Students can Download Maths Chapter 5 Information Processing Ex 5.3 Questions and Answers, Notes Pdf, Samacheer Kalvi 7th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

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

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

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,…
From Pascal’s Triangle, the triangular numbers are
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 3

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

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 4
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 5
From the above table we can conclude that the squares of the triangular numbers are the sum of cubes of natural numbers.

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

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 6
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 7
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 8
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.

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

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 9
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 10
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 11
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 12
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 13
56 × 210 × 126 = 70 × 84 × 252 = 1481760
∴ It form a part of Pascal’s Triangle

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