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AP Board Class 10 Maths Chapter 1 Real Numbers Optional Exercise Textbook Solutions PDF: Download Andhra Pradesh Board STD 10th Maths Chapter 1 Real Numbers Optional Exercise Book Answers |
Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise Textbooks Solutions PDF
Andhra Pradesh State Board STD 10th Maths Chapter 1 Real Numbers Optional Exercise Books Solutions with Answers are prepared and published by the Andhra Pradesh Board Publishers. It is an autonomous organization to advise and assist qualitative improvements in school education. If you are in search of AP Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise Books Answers Solutions, then you are in the right place. Here is a complete hub of Andhra Pradesh State Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise solutions that are available here for free PDF downloads to help students for their adequate preparation. You can find all the subjects of Andhra Pradesh Board STD 10th Maths Chapter 1 Real Numbers Optional Exercise Textbooks. These Andhra Pradesh State Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise Textbooks Solutions English PDF will be helpful for effective education, and a maximum number of questions in exams are chosen from Andhra Pradesh Board.Andhra Pradesh State Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise Books Solutions
Board | AP Board |
Materials | Textbook Solutions/Guide |
Format | DOC/PDF |
Class | 10th |
Subject | Maths |
Chapters | Maths Chapter 1 Real Numbers Optional Exercise |
Provider | Hsslive |
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AP Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise Textbooks Solutions with Answer PDF Download
Find below the list of all AP Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:Question 1.
Can the number 6n, n being a natural number, end with the digit 5? Give reason.
Answer:
Given number = 6n ; n ∈ N
6n to be end in 5; it should be divisible by 5
6n = (2 × 3)n
The prime factors of 6n are 2 and 3.
It can’t end with the digit 5.
Question 2.
Is 7 × 5 × 3 × 2 + 3 a composite number? Justify your answer.
Answer:
Given:
7 × 5 × 3 × 2 + 3
= 3 (7 × 5 × 2 + 1)
= 3 × (70 + 1)
= 3 × 71
∴ The given number has two factors namely 3 and 71.
Hence it is a composite number.
Question 3.
Prove that (2√3 + √5 ) is an irrational number. Also check whether (2√3 + √5) (2√3 – √5) is rational or irrational.
Answer:
To prove:
2√3 + √5 is an irrational number. On contrary, let us suppose that 2√3 + √5 be a rational number.
Then 2√3 + √5 = 𝑝𝑞
Squaring on both sides, we get
L.H.S = an irrational number.
R.H.S = p, q being integers, 𝑝2−17𝑞24𝑞2 is a rational number.
This is a contradiction to the fact that √l5 is an irrational. This is due to our assumption that 2√3 + √5 is a rational. Hence our assumption is wrong and 2√3 + √5 is an irrational number. Also,
(2√3 + √5) (2√3 – √5)
= (2√3)2 – (√5)2
[∵ (a + b) (a – b) = a2 – b2]
= 4 × 3 – 5
= 12 – 5 = 7, a rational number.
Question 4.
If x2 + y2 = 6xy, prove that 2 log (x + y) = log x + log y + 3 log 2.
Answer:
Given: x2 + y2 = 6xy
x2 + y2 + 2xy = 6xy + 2xy
(x + y)2 = 8xy
Taking logarithms on both sides log (x + y)2 = log8xy
⇒ 2log(x + y)= log8 + logx + logy [∵ logxm = mlogx]
[∵ logxy = logx + logy]
= log23 + logx + logy
⇒ 2log(x + y) = logx + logy + 3log2
Question 5.
Find the number of digits in 42013, if log102 = 0.3010.
Answer:
Given:
log102 = 0.3010
42013 = (22)2013 = 24026
∴ log10 24026 = 4026 log102
[∵ log xm = m log x]
= 4026 × 0.3010 = 1211.826.
So 1211 + 1 = 1212
∴ 42013 has 1212 digits in its expansion.
(∵ characteristic 1211)
AP Board Textbook Solutions PDF for Class 10th Maths
- AP Board Class 10 Maths Chapter 1 Real Numbers Ex 1.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 1 Real Numbers Ex 1.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 1 Real Numbers Ex 1.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 1 Real Numbers Ex 1.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 1 Real Numbers Ex 1.5 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 1 Real Numbers Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 1 Real Numbers InText Questions Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 2 Sets Ex 2.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 2 Sets Ex 2.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 2 Sets Ex 2.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 2 Sets Ex 2.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 2 Sets InText Questions Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 3 Polynomials Ex 3.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 3 Polynomials Ex 3.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 3 Polynomials Ex 3.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 3 Polynomials Ex 3.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 3 Polynomials Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 3 Polynomials InText Questions Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables Ex 4.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables Ex 4.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables Ex 4.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables InText Questions Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 5 Quadratic Equations Ex 5.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 5 Quadratic Equations Ex 5.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 5 Quadratic Equations Ex 5.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 5 Quadratic Equations Ex 5.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 5 Quadratic Equations Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 5 Quadratic Equations InText Questions Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 6 Progressions Ex 6.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 6 Progressions Ex 6.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 6 Progressions Ex 6.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 6 Progressions Ex 6.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 6 Progressions Ex 6.5 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 6 Progressions Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 6 Progressions InText Questions Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 7 Coordinate Geometry Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 7 Coordinate Geometry InText Questions Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 8 Similar Triangles Ex 8.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 8 Similar Triangles Ex 8.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 8 Similar Triangles Ex 8.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 8 Similar Triangles Ex 8.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 8 Similar Triangles Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 8 Similar Triangles InText Questions Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 9 Tangents and Secants to a Circle Ex 9.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 9 Tangents and Secants to a Circle Ex 9.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 9 Tangents and Secants to a Circle Ex 9.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 9 Tangents and Secants to a Circle Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 9 Tangents and Secants to a Circle InText Questions Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 10 Mensuration Ex 10.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 10 Mensuration Ex 10.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 10 Mensuration Ex 10.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 10 Mensuration Ex 10.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 10 Mensuration Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 10 Mensuration InText Questions Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 11 Trigonometry Ex 11.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 11 Trigonometry Ex 11.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 11 Trigonometry Ex 11.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 11 Trigonometry Ex 11.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 11 Trigonometry Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 11 Trigonometry InText Questions Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 12 Applications of Trigonometry Ex 12.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 12 Applications of Trigonometry Ex 12.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 12 Applications of Trigonometry Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 12 Applications of Trigonometry InText Questions Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 13 Probability Ex 13.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 13 Probability Ex 13.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 13 Probability Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 13 Probability InText Questions Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 14 Statistics Ex 14.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 14 Statistics Ex 14.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 14 Statistics Ex 14.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 14 Statistics Ex 14.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 14 Statistics InText Questions Textbook Solutions PDF
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