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

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.4 are the part of NCERT Solutions for Class 7 Maths. Here you can find the NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.4.

Ex 12.4 Class 7 Maths Question 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 6, 4, 8.

Solution:
(i) The number of line segments required to form n digits of 6 is given by the expressions:

For 5 figures, putting n =5, then the number of line segments = 5 × 5 + 1 = 25 + 1 = 26
For 10 figures, putting n = 10, then the number of line segments = 5 × 10 + 1
= 50 + 1 = 51
For 100 figures, putting n = 100, then the number of line segments = 5 × 100 + 1
= 500 + 1 = 501

(ii) The number of line segments required to form n digits of 4 is given by the expressions:

For 5 figures, putting n = 5, then the number of line segments = 3 × 5 + 1
= 15 + 1 = 16
For 10 figures, putting n = 10, then the number of line segments = 3 × 10 + 1
= 30 + 1 = 31
For 100 figures, putting n = 100, then the number of line segments = 3 × 100 + 1
= 300 + 1 = 301

(iii) The number of line segments required to form n digits of 8 is given by the expressions:

For 5 figures, putting n = 5, then the number of line segments = 5 × 5 + 2
= 25 + 2 = 27
For 10 figures, putting n = 10, then the number of line segments = 5 × 10 + 2
= 50 + 2 = 52
For 100 figures, putting n = 100, then the number of line segments = 5 × 100 + 2
= 500 + 2 = 502

Ex 12.4 Class 7 Maths Question 2.

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

S.No.	Expression	Terms
S.No.	Expression	1^st	2^nd	3^rd	4^th	5^th	…	10^th	…	100^th	…
(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	–	–	–	–	10,001	–

Solution:

(i) The given expression is 2n – 1.
Putting n = 100, we get 100^th term, that is, 2 × 100 – 1
= 200 – 1 = 199

(ii) The given expression is 3n + 2.
Putting n = 5, we get 5^th term, that is, 3 × 5 + 2 = 15 + 2 = 17
Putting n = 10, we get 10^th term, that is, 3 × 10 + 2 = 30 + 2 = 32
Putting n = 100, we get 100^th term, that is, 3 × 100 + 2 = 300 + 2 = 302

(iii) The given expression is 4n + 1.
Putting n = 5, we get 5^th term, that is, 4 × 5 + 1 = 20 + 1 = 21
Putting n = 10, we get 10^th term, that is, 4 × 10 + 1 = 40 + 1 = 41
Putting n = 100, we get 100^th term, that is, 4 × 100 + 1 = 400 + 1 = 401

(iv) The given expression is 7n + 20.
Putting n = 5, we get 5^th term, that is, 7 × 5 + 20 = 35 + 20 = 55
Putting n = 10, we get 10^th term, that is, 7 × 10 + 20 = 70 + 20 = 90
Putting n = 100, we get 100^th term, that is, 7 × 100 + 20 = 700 + 20 = 720

(v) The given expression is n² + 1.
Putting n = 5, we get 5^th term, that is, 5² + 1 = 25 + 1 = 26
Putting n = 10, we get 10^th term, that is, 10² + 1 = 100 + 1 = 101