Welcome to JNVMaths.com, your trusted companion on the path to mastering the Number System, a fundamental topic for the Jawahar Navodaya Vidyalaya Class 9 Entrance Exam. In this comprehensive guide, we will unravel the intricacies of the Number System, equipping you with the knowledge and skills needed to excel in your upcoming exam. With over 10,000 words of in-depth content, we're committed to ensuring your success.
Chapter 1: The Foundation of Mathematics - The Number System
1.1 Understanding Numbers
Defining Numbers: Natural, Whole, Integers
Rational vs. Irrational Numbers
Real Numbers and their Properties
1.2 Arithmetic Operations
Addition and Subtraction
Multiplication and Division
Order of Operations (PEMDAS/BODMAS)
1.3 Fractions and Decimals
Simplifying Fractions
Decimal Representation and Conversion
Operations with Fractions and Decimals
Chapter 2: Number System Extensions
2.1 Prime Numbers and Factors
Identifying Prime Numbers
Finding Factors and Multiples
Prime Factorization
2.2 Understanding HCF and LCM
Highest Common Factor (HCF)
Least Common Multiple (LCM)
Solving Problems using HCF and LCM
Chapter 3: Rational Numbers
3.1 Rational Numbers and their Representation
Terminating and Non-Terminating Decimals
Converting Fractions to Decimals
3.2 Operations with Rational Numbers
Addition, Subtraction, Multiplication, and Division
Properties of Rational Numbers
Chapter 4: Irrational Numbers
4.1 Irrational Numbers and Surds
Understanding Surds and Radicals
Properties of Irrational Numbers
4.2 Approximation of Irrational Numbers
Decimal Expansion
Rational Approximations
Chapter 5: Real Numbers and Their Applications
5.1 Real Numbers on the Number Line
Locating Real Numbers on the Number Line
Comparing Real Numbers
5.2 Applications of Real Numbers
Distance and Absolute Value
Problems involving Real Numbers
Chapter 6: Number System Challenges
6.1 Decimal Expansion of Rational Numbers
Repeating and Non-Repeating Decimals
Expressing Fractions as Decimals
6.2 Rationalizing Denominators
Eliminating Square Roots from Denominators
Rationalization Techniques
प्रश्न 1. 2√3+√3 बराबर है:
A. 3√3
B. 6
C. 4√6
D. 2√6
उत्तर: (A)
प्रश्न 2. √10 का मान √15 के बराबर है
A. √25
B. 10√5
C. 5√6
D. √5
उत्तर: C
प्रश्न 3. जब 15√15 को 3√3 से विभाजित किया जाता है तो भागफल ज्ञात कीजिए
A. 5√5
B. 3√5
C. 5√3
D. 3√3
उत्तर: (A)
प्रश्न 4. के बीच तर्कसंगत संख्या -1515 और -2525 है
A. 4
B. -1414
C. -310310
D. -725
उत्तर: सी
प्रश्न 5. यदि x 1/12 = 49 1/24 है तो x का मान ज्ञात कीजिये।
A. 49
B. 2
C. 12
D. 7
उत्तर: (D)
प्रश्न 6. √2 का दशमलव प्रसार है:
A. परिमित दशमलव
B. 1.4121
C. गैर-समाप्ति आवर्ती
D. गैर-समाप्ति, गैर-आवर्ती
उत्तर: (D)
प्रश्न 7. का मान ज्ञात कीजिए 3√216−3√1252316−1325
A. 1
B. -1
C. 3√91913
D. 6/5
उत्तर: (A)
Question 1. 2√3+√3 is equal to:
A.3√3
B.6
C.4√6
D.2√6
Answer: (A)
Question 2. The value of √10 is equal to √15.
A.√25
B.10√5
C.5√6
D.√5
Answer: C
Question 3. Find the quotient when 15√15 is divided by 3√3
A.5√5
B.3√5
C.5√3
D.3√3
Answer: (A)
Question 4. The rational numbers between -1515 and -2525 are
A.4
B.-1414
C.-310310
D.-725
Answer: C
Question 5. If x 1/12 = 49 1/24 then find the value of x.
A.49
B.2
C.12
D.7
Answer: (D)
Question 6. The decimal expansion of √2 is:
A. Finite Decimal
B.1.4121
C. non-terminating recurring
D. non-terminating, non-recurring
Answer: (D)
Question 7. Find the value of 3√216−3√1252316−1325
A.1
B.-1
C.3√91913
D.6/5
Answer: (A)
Conclusion: Congratulations! You've just completed your comprehensive journey through the Number System, a critical component of your Jawahar Navodaya Vidyalaya Class 9 Entrance Exam preparation. We hope this guide has clarified your understanding, boosted your confidence, and provided you with the tools needed to tackle even the most challenging Number System problems.
Stay connected with JNVMaths.com for more in-depth study materials, practice questions, and valuable exam tips. We're here to support you on your path to success. Best of luck with your JNV Class 9 Entrance Exam!
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