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 ~ HSSlive: Plus One & Plus Two Notes & Solutions for Kerala State Board

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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

AP Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise Textbooks Solutions and answers for students are now available in pdf format. Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise Book answers and solutions are one of the most important study materials for any student. The Andhra Pradesh State Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise books are published by the Andhra Pradesh Board Publishers. These Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise textbooks are prepared by a group of expert faculty members. Students can download these AP Board STD 10th Maths Chapter 1 Real Numbers Optional Exercise book solutions pdf online from this page.

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
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Optional Exercise 1

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 [∵ logx^m = 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 x^m = 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 Textbook Solutions PDF

AP Board Class 10 Maths Chapter 2 Sets Textbook Solutions PDF

AP Board Class 10 Maths Chapter 3 Polynomials Textbook Solutions PDF

AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables Textbook Solutions PDF

AP Board Class 10 Maths Chapter 5 Quadratic Equations Textbook Solutions PDF

AP Board Class 10 Maths Chapter 6 Progressions Textbook Solutions PDF

AP Board Class 10 Maths Chapter 7 Coordinate Geometry Textbook Solutions PDF

AP Board Class 10 Maths Chapter 8 Similar Triangles Textbook Solutions PDF

AP Board Class 10 Maths Chapter 9 Tangents and Secants to a Circle Textbook Solutions PDF

AP Board Class 10 Maths Chapter 10 Mensuration Textbook Solutions PDF

AP Board Class 10 Maths Chapter 11 Trigonometry Textbook Solutions PDF

AP Board Class 10 Maths Chapter 12 Applications of Trigonometry Textbook Solutions PDF

AP Board Class 10 Maths Chapter 13 Probability Textbook Solutions PDF

AP Board Class 10 Maths Chapter 14 Statistics Textbook Solutions PDF

Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise Textbooks for Exam Preparations

Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise Textbook Solutions can be of great help in your Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise exam preparation. The AP Board STD 10th Maths Chapter 1 Real Numbers Optional Exercise Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 10th Maths Chapter 1 Real Numbers Optional Exercise Books State Board syllabus with maximum efficiency.

FAQs Regarding Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise Textbook Solutions

How to get AP Board Class 10th Maths Chapter 1 Real Numbers Optional Exercise Textbook Answers??

Students can download the Andhra Pradesh Board Class 10 Maths Chapter 1 Real Numbers Optional Exercise Answers PDF from the links provided above.

Can we get a Andhra Pradesh State Board Book PDF for all Classes?

Yes you can get Andhra Pradesh Board Text Book PDF for all classes using the links provided in the above article.

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Tuesday, June 7, 2022