:

I. Nervous system in humans consists of
(a) brain and nerves
(b) brain and spinal cord
(c) brain, spinal cord and nerves
(d) none of the above.

II. Fill in the blanks:

1. Basic structural unit of the nervous system is the neuron.
2. Central nervous system consists of brain and spinal cord.
3. A neuron consists of cell body, dendrite and axon.
4. The neurons carrying impulses from the brain to the muscles are called motor or efferent neurons.
5. Peripheral nervous system consists of nerves.
6. The three main parts of the brain are cerebrum, cerebellum and medulla oblongata (brain stem).

III. State whether the following statements are true (T) or false (F):

1. Each neuron consists of three parts called cell body, cyton and axon.
 False. Each neuron consists of three parts called cell body, dendrite and axon.

2. The largest part of the brain is the cerebrum.
 True.

3. Cerebellum maintains balance of the body.
True.

4. There are 31 pairs of cranial nerves.
 False. There are 12 pairs of cranial nerves.

IV. Find the odd-one out, giving reasons:
Axon, cell body, dendrite, cerebellum
Ans. Cerebellum is the odd one out as it is a part of brain while rest three are parts of a neuron.

V. Define the following:
1. Reflex arc
2. Sensory neuron
3. Motor neuron
4. Neuron
Answer:

1. Reflex arc: The path that an impulse takes in a reflex action is called a reflex arc.
2. Sensory neuron: The neurons which carry impulses
   from the body parts to the spinal cord or the brain are called sensory or afferent neurons. For example, optic nerve of the eye.
3. Motor neuron: The neurons which carry impulses from the brain or spinal cord to the body parts are called motor or efferent neurons.
4. Neuron: A neuron or a nerve cell is the basic structural and functional unit of the nervous system.

VI. Answer the following:

Question 1.
 Describe the two parts of the nervous system.
Answer:
The nervous system of human has two parts:

1. Central Nervous System (CNS): It consists of the brain and the spinal cord. The brain lies protected inside the skull while the spinal cord is protected within the vertebral column.
2. Peripheral Nervous System (PNS): It consists of nerves arising from the spinal cord (spinal nerves) and the brain (cranial nerves). These nerves link the central nervous system with the various body organs.

Question 2.
What are nerves? Mention the types of nerves found in humans.
Answer:
A bundle of nerve fibres joined together as a tubular sheath that transmits impulses between brain or spinal cord and other body parts is called a nerve. The nerves constitute the peripheral nervous system.
Nerves are of two types in humans:

1. Cranial nerves: They emerge from the brain. There are 12 pairs of cranial nerves.
2. Spinal nerves: They emerge from the spinal cord. There are 31 pairs of spinal nerves.

Question 3.
Explain the structure of brain.
Answer:
The brain is the main control centre of the nervous system.
It is enclosed within the bony shell of cranium.
It consists ofthree main part:

1. 1. Cerebrum: It is the uppermost and largest part with many ridges and grooves. It is divided into right and left halves called cerebral hemispheres. It controls our thinking, reasoning, intelligence, memory and perception of pain, sound, touch, taste and smell.
   2. Cerebellum: It is located under the cerebrum at the back of the head. It maintains balance of the body and coordinates muscular activity.
   3. Brain stem (medulla oblongata): It joins the brain to the spinal cord. It controls the activity of internal organs like heartbeat and breathing.
      

Question 4.
Compare the nervous system and the endocrine system.
Answer:
Nervous system

1. Messages are sent through nerve fibres.
2. It consists of brain, spinal cord and nerves.
3. No hormones are secreted. Messages are sent as impulses.
4. Transmission of impulse is quick.

Endocrine system

1. Messages are sent through blood in the form of hormones.
2. It consists of endocrine glands.
3. Hormones secreted by glands regulate the body activities. .
4. Transmission takes time.

Selina Concise Chemistry Class 7 ICSE Solutions – Physical and Chemical Changes

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ICSESolutions.com provides step by step solutions for Selina Concise ICSE Solutions for Class 7 Chemistry. You can download the Selina Concise Chemistry ICSE Solutions for Class 7 with Free PDF download option. Selina Publishers Concise Chemistry for Class 7 ICSE Solutions all questions are solved and explained by expert teachers as per ICSE board guidelines.

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Selina Concise ICSE Solutions for Class 7 Chemistry Chapter 2 Physical and Chemical Changes

Points to Remember :

1. All changes are classified into two types
   (i) Physical change
   (ii) Chemical change.
2. Physical Change— A physical change is a temporary change in which no new substance is formed and chemical composition remains same. e.g. Melting of ice.
3. Chemical Change— A chemical change is a permanent change, in which a new substances are formed whose chemical composition and physical properties are different, e.g. Burning of a candle.
4. Chemical Reaction— Any chemical change in matter involving its transformation into one or more new substances is called a chemical reaction.
5. Chemical Equations— A chemical equation is the symbolic representation of a chemical reaction using the symbols and the formulae of the substances involved in the reaction.
6. The substances that react with one another are called reactants, and the new substances thus formed are called products.
7. A balanced chemical reaction is one in which the number of the atoms of each element on the
8. reactant side is equal to the number of atoms of that element on the product side.
9. The law of conservation of mass states that mass can neither be created nor be destroyed.
10. A chemical equation gives both qualitative and quantitative information about reactants aftd products.
11. The type of chemical reaction in which two substances combine to form a new substance is known as combination reaction.
12. The type of chemical reaction in which a substance breaks up on heating to form two or more simpler substances,
    which can be either elements or compounds, known as decomposition reaction.

Exercise

Question 1.
(a) Define:
(i) a physical change
(ii) a chemical change
(b) Give two examples for each of the above two changes.
Answer:
(a) (i) Physical chagne : A temporary change in which no new substance is formed, the composition of substance remains the same, though its state, shape and size may change.
(ii) Chemical change : A permanent change in which new substances are formed whose composition and properties are completely different from those of the original substances.
(b) Physical change:
(i) Change of water into its vapours.
(ii) Heating of iron rod.
Chemical change:
(i) Burning of wood.
(ii) Breathing.

Question 2.
What are reversible and irreversible changes ? Give one example for each.
Answer:

1. Reversible change : When a change in a substance can be reversed by changing the conditions, it is said to be a reversible change.
   Example : Melting of ghee or wax.
2. Irreversible change : When a substance can not be brought back to its original state after a change, it is said to be an irreversible change.
   Example : Souring of milk.

Question 3.
Mention a change which is always
Answer:

1. Desirable : Changes that are useful to man are desirable changes, e.g. change of milk into curd.
2. Undesirable : Change that brings about destruction is an undesirable change, e.g. floods and epidemics are undesirable changes.
3. Periodic : Changes that are repeated at regular intervals of time are called periodic changes, e.g. change of day and night.

Question 4.
Is burning a physical change or a chemical change? Why?
Answer:
Burning is a chemical change as new substance is formed with new properties and it cannot be reversed.

Question 5.
A burning candle shows both physical and chemical changes. Explain ?
Answer:
A burning candle produces wax vapours which solidify and form wax again is physical change. At the same time wax on burning produces water vapours and carbondioxide which escape into the atmosphere which are new substances with new properties. It is a chemical change.
Hence burning of candle shows both physical and chemcial changes.

Question 6.
State three differences between evaporation and boiling
Answer:

Evaporation	Boiling
Evaporation is a slow process. Evaporation takes place from the surface of the liquid. Evaporation takes place at all temperature.	Boiling is a fast process. Bgiling takes place from all parts of the liquid. Boiling takes place at a fixed temperature on heating.

Question 7.
State four differences between physical and chemical changes.
Answer:
Four differences are :

Physical change	Chemical change
No new substances with new properties are formed. It can be reversed by simple physical methods. It is temporary change. Energy is neither needed nor produced.	New substances with new properties are formed. Change cannot be reversed by simple physical methods. It is permanent change. Energy is either needed or evolved.

Question 8.
What do you observe when :

1. water is boiled
   On boiling water changes into steam (gas) physical change.
2. a piece of paper is burnt
   On burning piece of paper produces carbon dioxide and ash is left behind. Is a chemical change.
3. some ice cubes are kept in a glass tumbler
   Ice cubes (solid) turn into water (liquid) only state changes (physical change).
4. solid ammonium chloride is heated
   Solid ammonium chloride on heating changes into vapours (change of state) is physical change.
5. an iron nail is kept in tap water for few days
   We observe reddish brown coating on the nail called rust (entirely new substance) is chemical change.
6. a spoon of sugar is heated in a pan
   When a spoon of sugar is heated in a pan, black (charred sugar) (carbon) is seen. Is a chemical change.
7. lighted match stick is brought near the mouth of the test tube containing hydrogen gas.
   We observe that hydrogen bums at the mouth of test tube with blue flame and pop sound is heard. It is chemical change.
8. quick lime is dissolved in water.
   The following two observations will be observed
   (i) A hissing sound is observed.
   (ii) The mixture starts boiling and lime water is obtained.
9.  liittle ammount of curd is added to a bowl containing warm milk and kept for five hours.
   When a little amount curd is added to a bowl containing warm milk and kept for five hours, a permanent change occured.
   The milk will change to curd. On boiling water changes into steam (gas) physical change.

Question 9.
Name a chemical change which takes place in presence of:
Answer:
Heat:

1. Burning of paper.
2. Cooking of food need heat.

Light :

1. Formation of food by plants i.e. photosynthesis need light.
2. Hydrogen and chlorine react in presence of light

Electricity:

1. Water breaks into hydrogen and oxygen on passing electricity.
2. Sodium chloride solution breaks up into its components sodium and Chlorine on passing electric current through sodium chloride solution.

Objective Type Questions

Question 1.
Fill in the blanks.

1. A new substance is always formed in a chemical change.
2. Melting of ice is a physical change.
3. When a candle burns, wax melts. Melting of wax is a physical change.
4. Chemical change occurs as a result of rearrangement of atoms between two substances.
5. Burning of a fuel is a chemical change.
6. Revolution of the earth around the sun is a natural periodic change.
7. Growing of a seedling into a plant is chemical change.

Question 2.
State whether the following are physical or chemical changes.

1. glowing of a bulb — physical change,
2. burning of sugar — chemical change,
3. heating of water — physical change,
4. growing of a piglet into a pig — chemical change,
5. burning of wood — chemical change,
6. passing electric current through a heater rod — physical change.
7. water cycle in nature — physical change,
8. respiration in living beings — chemical change,
9. shaping a piece of glass — physical change,
10. lightning — chemical change,
11. (energy produced) dissolving sugar in water — physical change,
12. heating a mixture of iron filings and sulphur—chemical change.
13. mixing oil with water — physical change.
14. cutting wood into small pieces — physical change,
15. photosynthesis — chemical change.
16. Digestion of food — chemical change.
17. Melting of wax — physical change.
18. Boiling of an egg — chemical change.
19. Slaking of lime — chemical change.

Question 3.
Match the following:



Answer:

Question 4.
Write true or false against the following statements :

1. Cutting of paper into pieces is a chemical change.
   False
2. Rusting of iron is a chemical change.
   True
3. Earthquake is a desirable change.
   False
4. Melting of ice is a physical change.
   True
5. Burning of sugar is a temporary change.
   False

Multiple Choice Questions

Tick (√) the correct alternative from the choice given for the following statements :
Question 1.
A substance which can not sublime is
Answer:

1. iodine
2. camphor
3. sugar
4. dry ice

Question 2.
When you put some ice cubes in a glass, droplets of water are formed on the outerwall of the glass. This explains the phenomenon of
Answer:

1. melting
2. freezing
3. condensation
4. evaporation

Question 3.
Burning is a
Answer:

1. slow process
2. fast process
3. natural process
4. none of the above

Question 4.
Which one of the following is volatile in nature ?
Answer:

1. common salt
2. petrol
3. water
4. milk

Question 5.
An example of both physical and chemical change is
Answer:

1. burning of candle
2. melting of ice
3. cooking of food
4. blowing of bulb

Question 6.
The compound rust is a hydrated oxide of
Answer:

1. copper
2. aluminium
3. iron
4. gold

Question 7.
When sugar is heated, its colour changes into
Answer:

1. red
2. brown
3. black
4. grey

Question 8.
A pop sound is heard when a lighted match stick is brought
near the mouth of a jar. This indicates the release of gas.
Answer:

1. oxygen
2. hydrogen
3. nitrogen
4. water-vapour

Question 9.
When we add water to the following substances, which one will show a chemical change ?
Answer:

1. salt
2. sugar
3. oild
4. quick lime