NCERT Solutions for Class 7 Maths Exercise 12.4

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NCERT solutions for Maths Algebraic Expressions Download as PDF

NCERT Solutions for Class 7 Maths Exercise 12.4

NCERT Solutions for Class 7 Maths Algebraic Expressions

Class –VII Mathematics (Ex. 12.4)
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.

(a) … …

  1. 11 16 21… {tex}\left( {5n + 1} \right)…{/tex}

(b)

  1. 7 10 13… {tex}\left( {3n + 1} \right)…{/tex}

(c)

7 121722…

If the number of digits formed is taken to be {tex}n,{/tex} the number of segments required to form {tex}n{/tex} 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

Answer:

S. No.SymbolDigit’s numberPattern’s FormulaeNo. of Segments
(i)5{tex}5n + 1{/tex}26
1051
100501
(ii)5{tex}3n + 1{/tex}16
1031
100301
(iii)5{tex}5n + 2{/tex}27
1052
100502

Putting {tex}n = 5,{/tex} 5 x 5 + 1 = 25 + 1 = 26(i) {tex}5n + 1{/tex}

Putting {tex}n = 10,{/tex} 5 x 10 + 1 = 50 + 1 = 51

Putting {tex}n = 100,{/tex} 5 x 100 + 1 = 500 + 1 = 501

(ii) {tex}3n + 1{/tex}

Putting {tex}n = 5,{/tex} 3 x 5 + 1 = 15 + 1 = 16

Putting {tex}n = 10,{/tex} 3 x 10 + 1 = 30 + 1 = 31

Putting {tex}n = 100,{/tex} 3 x 100 + 1 = 300 + 1 = 301

(iii) {tex}5n + 2{/tex}

Putting {tex}n = 5,{/tex} 5 x 5 + 2 = 25 + 2 = 27

Putting {tex}n = 10,{/tex} 5 x 10 + 2 = 50 + 2 = 52

Putting {tex}n = 100,{/tex} 5 x 100 + 2 = 500 + 2 = 502


NCERT Solutions for Class 7 Maths Exercise 12.4

Question 2.Use the given algebraic expression to complete the table of number patterns:
S.No.ExpressionTerms
1st2nd3rd4th5th10th100th
(i){tex}2n – 1{/tex}1357919
(ii){tex}3n + 2{/tex}25811
(iii){tex}4n + 1{/tex}591317
(iv){tex}7n + 20{/tex}27344148
(v){tex}{n^2} + 1{/tex}25101710001

(i) {tex}2n – 1{/tex}Answer:

Putting {tex}n = 100,{/tex} 2 x 100 – 1 = 200 – 1 = 199

(ii) {tex}3n + 2{/tex}

Putting {tex}n = 5,{/tex} 3 x 5 + 2 = 15 + 2 = 17

Putting {tex}n = 10,{/tex} 3 x 10 + 2 = 30 + 2 = 32

Putting {tex}n = 100,{/tex} 3 x 100 + 2 = 300 + 2 = 302

(iii) {tex}4n + 1{/tex}

Putting {tex}n = 5,{/tex} 4 x 5 + 1 = 20 + 1 = 21

Putting {tex}n = 10,{/tex} 4 x 10 + 1 = 40 + 1 = 41

Putting {tex}n = 100,{/tex} 4 x 100 + 1 = 400 + 1 = 401

(iv) {tex}7n + 20{/tex}

Putting {tex}n = 5,{/tex} 7 x 5 + 20 = 25 + 20 = 55

Putting {tex}n = 10,{/tex} 7 x 10 + 20 = 70 + 20 = 90

Putting {tex}n = 100,{/tex} 7 x 100 + 20 = 700 + 20 = 720

(v) {tex}{n^2} + 1{/tex}

Putting {tex}n = 5,{/tex} 5 x 5 + 1 = 25 + 1 = 26

Putting {tex}n = 10,{/tex} 10 x 10 + 1 = 100 + 1 = 101

Putting {tex}n = 100,{/tex} 100 x 100 + 1 = 10000 + 1 = 10001

Now complete table is,

S.No.ExpressionTerms
1st2nd3rd4th5th10th100th
(i){tex}2n – 1{/tex}1357919199
(ii){tex}3n + 2{/tex}258111732302
(iii){tex}4n + 1{/tex}5913172141401
(iv){tex}7n + 20{/tex}273441485590720
(v){tex}{n^2} + 1{/tex}2510172610110001

NCERT Solutions for Class 7 Maths Exercise 12.4

NCERT Solutions for Class 7 Maths Exercise 12.4 PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 7 Maths includes text book solutions from Class 7 Maths Book . NCERT Solutions for CBSE Class 7 Maths have total 15 chapters. 7 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 7 solutions PDF and Maths ncert class 7 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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