Exercise 5.3 - Chapter 5 - Information Processing - Term 2 - 7th Maths Guide Samacheer Kalvi Solutions

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Ex 5.3
Miscellaneous Practice Problems
Question 1.
Choose the correct relationship between $x$ and $y$ for the given table.

(i) $\mathrm{y}=\mathrm{x}+4$
(ii) $y=x+5$
(iii) $y=x+6$
(iv) $y=x+7$
Answer:
(iii) $y=x+6$

Question $2 .$
Find the triangular numbers from the Pascal's Triangle and colour them.

Solution:
Triangular numbers are numbers the objects of which can be arranged in the form of equilateral triangle. Example: $1,3,6,10,15, \ldots$

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:

Numbers in the 3rd slanding row are $1,3,6,10,15,21, \ldots$
The squares are $1^{2}, 3^{2}, 6^{2}, 10^{2} .15^{2}, 21^{2}, \ldots=1,9,36,100,225,441, \ldots$

Challenge Problems
Question $4 .$
Tabulate and find the relationship between the variables ( $x$ and $y$ ) for the following patterns.

Solution:
(i) Let the number of steps be $x$ and the number of shapes be $y$. Tabulating the values of $x$ and $y$
Shapes (y) $1+4+9+16$

From the table
$\begin{aligned}
&x=1 \Rightarrow y=1=12 \\
&x=2 \Rightarrow y=4=22 \\
&x=3 \Rightarrow y=9=32 \\
&x=4 \Rightarrow y=16=42
\end{aligned}$
Hence the relationship between $x$ and $y$ is $y=x 2$.
(ii) Let the number of steps be $x$ and the number of shapes be $y$.
Tabulating the values of $x$ and $y$

From the table $x=1 \Rightarrow y=1=1$
$x=2 \Rightarrow y=2+1=3$
$x=3 \Rightarrow y=3+2=5$
$x=4 \Rightarrow y=4+3=7$
$x=5 \Rightarrow y=5+4=9$
Hence the relationship between $x$ and $y$ is $y=2 x-1$.
 

Question $5 .$
Verify whether the following hexogonal shapes form a part of the Pascal's Triangle.

Solution:
In Pascal's Triangle product of the 3 alternate numbers given around the hexagon is equal to the product of remaining three numbers.