NCERT Solutions for Class 7 Maths Chapter 12: Algebraic Expressions - Exercise 12.4

Exercise 12.4

1. Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.

(a)

61116

If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern.

How many segments are required to form 5, 10, 100 digits of the kind .

Ans: The number of segments required to generate n digits of the kind 6 is given as $( {5n + 1} )$.

The following is the number of segments that must be formed from 5 digits.

Substitute 5 in the place of n in the $( {5n + 1} )$ and simplify.

$   \Rightarrow ( {5 \times 5 + 1} ) $

$   \Rightarrow ( {25 + 1} ) $

$   \Rightarrow 26  $

The following is the number of segments that must be formed from 10 digits.

Substitute 10 in the place of n in the $( {5n + 1} )$ and simplify.

$   \Rightarrow ( {5 \times 10 + 1} ) $

$   \Rightarrow ( {50 + 1} ) $

$   \Rightarrow 51  $

The following is the number of segments that must be formed from $100$ digits.

Substitute $100$ in the place of $n$ in the  $( {5n + 1} )$ and simplify.

$   \Rightarrow ( {5 \times 100 + 1} ) $

$   \Rightarrow ( {500 + 1} ) $

$   \Rightarrow 501  $

Therefore, to create $5$, $10$, $100$ digits of the kind

$26$, $51$, $501$ segments are required.

Create a table of number patterns and substitute the obtained values.

(b)

How many segments are required to form $5$, $10$, $100$ digits of the kind .

Ans: The number of segments required to generate $n$ digits of the kind $4$ is given as $( {3n + 1} )$.

The following is the number of segments that must be formed from $5$ digits.

Substitute $5$ in the place of $n$ in the  $( {3n + 1} )$ and simplify.

$ \Rightarrow ( {3 \times 5 + 1} ) $

$   \Rightarrow ( {15 + 1} ) $

$   \Rightarrow 16 $

The following is the number of segments that must be formed from $10$ digits.

Substitute $10$ in the place of $n$ in the  $( {3n + 1} )$ and simplify.

$   \Rightarrow ( {3 \times 10 + 1} ) $

$   \Rightarrow ( {30 + 1} ) $

$   \Rightarrow 31  $

The following is the number of segments that must be formed from $100$ digits.

Substitute $100$ in the place of $n$ in the  $( {3n + 1} )$ and simplify.

$  \Rightarrow ( {3 \times 100 + 1} ) $

$   \Rightarrow ( {300 + 1} ) $

$   \Rightarrow 301  $

Therefore, to create  $5$, $10$, $100$ digits of the kind

$16$, $31$, $301$ segments are required.

Create a table of number patterns and substitute the obtained values.

(c)

How many segments are required to form $5$, $10$, $100$ digits of the kind.

Ans: The number of segments required to generate $n$ digits of the kind $8$ is given as $( {5n + 2} )$.

The following is the number of segments that must be formed from $5$ digits.

Substitute $5$ in the place of $n$ in the $( {5n + 2} )$ and simplify.

$   \Rightarrow ( {5 \times 5 + 2} ) $

 $  \Rightarrow ( {25 + 2} ) $

$   \Rightarrow 27  $

The following is the number of segments that must be formed from $10$ digits.

Substitute $10$ in the place of $n$ in the $( {5n + 2} )$ and simplify.

$   \Rightarrow ( {5 \times 10 + 2} ) $

$   \Rightarrow ( {50 + 2} ) $

$   \Rightarrow 52 $

The following is the number of segments that must be formed from $100$ digits.

Substitute $100$ in the place of $n$ in the $( {5n + 2} )$ and simplify.

$   \Rightarrow ( {5 \times 100 + 2} ) $

$   \Rightarrow ( {500 + 2} ) $

$   \Rightarrow 502  $

Therefore, to create  $5$, $10$, $100$ digits of the kind

$27$, $52$, $502$ segments are required.

Create a table of number patterns and substitute the obtained values.

2. Use the given algebraic expression to complete the table of number patterns:

Ans: 

1. The given expression in the table is $( {2n - 1} )$.

To find the 100th  term where $n = 100$, substitute $100$ in the place of $n$ and simplify.

$   \Rightarrow ( {2 \times 100 - 1} ) $

$  \Rightarrow ( {200 - 1} ) $

$   \Rightarrow 199  $

2. The given expression in the table is $( {3n + 2} )$.

To find the $5^{th}$ term where $n = 5$, substitute $5$ in the place of $n$ and simplify.

$ \Rightarrow ( {( {3 \times 5} ) + 2} ) $

$   \Rightarrow ( {15 + 2} ) $

$   \Rightarrow 17  $

Then, to find the $10^{th}$ term where $n = 10$, substitute $10$ in the place of $n$ and simplify.

$  \Rightarrow ( {( {3 \times 10} ) + 2} ) $

$   \Rightarrow ( {30 + 2} ) $

$   \Rightarrow 32  $

Then, to find the 100th  term where $n = 100$, substitute $100$ in the place of $n$ and simplify.

$   \Rightarrow ( {( {3 \times 100} ) + 2} ) $

$   \Rightarrow ( {300 + 2} ) $

$   \Rightarrow 302  $

3. The given expression in the table is $( {4n + 1} )$.

To find the $5^{th}$ term where $n = 5$, substitute $5$ in the place of $n$ and simplify.

$   \Rightarrow ( {( {4 \times 5} ) + 1} ) $

$   \Rightarrow ( {20 + 1} ) $

$   \Rightarrow 21  $

Then, to find the $10^{th}$ term where $n = 10$, substitute $10$ in the place of $n$ and simplify.

$  \Rightarrow ( {( {4 \times 10} ) + 1} ) $

$   \Rightarrow ( {40 + 1} ) $

$   \Rightarrow 41  $

Then, to find the 100th  term where $n = 100$, substitute $100$ in the place of $n$ and simplify.

$   \Rightarrow ( {( {4 \times 100} ) + 1} ) $

$   \Rightarrow ( {400 + 1} ) $

$   \Rightarrow 401  $

4. The given expression in the table is $( {7n + 20} )$.

To find the $5^{th}$ term where $n = 5$, substitute $5$ in the place of $n$ and simplify.

$  \Rightarrow ( {( {7 \times 5} ) + 20} ) $

$   \Rightarrow ( {35 + 20} ) $

$   \Rightarrow 55  $

Then, to find the $10^{th}$ term where $n = 10$, substitute $10$ in the place of $n$ and simplify.

$   \Rightarrow ( {( {7 \times 10} ) + 20} ) $

$   \Rightarrow ( {70 + 20} ) $

$   \Rightarrow 90 $

Then, to find the 100th  term where $n = 100$, substitute $100$ in the place of $n$ and simplify.

$   \Rightarrow ( {( {7 \times 100} ) + 20} ) $

$   \Rightarrow ( {700 + 20} ) $

$   \Rightarrow 720 $

5. The given expression in the table is $( {{n^2} + 1} )$.

To find the $5^{th}$ term where $n = 5$, substitute $5$ in the place of $n$ and simplify.

$   \Rightarrow ( {{{( 5 )}^2} + 1} ) $

$   \Rightarrow ( {25 + 1} ) $

$   \Rightarrow 26 $

Then, to find the $10^{th}$ term where $n = 10$, substitute $10$ in the place of $n$ and simplify.

$   \Rightarrow ( {{{( {10} )}^2} + 1} ) $

$   \Rightarrow ( {100 + 1} ) $

$   \Rightarrow 101 $

Then, to find the 100th  term where $n = 100$, substitute $100$ in the place of $n$ and simplify.

$   \Rightarrow ( {{{( {100} )}^2} + 1} ) $

$   \Rightarrow ( {10000 + 1} ) $

$   \Rightarrow 10001 $

Therefore, the completed table is as follows.

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Exercise 12.4

Opting for the NCERT solutions for Ex 12.4 Class 7 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 12.4 Class 7 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

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