CBSE Class 10 Maths Real Numbers RD Sharma Solutions
CBSE Class 10 board exams score is vital for the student so that he can take the admission in the branch of his choice. Class 10 Maths requires the students to attain a clear understanding of the concepts, formulas and their application. Thus, RD Sharma solutions are of great help to them here to excel in the board exams. These solutions contain all sorts of questions that a student needs to practice in order to score excellent marks. It also contains a lot of practice questions as well as well explained step by step solutions and illustrations. Chapter 1 Real Numbers is a very important chapter for the students of class 10. Real Numbers chapter deals with the properties of integers which are very well explained in the RD Sharma solutions for class 10 maths chapter 1.
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RD Sharma Solutions for Class 10 Chapter 1 will assist students to understand the chapter in a proper and clear manner. These solutions have easy solutions to even complex problems. Also, these have an algorithmic approach to solving the problem and explains each step clearly. Hence, RD Sharma Solutions for Class 10 Chapter 1 is all you need for studying Real Numbers. The students can practice a variety of problems given in the exercises to build a strong understanding and foundation of the subject. These solutions thus prepare the students to solve any problem in the exam paper. Real Numbers chapter covers various concepts such as Euclid’s division Lemma, Euclid’s division algorithm, Fundamental Theorem of Arithmetic, etc.
Sub-topics covered under RD Sharma Solutions for Class 10 Maths Chapter 1
- Class 10 Chapter 1Â Real Numbers Exercise 1.1
- Class 10 Chapter 1Â Real Numbers Exercise 1.2
- Class 10 Chapter 1Â Real Numbers Exercise 1.3
- Class 10 Chapter 1Â Real Numbers Exercise 1.4
- Class 10 Chapter 1 Real Numbers Exercise 1.5
- Class 10 Chapter 1Â Real Numbers Exercise 1.6
Solved Examples from RD Sharma Class 10 Solutions – Chapter 1
Question 1: The product of two consecutive positive integers is divisible by 2.
- True
- False
Answer:
Let the 2 consecutive numbers be, x, x+1
product of these consecutive numbers, =x(x+1)
(1) even
let, x=2k
product =2k[2k+1]
from the above equation, it is clear that the product is divisible by 2
(2) odd
let, x=2k+1
product =(2k+1) [(2k+1)+1]
=2(2k2+3k+1)
from the above equation, it is clear that the product is divisible by 2.
Question 2: Prove that the square of any positive integer of the form 5q+1 is of the same form.
Answer:
Let n=5q+1. Then,
n2=25q2 + 10q + 1 = 5 (5q2 + 2q) + 1 = 5m + 1, where m = 5q2 + 2q
⇒ n2 is of the form 5m + 1
Question 3: Find the HCF of the following pair of integers and express it as a linear combination of them.
963 and 657
Answer:
We can use Euclid division linear to find
HCF of 963 and 657
963=657×1+306
657=306×2+45
306=45×6+36
45=36×1+9
36=9×4+0
Since Remainder =0
∴HCF(963,657)=9
Now, we will do the backward calculation ⇒
9=45−36
9=45−(306−45×6)
9=45×7−306
9=(657−306×2)×7−306
9=657×7−306×15
9=657×7−(963−657)×15
9=657×22−963×15
∴9=657×22−963×15
HCF(657, 963) as their linear combination.
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