Monthly Archives: October 2022

Statistics

Statistics is the study of collection, organization, analysis and interpretation of data.

Data

A distinct piece of information in the form of fact or figures collected or represented for any specific purpose is called Data.  In Latin, it is known as the Datum.

Collection of Data

Data are generally of two types

• Primary Data
• Secondary Data

Primary Data

Data collected from any firsthand experience for an explicit use or purpose is known as Primary Data

Secondary data

Data collected by any third party for a different purpose other than the user is known as Secondary Data.

Presentation of Data

After collecting data it is important to present it in a meaningful manner. There are many ways to present data.

1. Ungrouped Data

a. Raw Data– If there is no change in the data and it is in the same form as it is collected then it is said to be raw data.

Example

The marks obtained by 10 students in a Sanskrit test are

 55 36 95 73 60 42 25 78 75 62

Range- The difference between the highest and the lowest number of data is called Range.

b. Frequency Distribution– When the number of items is large then we can convert it into the tabular form which is called a Frequency Distribution Table.

Frequency is the number of times the item comes in the table.

2. Grouped Data

To present the very large number of items in a data we use grouped distribution table.

a. Class Interval – The group used to classify the data is called the class interval i.e. 20 – 30, 30 – 40.

b. Upper Limit – In each class interval, the greatest number is the upper-class limit.

c. Lower Limit – In each class interval, the smallest number is the lower class limit.

d. Class Size – It is the difference between the upper limit and the lower limit i.e. 10.

e. Class Mark – The midpoint of each class interval is the class mark.

Grouped data could be of two types as below:–

Inclusive or discontinuous Frequency Distribution – If the upper limit of one class is different from the lower limit next class then it is said to be an Inclusive or discontinuous Frequency Distribution.

Exclusive or continuous Frequency Distribution – If the upper limit of one class is the same as the lower limit of the next class then it is said to be exclusive or continuous Frequency Distribution

Graphical Representation of Data

As you know a picture is better than thousand words so represent data in an easier way is to represent it graphically. Some of the methods of representing the data graphically are

1. Bar Graph

It is the easiest way to represent the data in the form of rectangular bars so it is called Bar graph.

• The thickness of each bar should be the same.
• The space between in bar should also be same.
• The height of the bar should be according to the numerical data to be represented.

Example

Represent the average monthly rainfall of Nepal for the first six months in the year 2014.

Month	Jan	Feb	Mar	Apr	May	Jun
Average rainfall	45	65	40	60	75	30

Solution

• On the x-axis mark the name of the months.
• On the y-axis mark the class interval which we have chosen.
• Then mark the average rainfall respective to the name of the month by the vertical bars.
• The bars could be of any width but should be same.
• This is the required bar graph.

2. Histogram

It is like the Bar graph only but it is used in case of a continuous class interval.

• The class intervals are to be taken along an x-axis.
• The height represents the frequencies of the respective class intervals.

Example

Draw the histogram of the following frequency distribution.

Daily earnings (in Rs)	700 – 750	750 – 800	800 – 850	850 – 900	900 – 950	950 – 1000
No. of stores	6	9	2	7	11	5

Solution

• Mark the daily earnings on the x-axis.
• Mark the no. of stores on the y-axis.
• As the scale is starting from 700 so we will mark the zigzag to show the break.
• Mark the daily earnings through the vertical bars.

3. Frequency Polygon

To draw the frequency polygon

• First, we need to draw a histogram
• Then join the midpoint of the top of the bars a line segment and the figure so obtained is required frequency polygon.
• The midpoint of the first bar is to be joined with the midpoint of the imaginary interval of the x-axis
• The midpoint of the last bar is to be joined with the midpoint of the next interval of the x-axis. 

If we need to draw the frequency polygon without drawing the histogram then first we need to calculate the class mark of each interval and these points will make the frequency polygon.

Example

Draw the frequency polygon of a city in which the following weekly observations were made in a study on the cost of living index without histogram.

Step 1: First of all we need to calculate the class mark of each class interval.

Step 2: Take the suitable scale and represent the class marks on the x-axis.

Step 3: Take the suitable scale and represent the frequency distribution on the y-axis.

Step 4: To complete the frequency polygon we will join it with the x-axis before the first class and after the last interval.

Step 5: Now plot the respective points and join to make the frequency polygon.

Measures of Central Tendency

To make all the study of data useful, we need to use measures of central tendencies. Some of the tendencies are

1. Mean

The mean is the average of the number of observations. It is calculated by dividing the sum of the values of the observations by the total number of observations.

It is represented by x bar or.

The meanof n values x₁, x₂, x₃, …… x_n is given by

Mean of Grouped Data (Without Class Interval)

If the data is organized in such a way that the frequency is given but there is no class interval then we can calculate the mean by

where, x₁, x₂, x₃,…… x_n are the observations

f₁, f2, f3, …… f_n are the respective frequencies of the given observations.

Example

Here, x₁, x₂, x₃, x₄, and x₅ are 20, 40, 60, 80,100 respectively.

and f₁ , f₂ , f₃ , f₄, f₅ are 40, 60, 30, 50, 20 respectively.

2. Median

The median is the middle value of the given number of the observation which divides into exactly two parts.

For median of ungrouped data, we arrange it in ascending order and then calculated as follows

• If the number of the observations is odd then the median will beAs in the above figure the no. of observations is 7 i.e. odd, so the median will beterm.

= 4^th term.

The fourth term is 44.

• If the number of observations is even then the median is the average of n/2 and (n/2) +1 term.

Example

Find the median of the following data.

1. First, we need to arrange it in ascending order.

4, 6, 7,8,10,12,12,13

2. The no. of observation is 8. As the no. of observation is even the median is the average of n/2 and (n/2)+1.

3.

4.  4^th term is 8 and the 5^th term is 10.

5. So the median

3. Mode

The mode is the value of the observation which shows the number that occurs frequently in data i.e. the number of observations which has the maximum frequency is known as the Mode.

Example

Find the Mode of the following data:

15, 20, 22, 25, 30, 20,15, 20,12, 20

Solution

Here the number 20 appears the maximum number of times so

Mode = 20.

Remark: The empirical relation between the three measures of central tendency is

3 Median = Mode + 2 Mean

Introduction to Circles

There are lot many objects in our life which are round in shape. Few examples are the clock, dart board, cartwheel, ring, Vehicle wheel, Coins, etc.

Circles

• Any closed shape with all points connected at equidistance from centre forms a Circle.
• Any point which is at equidistance from anywhere from its boundary is known as the Centre of the Circle.
• Radius is a Latin word which means ‘ray’ but in the circle it is the line segment from the centre of the Circle to its edge. So any line starting or ending at the centre of the circle and joining anywhere on the border on the circle is known as the Radius of Circle.

Interior and Exterior of a Circle

In a flat surface, the interior of a circle is the line whose distance from the centre is less than the radius. 

The exterior of a circle is the line in the plane whose distance from the centre is larger than the radius.

Terms related to circle

• Chord: Any straight line segment that’s both endpoints falls on the boundary of the circle is known as Chord. In Latin, it means ‘bowstring’.
• Diameter: Any straight line segment or Chord which passes through the centre of the Circle and its endpoints connects on the boundary of the Circle is known as the Diameter of Circle. So in a circle Diameter is the longest chord possible in a circle.
• Arc: Any smooth curve joining two points is known as Arc. So in Circle, we can have two possible Arcs, the bigger one is known as Major Arc and the smaller one is known as Minor Arc.
• Circumference: It is the length of the circle if we open and straightened out to make a line segment.

Segment and Sector of the Circle

A segment of the circle is the region between either of its arcs and a chord. It could be a major or minor segment.

Sector of the circle is the area covered by an arc and two radii joining the centre of the circle. It could be the major or minor sector.

Angle Subtended by a Chord at a Point

If in a circle AB is the chord and is making ∠ACB at any point of the circle then this is the angle subtended by the chord AB at a point C.

 Likewise, ∠AOB is the angle subtended by chord AB at point O i.e. at the centre and ∠ADB is also the angle subtended by AB at point D on the circle.

Theorem 1: Any two equal chords of a circle subtend equal angles at the centre.

Here in the circle, the two chords are given and PQ = RS with centre O.

So OP = OS = OQ = OR (all are radii of the circle)

∆POQ ≅ ∆SOR

∠POQ = ∠SOR  

This shows that the angles subtended by equal chords to the centre are also equal.

Theorem 2: If the angles made by the chords of a circle at the centre are equal, then the chords must be equal.

This theorem is the reverse of the above Theorem 1.

Perpendicular from the Centre to a Chord

Theorem 3: If we draw a perpendicular from the centre of a circle to any chord then it bisects the chord.

If we draw a perpendicular from the centre to the chord of the circle then it will bisect the chord. And the bisector will make 90° angle to the chord.

Theorem 4: The line which is drawn from the centre of a circle to bisect a chord must be perpendicular to the chord.

If we draw a line OB from the centre of the circle O to the midpoint of the chord AC i.e. B, then OB is the perpendicular to the chord AB.

If we join OA and OC, then

In ∆OBA and ∆OBC,

AB = BC (B is the midpoint of AC)

OA = OC (Both are the radii of the same circle)

OB = OB (same side)

Hence, ΔOBA ≅ ΔOBC (both are congruent by SSS congruence rule)

⇒ ∠OBA = ∠OBC (respective angles of congruent triangles)

∠OBA + ∠OBC = ∠ABC = 180° [Linear pair]

∠OBC + ∠OBC = 180° [Since ∠OBA = ∠OBC]

2 x ∠OBC = 180°

∠OBC = 90^o

∠OBC = ∠OBA = 90°

∴ OB ⊥ AC

Circle through Three Points

Theorem 5: There is one and only one circle passing through three given non-collinear points.

In this figure, we have three non-collinear points A, B and C. Let us join AB and BC and then make the perpendicular bisector of both so that RS and PQ the perpendicular bisector of AB and BC respectively meet each other at Point O.

Now take the O as centre and OA as the radius draw the circle which passes through the three points A, B and C.

This circle is known as Circumcircle. Its centre and radius are known as the Circumcenter and Circumradius.

Equal Chords and Their Distances from the Centre

Theorem 6: Two equal chords of a circle are at equal distance from the centre.

AB and CD are the two equal chords in the circle. If we draw the perpendicular bisector of these chords then the line segment from the centre to the chord is the distance of the chord from the centre.

If the chords are of equal size then their distance from the centre will also be equal.

Theorem 7: Chords at equal distance from the centre of a circle are also equal in length. This is the reverse of the above theorem which says that if the distance between the centre and the chords are equal then they must be of equal length.

Angle Subtended by an Arc of a Circle

The angle made by two different equal arcs to the centre of the circle will also be equal.

There are two arcs in the circle AB and CD which are equal in length.

So ∠AOB = ∠COD.

Theorem 8: The angle subtended by an arc at the centre is twice the angle subtended by the same arc at some other point on the remaining part of the circle.

In the above figure ∠POQ = 2∠PRQ.

Theorem 9: Angles from a common chord which are on the same segment of a circle are always equal.

If there are two angles subtended from a chord to any point on the circle which are on the same segment of the circle then they will be equal.

∠a = (1/2) ∠c (By theorem 8)

∠b = (1/2) ∠c

∠a = ∠b

Cyclic Quadrilaterals

If all the vertex of the quadrilateral comes on a circle then it is said to be a cyclic quadrilateral.

Theorem 10: Any pair of opposite angles of a cyclic quadrilateral has the sum of 180º.

∠A + ∠B + ∠C + ∠D = 360º (angle sum property of a quadrilateral)

∠A + ∠C = 180°

∠B + ∠D = 180º

Theorem 11: If the pair of opposite angles of a quadrilateral has sum of 180º, then the quadrilateral will be cyclic.

This is the reverse of the above theorem.

Area of a Closed Shape

The part of any plane which is enclosed with the closed figure is known as the Planar Region. And the measure of this region is called the Area of that figure. This is expressed in the form of numbers using any unit.

Properties of the Area of a figure

• If the shape and size of the two figures are the same then these are said to be congruent. And if the two figures are congruent then their area will also be the same. If ∆ABC and ∆DEF are two congruent figures then ar (∆ABC) = ar (∆DEF).

• But if the two figures have the same area they need not be congruent.

• If the two non-overlapping plane regions form a new planner region. Let Area of the square be ar(S) and Area of Triangle be ar (T). So Area of the new figure is Ar (P) = ar(S) + ar (T) 

Figures on the Same Base and Between the Same Parallels

If the two figures have the same base and the vertices opposite to the base is also on the line parallel to the base then the two figures are said to be on the same base and between the same parallels.

∆ABC and ∆BDC have the same base and the opposite vertex is on the parallel line.

Parallelograms on the same Base and between the same Parallels

If the two parallelograms have the same base and are between the same parallel lines then these two parallelograms must have equal area.

Here, ABCD and ABGH are the two parallelograms having common base i.e. AB and between the two parallel lines i.e. AB and HC.

ar (ABCD) = ar (ABGH)

Remark: The parallelograms having the same base and equal area than these two parallelograms must lie between the same parallels.

Area of Parallelogram

Area of parallelogram = base × height

Height is the perpendicular on the base.

If the Area is given and one of the height or base is missing then we can find it as

Remark: The formula of area of the parallelogram is base × height that’s why the two parallelograms having the same base and between the same parallel lines have equal area.

Example:

Calculate the Area of the parallelogram if the base is 15 ft and the height is 3 ft.

Solution:

Given b = 15 ft

h = 3 ft

Area of parallelogram = b × h

= 15 × 3

= 45 ft²

Triangles on the same Base and between the same Parallels

If the two triangles are on the same base and their opposite vertex is on the parallel line then their area must be equal.

Here, ABC and DBC are the two triangles having common base i.e. BC and between the two parallel lines i.e. XY and BC.

ar (ABC) = ar (DBC)

Remark: If the triangles have the same base and equal area then these two triangles must lie between the same parallels.

Area of Triangle

Median of a Triangle

The line segment from any vertex of the triangle to the midpoint of the opposite side is the Median.

There are three medians of a triangle and the intersection of all the three medians is known as the Centroid.

The median divides the triangle into two equal parts.

In ∆ABC AE, CD and BF are the three medians and the centroid is the point O.

AE divides the triangle into two equal parts i.e. ∆ACE and ∆AEB,

CD divides the triangle into two equal parts i.e. ∆CBD and ∆CDA

BF divides the triangle into two equal parts i.e. ∆BFA and ∆BFC.

A Parallelogram and a Triangle on the same base and also between same parallel

If a triangle is on the base which is same with a parallelogram and between the same parallel line then the area of the triangle is half of the area of the parallelogram.

Here ∆ ABC and parallelogram ABCE are on the same base and between same parallel lines i.e. XY and BC so 

Quadrilateral

Any closed polygon with four sides, four angles and four vertices are called Quadrilateral. It could be regular or irregular.

Angle Sum Property of a Quadrilateral

The sum of the four angles of a quadrilateral is 360°

If we draw a diagonal in the quadrilateral, it divides it into two triangles.  

And we know the angle sum property of a triangle i.e. the sum of all the three angles of a triangle is 180°.

The sum of angles of ∆ADC = 180°.

The sum of angles of ∆ABC = 180°.

By adding both we get ∠A + ∠B + ∠C + ∠D = 360°

Hence, the sum of the four angles of a quadrilateral is 360°.

Example

Find ∠A and ∠D, if BC∥ AD and ∠B = 52° and ∠C = 60° in the quadrilateral ABCD.

Solution:

Given BC ∥ AD, so ∠A and ∠B are consecutive interior angles.

So ∠A + ∠B = 180° (Sum of consecutive interior angles is 180°).

∠B = 52°

∠A = 180°- 52° = 128°

∠A + ∠B + ∠C + ∠D = 360° (Sum of the four angles of a quadrilateral is 360°).

∠C = 60°

128° + 52° + 60° + ∠D = 360°

∠D = 120°

∴ ∠A = 128° and ∠D = 120 °.

Types of Quadrilaterals

S No.	Quadrilateral	Property	Image
1.	Trapezium	One pair of opposite sides is parallel.
2.	Parallelogram	Both pairs of opposite sides are parallel.
3.	Rectangle	a. Both the pair of opposite sides is parallel. b. Opposite sides are equal. c. All the four angles are 90°.
4.	Square	a. All four sides are equal. b. Opposite sides are parallel. c. All the four angles are 90°.
5.	Rhombus	a. All four sides are equal. b. Opposite sides are parallel. c. Opposite angles are equal. d. Diagonals intersect each other at the centre and at 90°.
6.	Kite	Two pairs of adjacent sides are equal.

Remark: A square, Rectangle and Rhombus are also a parallelogram.

Properties of a Parallelogram

Theorem 1: When we divide a parallelogram into two parts diagonally then it divides it into two congruent triangles.

∆ABD ≅ ∆CDB

Theorem 2: In a parallelogram, opposite sides will always be equal.

Theorem 3: A quadrilateral will be a parallelogram if each pair of its opposite sides will be equal.

Here, AD = BC and AB = DC

Then ABCD is a parallelogram.

Theorem 4: In a parallelogram, opposite angles are equal.

In ABCD, ∠A = ∠C and ∠B = ∠D

Theorem 5: In a quadrilateral, if each pair of opposite angles is equal, then it is said to be a parallelogram. This is the reverse of Theorem 4.

Theorem 6: The diagonals of a parallelogram bisect each other.

Here, AC and BD are the diagonals of the parallelogram ABCD.

So the bisect each other at the centre.

DE = EB and AE = EC

Theorem 7: When the diagonals of the given quadrilateral bisect each other, then it is a parallelogram.

This is the reverse of the theorem 6.

The Mid-point Theorem

1. If a line segment joins the midpoints of the two sides of the triangle then it will be parallel to the third side of the triangle.

If AB = BC and CD = DE then BD ∥ AE.

2. If a line starts from the midpoint of one line and that line is parallel to the third line then it will intersect the midpoint of the third line. 

If D is the midpoint of AB and DE∥ BC then E is the midpoint of AC.

Example

Prove that C is the midpoint of BF if ABFE is a trapezium and AB ∥ EF.D is the midpoint of AE and EF∥ DC.

Solution:

Let BE cut DC at a point G.

Now in ∆AEB, D is the midpoint of AE and DG ∥ AB.

By midpoint theorem, G is the midpoint of EB.

Again in ∆BEF, G is the midpoint of BE and GC∥ EF.

So, by midpoint theorem C is the midpoint of BF.

Hence proved.

Triangle

A closed figure with three sides is called a Triangle. It has three vertex, sides and Angles.

Types of Triangle

1. There are three types of triangles on the basis of the length of the sides.

Name of Triangle	Property	Image
Scalene	Length of all sides are different
Isosceles	Length of two sides are equal
Equilateral	Length of all three sides are equal

2. There are three types of triangles on the basis of angles.

Name of Triangle	Property	Image
Acute	All the three angles are less than 90°
Obtuse	One angle is greater than 90°
Right	One angle is equal to 90°

Congruence

If the shape and size of two figures are same then these are called Congruent.

1. Two circles are congruent if their radii are same.

2. Two squares are congruent if their sides are equal.

Congruence of Triangles

A triangle will be congruent if its corresponding sides and angles are equal.

The symbol of congruent is “≅”.

AB = DE, BC = EF, AC = DF

m∠A = m∠D, m∠B = m∠E, m∠C = m∠F

Here ∆ABC ≅ ∆DEF

Criteria for Congruence of Triangles

S.No.	Rule	Meaning	Figure
1.	SAS (Side-Angle-Side) Congruence rule	If the two sides and the including angle of one triangle is equal to another triangle then they are called congruent triangles.
2.	ASA (Angle-Side-Angle) Congruence rule	If the two angles and the including side of one triangle is equal to another triangle then they are called congruent triangles.
3.	AAS (Angle-Angle-Side) Congruence rule	If any two pairs of angles and a pair of the corresponding side is equal in two triangles then these are called congruent triangles.
4.	SSS (Side-Side-Side) Congruence rule	If all the three sides of a triangle are equal with the three corresponding sides of another triangle then these are called congruent triangles.
5.	RHS (Right angle-Hypotenuse-Side) Congruence rule	If there are two right-angled triangles then they will be congruent if their hypotenuse and any one side are equal.

Remark

1. SSA and ASS do not show the congruency of triangles.

2. AAA is also not the right condition to prove that the triangles are congruent.

Example

Find the ∠P, ∠R, ∠N and ∠M if ∆LMN ≅ ∆PQR.

Solution

If ∆ LMN ≅ ∆PQR, then

∠L=∠P

∠M =∠Q

∠N =∠R

So,

∠L=∠P = 105°

∠M =∠Q = 45°

∠M + ∠N + ∠L = 180° (Sum of three angles of a triangle is 180°)

45° + 105° + ∠N = 180°

∠N = 180°- 45° + 105°

∠N = 30°

∠N = ∠R = 30°

Some Properties of a Triangle

If a triangle has two equal sides then it is called an Isosceles Triangle.

1. Two angles opposite to the two equal sides of an isosceles triangle are also equal.

2. Two sides opposite to the equal angles of the isosceles triangle are also equal. This is the converse of the above theorem.

Inequalities in a Triangle

Theorem 1: In a given triangle if two sides are unequal then the angle opposite to the longer side will be larger.

a > b, if and only if ∠A > ∠B

Longer sides correspond to larger angles.

Theorem 2: In the given triangle, the side opposite to the larger angle will always be longer. This is the converse of above theorem.

Theorem 3: The sum of any two sides of a triangle will always be greater than the third side.

Example

Show whether the inequality theorem is applicable to this triangle or not?

Solution

The three sides are given as 7, 8 and 9.

According to inequality theorem, the sum of any two sides of a triangle will always be greater than the third side.

Let’s check it

7 + 8 > 9

8 + 9 > 7

9 + 7 > 8

This shows that this theorem is applicable to all the triangles irrespective of the type of triangle.

• To protect people from exploitation the government makes certain laws. These laws try to ensure that the unfair practices are kept at a minimum in the markets.
• To ensure that workers are not underpaid but are paid fairly, minimum wages has been set by governments.
• There are laws that protect the interests of producers and consumers in the market.
• The government has to ensure that these laws are implemented which means that the law must be enforced.
• Enforcement becomes even more important when the laws, the government can control the activities of individuals or private companies so as to ensure social justice.
• Fundamental Rights guaranteed by the Indian Constitution like ‘Right against Exploitation’ say that no one can be forced to work for low wages or under bondage.
• The Constitution lays down no child below the age of 14 years shall be employed to work in any factory or mines or engaged in any other hazardous employment.
• The Constitution has also make provisions against any sort of exploitation of human being irrespective of gender and sex.
• By making constitutional rights governments always try to ensure social justice to every section of society.
• The Social and Just society makes the basis of Gandhian socialism and avail the resources to everyone and stop the discrimination.

Bhopal Gas Tragedy:

• The world’s worst industrial tragedy took place in Bhopal 24 years ago.
• Union Carbide (UC) an American company had a factory in the city in which it produced pesticides. MIC, a highly poisonous gas, started leaking on 2 December 1984, at midnight from the factory.
• Within three days more than 8,000 people were dead, Hundreds of thousands were maimed.
• US stopped its operations but left behind tons of toxic chemicals.
• 24 years later, people are still fighting for justice, for safe drinking water, for healthcare facilities and jobs for the people poisoned by UC. After effects still haunts the generations of victims.
• Governments come and go but people are waiting for justice. To stop any such sort of incidents in future the developers and business class should make liable by making strict laws.So that such incidents could not take place in future.

What is a Worker’s worth:

• Foreign companies come to India for cheaper labor.
• Wages in USA are higher than that compared to workers in poorer countries like in India.
• For lower pay, companies can get longer hours of work.
• Cost cutting can be done by other more dangerous means, e.g., lower working conditions including lower safety measures are used as ways of cutting costs.
• Since there is as much unemployment, there are many workers who are willing to work in unsafe conditions in return for a wage.
• In the grave situation of unemployment where people are ready to work in corrosive situation as well, it become the duty of government to ensure the safety of its citizens.
• Proper safety laws should be present to protect the people from damages and incidents.

Enforcement of Safety Laws:

• As the lawmaker and enforcer, the government is supposed to ensure that safety laws are implemented.
• It is the duty of the government to ensure that the Right to Life guaranteed under Article 21 of the Constitution is not violated.
• Instead of protecting the interests of the people, their safety was being disregarded both by the government and by private companies.
• With more industries being set up both by local and foreign business in India, there is a great need for stronger laws protecting workers rights and better enforcement of these laws.
• Before approval of any industry laws and codes must be satisfied with and after assessment permission should be given.

New Laws to Protect the Environment:

• In 1984, there were very few laws protecting environment (Environment protection act 1986)in India and there was hardly any enforcement of these laws.
• Environment was treated as a ‘free’ entity and industry could pollute the air and water without any restricted.
• Whether it was our rivers, air or groundwater the environment was being polluted and the health of people disregarded.
• The polluter was to be held accountable for the damage done to environment.
• The Government is responsible for setting up laws and procedures that can check pollution, clean rivers and introduce heavy fines for those who pollute.
• Supreme Court in many of judgments has also said about the right to healthy life and safe drinking water as essential part of article 21 that is right to life.
• Recently by invoking swatch Bharat Abhiyan, Namami Gangay and Rally for rivers government has shown its commitment towards environment protection.
• By imposing high carbon tax and high taxes of petroleum government is deterring individual from misusing these resources.
• At international level as well India is showing its commitment towards environment issue.

Environment as a Public Facility:

• Environment issue in India has highlighted the fact that the growing concern for the environment among the middle classes is often at the expense of the poor.
• The challenge is to look for solutions where everyone can benefit from a clean environment.
• The government has to encourage and support factories to gradually move to cleaner technologies.
• This will ensure that the workers livelihoods are protected and both workers and communities living around the factories enjoy a safe environment.
• By heavy dependency of rich on air condition and vehicles the problem of pollution is getting enhanced and burnt has to be faced by poor.

Conclusion:

• Laws are necessary in many situations, whether this be the market, office or factory so as to protect people from unfair practices.
• Laws that are weak and poorly enforced can cause serious harm.
• While the government has a leading role in the respect, people can exert pressure so that both private companies and the government act in the interests of society.
• Here the role has to be played by government by making better policies and by implementing them in effective manner.

Public facilities are the facilities provided to the people by the government. They are important to sustain and lead a comfortable life.

Water and the People of Chennai:

• Mr. Ramgopal lives in Anna Nagar, Chennai. This area looks lush and green with lawns maintained by generous spraying of water.
• Likewise, in an apartment where Mr.Subramaniam lives water supply is inadequate. They have to spend Rs 500-600 per month to buy water.
• Siva lives in Madipakkam, Chennai. She gets water once in 4 days. For drinking, she buys bottled water.
• Water as a public utility is available in different quantity to different people.
• Safe drinking water comes under the fundamental right of an individual and it is the responsibility of government ot avail it to its citizens.

Water as Part of the Fundamental Rights to Life:

• Water is essential for life and for good health.
• India has one of the largest numbers of causes of water-related diseases such as diarrhea, dysentery, cholera. More than 1600 Indians, mostly children below the age of five die every day because of water-related diseases.
• The Constitution of India recognizes the right to water as being a part of the Right to Life under Article 21. That means there should be “universal access” to water.
• The High Courts and Supreme Court have held that the right to safe drinking water is a Fundamental Right.
• Verdicts given by courts make it as the responsibility of government to ensure the supply of fresh drinking water.

Public Facilities:

• Things like electricity, public transport, schools, and colleges, etc.which are necessary for survival are known as public facilities.
• Public facilities are provided so that its benefits can be shared by many people.
• This is the responsibility of government to make public facilities available to every individual and no one should be discriminated just on the basis of social or economic division.

The Government’s Role:

• One of the most important functions of the government is to ensure that these public facilities are made available to everyone:
  • Making provision for education & setting up of schools & colleges.
  • Improving health & sanitation facilities.
  • Ensuring equal distribution of food throughout the country.
  • Improving the means of transport
  • Maintenance of public utility works like post offices, railways and roads
• Private companies operate for profit in the market. Public facilities are related to people’s basic needs.
• The main source of revenue for the government is the taxes collected from the people and the government is empowered to collect these taxes and use them for such programmes.
• For instance, to supply water, the government has to incur costs in pumping water, carrying it over long distances, laying down pipes for its distribution, treating the water for impurities and finally collecting and treating wastewater.
• It meets these expenses partly from the various taxes that it collects and partly by charging a price for water. This price is set so that most people can afford a certain minimum amount of water for daily use.
• One of the most important tasks of government is to ensure the availability of resources to everyone.
• By making the administration strict and effectively implementing the schemes government can help underprivilaged.
• The government by utilising the revenue collected in better social schemes and using the resources in better manner can ensure the well being to maximum of the population.

Water supply to Chennai: is it Available to All:

• Water supply in Chennai is marked by shortage. Municipal supply meets only about half the needs of the people of the city, on an average.
• The burden of shortfalls in water supply falls mostly on the poor.
• In search of Alternatives, the scenario of shortage and acute crisis during the summer months is common to other cities of India.
• A shortage of municipal water is often taken as a sign of failure of the government.
• Throughout the world, water supply is the responsibility of the government. There are very few instances of private water supply.
• In this era of industrialisation, water pollution has become a major problem.
• To avail the clean drinking water to a large population can be done through the technology advancement which needs investment by the government.

Conclusion:

• Public facilities are related to our basic needs and the Indian Constitution has recognised the right to water, health, education, etc. as being a part of the Right to Life.
• The major role of the government is to ensure adequate public facilities for everyone.
• Public facilities provided to everyone give rise to better living indices and help any country to get recognised at international level in terms of development.
• The success of any government is also acknowledged through the facilities and basic needs provided to all the individuals.
• These facilities finally become the building blocks of the development of a nation.

OBC (Other Backward Classes)

The weaker sections of the society other than the Schedule Castes and Scheduled Tribes are called the Other Backward Classes (OBCs).

The Kaka Kelkar Commission which gave its report for OBCs in 1953’s was accepted by government. In 1978, B.P. Mandal gave another report making recommendations for OBCs.

The provisions were implemented in 1990 by V.P. Singh. After a great deal of controversy, the Supreme Court gave the following judgment on OBCs :

(i) The court allowed 27% reservation for the backward caste/classes, but it announced that the ‘creamy layer of the backward class should be excluded. Government was to identify this creamy layer.

(ii) The armed forces and sensitive higher civilian posts like Scientists, Pilots, University Professors, etc. were to be kept outside the purview of the caste reservation.

(iii) The number of backward castes was reduced to 1,238 from 3,743 as recommended by the Mandal Report.

(iv) Those classes which had adequate representation in the government services were to be excluded from the list of OBCs.

(v) While Mandal Commission had recommended reservation policy in the field of promotions also the Supreme Court recommended reservation only  in original appointments.

(vi) The Supreme Court directed that the reservation quota should not exceed 50 percent in any eventuality.

Implementation of Mandal Report

(i) On the Supreme Court’s verdict, the Union government implemented the reservation of 27% quota for 1,238 backward castes in Central Services and Public Undertakings.

(ii) The government has given them relaxation in qualifying marks in written examinations and in interviews.

(iii) Relaxation in upper age limit by 3 years in direct recruitment has also been given to OBCs.(iv) The OBCs are given relaxation to clear the Civil Services examinations in seven attempts. The verdict of the Supreme Court on PIL filed by the Safai Karamchari Andolan and other organisations

The court had directed the departments of central and state government to verify the condition of manual scavenging and to introduce time-bound programme for their liberation and rehabilitation.

Kabir was a fifteenth century poet and weaver. He belonged to the Bhakti tradition. Kabir’s poetry spoke about his love for the supreme being, free of rituals and priests. According to Kabir, untouchability was the highest state of knowledge, i.e. not touched by narrow limiting ideas, so he changed a lower concept to the highest one.

Legal measure taken by the Indian Government against the practice of untouchability are :

(i) The practice of untouchability is a form of social discrimination against certain groups based on their castes. India has been a severe victim of this social evil since ages.

(ii) Framers of the Indian Constitution were unanimous on making a strong law to end this in human practice.

(iii) Article 17 of the Constitution of India declares abolition of the practice of untouchability. In according with the Constitutional provisions, the Government of India has passed the Untouchability (Offences) Act, 1955 and later the Scheduled Caste and Scheduled Tribes (Prevention of Atrocities) and Act, 1989 to eradicate caste based discrimination and upliftment of the people belonging to deprived sections of the society.

(iv) The government has introduced reservation system in educational institutes, government services and elected institutions.

The government made various laws to protect marginalised citizens. There are some specific laws and policies for the marginalised groups in our Country. There are policies or schemes that emerge through other means like setting up a committee or by undertaking a survey, etc. The government also makes efforts to promote such policies.

The State Governments of India keep a list of Scheduled Castes (or Dalits), Scheduled Tribes, backward and most backward castes. The Central Government also has a list. The students applying to educational institutions of government and those applying for posts in government are  expected to show the proof of their caste or tribe status in the form of caste and tribe certificates issued by the government agencies. If a particular caste or a certain tribe is on the government list, then a candidate from that caste or tribe can gain the benefit of reservation.

C.K. Janu point about the violation of the rights of the tribes

In her observation, C.K. Janu, an Adivasi activist, had pointed out violations of the Constitutional rights assured to tribal people of the various state government of India. They allow non-tribal encroachers in the form of timber merchants, paper mills, etc. to exploit tribal land, and forcibly evict tribal people from their traditional forests in the process of declaring forests as reserved or as sanctuaries. She has also noted out the cases where tribal people have already been expelled and are not allowed to go back to their lands.

The dalits are enlightened about their rights and they utilize the Fundamental Rights if they are discriminated by the individual, community or by the government. Now, they have drawn the attention of the government of India to follow the Constitution and to ensure justice for them.

The minorities like Parsi, Muslims, Sikhs, etc. use the Fundamental Rights to secure themselves. They become the guardian of their cultural content and to preserve it in the best way. The Constitution of India guarantees the cultural justice to cultural, religious or linguistic minorities. The Constitution makes sure that no majority community will dominate or eliminate them. The Constitution provides them the freedom to practice their religion.

The Schedule Castes and Schedule Tribes Act 1989 states that the actions that deprive the Dalits and Adivasis of their small resources or which force them into slaved labour are punishable. It means that if someone tries to occupy or cultivate any land owned by or allotted to a member of Schedule Caste or Tribe, he will be punished by law.

Article 15 of the Constitution states that no citizen of India shall be discriminated on the basis of religion, race, caste, sex or place of birth.

Article 17 of the Constitution states that untouchability has been abolished and no one can prevent Dalits from getting education, entering temples, using public facilities.

1. MARGINALISED SECTIONS.
   • A marginal group is one that does not belong or which dwells at the margin of two cultures and two societies and possesses a marginal mentality with its unresolved identity crises.”
   • It is first seen as a distinctive social group, with their own characteristic’s features, victimised by the dominant members of the host society.
   • They are subjected to unequal treatment by way of acts of discrimination.
   • In India, large numbers of people have experienced marginalisation because of the caste system.
2. ADIVASIS.
   • The term literally means ‘original inhabitants’ – are communities who lived, and often continued to live, in close association with forests.
   • Around 8 per cent of India’s population is Adivasi and many of India’s most important mining and Industrial centres are in Adivasi areas – Jamshedpur, Rourkela, Bokaro and Bhilai among others.
   • Adivasis are not homogeneous population: there are over 500 different Adivasi groups in India.
   • Adivasis are particularly numerous in states like Chhattisgarh, Jharkhand, Madhya Pradesh, Orissa, Gujarat, Maharashtra, Rajasthan, Andhra Pradesh, West Bengal and in the north-eastern states of Arunachal Pradesh, Assam, Manipur, Meghalaya, Mizoram, Nagaland and Tripura.
   • Adivasi societies are also most distinctive because there is often very little hierarchy among them. Thus, makes them radically different from communities organised around principles of jati-varna or those that were ruled by Kings.
   • Adivasis have their own language, which have often deeply influenced the formation of ‘mainstream’ Indian languages, like Bengali.
3. ADIVASIS AND STEREOTYPING.
   • In India, we usually ‘showcase’ Adivasi communities in particular way. Thus, during school functions or other official events or on books and movies, Adivasis are invariably portrayed in very stereotypical ways – in colourful costumes, headgear and through their dancing.
   • This often wrongly leads people believing that they are exotic, primitive and backward. Often Adivasis are blamed for their lack of advancement as they are believed to be resistant to change or new ideas.
4. ADIVASIS AND DEVELOPMENT.
   • Forests covered the major part orb our country till the nineteenth century and the Adivasis had a deep knowledge of, access to, as well as control over most of these vast tracts at least till the middle of the nineteenth century.
   • This meant that they were not ruled by large States and Empires. Instead, often empires heavily depended on Adivasis for the crucial access to forest resources.
   • This is radically contrary to our image of Adivasis today as somewhat marginal and powerless communities. In the pre-colonial world, they were traditionally ranged Hunter-gatherers and nomads and lived by shifting agriculture and cultivating in one place.
   • For the past 200 years Adivasis have been increasingly forced – through economic changes, forest policies and political force applied by the State and private industry – to migrate to live as workers in plantations, at construction sites, in industries and as domestic workers.
   • Adivasis have also lived in areas that are rich in minerals and other large industrial projects.
   • Losing their lands and access to the forest means that tribals lose their main source of livelihood and food. Having gradually lost access to their traditional homelands, many Adivasis have migrated to cities in search of work where they are employed for very low wages in local industries or at building or construction sites.
5. MINORITIES AND MARGINALISATION.
   • Constitution provides safeguard to religious and linguistic minorities as part of our Fundamental Rights.
   • The term minority is most commonly used to refer to communities that are numerically small in relation to the rest of the population.
   • The Indian Constitution recognised that the culture of the majority influences the way in which society and government might express themselves. In such cases, size can be a disadvantage and lead to the marginalisation of the relatively smaller communities.
   • Safeguards are needed to protect minority communities against the possibility of being culturally dominated by the majority. They also protect them against any discrimination and disadvantage that they may face.
   • The Constitution provides these safeguards because it is committed to protecting India’s cultural diversity and promoting equality as well as justice.
6. MUSLIMS AND MARGINALISATION.
   • According to 2001 census, Muslims are 13.4 per cent if India’s population and are a marginalised community in India today because in comparison to other communities, they have over the years been deprived of the benefits of socio-economic development
   • Recognising that Muslims in India were lagging in terms of various development indicators, the government set up a high-level Committee examined the social, economic and Educational status of the Muslim community.

Key Players of Our Criminal Justice System

• The four key players in the criminal justice system are:
→ the police,
→ the Public Prosecutor
→ the defence lawyer
→ the judge

What is the Role of the Police in Investigating a Crime?

• The main function of police is to investigate any complaint about the commission of a crime.
→ An investigation includes recording statements of witnesses and collecting different kinds of evidence.

• On the basis of the investigation, the police are required to form an opinion.
→ Police file a chargesheet in the court if they think accused person is guilty.

• The police can’t decide whether a person is guilty or innocent, that is for the judge to decide.

• The police investigations always have to be conducted in accordance with law and with full respect for human rights.

• Every arrested person has following Fundamental Rights as per Article 22 of the Constitution and criminal law

→ The Right to be informed at the time of arrest of the offence for which the person is being arrested.
→ The Right to be presented before a magistrate within 24 hours of arrest.
→ The Right not to be ill treated or tortured during arrest or in custody.
→ Confessions made in police custody cannot be used as evidence against the accused.

→ A boy under 15 years of age and women cannot be called to the police station only for questioning.

What is the Role of the Public Prosecutor?

• The role of the Prosecutor begins once the police has conducted the investigation and filed the chargesheet in the court.

• The Prosecutor duty to act impartially and present the full and material facts, witnesses and evidence before the court to enable the court to decide the case.

What is the Role of the Judge?

• The judge hears all the witnesses and any other evidence presented by the prosecution and the defence.

• The judge decides whether the accused person is guilty or innocent on the basis of the evidence presented and in accordance with the law.

• He may send the person to jail or impose a fine or both, depending on what the law prescribes.

What is a Fair Trial?

• Article 21 of the Constitution that guarantees the Right to Life states that a person’s life or liberty can be taken away only by following a reasonable and just legal procedure.

Essential elements of a fair trial:

• The trial should be held in an open court, in public view.
• The trial should be held in the presence of the accused.
• The accused must be defended by a lawyer.
• Defence lawyer must have opportunity to cross-examine all the prosecution witnesses. Also, have an opportunity to present witnesses in accused’s defence.
• It was the responsibility of the prosecution to prove beyond reasonable doubt that accused was guilty.
• The judge should decide the matter only on the basis of the evidence before the court. He/She must remain impartial.