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. 256 x 0.16 ( 256) 0.09 का मान है:
A. 256.25
B. 64
C. 4
D.16
उत्तर: (C)
प्रश्न 2. का मान है:4√16−216−24
A. 1/2
B. 4
C. 1/4
D. 1/16
उत्तर: (A)
प्रश्न 3. √12 X √15 किसके बराबर है:
A. √25
B. 10√5
C. 5√6
D. 6√5
उत्तर: (D)
प्रश्न 4. 4√5 + 5√5 बराबर है:
A. 9√10
B. 9√5
C. 7√5
D. 5√10
उत्तर: (B)
प्रश्न 5. √2 और √3 के बीच एक परिमेय संख्या:
A. (√2. √3)/2
B. 1.5
C. 1.8
D. 1.9
उत्तर: (B)
प्रश्न 6. एक परिमेय और एक अपरिमेय संख्या का गुणनफल है:
A. कभी तर्कसंगत तो कभी अतार्किक
B. सदैव एक पूर्णांक
C. हमेशा एक तर्कसंगत संख्या
D. सदैव एक अपरिमेय संख्या
उत्तर: (D)
प्रश्न 7. प्रत्येक परिमेय संख्या है:
A. वास्तविक संख्या
B. प्राकृतिक संख्या
C. पूरा नंबर
D. पूर्णांक
उत्तर: (A)
8. तर्कसंगत बनाने के बाद हर क्या होगा ?7(5√3−9√2)7(53−92)
A. 19
B. 20
C. 25
D. इनमें से कोई नहीं
उत्तर: (D)
प्रश्न 9. एक अपरिमेय संख्या का दशमलव प्रसार हो सकता है:
A. पुनरावर्ती
B. गैर-समाप्ति और गैर-आवर्ती
C. समाप्त
D. या तो समाप्त होने वाला या गैर-समाप्त होने वाला
उत्तर: (B)
Question 1. The value of 256 x 0.16 (256) 0.09 is:
A.256.25
B.64
C.4
D.16
Answer: (c)
Question 2. The value of is:4√16−216−24
A. 1/2
B.4
C. 1/4
D.1/16
Answer: (A)
Question 3. √12 X √15 is equal to:
A.√25
B.10√5
C.5√6
D.6√5
Answer: (D)
Question 4. 4√5 + 5√5 is equal to:
A.9√10
B.9√5
C.7√5
D.5√10
Answer: (B)
Question 5. A rational number between √2 and √3:
A. (√2. √3)/2
B.1.5
C.1.8
D.1.9
Answer: (B)
Question 6. The product of a rational and an irrational number is:
A. Sometimes rational and sometimes irrational
B. Always an integer
C. Always a rational number
D. Always an irrational number
Answer: (D)
Question 7. Every rational number is:
A. Real numbers
B. Natural numbers
C. whole number
D. integer
Answer: (A)
8. What will be the denominator after rationalizing?7(5√3−9√2)7(53−92)
A.19
B.20
C.25
D. None of these
Answer: (D)
Question 9. Decimal expansion of an irrational number can be:
A. recurring
B. Non-terminating and non-recurring
C. finished
D. Either terminating or non-terminating
Answer: (B)
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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