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Class 9 Maths - Number System Previous Year Questions

Very Short Answer Type Questions

Q1.Complete the following:

(i) Every point on the number line corresponds to a _______ number which may be either _______ or _______.

(ii) The decimal form of an irrational number is neither _______nor _______ .

(iii) The decimal representation of the rational number8/27\frac{8}{27} is _______ .

(iv) 0 is _______number. [Hint: a rational / an irrational]

Sol:

Class 9 Maths - Number System Previous Year Questions  View Answer

(i) Every point on the number line corresponds to a real number which may be either rational or irrational.

(ii) The decimal form of an irrational number is neither recurring nor terminating.

(iii) The decimal representation of the rational number 827  is 0.296.

(iv) 0 is a rational number.

Q2: Find the value of’(0.6)0 − (0.1)−1(3/8)−1 × (3/2)3 + (-1/3)−1

Class 9 Maths - Number System Previous Year Questions  View Answer

Sol:
(0.6)0 − (0.1)−1(3/8)−1 × (3/2)3 + (-1/3)−1

= 1 x 1/0.18/3 × 27/8 + (3)
= 1 − 109 − 3 = −96 = −32

Q3: Find the value of 4(216)-2/3− 1(256)-3/4

Class 9 Maths - Number System Previous Year Questions  View Answer

Sol:
4(216)-2/3− 1(256)-3/4

= 4 × (216)2/3 − (256)3/4

= 4 × (6 × 6 × 6)2/3 − (4 × 4 × 4 × 4)3/4

= 4 × 63 × 2/3 − 44 × 3/4

= 4 × 62 − 43

= 4 × 36 − 64

= 144 − 64 = 80

Short Answer Type Questions

Q1: Give three rational numbers lying between 13 and 12 .

Class 9 Maths - Number System Previous Year Questions  View Answer

Sol:The rational number lying between 13  and  12 is calculated as follows:

12 × ( 13 + 12 )  =  1 × (2 + 3)3 × 2  =  512.

Therefore, 13  < 512  < 12.

Now, the rational number lying between 13 and 512 is calculated as:

12 × ( 13 + 512 )  =  1 × (4 + 5)12 × 2  =  38.

Therefore, 13  <  38  <  512.

The rational number lying between 512 and 12 is:

12 × ( 512 + 12 )  = 1 × (5 + 6)12 × 2  = 1124.

Therefore, 512 < 1124 < 12.

Hence, the three rational numbers lying between 13  and  12  are:  38,  512,  and  1124.

Q2.Identify a rational number among the following numbers :
14 + √3,  2√2,  1 and π/4

Class 9 Maths - Number System Previous Year Questions  View Answer

Sol: 1 is a rational number.

Q3.Simplify: (√5 + √3)2.

Class 9 Maths - Number System Previous Year Questions  View Answer

Sol:
Here,using (a+b)= a+ 2ab +b2
we get, 
(√5 + √3)
2= (√5)2+ 2(√5)(√3) + (√3)2
= 5 + 2√15 + 3 
= 8 + 2√15

Q4.Simplify : √45 – 3√20 + 4√5

Class 9 Maths - Number System Previous Year Questions  View Answer

Sol: Simplify each square root.

√45 = √9 × 5 = 3√5

√20 = √4 × 5 = 2√5
Substitute these value in given equation : √45 – 3√20 + 4√5 
we get , 
= 3√5 – 6√5 + 4√5 
= √5.

Q5.Express 1.8181… in the form pq where p and q are integers and q ≠ 0.

Class 9 Maths - Number System Previous Year Questions  View Answer

Sol:Let x =1.8181… …(i)
[multiplying eqn. (i) by 100] 
we get , 
100x = 181.8181… …(ii) 
99x = 180 
[subtracting (i) from (ii)] 
we get, 
x = 180/99

Hence, 1.8181… = 180/99 = 20/11

Long Answer Type Questions

Q1.Simplify the expression: (11 + √11) (11 – √11)

Class 9 Maths - Number System Previous Year Questions  View Answer

Sol:Using Identity: (a – b) (a+b) = a2 – b2

(i) (11 + √11) (11 – √11)

= 112 – (√11)2

= 121 – 11

= 110

Q2.Rationalise the denominator :

3√2 + 12√5 − 3

Class 9 Maths - Number System Previous Year Questions  View Answer

Sol:Multiply and divide the given number by 2√5 + 3

3√2 + 12√5 − 3

= (3√2 + 1) × (2√5 + 3)(2√5 − 3)(2√5 + 3)

= 6√10 + 9√2 + 2√5 + 3(20 − 9)

= 6√10 + 9√2 + 2√5 + 311

Q3Simplify and find the value of
(a) (729)1/6
(b) (64)2/3
(c) (243)6/5
(d) (21)3/2 x  (21)5/2
(e) (81)1/3(81)1/12

Class 9 Maths - Number System Previous Year Questions  View Answer

Sol:
(a) (729)1/6
Prime factorize 729 = 3 × 3 × 3 × 3 × 3 × 3 = 36

(729)1/6 = (36)1/6 = (3)(6/6) = 3

( Used : Rule of exponents used: (ax)y = axy
(b) (64)2/3
Prime factorize 64 = 2 × 2 × 2 × 2 × 2 × 2 = 26
(64)2/3 = (26)2/3 = (2)(12/3) = (2)4 = 16

Rule of exponents used: (ax)y = axy
(c) (243)6/5  
(243)6/5 = (35)6/5 = 36 = 729
( Used : Rule of exponents used: (ax)y = axy
(d) (21)3/2 x  (21)5/2
(21)3/2 x (21)5/2 = (21) 3/2+5/2 = (21)8/2 = 214
Rule of exponents used: (ax) × (ay) = ax + y
(e) 
(81)1/3(81)1/12
= (81)1/3(81)1/12 = (81)1/3 − 1/12
= (81)(4 − 1)/12 = (81)3/12
= (81)1/4
Prime factorize 81 = 3 × 3 × 3 × 3 = 34
(81)1/4 = (34)1/4 = (3)4/4 = 3
Rule of exponents used: axay = ax − y

Q4. Rationalize the denominator: 

 18 + 3√5

Class 9 Maths - Number System Previous Year Questions  View Answer

Sol: Multiply and divide by the (8 - 3√5): 

= 18 + 3√5 × 8 − 3√58 − 3√5

= 8 − 3√582 − (3√5)2

= 8 − 3√564 − 45

= 8 − 3√519

Q5 : What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.

Class 9 Maths - Number System Previous Year Questions  View Answer

Sol: Class 9 Maths - Number System Previous Year Questions

Thus, 1/17 = 0.0588235294117647….
Therefore, 1/17 has 16 digits in the repeating block of digits in the decimal expansion.

The document Class 9 Maths - Number System Previous Year Questions is a part of the Class 9 Course Mathematics (Maths) Class 9.
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FAQs on Class 9 Maths - Number System Previous Year Questions

1. What is the importance of number systems in mathematics?
Ans. Number systems are fundamental in mathematics as they provide a framework for representing and manipulating numbers. They enable us to perform arithmetic operations, solve equations, and understand numerical relationships. Different number systems, such as natural numbers, integers, rational numbers, and real numbers, each serve specific purposes in mathematical theory and applications.
2. What are the different types of number systems commonly used?
Ans. The most commonly used number systems include: 1. Natural Numbers (N): The set of positive integers starting from 1. 2. Whole Numbers (W): The set of natural numbers including zero. 3. Integers (Z): The set of whole numbers and their negative counterparts. 4. Rational Numbers (Q): Numbers that can be expressed as the quotient of two integers. 5. Real Numbers (R): All numbers on the number line, including rational and irrational numbers.
3. How do you convert a decimal number to a binary number?
Ans. To convert a decimal number to a binary number, you can use the following method: 1. Divide the decimal number by 2. 2. Write down the remainder (0 or 1). 3. Divide the quotient by 2 and repeat the process until the quotient is 0. 4. The binary number is read from the bottom remainder to the top.
4. What are some common operations performed on number systems?
Ans. Common operations performed on number systems include addition, subtraction, multiplication, and division. These operations can vary in complexity depending on the number system in use. For example, adding binary numbers involves carrying over when the sum exceeds 1, while operations in the decimal system follow our standard base-10 rules.
5. Why is it essential to understand number systems for competitive exams?
Ans. Understanding number systems is crucial for competitive exams because they form the basis for many mathematical concepts and problems. Questions related to number systems test a candidate's analytical skills and problem-solving abilities. Mastery of these concepts can lead to better performance in quantitative sections of exams.
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