*According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 10.
NCERT Solutions for Class 7 Maths Exercise 12.4 Chapter 12 Algebraic Expressions are given here in a detailed though simple way. Using algebraic expressions – formulas and rules is the only topic covered in this exercise of NCERT Solutions for Maths Class 7 Chapter 12. These solutions can be beneficial for the students to clear all their doubts quickly and understand the concepts of this chapter. Students can use them as worksheets to prepare for their exams.
NCERT Solutions for Class 7 Maths Chapter 12 Perimeter and Area – Exercise 12.4
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Access Answers to NCERT Class 7 Maths Chapter 12 – Algebraic Expressions 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.
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 
Solution:-
(a) From the question it is given that the numbers of segments required to form n digits of the kind
is (5n + 1)
Then,
The number of segments required to form 5 digits = ((5 × 5) + 1)
= (25 + 1)
= 26
The number of segments required to form 10 digits = ((5 × 10) + 1)
= (50 + 1)
= 51
The number of segments required to form 100 digits = ((5 × 100) + 1)
= (500 + 1)
= 501
(b) From the question it is given that the numbers of segments required to form n digits of the kind
is (3n + 1)
Then,
The number of segments required to form 5 digits = ((3 × 5) + 1)
= (15 + 1)
= 16
The number of segments required to form 10 digits = ((3 × 10) + 1)
= (30 + 1)
= 31
The number of segments required to form 100 digits = ((3 × 100) + 1)
= (300 + 1)
= 301
(c) From the question it is given that the numbers of segments required to form n digits of the kind
is (5n + 2)
Then,
The number of segments required to form 5 digits = ((5 × 5) + 2)
= (25 + 2)
= 27
The number of segments required to form 10 digits = ((5 × 10) + 2)
= (50 + 2)
= 52
The number of segments required to form 100 digits = ((5 × 100) + 1)
= (500 + 2)
= 502
2. Use the given algebraic expression to complete the table of number patterns.
| S. No. | Expression | Terms | |||||||||
| 1st | 2nd | 3rd | 4th | 5th | … | 10th | … | 100th | … | ||
| (i) | 2n – 1 | 1 | 3 | 5 | 7 | 9 | – | 19 | – | – | – |
| (ii) | 3n + 2 | 5 | 8 | 11 | 14 | – | – | – | – | – | – |
| (iii) | 4n + 1 | 5 | 9 | 13 | 17 | – | – | – | – | – | – |
| (iv) | 7n + 20 | 27 | 34 | 41 | 48 | – | – | – | – | – | – |
| (v) | n2 + 1 | 2 | 5 | 10 | 17 | – | – | – | – | 10001 | – |
Solution:-
(i) From the table (2n – 1)
Then, 100th term =?
Where n = 100
= (2 × 100) – 1
= 200 – 1
= 199
(ii) From the table (3n + 2)
5th term =?
Where n = 5
= (3 × 5) + 2
= 15 + 2
= 17
Then, 10th term =?
Where n = 10
= (3 × 10) + 2
= 30 + 2
= 32
Then, 100th term =?
Where n = 100
= (3 × 100) + 2
= 300 + 2
= 302
(iii) From the table (4n + 1)
5th term =?
Where n = 5
= (4 × 5) + 1
= 20 + 1
= 21
Then, 10th term =?
Where n = 10
= (4 × 10) + 1
= 40 + 1
= 41
Then, 100th term =?
Where n = 100
= (4 × 100) + 1
= 400 + 1
= 401
(iv) From the table (7n + 20)
5th term =?
Where n = 5
= (7 × 5) + 20
= 35 + 20
= 55
Then, 10th term =?
Where n = 10
= (7 × 10) + 20
= 70 + 20
= 90
Then, 100th term =?
Where n = 100
= (7 × 100) + 20
= 700 + 20
= 720
(v) From the table (n2 + 1)
5th term =?
Where n = 5
= (52) + 1
= 25+ 1
= 26
Then, 10th term =?
Where n = 10
= (102) + 1
= 100 + 1
= 101
So the table is completed below.
| S. No. | Expression | Terms | |||||||||
| 1st | 2nd | 3rd | 4th | 5th | … | 10th | … | 100th | … | ||
| (i) | 2n – 1 | 1 | 3 | 5 | 7 | 9 | – | 19 | – | 199 | – |
| (ii) | 3n + 2 | 5 | 8 | 11 | 14 | 17 | – | 32 | – | 302 | – |
| (iii) | 4n + 1 | 5 | 9 | 13 | 17 | 21 | – | 41 | – | 401 | – |
| (iv) | 7n + 20 | 27 | 34 | 41 | 48 | 55 | – | 90 | – | 720 | – |
| (v) | n2 + 1 | 2 | 5 | 10 | 17 | 26 | – | 101 | – | 10001 | – |
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NCERT Solutions for Class 7 Maths
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