Category: Class 6

MP Board Class 6th Maths Solutions Chapter 10 Mensuration Ex 10.3

Question 1.
Find the areas of the rectangles whose sides are:
(a) 3 cm and 4 cm
(b) 12 m and 21m
(c) 2 km and 3 km
(d) 2 m and 70 cm
Solution:
(a) Area of rectangle = length × breadth
= 3 cm × 4 cm = 12 cm²

(b) Area of rectangle = length × breadth
= 12 m × 21 m = 252 m²

(c) Area of rectangle = length × breadth
= 2 km × 3 km = 6 km²

(d) Area of rectangle = length × breadth
= 2 m × 70 cm = 2 m × 0.7 m = 1.4 m²

Question 2.
Find the areas of the squares whose sides are:
(a) 10 cm
(b) 14 cm
(c) 5 m
Solution:
(a) Area of square = side × side
= 10 cm × 10 cm = 100 cm²

(b) Area of square = side × side
= 14 cm × 14 cm = 196 cm²

(c) Area of square = side × side
= 5 m × 5 m = 25 m²

Question 3.
The length and breadth of three rectangles are as given below:
(a) 9 m and 6 m
(b) 17 m and 3 m
(c) 4 m and 14 m
Which one has the largest area and which one has the smallest?
Solution:
(a) Area of rectangle = length × breadth
= 9m × 6m = 54m²

(b) Area of rectangle = length × breadth
= 17 m × 3 m = 51 m²

(c) Area of rectangle = length × breadth
= 4 m × 14 m = 56 m²
Thus, rectangle (c) has the largest area, i.e. 56 m² and rectangle (b) has the smallest area, i.e., 51 m².

Question 4.
The area of a rectangular garden 50 m long is 300 sq m. Find the width of the garden.
SolutionL
Length of rectangle = 50 m
Area of rectangle = 300 m²
Since, area of rectangle = length × breadth
Therefore, breadth = \(\frac{\text { area of rectangle }}{\text { length }}\)
= \(\frac{300}{50}\) m = 6 m
Thus, the breadth of the garden is 6 m.

Question 5.
What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of Rs. 8 per hundred sq m?
Solution:
Length of land = 500 m
Breadth of land = 200 m
Area of land = length × breadth
= 500 m × 200 m = 1,00,000 sq m
Cost of tiling 100 sq m of land = Rs. 8
∴ Cost of tiling 1,00,000 sq m of land
= Rs. \(\frac{8 \times 100000}{100}\) = Rs. 8000

Question 6.
A table-top measures 2 m by 1 m 50 cm. What is its area in square metres?
Solution:
Length of table-top = 2 m
Breadth of table-top = 1 m 50 cm = 1.50 m
∴ Area of table-top = length × breadth
= 2 m × 1.50 m = 3 m²

Question 7.
A room is 4 m long and 3 m 50 cm wide. How many square metres of carpet is needed to cover the floor of the room?
Solution:
Length of room = 4 m
And breadth of room = 3 m 50 cm = 3.50 m
∴ Area of carpet = length × breadth
= 4 m × 3.50 m = 14 m²

Question 8.
A floor is 5 m long and 4 m wide. A square carpet of sides 3 m is laid on the floor. Find the area of the floor that is not carpeted.
Solution:
Length of floor = 5 m
And breadth of floor = 4 m
Area of floor = length × breadth
= 5m × 4m = 20m²
Now, side of square carpet = 3 m
Area of square carpet = side × side
= 3m × 3m = 9m²
∴ Area of floor that is not carpeted
= 20 m² – 9 m² = 11 m²

Question 9.
Five square flower beds each of sides 1 m are dug on a piece of land 5 m long and 4 m wide. What is the area of the remaining part of the land?
Solution:
Side of square flower bed = 1 m Area of square flower bed = side × side
= 1m × 1m = 1m²
∴ Area of 5 square flower beds = (1 × 5) m²
= 5 m²
Now, length of land = 5 m
And breadth of land = 4 m
∴ Area of land = length × breadth = 5m × 4m
= 20 m²
∴ Area of remaining part
= Area of land – Area of 5 flower beds
= 20 m² – 5 m² = 15 m²

Question 10.
By splitting the following figures into rectangles, find their areas (The measures are given in centimeters).

Solution:
(a) We have,

Area of square HKLM = 3 × 3 cm² = 9 cm²
Area of rectangle I]CH = 1 × 2 cm² = 2 cm²
Area of square FEDG = 3 × 3 cm² = 9 cm²
Area of rectangle ABCD = 2 × 4 cm² = 8 cm²
∴ Total area of the figure = (9 + 2 + 9 + 8) cm² = 28 cm²

(b) We have,

Area of rectangle ABCD = 3 × 1 cm² = 3 cm²
Area of rectangle BJEF = 3 × 1 cm² = 3 cm²
Area of rectangle FGHI = 3 × 1 cm² = 3 cm²
∴ Total area of the figure = (3 + 3 + 3) cm² = 9 cm²

Question 11.
Split the following shapes into rectangles and find their areas. (The measures are given in centimetres).

Solution:
(a) We have,

Area of rectangle ABCD = 2 × 10 cm² = 20 cm²
Area of rectangle DEFG = 10 × 2 cm² = 20 cm²
∴ Total area of the figure = (20 + 20) cm²
= 40 cm²

(b) We have,

There are 5 squares each of side 7 cm.
Area of one square = 7 × 7 cm² = 49 cm²
∴ Area of 5 squares = 5 × 49 cm² = 245 cm²

(c) We have,

Area of rectangle ABCD = 5 × 1 cm² = 5 cm²
Area of rectangle EFGH = 4 × 1 cm² = 4 cm²
∴ Total area of the figure = (5 + 4) cm²
= 9 cm²

Question 12.
How many tiles whose length and breadth are 12 cm and 5 cm respectively will be needed to fit in a rectangular region whose length and breadth are respectively:
(a) 100 cm and 144 cm
(b) 70 cm and 36 cm.
Solution:
(a) Area of rectangular region
= length × breadth = 100 cm × 144 cm = 14400 cm²
Area of one tile = 12 cm × 5 cm = 60 cm²

Thus, 240 tiles are required.

(b) Area of rectangular region
= length × breadth = 70 cm × 36 cm = 2520 cm²
Area of one tile = 12 cm × 5 cm = 60 cm²
∴ Number of tiles
= \(\frac{\text { Area of rectangular region }}{\text { Area of one tile }}=\frac{2520}{60}\) = 40
Thus, 42 tiles are required.

MP Board Class 6th Maths Solutions

MP Board Class 6th Maths Solutions Chapter 9 Data Handling Ex 9.2

Question 1.
Total number of animals in five villages are as follows:
Village A : 80 Village B : 120
Village C : 90 Village D : 40
Village E : 60
Prepare a pictograph of these animals using one symbol to represent 10 animals and answer the following questions :
(a) How many symbols represent animals of village E?
(b) Which village has the maximum number of animals?
(c) Which village has more animals : village A or village C?
Solution:

(a) 6 symbols represent animals of village E.
(b) Village B has the maximum number of animals.
(c) Village C has more animals than village A.

Question 2.
Total number of students of a school in different years is shown in the following table.

A. Prepare a pictograph of students using one symbol img 2 to represent 100 students and answer the following questions:
(a) How many symbols represent total number of students in the year 2002?
(b) How many symbols represent total number of students for the year 1998?
B. Prepare another pictograph of students using any other symbol each representing 50 students. Which pictograph do you find more informative?
Solution:
A.

(a) 6 symbols represent total number of students in the year 2002.
(b) Five completed and one incomplete symbols represent total number of students for the year 1998.
B.

Pictograph B is more informative than pictograph A.

MP Board Class 6th Maths Solutions

MP Board Class 6th Maths Solutions Chapter 10 Mensuration Ex 10.2

Question 1.
Find the areas of the following figures by counting square:

Solution:
(a) Number of filled squares = 9
∴ Area covered by filled squares
= (9 × 1) sq units = 9 sq units

(b) Number of filled squares = 5
∴ Area covered by filled squares
= (5 × 1) sq units = 5 sq units

(c) Number of fully-filled squares = 2
Number of half-filled squares = 4
∴ Area covered by fully-filled squares
= (2 × 1) sq units = 2 sq units
Area covered by half-filled squares
= (4 × \(\frac{1}{2}\)) sq units = 2 sq units
∴ Total area = (2 + 2) sq units = 4 sq units

(d) Number of filled squares = 8
∴ Area covered by filled squares
= (8 × 1) sq units = 8 sq units

(e) Number of filled squares = 10
∴ Area covered by filled squares
= (10 × 1) sq units = 10 sq units

(f) Number of fully-filled squares = 2
Number of half-filled squares = 4
∴ Area covered by fully-filled squares
= (2 × 1) sq units = 2 sq units
Area covered by half-filled squares
= (4 × \(\frac{1}{2}\)) sq units = 2 sq units
∴ Total area = (2 + 2) sq units = 4 sq units

(g) Number of fully-filled squares = 4
Number of half-filled squares = 4
∴ Area covered by fully-filled squares
= (4 × 1) sq units = 4 sq units
Area covered by half-filled squares
= (4 × \(\frac{1}{2}\)) sq units = 2 sq units
∴ Total area = (4 + 2) sq units = 6 sq units

(h) Number of filled squares = 5 .
∴ Area covered by filled squares
= (5 × 1) sq units = 5 sq units

(i) Number of filled squares = 9
∴ Area covered by filled squares
= (9 × 1) sq units = 9 sq units

(j) Number of fully-filled squares = 2
Number of half-filled squares = 4
∴ Area covered by fully-filled squares
= (2 × 1) sq units = 2 sq units
Area covered by half-filled squares
= (4 × \(\frac{1}{2}\)) sq units = 2 sq units
∴ Total area = (2 + 2) sq units = 4 sq units

(k) Number of fully-filled squares = 4
Number of half-filled squares = 2
∴ Area covered by fully-filled squares
= (4 × 1) sq units = 4 sq units
Area covered by half-filled squares
= (2 × \(\frac{1}{2}\)) sq units = 1 sq units
∴ Total area = (4 + 1) sq units = 5 sq units

(l) Number of fully-filled squares = 3,
Number of half-filled squares = 2,
Number of more than half-filled squares = 4
and number of less than half-filled squares = 4.
Now, estimated area covered by
fully-filled squares = 3 sq units,
half-filled squares = (2 × \(\frac{1}{2}\)) sq units
= 1 sq unit,
more than half-filled squares = 4 sq units
and less than half-filled squares
= 0 sq unit
∴ Total area = (3 + 1 + 4 + 0) sq units
= 8 sq units.

(m) Number of fully-filled squares = 7,
Number of more than half-filled squares = 7
and number of less than half-filled squares = 5
Estimated area covered by
fully-filled squares = 7 sq units,
more than half-filled squares = 7 sq units
and less than half-filled squares = 0 sq unit
∴ Total area = (7 + 7 + 0) sq units = 14 sq units

(n) Number of fully-filled squares = 10,
Number of more than half-filled squares = 8
and number of less than half-filled squares = 5
Estimated area covered by
fully-filled squares = 10 sq units,
more than half-filled squares = 8 sq units
less than half-filled squares = 0 sq unit
∴ Total area = (10 + 8 + 0) sq units
= 18 sq units.

MP Board Class 6th Maths Solutions

MP Board Class 6th Maths Solutions Chapter 9 Data Handling Ex 9.1

Question 1.
In a Mathematics test, the following marks were obtained by 40 students. Arrange these marks in a table using tally marks.

(a) Find how many students obtained marks equal to or more than 7.
(b) How many students obtained marks
Solution:

(a) 5 + 4 + 3 = 12 students obtained marks equal to or more than 7.
(b) 2 + 3 + 3 = 8 students obtained marks below 4.

Question 2.
Following is the choice of sweets of 30 students of Class VI.
Ladoo, Barfi, Ladoo, Jalebi, Ladoo, Rasgulla, Jalebi, Ladoo, Barfi, Rasgulla, Ladoo, Jalebi, Jalebi, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo, Rasgulla, Ladoo, Ladoo, Barfi, Rasgulla, Rasgulla, Jalebi, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo.
(a) Arrange the names of sweets in a table using tally marks.
(b) Which sweet is preferred by most of the students?
Solution:

(b) Ladoo is preferred by most of the students.

Question 3.
Catherine threw a dice 40 times and noted the number appearing each time as shown below:

Make a table and enter the data using tally marks. Find the number that appeared
(a) The minimum number of times.
(b) The maximum number of times.
(c) Find those numbers that appear an equal number of times
Solution:

(a) 4 appeared minimum number of times.
(b) 5 appeared maximum number of times.
(c) 1 and 6 appeared equal number of times.

Question 4.
Following pictograph shows the number of tractors in five villages.

Observe the pictograph and answer the following questions.
(i) Which village has the minimum number of tractors?
(ii) Which village has the maximum number of tractors?
(iii) Flow many more tractors village C has as compared to village B.
(iv) What is the total number of tractors in all the five villages?
Solution:
(i) Village D has the minimum number of tractors.
(ii) Village C has the maximum number of tractors.
(iii) Village C has 8 – 5 = 3 more tractors than village B.
(iv) Total number of tractors = 6 + 5 + 8 + 3 + 6 = 28

Question 5.
The number of girl students in each class of a co-educational middle school is depicted by the pictograph:

Observe this pictograph and answer the following questions:
(a) Which class has the minimum number of girl students?
(b) Is the number of girls in Class VI less than the number of girls in Class V?
(c) Flow many girls are there in Class VII?
Solution:

(a) Class VIII has the minimum number of girl students.
(b) No, the number of girls in Class VI is greater than the number of girls in Class V.
(c) There are 12 girls in Class VII.

Question 6.
The sale of electric bulbs on different days of a week is shown below:

Observe the pictograph and answer the following questions:
(a) How many bulbs were sold on Friday?
(b) On which day were the maximum number of bulbs sold?
(c) On which of the days same number of bulbs were sold?
(d) On which of the days minimum number of bulbs were sold?
(e) If one big carton can hold 9 bulbs. How many cartons were needed in the given week ?
Solution:

(a) Number of bulbs sold on Friday is 14.
(b) Maximum number of bulbs were sold on Sunday.
(c) Same number of bulbs were sold on Wednesday and Saturday.
(d) Minimum number of bulbs were sold on Wednesday and Saturday.
(e) The total number of bulbs were sold in the given week = 86
Number of cartons required for 9 bulbs = 1
∴ Number of cartons required for 86 bulbs = 86 ÷ 9 = 9.55 = 10
Therefore, 10 cartons were needed in the given week.

Question 7.
In a village six fruit merchants sold the following number of fruit baskets in a particular season:

Observe this pictograph and answer the following questions:
(a) Which merchant sold the maximum number of baskets?
(b) How many fruit baskets were sold by Anwar?
(c) The merchants who have sold 600 or more number of baskets are planning to buy a godown for the next season. Can you name them?
Solution:

(a) Martin sold the maximum number of baskets.
(b) 700 fruit baskets were sold by Anwar.
(c) Anwar, Martin and Ranjit Singh have sold more than 600 baskets.

MP Board Class 6th Maths Solutions

MP Board Class 6th Maths Solutions Chapter 10 Mensuration Ex 10.1

Question 1.
Find the perimeter of each of the following figures:

Solution:
(a) Perimeter = Sum of all the sides
= 4 cm + 2 cm + 1 cm + 5 cm = 12 cm

(b) Perimeter = Sum of all the sides
= 23 cm + 35cm + 40 cm + 35cm = 133 cm

(c) Perimeter = Sum of all the sides
= 15 cm + 15 cm + 15 cm + 15 cm = 60 cm

(d) Perimeter = Sum of all the sides
= 4 cm + 4 cm + 4 cm + 4 cm + 4 cm = 20 cm

(e) Perimeter = Sum of all the sides
= 1 cm + 4 cm + 0.5 cm + 2.5 cm + 2.5 cm + 0.5 cm + 4 cm = 15 cm

(f) Perimeter = Sum of all the sides
= 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm = 52 cm

Question 2.
The lid of a rectangular box of sides 40 cm by 10 cm is sealed all round with tape. What is the length of the tape required?
Solution:
Total length of tape required
= Perimeter of rectangle
= 2 (length + breadth)
= 2 (40 +10) cm = 2 × 50 cm = 100 cm = 1 m

Thus, the total length of tape required is 100 cm or 1 m.

Question 3.
A table-top measures 2 m 25 cm by 1 m 50 cm. What is the perimeter of the table-top?
Solution:
Length of table-top = 2 m 25 cm = 2.25 m
Breadth of table-top = 1 m 50 cm = 1.50 m
Perimeter of table-top = 2 × (length + breadth)
= 2 × (2.25 + 1.50) m
= 2 × 3.75 m = 7.50 m
Thus, perimeter of table-top is 7.5 m.

Question 4.
What is the length of the wooden strip required to frame a photograph of length and breadth 32 cm and 21 cm respectively?
Solution:
Length of wooden strip
= Perimeter of photograph
= 2 × (length + breadth)
= 2 (32 + 21) cm = 2 × 53 cm = 106 cm
Thus, the length of the wooden strip required is 106 cm.

Question 5.
A rectangular piece of land measures 0.7 km by 0.5 km. Each side is to be fenced with 4 rows of wires. What is the length of the wire needed?
Solution:
Since 4 rows of wires are needed. Therefore, the total length of wire is equal to 4 times the perimeter of land.
Perimeter of land = 2 × (length + breadth)
= 2 × (0.7 + 0.5) km = 2 × 1.2 km = 2.4 km
= 2.4 × 1000 m = 2400 m
Thus, the length of wire
= 4 × 2400 m = 9600 m = 9.6 km

Question 6.
Find the perimeter of each of the following shapes:
(a) A triangle of sides 3 cm, 4 cm and 5 cm.
(b) An equilateral triangle of side 9 cm.
(c) An isosceles triangle with equal sides 8 cm each and third side 6 cm.
Solution:
(a) Perimeter of ∆ABC
= AB + BC + CA
= 3 cm+ 5 cm+ 4 cm
= 12 cm

(b) Perimeter of equilateral ∆ABC
= 3 × side
= 3 × 9 cm
= 27 cm

(c) Perimeter of ∆ABC
= AB + BC + CA
= 8 cm + 6 cm + 8 cm
= 22 cm

Question 7.
Find the perimeter of a triangle with sides measuring 10 cm, 14 cm and 15 cm.
Solution:
Perimeter of triangle
= Sum of all three sides
= 10 cm + 14 cm + 15 cm = 39 cm
Thus, perimeter of triangle is 39 cm.

Question 8.
Find the perimeter of a regular hexagon with each side measuring 8 m.
Solution:
Perimeter of a regular hexagon
= 6 × length of one side
= 6 × 8m
= 48m
Thus, the perimeter of the regular hexagon is 48 m.

Question 9.
Find the side of the square whose perimeter is 20 m.
Solution:
Perimeter of square = 4 × side
⇒ 20 m = 4 × side ⇒ side = \(\frac{20}{4}\) m = 5m
Thus, the side of square is 5 m.

Question 10.
The perimeter of a regular pentagon is 100 cm. How long is its each side?
Solution:
Perimeter of regular pentagon = 5 × side
⇒ 100 cm = 5 × side ⇒ side = \(\frac{100}{5}\) cm = 20 cm
Thus, the side of regular pentagon is 20 cm.

Question 11.
A piece of string is 30 cm long. What will be the length of each side if the string is used to form:
(a) a square?
(b) an equilateral triangle?
(c) a regular hexagon?
Solution:
Length of string = Perimeter of each shape
(a) Perimeter of square = 4 × side
⇒ 30 cm = 4 × side ⇒ side = \(\frac{30}{4}\) cm = 7.5 cm
Thus, the length of each side of square will be 7.5 cm.

(b) Perimeter of equilateral triangle = 3 × side
⇒ 30 cm = 3 × side ⇒ side = \(\frac{30}{3}\) cm = 10 cm
Thus, the length of each side of equilateral triangle will be 10 cm.

(c) Perimeter of regular hexagon = 6 × side
⇒ 30 cm = 6 × side ⇒ side = \(\frac{30}{6}\) cm = 5 cm
Thus, the length of each side of regular hexagon will be 5 cm.

Question 12.
Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is its third side?
Solution:
Let the length of third side be x cm. Length of other two sides are 12 cm and 14 cm.
Now, perimeter of triangle = 36 cm
⇒ 12 + 14 + x = 36 ⇒ 26 + x = 36
⇒ x = 36 – 26 ⇒ x = 10
Thus, the length of third side is 10 cm.

Question 13.
Find the cost of fencing a square park of side 250 m at the rate of Rs. 20 per metre.
Solution:
Side of square park = 250 m
Perimeter of square park = 4 × side
= 4 × 250 m = 1000 m
Since, cost of fencing for 1 metre = Rs. 20
Therefore, cost of fencing for 1000 metres
= Rs. 20 × 1000 = Rs. 20,000

Question 14.
Find the cost of fencing a rectangular park of length 175 m and breadth 125 m at the rate of Rs. 12 per metre.
Solution:
Length of rectangular park = 175 m
Breadth of rectangular park = 125 m
Perimeter of park = 2 × (length + breadth)
= 2 × (175 + 125) m = 2 × 300 m = 600 m
Since, cost of fencing park for 1 metre = Rs. 12
Therefore, cost of fencing park for 600 m = Rs. 12 × 600 = Rs. 7,200

Question 15.
Sweety runs around a square park of side 75 m. Bulbul runs around a rectangular park with length 60 m and breadth 45 m. Who covers less distance?
Solution:
Distance covered by Sweety
= Perimeter of square park = 4 × side
= 4 × 75 m = 300 m
Thus, distance covered by Sweety is 300 m.
Now, distance covered by Bulbul
= Perimeter of rectangular park
= 2 × (length + breadth)
= 2 × (60 + 45) m = 2 × 105 m = 210 m
Thus, Bulbul covers a distance of 210 m.
So, Bulbul covers less distance.

Question 16.
What is the perimeter of each of the following figures? What do you infer from the answers?

Solution:
(a) Perimeter of square = 4 × side
= 4 × 25 cm = 100 cm

(b) Perimeter of rectangle
= 2 × (length + breadth)
= 2 × (40 + 10) cm = 2 × 50 cm = 100 cm

(c) Perimeter of rectangle
= 2 × (length + breadth)
= 2 × (30 + 20) cm = 2 × 50 cm = 100 cm

(d) Perimeter of triangle = Sum of all sides
= 30 cm + 30 cm + 40 cm
= 100 cm
Thus, all the figures have same perimeter.

Question 17.
Avneet buys 9 square paving slabs, each with side of \(\frac{1}{2}\) m. He lays them in the form of a square.
(a) What is the perimeter of his arrangement [see fig. (i)]?
(b) Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement [see fig. (ii)]?
(c) Which has a greater perimeter?
(d) Avneet wonders if there is a way of getting an even greater perimeter. Can you find a way of doing this? (The paving slabs must meet along complete edges i.e. they cannot be broken.)

Solution:
(a) Side of one small square = \(\frac{1}{2}\) m
∴ Side of given square = \(\frac{3}{2}\) m
Perimeter of square = 4 × side
= 4 × \(\frac{3}{2}\) m = 6 m

(b) Perimeter of given figure
= Sum of all sides = 20 × \(\frac{1}{2}\) m = 10 m

(c) The arrangement cross has greater perimeter.
(d) It is not possible to determine the arrangement with perimeter greater than 10 m.

MP Board Class 6th Maths Solutions

MP Board Class 6th Social Science Solutions Miscellaneous Questions 1

MP Board Class 6th Social Science Miscellaneous Questions 1 Short Answer Type Questions

Question 1.
What do you understand by History?
Answer:
History is one way of knowing the past.

Question 2.
Name four sources of knowing History?
Answer:
Inscriptions on stone are called Petrograph.

Question 3.
What is a petrography?
Answer:
Petrography is a branch of petrology that focuses on detailed descriptions of rocks. Someone who studies petrography is called a petrographer. The mineral content and the textural relationships within the rock are described in detail.

Question 4.
What is a Bhojpatra?
Answer:
The bark of birch tree on which ancient books were written, is called as Bhojpatra.

Question 5.
What is a record?
Answer:
Records are the old historic information. These are found on dried palm leaves, the bark of the brich tree, plates of copper and hand written papers.

Question 6.
Who is primitive man?
Answer:
The man who lived thousands of years ago, was called primitive man.

Question 7.
How did primitive man protect themselves from wild animals?
Answer:
The primitive man protected themselves from animals by burning the fire at the entrance of the caves.

Question 8.
Why is the age of primitive man called the stone age?
Answer:

1. The man of stone age was having the tools, weapons and pots made of stones.
2. So this age is called as stone age.

Question 9.
In how many parts stone age has been divided? Name them?
Answer:
The stone age have been divided in to three parts:

1. Palaeotithic or the Old stone age.
2. Mesolithic or the Middle Stone Age.
3. Neolithic or the New Stone Age.

Question 10.
How was fire discovered?
Answer:
It is assumed that the discovery of fire was by accident. When two flint stones were struck against each other, it created sparks which caused leaves to burn. In this way man learnt to light a fire. Fire was very useful to them for light, roasting meat and protection from wild animals.

Question 11.
Which animals were used by primitive man?
Answer:
The primitive man used animals for different purposes, the dog for hunting, the cow, the buffalo and the goat for milk,the goat, the sheep and the buffalo for meat.

Question 12.
How did the discovery of wheel proved a boon to human beings?
Answer:
Discovery and uses of wheel. Wheel was a very important discovery of the early man. It led to a big advance in the pattern of man’s living. Its discovery made life very much easy in a number of ways. Man now discovered carts which were drawn by animals. People now could travel easily from one place to other. It also helped in movement of objects. It improved the making of pottery.

Question 13.
How did primitive man travel from one place to another?
Answer:
There were no means of transport. The primitive man used to walk for going from one place to another.

Question 14.
What is the importance of the family to a person?
Answer:
Father, mother, brother and sister together constitute a family. In bigger families grandfather, grandmother, uncles, aunts also live with their children. This type of family is called joint family.

Question 15.
What is the unit of a society?
Answer:
A family is the unit of society.

Question 16.
Write two characteristics of a developed society?
Answer:
The two characteristics of a developed society:

1. The spirit, of working together
2.  Respect for the ideas of other.

Question 17.
What do you understand by interdependence?
Answer:
The dependence on each other to complete a work or fulfill a need is called interdependence.

Question 18.
How many planets are there in the Solar System? Which is called the living planet?
Answer:
1. The Sun and the nine planets which revolve around it make up the ‘Family of the Sun’ or the Solar System.

2. The Solar System consists of the Sun as the centre and Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto as planets. In addition, there are in all 44 satellites in our Solar System.

Question 19.
Explain interdependence between two countries with examples?
Answer:
1. The increase and diversity of the needs became the reason for interdependence. Countries depend on each other for things which are not available or available in very little quantity.

2. For example, our country has to depend on other countries for petroleum products i.e., diesel, petrol and kerosene modern equipments and arms for the army. We get these from countries which produce them.

3. On the other hand, we send spices, tea, cement, ready – made garments to other countries.

Question 20.
Write the name of the head of the solar system?
Answer:
Sun is the head of the solar system.

Question 21.
In how many days does the earth go round the sun once?
Answer:
The earth takes 365 days to rotate round the sun.

Question 22.
Write the names of the nearest and farthest planet from the sun?
Answer:
Mercury and Pluto.

Question 23.
The Moon is the satellite of which planet?
Answer:
Earth.

Question 24.
Which is called the red planet?
Answer:
Mars is called the red planet.

Question 25.
What is a light year?
Answer:
A light – year is a unit of distance. It is the distance that light can travel in one year. Light moves at a velocity of about 300,000 kilometers (km) each second. So in one year, it can travel about 10 trillion km. More precisely, one light – year is equal to 9,500,000,000,000 kilometers.

Question 26.
What are latitudes and longitudes?
Answer:
1. The spherical and horizontal lines drawn parallel to the equator are called latitudes.

2. There are 90 latitudes in the northern hemisphere and 90 latitudes in the southern hemisphere. In all there are 180 latitudes drawn on the globe. The equator is the largest latitude drawn on the globe. The equator is also known as the 0° latitude.

3. The 23\(\frac { 1 }{ 2 }\)° W latitude north, in the northern hemisphere is called the tropic of cancer.

4. Similarly the 23\(\frac { 1 }{ 2 }\)° latitude south, in the southern hemisphere is called the tropic of capricorn.

5. The Arctic Circle lies at the distances of 66\(\frac { 1 }{ 2 }\)° N of the equator.

6. The Antarctic Circle 66\(\frac { 1 }{ 2 }\)° S is similar to the Arctic Circle but lies in the southern hemisphere.

7. The vertical lines drawn from north to south are called longitudes.

8. The longitude passes through Greenwich Observatory near London in England is called 0° longitude, Prime Meridian.

9. The other longitudes are drawn east and west of the Prime Meridian.

10. The Prime Meridian divides the world into Eastern (E) and Western (W) hemisphere.

Question 27.
What is a globe?
Answer:
Globe is a three dimensional model of earth or sphere, which gives us the correct idea of the shape of the earth.

Question 28.
What is a map?
Answer:
The following information we can get from a globe:

1. The earth is a bit flat at the poles.
2. The shape of earth is spheroid.
3. The earth is not straight on its axis but a little tilted.
4. The globe shows the location of oceans, islands, continents, main mountains and countries, etc.
5. The characteristics of the horizontal and vertical lines drawn on the globe.

Question 29.
Write the names of the continents and the oceans of the world?
Answer:
List of Continents:

1. North America
2. South America
3. Asia
4. Europe
5. Africa
6. Australia
7. Antractica .

List of Oceans:

1. Pacific Ocean
2. Atlantic Ocean
3. Indian Ocean
4. Arctic Ocean

List of Seas:

1. Arabian sea.

List of Islands:

1. Andaman and Nicobar Islands.

Question 30.
Why latitudes and longitudes are drawn on a globe?
Answer:
To locate the exact position of places on earth, latitudes and longitudes lines are drawn on a globe or a map. We can easily locate the geographical position of any village, city, town, country, or any place with the help of these lines.

Question 31.
Which latitude passes through the centre of India?
Answer:
Latitude.

Question 32.
In which Hemispheres India is situated?
Answer:
Northern Hemisphere.

Question 33.
What is the name given to the biggest latitude?
Answer:
Equator.

Question 34.
What is Prime Meridian?
Answer:
Equator:
Equator is an imaginary line which is drawn on the globes (the model of earth) in such a way that at all points it lies exactly half way between the north pole and the south pole.

Prime Meridian:

1. Like the main latitude (0° equator), there is a main longitude. This longitude passes through Greenwich Observatory near Landon in England. This is called 0° longitude, Prime Meridian.
2. The world has been divided by these lines into four hemisphere.

Question 35.
What is the name given to 23\(\frac { 1 }{ 2 }\)° South latitude?
Answer:
Tropic of capricorn.

Question 36.
What are the differences between latitude and longitude? Write any three?
Answer:
Latitude:

1. The line drawn horizontally parallel to the equator on the globe is latitude.
2. All the horizontally parallel lines are not in equal size.
3. There are 180 latitude lines.

Longitude:

1. The line drawn horizontally parallel to the equator on the globe is latitude.
2. All the horizontally parallel lines are not in equal size.
3. There are 180 latitude lines.

Question 37.
How many realms of earth are there? Name them.
Answer:
There are three realms of earth. The three realms of the earth are:

1. Land
2. Water
3. Air.

Question 38.
What is the percentage of water on earth?
Answer:
71%.

Question 39.
What is lithosphere?
Answer:
The realm of the earth consisting of rocks, stones and soil is called lithosphere.

Question 40.
What is hydrosphere?
Answer:
Hydrosphere is the realm of water on the earth.

Question 41.
Which gas is found the most in the atmosphere?
Answer:
Nitrogen.

Question 42.
What is the difference between a mountain and a plateau?
Answer:
Mount Everest.

Mountain:

1. Mountain are highly elevated lands with steep slopes. by the rivers.
2. They are higher than the surrounding areas.

Plateau:

1. Plateaus are moderately elevated lands with flat tops.
2. They rise abruptly from the surrounding areas.

Question 43.
What is an island?
Answer:
The small parts of land surrounded by water are called islands.

Answer the following Questions:

Question 1.
What do you understand by History? What are the different sources of knowing History?
Answer:
The different ways of knowing History are through:

1. Oral information
2. Written information
3. Evidences.

1. Oral information:
The old proverbs, stories and ancedotes come under oral in formations.

2. Written information:
These are the writings which can be read.

3. Evidences:
These are the things which were used by the people at that time.

Question 2.
How did the primitive man start agriculture and animal husbandry? Explain in detail.
Answer:
In India cultivation started 5,000 to 6,000 years ago, growing plants and grain was an important discovery. Now, man had learnt that by putting seeds into the soil and watering the soil, plants would grow. This was the beginning of agriculture. He could grow his own food. So, he started living at one place and settled him as an agriculturist. Along with cultivation man also learnt animal husbandary. He began rearing a number of useful animals. He used them for different tasks:

1. Use of dogs in hunting.
2. Use of bullocks in farming.
3. Cows, goats and buffaloes for milk.
4. Sheep, bulls and goats for meat.
5. Horses for riding.

Question 3.
What is a society and what type of evils can be controlled by the society?
Answer:
A society is a network of social relations. In fact, a society is formed by the relationship among many families. Man is a social animal, so man lives in a family and society. Many problems come in the life of a man, like selection of a partner for marriage and bringing up children and educating them. The members of the family and their family friends help to resolve these problems. A society can control many social evils like child – marriage, large families not giving elementary education to children.

Question 4.
Explain the interdependence of villages and cities and give examples of things produced by the village and the things produced by the cities?
Answer:
The items like wheat, gram, kolikeheda, cotton, milk etc. are brought to village or town from villages. The items like diesel, petrol, kerosene, clothes, medicine, sugar, radio, T.V, bicycle, fruits are brought to village or town from towns.

Question 5.
What is the interdependence and how does it affect civic life?
Answer:
The citizen’s life is dependent on mutual help. In the family, school and neighbourhood, there is a need of mutual help. In your school you must have some rules which are essential for every teacher and student to follow. The work, we do as a rule, is called duty. The life of citizens depend on mutual help and performance of duty.

Question 6.
What is the Solar System? Why is the earth called a unique planet?
Answer:
The Sun and the nine planets which revolve around it make up the family of the Sun or the Solar System. In addition to the nine planets, there are 44 satellites in the Solar System.

The earth is a small member of the Solar System. It is the fifth in size of the nine major planets and the third in distance. But it occupies a very unique position in the Solar System, for the following reasons:

1. Around the Earth is a gaseous envelope known as the atmosphere. It saves us from the extreme heat of the Sun.
2. The Earth has land, water and air unlike the other planets which makes life possible. All this had made the Earth a sweet home for us.

Question 7.
Explain the solar system with a diagram?
Answer:
The Sun and the nine planets which revolve around it make up the family of the Sun or the Solar System. In addition to the nine planets, there are 44 satellites in the Solar System.

Question 8.
What is a globe? What information can we get from a globe?
Answer:
Globe is a three dimensional model of earth or sphere, which gives us the correct idea of the shape of the earth.

The following information we can get from a globe:

1. The earth is a bit flat at the poles.
2. The shape of earth is spheroid.
3. The earth is not straight on its axis but a little tilted.
4. The globe shows the location of oceans, islands, continents, main mountains and countries, etc.
5. The characteristics of the horizontal and vertical lines drawn on the globe.

Question 9.
What should one know to read a map?
Answer:

1. A map can be read and understand as a book is read and information is gathered from it.
2. A map can be made and read on four basic points.

These are :

1. Symbol
2. Direction
3. Headings
4. Scale

1. Symbol:
It is the third important component of any map. When an area or locality is shown on a map, it is not possible to show various features, e.g., roads, building, trees, railway lines in their actual shape and size. To overcome this difficulty, the features are shown by different symbols.

The use of symbols saves space and a lot of information can be given in a single map. Various colours in maps are chosen for the same purpose. All over the world there has been some kind of agreement regarding the use of symbols and colours. The symbols used all over the world in various maps are called conventional symbols.

2. Direction:
It is another very important component of any map. A map has four directions i.e., north, south, east and west. While knowing any one direction on map we fan find all the remaining directions.

3. Headings:
Heading is the one of the component of read a map. “Structure” to their code that identifies main headings and subheadings. Headings Map creates a visual heading structure of the webpage by generating an index or ‘map’ of the headings created by the author.

4. Scale:
When human being did not have the knowledge of scripts, they expressed themselves through pictures and figures drawn on rocks. These pictures are called rock paintings. The rock paintings at Bhimbetka near Bhopal is a living example of ancient rock painting. The most of the rock paintings in India have been found in the Vindhyachal and Satpura ranges in Madhya Pradesh.

Question 10.
What are latitudes and longitudes? Why they have been drawn on the globe?
Answer:
To locate the exact position of places on earth, latitudes and longitudes lines are drawn on a globe or a map. We can easily locate the geographical position of any village, city, town, country, or any place with the help of these lines.

The spherical and horizontal lines drawn parallel to the equator are called latitudes. There are 90 latitudes in the northern hemisphere and 90 latitudes in the southern hemisphere. In all there are 180 latitudes drawn on the globe. The equator is the largest latitude drawn on the globe. The equator is also known as the 0° latitude.

The 23\(\frac { 1 }{ 2 }\)° W latitude north, in the northern hemisphere is called the tropic of cancer. Similarly the 23\(\frac { 1 }{ 2 }\) ° latitude south, in the southern hemisphere is called the tropic of capricorn. The Arctic Circle lies at the distances of 66\(\frac { 1 }{ 2 }\)° N of the equator. The Antarctic Circle 66\(\frac { 1 }{ 2 }\)° S is similar to the Arctic Circle but lies in the southern hemisphere.

The vertical lines drawn from north to south are called longitudes. The longitude passes through Greenwich Observatory near London in England is called 0° longitude, Prime Meridian. The other longitudes are drawn east and west of the Prime Meridian. The Prime Meridian divides the world into Eastern (E) and Western (W) hemisphere.

Question 11.
How many realms are there on the earth? Write their names and describe the different forms of the lithosphere?
Answer:
There are three realms of earth. The three realms of the earth are:

1. Land
2. Water
3. Air.

The realm of the earth consisting of rocks, stones and soil is called lithosphere.

Fill in the blanks:

1. The picture drawn on rocks are called ……………….
2. The words engraved on stone are called …………….
3. Our civic life depends on and …………….
4. The planets and the satellites are illuminated by …………………..
5. The only satellite of our earth is ………………..
6. The small and temporary planets made by humans are called ……………….
7. The large area of water stretched on earth is called ……………
8. The shape of the earth is ………………
9.  …………… colour is seen the most on a globe.
10. The uppermost point on the globe is called …………… pole and the Southern most point is called the ……………….
11. Longitude are ………………. lines.
12. The world is ……………….. on its axis.
13. Land is on …………… percent part of the earth.
14. The piece of land surrounded by water on all sides is called ………………..
15. The gas over the earth is called …………………

Answer:

1. rock paintings
2. inscriptions
3. mutual help, performance of duty
4. sun
5. moon
6. artificial setellites
7. oceans
8. bit flattened at the poles
9. Blue
10. north, south
11. vertical
12. rotate
13.  29
14. island
15. air

Choose the correct alternative:

Question (a)
What among the following is a source of knowing History?
(i) water
(ii) tree
(iii) earthen utensils
(iv) pen
Answer:
(iii) earthen utensils

Question (b)
How did the primitive man get their food?
(i) By agriculture
(ii) by collecting tubers and fruits
(iii) from the sea
(iv) none of these
Answer:
(ii) by collecting tubers and fruits

Question (c)
What among these is a not the characteristic of the society?
(i) Food habits
(ii) blood relation
(iii) life style
(iv) customs
Answer:
(iv) customs

Question (d)
What among the following is not our basic need?
(i) Food
(ii) clothes
(iii) electricity
(iv) shelter
Answer:
(iii) electricity

Question (e)
Which among the following is a star?
(i) the Sun
(ii) the Moon
(iii) the Earth
(iv) the Mars
Answer:
(i) the Sun

Question (f)
The infinite space in which all the galaxies and energy are stretched is called:
(i) the Solar System
(ii) The Sun
(iii) the universe
(iv) Akashganga
Answer:
(iii) the universe

Question (g)
Which among the following is called a living planet?
(i) the moon
(ii) the earth
(iii) the Mercury
(iv) the Mars
Answer:
(ii) the earth

Question (h)
Which among the following is called the red planet?
(i) the Earth
(ii) the Mars
(iii) the Jupiter
(iv) the Mercury
Answer:
(ii) the Mars

Question (i)
Which among the following is the life saving gas?
(i) Oxygen
(ii) Nitrogen
(iii) Helium
(iv) Ozone
Answer:
(i) Oxygen

Question (j)
The night when the total moon is seen is called?
(i) Dark day
(ii) New moon
(iii) Full moon
(iv) the eleventh day
Answer:
(iii) Full moon

Question (k)
The nearest celestial body to earth is?
(i) the Sun
(ii) the Mercury
(iii) the Moon
(iv) the Venus
Answer:
(ii) the Mercury

Question (l)
The model of the earth is called?
(i) map
(ii) measurer
(iii) globe
(iv) moon.
Answer:
(iii) globe

Question (m)
The number of continents on earth are?
(i) 4
(ii) 5
(iii) 6
(iv) 7
Answer:
(iv) 7

Question (n)
The latitudes are:
(i) semi circles
(ii) of equal length
(iii) spherical
(iv) vertical lines.
Answer:
(iii) spherical

Pick the odd one out:

Question (a)
(i) Palaeolithic
(ii) black stone age
(iii) Mesolithic
(iv) Neolithic
Answer:
(i) Palaeolithic

Question (b)
(i) cow
(ii) buffalo
(iii) tiger
(iv) goat
Answer:
(iii) tiger

Question (c)
(i) rock-painting
(ii) documentary
(iii) cave painting
(iv) mural
Answer:
(ii) documentary

Question (d)
(i) family
(ii) community
(iii) marriage
(iv) society
Answer:
(iii) marriage

Question (e)
(i) petrol
(ii) clothes
(iii) diesel
(iv) kerosene.
Answer:
(ii) clothes

Question (f)
(i) crops
(ii) foodgrains
(iii) food
(iv) produce
Answer:
(iv) produce

Question (g)
(i) the Mercury
(ii) the Venus
(iii) the Mars
(iv) the Moon
Answer:
(iv) the Moon

Question (h)
(i) Aryabhatta
(ii) Rohini
(iii) Moon
(iv) Bhaskar
Answer:
(iii) Moon

Question (i)
(i) Asia
(ii) Africa
(iii) Pacific
(iv) America
Answer:
(iii) Pacific

Question (j)
(i) Tropic of Cancer
(ii) Equator
(iii) Lapic of Capricorn
(iv) Greenwich Meridian.
Answer:
(iv) Greenwich Meridian.

Question (k)
(i) Lithosphere
(ii) Biosphere
(iii) Atmosphere
(iv) Solar family
Answer:
(iv) Solar family

Question (l)
(i) mountain
(ii) sea
(iii) plateau
(iv) plains
Answer:
(ii) sea

Question (m)
(i) nitrogen
(ii) oxygen
(iii) vapours
(iv) carbondioxide.
Answer:
(iii) vapours

Match the following:

1. The mixture of gases – family
2. The vertical lines – the earth
3. The horizontal lines – Petrograph
4. Spheroid – stone age
5. The model of the earth – globe
6. The largest planet – the Jupiter
7. The interdependence as per need – interdependence
8. The unit of the society – family
9. The era of stone – stone age
10. The information engraved On stone – Interdependence

Answer:

1. The mixture of gases – atmosphere
2. The vertical lines – longitudes
3. The horizontal lines – latitudes
4. spheroid – the earth
5. The model of the earth – globe
6. The largest planet – the Jupiter
7. The interdependence as per need interdependence
8. The unit of the society – family
9. The era of stone – stone age
10. The information engraved On stone – Petrograph

Project work:

Question 1.
Move around your village/school and talk to people to gather history of your village?
Answer:
Do with the help of your teacher.

Question 2.
Collect information about the postal, telegraph/rail department and find our dependence on these departments?
Answer:
Do with the help of your teacher.

Question 3.
Make a big labelled diagram of the solar system?
Answer:
The Sun and the nine planets which revolve around it make up the family of the Sun or the Solar System. In addition to the nine planets, there are 44 satellites in the Solar System.

Show the following on the world map.

1. The Equator
2. Asia
3. The Indian Ocean Meridian
4. Greeenwich
5. The Pacific Ocean
6. The Himalaya
7. The Plateau of Pamir
8. The Decean Plateau
9. The plains of Ganga – yamuna
10. India.

Answer:
Do Yourself.

MP Board Class 6th Social Science Solutions

MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.6

पाठ्य-पुस्तक पृष्ठ संख्या # 91

प्रश्न 1.
संलग्न आकृति देखकर लिखिए :
(a) वृत्त का केन्द्र
(b) तीन त्रिज्याएँ
(c) एक व्यास
(d) एक जीवा
(e) अभ्यन्तर में दो बिन्दु
(f) बहिर्भाग में एक बिन्दु
(g) एक त्रिज्यखण्ड
(h) एक वृत्तखण्ड

हल :
(a) वृत्त का केन्द्र- O
(b) तीन त्रिज्याएँ- \(\overline{O A}, \overline{O B}\) और \(\overline{O C}\)
(c) एक व्यास- \(\overline{A C}\)
(d) एक जीवा- \(\overline{E D}\)
(e) अभ्यन्तर में दो बिन्दु- O और P
(f) बहिर्भाग में एक बिन्दु- Q
(g) एक त्रिज्यखण्ड- OAB (छायांकित भाग)
(h) एक वृत्तखण्ड-रेखाखण्ड ED (छायांकित भाग)

प्रश्न 2.
(a) क्या वृत्त का प्रत्येक व्यास उसकी एक जीवा भी होता है ?
(b) क्या वृत्त की प्रत्येक जीवा उसका एक व्यास भी होती है ?
हल :
(a) हाँ, वृत्त का प्रत्येक व्यास उसकी सबसे बड़ी जीवा होती है। .
(b) नहीं, वृत्त की प्रत्येक जीवा हमेशा उसका व्यास नहीं होती है।

प्रश्न 3.
कोई वृत्त खींचिए और निम्न को अंकित कीजिए:
(a) उसका केन्द्र
(b) एक त्रिज्या
(c) एक व्यास
(d) एक त्रिज्यखण्ड
(e) एक वृत्तखण्ड
(f) उसके अभ्यन्तर में एक बिन्दु
(g) उसके बहिर्भाग में एक बिन्दु
(h) एक चाप
हल :
(a) वृत्त का केन्द्र- O,
(b) त्रिज्या- \(\overline{O C}\)
(c) व्यास- \(\overline{A B}\),
(d) त्रिज्यखण्ड- OAD

(e) वृत्तखण्ड- JKL,
(f) अभ्यन्तर में एक बिन्दु- P
(g) बहिर्भाग में एक बिन्दु- Q,
(h) एक चाप- MN

प्रश्न 4.
सत्य या असत्य बताइए :
(a) वृत्त के दो व्यास अवश्य ही प्रतिच्छेद करेंगे।
(b) वृत्त का केन्द्र सदैव उसके अभ्यन्तर में स्थित होता है।
हल :
(a) सत्य,
(b) सत्य।

MP Board Class 6th Maths Solutions

MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.5

पाठ्य-पुस्तक पृष्ठ संख्या # 89

प्रश्न 1.
चतुर्भुज PQRS का एक रफ चित्र खींचिए। इसके विकर्ण खींचिए। क्या विकर्णों का प्रतिच्छेद बिन्दु चतुर्भुज के अभ्यन्तर में स्थित है या बहिर्भाग में स्थित है ?
हल :
(a) PQRS एक चतुर्भुज है।

(b) इसके विकर्ण \(\overline{P R}\) और \(\overline{Q S}\) हैं। इनका प्रतिच्छेद बिन्दु O चतुर्भज PQRS के अभ्यन्तर में स्थित है।

प्रश्न 2.
चतुर्भुज KLMN का एक रफ चित्र खींचिए। बताइए:
(a) सम्मुख भुजाओं के दो युग्म
(b) सम्मुख कोणों के दो युग्म
(c) आसन्न भुजाओं के दो युग्म
(d) आसन्न कोणों के दो युग्म
हल:

(a) सम्मुख भुजाओं के दो युग्म- \(\overline{K L}, \overline{N M}\) और \(\overline{K N}, \overline{M L}\)
(b) सम्मुख कोणों के दो युग्म- ∠K, ∠M और ∠N, ∠L
(c) आसन्न भुजाओं के दो युग्म- \(\overline{K L}, \overline{K N}\) और \(\overline{N M}, \overline{M L}\) अथवा \(\overline{K L}, \overline{L M}\) और \(\overline{N M}, \overline{N K}\)
(d) आसन्न कोणों के दो युग्म- ∠K, ∠L और ∠M, ∠N अथवा ∠K, ∠N और ∠L, ∠M आदि।

प्रश्न 3.
खोज कीजिए :
पट्टियाँ और इन्हें बाँधने की वस्तुएँ लेकर एक त्रिभुज बनाइए और एक चतुर्भुज बनाइए। त्रिभुज के किसी एक शीर्ष पर पट्टियों को अन्दर की ओर दबाने का प्रयत्न कीजिए। यही कार्य चतुर्भुज के लिए भी कीजिए। क्या त्रिभुज में कोई परिवर्तन आया ? क्या चतुर्भुज में कोई परिवर्तन हुआ? क्या त्रिभुज एक दृढ़ (rigid) आकृति है ? क्या कारण है कि विद्युत् टॉवरों (Electric Towers) जैसी संरचनाओं में त्रिभुजीय आकारों का प्रयोग किया जाता है; चतुर्भुजीय आकारों का नहीं ?
हल :

1. त्रिभुज के किसी एक शीर्ष पर पट्टियों को अन्दर की ओर दबाने से त्रिभुज में कोई परिवर्तन नहीं हुआ जबकि चतुर्भुज के साथ ऐसा करने से उसमें परिवर्तन हुआ है।
2. त्रिभुज एक दृढ़ आकृति है।
3. विद्युत् टॉवरों जैसी संरचनाओं में त्रिभुजीय आकारों का प्रयोग इसलिए करते हैं, क्योंकि त्रिभुज का आकार अधिक दृढ़ होता है।

MP Board Class 6th Maths Solutions

 MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.4

पाठ्य-पुस्तक पृष्ठ संख्या # 88

प्रश्न 1.
त्रिभुज ABC का एक रफ चित्र खींचिए। इस त्रिभुज के अभ्यन्तर में एक बिन्दु P अंकित कीजिए और उसके बहिर्भाग में एक बिन्दु Q अंकित कीजिए। बिन्दु A इसके अभ्यन्तर में स्थित है या बहिर्भाग में स्थित है ?
हल :
संलग्न चित्र में ABC एक त्रिभुज है।
(i) बिन्दु P, ∆ABC के अभ्यन्तर में है।
(ii) बिन्दु Q त्रिभुज के बहिर्भाग में है।
(iii) नहीं, बिन्दु A न तो इसके अभ्यन्तर में स्थित है और न ही इसके बहिर्भाग में।

प्रश्न 2.
(a) संलग्न आकृति में तीन त्रिभुजों की पहचान कीजिए।
(b) ज्ञात कोणों के नाम लिखिए।
(c) इसी आकृति में छः रेखाखण्डों के नाम लिखिए।
(d) किन दो त्रिभुजों में ∠B उभयनिष्ठ है ?

हल :
(a) तीन त्रिभुज- ∆ABC, ∆ABD, ∆ADC
(b) सात कोण- ∠B, ∠C, ∠BAC, ∠BAD, ∠CAD, ∠ADB, ∠ADC
(c) छः रेखाखण्ड- \(\overline{A B}, \overline{A C}, \overline{B C}, \overline{A D}, \overline{B D}, \overline{D C}\)
(d) ∆ABC और ∆ABD में ∠B उभयनिष्ठ है।

MP Board Class 6th Maths Solutions

MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.3

पाठ्य-पुस्तक पृष्ठ संख्या # 87

प्रश्न 1.
नीचे दी आकृति में, कोणों के नाम लिखिए :

हल :
∠A अथवा ∠DAB ; ∠B अथवा ∠ABC ; ∠C अथवा ∠BCD; ∠D अथवा ∠CDA

प्रश्न 2.
संलग्न आकृति में, वे बिन्दु लिखिए जो
(a) ∠DOE के अभ्यन्तर में स्थित हैं।
(b) ∠EOF के बहिर्भाग में स्थित हैं।
(c) ∠EOF पर स्थित हैं।

हल :
(a) ∠DOE के अभ्यंतर में बिन्दु A है।
(b) ∠EOF के बहिर्भाग में बिन्दु A,C और D हैं।
(c) ∠EOF पर स्थित बिन्दु हैं, E,B,O और F।

प्रश्न 3.
दो कोणों की रफ आकृतियाँ खींचिए जिससे
(a) उनमें एक बिन्दु उभयनिष्ठ हो।
(b) उनमें दो बिन्दु उभयनिष्ठ हों।
(c) उनमें तीन बिन्दु उभयनिष्ठ हों।
(d) उनमें चार बिन्दु उभयनिष्ठ हों।
(e) उनमें एक किरण उभयनिष्ठ हो।
हल :
(a) ∠PQS और ∠RQS में एक बिन्दु Q उभयनिष्ठ है।

(b) ∠AOB और ∠ODC में दो बिन्दु O तथा D उभयनिष्ठ है।

(c) ∠ABC और ∠QPR में तीन बिन्दु D, E तथा F उभयनिष्ठ हैं। .

(d) ∠BAC और ∠PQR में चार बिन्दु E, F G तथा H उभयनिष्ठ हैं।

(e) ∠RQS और ∠PQS में किरण QS उभयनिष्ठ है।

MP Board Class 6th Maths Solutions