Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3

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Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3

Miscellaneous Practice Problems

Question 1.
Choose the correct relationship between x and y for the given table.
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 1
(i) y = x + 4
(ii) y = x + 5
(iii) y = x + 6
(iv) y = x + 7
Answer:
(iii) y = x + 6

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Question 2.
Find the triangular numbers from the Pascal’s Triangle and colour them.
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 2
Solution:
Triangular numbers are numbers the objects of which can be arranged in the form of equilateral triangle.
Example : 1, 3, 6, 10, 15,…
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 3
From Pascal’s Triangle, the triangular numbers are
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 4

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Question 3.
Write the first five numbers in the third slanting row of the Pascal’s Triangle and find their squares. What do you infer?
Solution:
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 5
Numbers in the 3rd slanding row are 1, 3, 6, 10, 15, 21,….
The squares are 12, 32, 62, 102. 152, 212,…. = 1, 9, 36, 100, 225, 441,…
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 6
From the above table we can conclude that the squares of the triangular numbers are the sum of cubes of natural numbers.

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Challenge Problems

Question 4.
Tabulate and find the relationship between the variables (x and y) for the following patterns.
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 7
Solution:
(i) Let the number of steps be x and the number of shapes be y.
Tabulating the values of x and y
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 8
From the table
x = 1 ⇒ y = 1 = 12
x = 2 ⇒ y = 4 = 22
x = 3 ⇒ y = 9 = 32
x = 4 ⇒ y = 16 = 42
Hence the relationship between x and y is y = x2.

(ii) Let the number of steps be x and the number of shapes be y.
Tabulating the values of x and y
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 9
From the table x = 1 ⇒ y = 1 = 1
x = 2 ⇒ y = 2 + 1 = 3
x = 3 ⇒ y = 3 + 2 = 5
x = 4 ⇒ y = 4 + 3 = 7
x = 5 ⇒ y = 5 + 4 = 9
Hence the relationship between x and y is y = 2x-1.

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Question 5.
Verify whether the following hexogonal shapes form a part of the Pascal’s Triangle.
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 10
Solution:
In Pascal’s Triangle product of the 3 alternate numbers given around the hexagon is equal to the product of remaining three numbers.
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 11
1 × 13 × 66 = 11 × 1 × 78 = 858
∴ It form a part of Pascal’s Triangle.

Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 12
5 × 21 × 20 = 10 × 6 × 35 = 2100
∴ It form a part of Pascal’s Triangle

Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 13
8 × 45 × 84 = 28 × 9 × 120 = 30240
∴ It form a part of Pascal’s Triangle

Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 14
56 × 210 × 126 = 70 × 84 × 252 = 1481760
∴ It form a part of Pascal’s Triangle

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