# NCERT Solutions for Class 9 Maths Chapter 14 Statistics

**NCERT solutions for class 9 maths chapter 14 Statistics: **Statistics is one of the important topics in class 9 NCERT syllabus. You must have seen information like the temperature of cities, cricket batsman or bowler ranking, results of particular exams either in news, tv, online sites or magazines. All the mentioned examples are represented through a table or graphs. NCERT solutions for class 9 maths chapter 14 Statistics is covering the solutions for this particular topic in detail. In statistics class 9, the numbers or facts are collected for a purpose and the collection is called data. From these collected data you can understand and conclude some results.

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For example, if we have data on the temperature of 40 cities for a particular day, we can infer which city has a higher temperature, which city has a lower temperature, what is the average temperature of 40 cities, which value of temperature is most repeated, what is the middle value of temperature if we arranged the temperature in either increasing or decreasing order, etc. In this, you are arranging the collected data and then analyzing it and can infer certain things. In NCERT solutions for class 9 maths chapter 14 Statistics the answers to the questions of mode, average, median, etc are covered. Statistics is the part of maths in which you learn to get some results based on the collected data. In this NCERT Book chapter, there are a total of 4 exercises consisting of a total of 35 questions. NCERT solutions for class 9 maths chapter 14 Statistics is covering every question in a step-by-step manner so that you do not lose a single mark in any question. Apart from this particular ch 14 maths class 9 NCERT solutions are available for other chapters as well. Here you will get NCERT solutions for class 9 also.

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## ** Statistics Class 9 NCERT Excercise: 14.1 **

** Q1 ** Give five examples of data that you can collect from your day-to-day life.

** Answer: **

Five examples of data that we can collect in our daily life are

(i) Number of students in a class.

(ii) The number of books in a library.

(iii) Toys sold on a particular day at a shop.

(iv) People who voted for a particular candidate.

(v) Runs scored by a batsman on each ball in a particular evening.

** Q2 ** Classify the data in Q.1 above as primary or secondary data.

** Answer: **

(i) The number of students in a class.

(ii) The number of books in a library.

(iii) Toys sold on a particular day at a shop.

(iv) People who voted for a particular candidate.

(v) Runs scored by a batsman on each ball on a particular evening.

All of the data in Q.1 is primary data.

## ** ****Statistics Class 9 NCERT Excercise**: 14.2

**Statistics Class 9 NCERT Excercise**: 14.2

** Q1 ** The blood groups of 30 students of Class VIII are recorded as follows:

A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O,

A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.

Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students?

** Answer: **

The representation of the given data in the form of a frequency distribution table is as follows.

From the table we can see that O is the most common and AB is the rarest blood group.

** Q2 ** The distance (in km) of engineers from their residence to their place of work were found as follows:

5 3 10 20 25 11 13 7 12 31

19 10 12 17 18 11 32 17 16 2

7 9 7 8 3 5 12 15 18 3

12 14 2 9 6 15 15 7 6 12

Construct a grouped frequency distribution table with class size for the data given above taking the first interval as ( not included). What main features do you observe from this tabular representation?

** Answer: **

As the minimum and maximum distances of an engineer from his place of work is 2 and 32 respectively the class intervals with class size 5 would be the following.

0 - 5, 5 - 10, 10 - 15, 15 - 20, 20 - 25, 25 - 30, 30 - 35

The representation of the given data in the form of a grouped frequency distribution table is as follows

Frequencies of the class intervals 5 - 10 and 10 - 15 are maximum and equal to 11 each and frequencies of the class intervals 20 - 25 and 125 - 30 are minimum and equal to 1 each.

** Q3 (i) ** The relative humidity (in ) of a certain city for a month of days was as follows:

98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2 95.1

89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3 95.2 97.3

96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89

Construct a grouped frequency distribution table with classes 84 - 86, 86 - 88, etc.

** Answer: **

** Q3 (ii) ** The relative humidity (in ) of a certain city for a month of days was as follows:

98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2 95.1

89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3 95.2 97.3

96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89

Which month or season do you think this data is about?

** Answer: **

As from the table we can see relative humidity in most of the days is above 92% we can conclude the data is from a month of the rainy season. The leaast humidity recorded is 84.9% which also is prettry high.

** Q3 (iii) ** The relative humidity (in ) of a certain city for a month of days was as follows:

98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2 95.1

89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3 95.2 97.3

96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89

What is the range of this data?

** Answer: **

Range of a given data = Highest observation - Lowest Observation

Highest recorded humidity = 99.2%

Lowest recorded humidity = 84.9%

Therefore range of the given data = 99.2 - 84.9 = 14.3%

** Q4 (i) ** The heights of 50 students, measured to the nearest centimetres, have been found to be as follows:

161 150 154 165 168 161 154 162 150 151

162 164 171 165 158 154 156 172 160 170

153 159 161 170 162 165 166 168 165 164

154 152 153 156 158 162 160 161 173 166

161 159 162 167 168 159 158 153 154 159

Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160 - 165, 165 - 170, etc.

** Answer: **

The highest recorded height of a student is 173 cm.

The lowest recorded height of a student is 150 cm.

The class intervals would therefore be 150 -155, 155 - 160, 160 - 165, 165 - 170, 170 - 175

The representation of the given data in the form of a grouped frequency distribution table is as follows.

** Q4 (ii) ** The heights of 50 students, measured to the nearest centimetres, have been found to be as follows:

161 150 154 165 168 161 154 162 150 151

162 164 171 165 158 154 156 172 160 170

153 159 161 170 162 165 166 168 165 164

154 152 153 156 158 162 160 161 173 166

161 159 162 167 168 159 158 153 154 159

What can you conclude about their heights from the table?

** Answer: **

From the table we can conclude that maximum students have height in the range 160 - 165 cm and more than half of the students are shorter than 165 cm.

0.03 0.08 0.08 0.09 0.04 0.17

0.16 0.05 0.02 0.06 0.18 0.20

0.11 0.08 0.12 0.13 0.22 0.07

0.08 0.01 0.10 0.06 0.09 0.18

0.11 0.07 0.05 0.07 0.01 0.04

Make a grouped frequency distribution table for this data with class intervals as 0.00 - 0.04, 0.04 - 0.08, and so on.

** Answer: **

The lowest value of the concentration of sulphur dioxide in the air is 0.01 ppm

The highest value of the concentration of sulphur dioxide in the air is 0.22 ppm

The representation of the given data in the form of a frequency distribution table is as follows.

0.03 0.08 0.08 0.09 0.04 0.17

0.16 0.05 0.02 0.06 0.18 0.20

0.11 0.08 0.12 0.13 0.22 0.07

0.08 0.01 0.10 0.06 0.09 0.18

0.11 0.07 0.05 0.07 0.01 0.04

For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million?

** Answer: **

From the frequency distribution table, we can see the concentration of sulphur dioxide was more than 0.11 ppm for 8 days.

It was in the range 0.12 - 0.16 for 2 days, 0.16 - 0.20 for 4 days and 0.20 - 0.24 for 2 days.

0 1 2 2 1 2 3 1 3 0

1 3 1 1 2 2 0 1 2 1

3 0 0 1 1 2 3 2 2 0

Prepare a frequency distribution table for the data given above

** Answer: **

A frequency distribution table for the data given above is as follows.

** Q7 (i) ** The value of upto decimal places is given below:

3.14159265358979323846264338327950288419716939937510

Make a frequency distribution of the digits from 0 to 9 after the decimal point.

** Answer: **

The representation of the given data in the form of a frequency distribution table is as follows.

** Q7 (ii) ** The value of up to decimal places is given below:

3.14159265358979323846264338327950288419716939937510

What are the most and the least frequently occurring digits?

** Answer: **

The most frequently occurring digits are 3 and 9 with a frequency of 8.

1 6 2 3 5 12 5 8 4 8

10 3 4 12 2 8 15 1 17 6

3 2 8 5 9 6 8 7 14 12

Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 - 10.

** Answer: **

The highest number of hours for which a child watched TV = 17

The lowest number of hours for which a child watched TV = 1

The class intervals with class width 5 would, therefore, be 1 - 5, 5 - 10, 10 - 15, 15 - 20

The representation of the given data in the form of a frequency distribution table is as follows.

1 6 2 3 5 12 5 8 4 8

10 3 4 12 2 8 15 1 17 6

3 2 8 5 9 6 8 7 14 12

How many children watched television for 15 or more hours a week?

** Answer: **

2 children watched television for 15 or more hours a week as we can see from the frequency distribution table. Frequency of the class interval 15 - 20 is 2.

2.6 3.0 3.7 3.2 2.2 4.1 3.5 4.5

3.5 2.3 3.2 3.4 3.8 3.2 4.6 3.7

2.5 4.4 3.4 3.3 2.9 3.0 4.3 2.8

3.5 3.2 3.9 3.2 3.2 3.1 3.7 3.4

4.6 3.8 3.2 2.6 3.5 4.2 2.9 3.6

Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the interval 2 - 2.5.

** Answer: **

The least value of life of a battery recorded = 2.2

The highest value of life of a battery recorded = 4.6

The class intervals with interval size 0.5 would therefore be 2.0 - 2.5, 2.5 - 3.0, 3.0 - 3.5, 3.5 - 4.0, 4.0 - 4.5, 4.5 - 5.0

The representation of the given data in the form of a frequency distribution table is as follows.

## ** ****Statistics Class 9 NCERT Excercise**: 14.3

**Statistics Class 9 NCERT Excercise**: 14.3

Serial Number | Causes | Female fatality rate (%) |

1. | Reproductive health conditions | 31.8 |

2. | Neuropsychiatric conditions | 25.4 |

3. | Injuries | 12.4 |

4. | Cardiovascular conditions | 4.3 |

5. | Respiratory conditions | 4.1 |

6. | Other causes | 22.0 |

Represent the information given above graphically

** Answer: **

The graphical representation of the given data is as follows

Serial Number | Causes | Female fatality rate (%) |

1. | Reproductive health conditions | 31.8 |

2. | Neuropsychiatric conditions | 25.4 |

3. | Injuries | 12.4 |

4. | Cardiovascular conditions | 4.3 |

5. | Respiratory conditions | 4.1 |

6. | Other causes | 22.0 |

Which condition is the major cause of women’s ill health and death worldwide?

** Answer: **

From the graph we can see reproductive health conditions is the major cause of women’s ill health and death worldwide. The female fatality rate is 31.8% due to reproductive health conditions.

Serial Number | Causes | Female fatality rate (%) |

1. | Reproductive health conditions | 31.8 |

2. | Neuropsychiatric conditions | 25.4 |

3. | Injuries | 12.4 |

4. | Cardiovascular conditions | 4.3 |

5. | Respiratory conditions | 4.1 |

6. | Other causes | 22.0 |

Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause

** Answer: **

Due to poor financial conditions and failure of the government to provide necessary healthcare condition to women, reproductive health conditions is the major cause of ill health and death of women worldwide.

Section | Number of girls per thousand boys |

Schedule Caste (SC) | 940 |

Schedule Tribe (ST) | 970 |

Non SC/ST | 920 |

Backward districts | 950 |

Non-backward districts | 920 |

Rural | 930 |

Urban | 910 |

Represent the information above by a bar graph.

** Answer: **

The graphical representation of the given information is as follows

Section | Number of girls per thousand boys |

Schedule Caste (SC) | 940 |

Schedule Tribe (ST) | 970 |

Non SC/ST | 920 |

Backward districts | 950 |

Non-backward districts | 920 |

Rural | 930 |

Urban | 910 |

In the classroom discuss what conclusions can be arrived at from the graph

** Answer: **

From the graph, we can see that the number of girls per thousand boys is the least in urban society and the highest in the Scheduled Tribes.

910 in case of urban society and 970 in that of Scheduled Tribes.

Political Party | A | B | C | D | E | F |

Seats Won | 75 | 55 | 37 | 29 | 10 | 37 |

Draw a bar graph to represent the polling results.

** Answer: **

The representation of the given data in the form of a bar graph is as follows.

Political Party | A | B | C | D | E | F |

Seats Won | 75 | 55 | 37 | 29 | 10 | 37 |

Which political party won the maximum number of seats?

** Answer: **

Party A has won the maximum number of seats. Party A has won 75 seats.

Length (in mm) | Number of leaves |

118-126 | 3 |

127-135 | 5 |

136-144 | 9 |

145-153 | 12 |

154-162 | 5 |

163-171 | 4 |

172-180 | 2 |

Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]

** Answer: **

As we can see from the given table that the data is discontinous and the difference between the upper limit of a class and the lower limit of the next class is 1 and therefore we change both of them by a value 1/2.

e.g 127 - 135 would become 126.5 - 235.5

The modified table therefore is

The representation of the above data through a histogram is as follows

Length (in mm) | Number of leaves |

118-126 | 3 |

127-135 | 5 |

136-144 | 9 |

145-153 | 12 |

154-162 | 5 |

163-171 | 4 |

172-180 | 2 |

Is there any other suitable graphical representation for the same data?

** Answer: **

A frequency polygon could be another suitable graphical representation for the same data.

Length (in mm) | Number of leaves |

118-126 | 3 |

127-135 | 5 |

136-144 | 9 |

145-153 | 12 |

154-162 | 5 |

163-171 | 4 |

172-180 | 2 |

Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

** Answer: **

No it is certainly not correct to conclude that the maximum number of leaves are 153 mm long because the given data does not tell us about the exact length of the leaves. It only tells us about the range in which their lengths lie. We can only conclude that the maximum number of leaves (12) have their lengths in the region 145 - 153.

** Q5 (i) ** The following table gives the life times of 400 neon lamps:

Life time (in hours) | Number of lamps |

300-400 | 14 |

400-500 | 56 |

500-600 | 60 |

600-700 | 86 |

700-800 | 74 |

800-900 | 62 |

900-1000 | 48 |

Represent the given information with the help of a histogram.

** Answer: **

The representation of the given information in the form of a histogram is as follows.

** Q5 (ii) ** The following table gives the life times of 400 neon lamps:

Life time (in hours) | Number of lamps |

300-400 | 14 |

400-500 | 56 |

500-600 | 60 |

600-700 | 86 |

700-800 | 74 |

800-900 | 62 |

900-1000 | 48 |

How many lamps have a life time of more than 700 hours?

** Answer: **

Lamps having life time in the range 700 - 800 = 74

Lamps having life time in the range 800 - 900 = 62

Lamps having life time in the range 900 - 1000 = 48

Lamps having a life time of more than 700 hours = 74 + 62 + 48 = 184.

Section A | Section B | ||

Marks | Frequency | Marks | Frequency |

0-10 | 3 | 0-10 | 5 |

10-20 | 9 | 10-20 | 19 |

20-30 | 17 | 20-30 | 15 |

30-40 | 12 | 30-40 | 10 |

40-50 | 9 | 40-50 | 1 |

Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections

** Answer: **

To make the frequency polygon we first modify the table as follows

To make the frequency polygon we mark the marks on the x-axis and the number of students on the y-axis.

The representation of the given information in the form of frequency polygon is as follows.

From the frequency polygon we can see that the performance of section A is better.

** Q7 ** The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:

Number of balls | Team A | Team B |

1-6 | 2 | 5 |

7-12 | 1 | 6 |

13-18 | 8 | 2 |

19-24 | 9 | 10 |

25-30 | 4 | 5 |

31-36 | 5 | 6 |

37-42 | 6 | 3 |

43-48 | 10 | 4 |

49-54 | 6 | 8 |

55-60 | 2 | 10 |

Represent the data of both the teams on the same graph by frequency polygons. [ ** Hint ** : First make the class intervals continuous.]

** Answer: **

The given data is not continous we therefore modify the limits of the class intervals as well to make the class intervals continous.

To make the frequency polygon we first modify the table as follows

To make the frequency polygon we mark the number of balls on the x-axis and the runs scored on the y-axis.

The representation of the given information in the form of frequency polygon is as follows.

Age (in years) | Number of children |

1-2 | 5 |

2-3 | 3 |

3-5 | 6 |

5-7 | 12 |

7-10 | 9 |

10-15 | 10 |

15-17 | 4 |

Draw a histogram to represent the data above.

** Answer: **

Since the class sizes vary to make the histogram we have to calculate the weighted frequency for each rectangle as per its width

Minimum class size = 2 - 1 = 1

The modified table showing the weighted frequency as per the size of the class intervals is as follows.

The histogram representing the information given in the above table is as follows.

Number of letters | Number of surnames |

1-4 | 6 |

4-6 | 30 |

6-8 | 44 |

8-12 | 16 |

12-20 | 4 |

** Answer: **

Since the class sizes vary to make the histogram we have to calculate the weighted frequency for each rectangle as per its width

Minimum class size = 6 - 4 = 2

The modified table showing the weighted frequency as per the size of the class intervals is as follows.

The histogram representing the information given in the above table is as follows.

Number of letters | Number of surnames |

1-4 | 6 |

4-6 | 30 |

6-8 | 44 |

8-12 | 16 |

12-20 | 4 |

Write the class interval in which the maximum number of surnames lie.

** Answer: **

The class interval in which the maximum number of surnames lie is 6 - 8

The weighted frequency of this class interval (taking 2 as the minimum class size) is 44.

**Statistics Class 9 NCERT Excercise****: 14.4 **

** Q1 ** The following number of goals were scored by a team in a series of 10 matches:

2, 3, 4, 5, 0, 1, 3, 3, 4, 3

Find the mean, median and mode of these scores.

** Answer: **

Number of observations, n = 10

Mean is 2.8

To find the median we have to arrange the given data in ascending order as follows:

0, 1, 2, 3, 3, 3, 3, 4, 4, 5

n = 10 (even)

In the given data 3 occurs the maximum number of times (4)

Therefore, Mode = 3

** Q2 ** In a mathematics test given to 15 students, the following marks (out of 100) are recorded:

41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60

Find the mean, median and mode of this data.

** Answer: **

Number of observations, n = 15

Mean is 54.8

To find the median we have to arrange the given data in ascending order as follows:

39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

n = 15 (odd)

In the given data 52 occurs the maximum number of times ()

Therefore, Mode = 52

29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

** Answer: **

The given data is already in ascending order

Number of observations, n = 10 (even)

x + 1 = 63

x = 62

** Q4 ** Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.

** Answer: **

In the given data 14 is occuring the maximum number of times (4)

Mode of the given data is therefore 14.

** Q5 ** Find the mean salary of 60 workers of a factory from the following table:

Salary (in Rs) | Number of workers |

3000 | 16 |

4000 | 12 |

5000 | 10 |

6000 | 8 |

7000 | 6 |

8000 | 4 |

9000 | 3 |

10000 | 1 |

Total | 60 |

** Answer: **

Salary ( in Rs)(x _{ i } ) | Number of workers(f _{ i } ) | f _{ i } x _{ i } |

3000 | 16 | 48000 |

4000 | 12 | 48000 |

5000 | 10 | 50000 |

6000 | 8 | 48000 |

7000 | 6 | 42000 |

8000 | 4 | 32000 |

9000 | 3 | 27000 |

10000 | 1 | 10000 |

Total |

The mean of the above data is given by

The mean salary of the workers working in the factory is Rs 5083.33

** Q6 (i) ** Give one example of a situation in which the mean is an appropriate measure of central tendency.

** Answer: **

The mean is an appropriate measure of central tendency in case the observations are close to each other. An example of such a case is height of the students in a class.

Statistics Excercise: 14.4

** Answer: **

The mean is not an appropriate measure of central tendency in case the observations are not close to each other. An example of such a case is prices of the toys in a toy shop.

**Students who are the interested in consolidated solutions in a single place can access from following links**

- Statistics Class 9 NCERT Excercise 14.1
- Statistics Class 9 NCERT Excercise 14.2
- Statistics Class 9 NCERT Excercise 14.3
- Statistics Class 9 NCERT Excercise 14.4

**NCERT solutions for class 9 maths chapter wise **

Chapter No. | Chapter Name |

Chapter 1 | Number Systems |

Chapter 2 | Polynomials |

Chapter 3 | Coordinate Geometry |

Chapter 4 | Linear Equations In Two Variables |

Chapter 5 | Introduction to Euclid's Geometry |

Chapter 6 | Lines And Angles |

Chapter 7 | Triangles |

Chapter 8 | Quadrilaterals |

Chapter 9 | Areas of Parallelograms and Triangles |

Chapter 10 | Circles |

Chapter 11 | Constructions |

Chapter 12 | Heron’s Formula |

Chapter 13 | Surface Area and Volumes |

Chapter 14 | Statistics |

Chapter 15 | Probability |

** NCERT solutions for class 9 subject wise **

** How to use NCERT solutions for class 9 maths chapter 14 Statistics? **

- Go through some tables and understand that representation of data.
- Take a look through some examples to understand the calculation of mean, median, mode.
- Memorize the formulas to calculate mean, median, mode.
- Implement the application of all the concepts and formulas on the practice problems.
- While practicing you can use NCERT solutions for class 9 maths chapter 14 Statistics.

* Keep working hard and happy learning! *

**Also Check NCERT Books and NCERT Syllabus here:**

## Frequently Asked Question (FAQs) - NCERT Solutions for Class 9 Maths Chapter 14 Statistics

**Question: **What are the important topics in chapter Statistics ?

**Answer: **

Mean, median, mode, variance, and standard deviation are the important topics of this NCERT Book chapter. having command in the concepts of statistics will help students not only in exams but in understanding data in daily life and professional life as well.

**Question: **How does the NCERT solutions are helpful ?

**Answer: **

NCERT solutions are helpful for the students if they stuck while solving NCERT problems. Also, these solutions are provided in a very detailed manner which will give them conceptual clarity.

**Question: **Does CBSE class 9 maths is tough ?

**Answer: **

CBSE class 9 maths is not tough at all. There are some new topics and in the previous classes we have study maths basic and damn simple, so students may find it tough but overall it is not tough.

**Question: **Where can I find the complete solutions of NCERT for class 9 maths ?

**Answer: **

Here you will get the detailed NCERT solutions for class 9 maths by clicking on the link.

**Question: **Where can I find the complete solutions of NCERT for class 9 ?

**Answer: **

Here you will get the detailed NCERT solutions for class 9 by clicking on the link.

**Question: **Does CBSE provides the solutions of NCERT for class 9 maths ?

**Answer: **

No, CBSE doesn’t provide NCERT solutions for any class or subject. students who are really fascinated by NCERT Book solutions consolidated way can above in this article listed chapter as well as subject wise.

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