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False.

Difference of two natural numbers are not always a natural number.

Therefore, natural numbers are not closed under subtraction.

True.

We know that, sum of two natural numbers is always natural number.

Therefore, natural numbers are closed under addition.

Natural numbers are closed under addition and under multiplication.

Addition of a and b is a + b which is again a natural number, therefore natural numbers are closed under addition.

Multiplication of a and b is (a x b) which is again a natural number, therefore natural numbers are closed under multiplication.

(i) Every point on the number line corresponds to a REAL number which many be either RATIONAL or IRRATIONAL 

(ii) The decimal from of an irrational number is neither TERMINATING Nor REPEATING. 

(iii) The decimal representation of a rational number is either TERMINATING or NON TERMINATING 

(iv) Every real number is either RATIONAL number or IRRATIONAL Number

If n can be written in the form of p/q, where q≠0, then it is a rational number else irrational.

No, because 39 is not a prime number.

25 is the total number of primes up to 100.

(i) 12

(ii) 31

(iii) 3

(iv) 2

(v) 10

Twin primes

A pair of prime numbers whose difference is 2, is called twin primes.

(d) impossible

100 years = 1 Century

Scalene Triangle

(i) Loss = CP – SP

(ii) 526 ml = 0.526 L

(a) 2

If the number 6354*97 is divisible by 9, then the value * is 2.

(i) 15

(ii) 156

(iii) 2

(iv) 3

(v) 3

Take the first five consecutive natural numbers 1, 2, 3, 4 and 5.

Their sum 1 + 2 + 3 + 4 + 5 = 15, divisible by 5.

Also, 2 + 3 + 4 + 5 + 6 = 20, divisible by 5.

3 + 4 + 5 + 6 + 7 = 25, divisible by 5.

Generally, the sum of 5 consecutive natural numbers is divisible by 5.

2 × 3 × 4 = 24 is divisible by 6.

Yes, because it has two factors.

(i) False 42 is divisible by 3 but it is not divisible by 9

(ii) True 36 is divisible by 12. Also divisible by 6.

The first four-digit number is 1000.

Sum of the digits is 1 + 0 + 0 + 0 = 1, not divisible by 3.

1000 is not divisible by 3.

(i) A number is divisible by 2 if it is an even number.

Greatest 2 digit even number is 98.

∴ A = 8

(ii) A number is divisible by 3 if the sum of its digits is divisible by 3

Sum of digits of 567A = 5 + 6 + 7+ A = 18 + A

∴ 18 is divisible by 3

∴ A may be 0

The number will be 5670

(iii) A number is divisible by 6 if it is divisible by both 2 and 3

9A6 is even and so divisible by 2

If A = 9 then the sum of digits will be = 24 which is divisible by 3.

The number will be 996 and A = 9

(iv) 08 is divisible by 4, so A08 is divisible by 4.

If A = 1 then the sum of digits will be 9 which is divisible by 9.

The number will be 108 and A = 1

(v) 5 + A + 2 – (8 + 5 + 2) 

= 7 + A – 15 

= -8 + A

∴ A = 8

Leap years are divisible by 4.

Leap years are divisible by 2.

True, as we know, that, “the sum of any three odd numbers is always an odd number”.

Example: 3 + 7 + 9 = 19 is odd.

(3, 5, 7)

Prime triplet (3, 5, 7).

False 12 is divisible by both 4 and 6. But not divisible by 24.

(c) 40

The sum of the factors of 27 is 40.

(D) 39

The prime factors of 1729 = 7 × 13 × 19

Therefore, the sum of prime numbers = 7 + 13 + 19

= 39

Class 9 Maths MCQ Questions of Number system will shape a huge part of the Mathematics question paper in final exams. Students can score full marks without much of a stretch in these objective type questions with a little difficult work and great practice. We are giving here the MCQ questions of the Number System which are set up by subject specialists. 

Class 9 Maths syllabus incorporates some early on parts of various numerical branches. The branches are arithmetic, algebra, geometry, trigonometry, etc. The students should become familiar with the number system effectively for their future accommodation. The number system is quite possibly the main basic subjects of science.

They should be taken care of different numerical issues all alone on this subject. It will assist the students with being more productive and certain.Following are some number system MCQ Questions for class 9 maths with answers. Each question comprises 4 choices, out of which one is right.

Practice Class 9 Maths MCQ Questions 

1. Write three rational numbers between 4 and 5?

(a) 12/6, 13/6, 14/6
(b) 12/7, 13/7, 14/7
(c) 17/4, 18/4, 19/4
(d) 17/2, 18/13, 19/23

2.  In between two rational number there is/are:

(a) Exactly one rational number
(b) Infinitely many rational number
(c) Many irrational numbers
(d) Only irrational numbers

3. The product of a rational and an irrational numbers is:

(a) Always an integer
(b) Always a rational number
(c) Always an irrational number
(d) Sometimes rational and sometimes irrational

4. The decimal expansion of an irrational number may be:

(a) Terminating
(b) Recurring
(c) Either terminating or non- terminating
(d) Non-terminating and non-recurring

5.  A rational number between √2 and √3:

(a) 1.9
(b) (√2. √3)/2
(c) 1.5
(d) 1.8

6. Can we write 0 in the form of p/q?

(a) Yes
(b) No
(c) Cannot be explained
(d) None of the above

7. The three rational numbers between 3 and 4 are:

(a) 5/2, 6/2, 7/2
(b) 13/4, 14/4, 15/4
(c) 12/7, 13/7, 14/7
(d) 11/4, 12/4, 13/4

8. Every rational number is:

(a) Whole number
(b) Natural number
(c) Integer
(d) Real number

9. √9 is  __________ number.

(a) A rational
(b) An irrational
(c) Neither rational nor irrational
(d) None of the above

10. Which of the following is an irrational number?

(a) √16
(b) √(12/3)
(c) √12
(d) √100

11. 3√6 + 4√6 is equal to:

(a) 6√6
(b) 7√6
(c) 4√12
(d) 7√12

12. √6 x √27 is equal to:

(a) 9√2
(b) 3√3
(c) 2√2
(d) 9√3

13.  Which of the following is equal to x³?

(a) x⁶-x³
(b) x⁶.x³
(c) x⁶/x³
(d) (x⁶)³

14. 4√5 + 5√5 is equal to:

(a) 9√5
(b) 9√10
(c) 5√10
(d) 7√5

15. Which of the following is an irrational number?

(a) √23
(b) √225
(c) 0.3796
(d) 7.478478

16. Which of the following is an irrational number?

(a) 0.14
(b) 0.14\(\overline{16}\)
(c) 0.\(\overline{1416}\)
(d) 0.4014001400014…

17. 2√3+√3 = 

(a) 6
(b) 2√6
(c) 3√3
(d) 4√6

18. Which of the following is rational?

(a) 4/0
(b) 0/4
(c) √3
(d) π

19. The irrational number between 2 and 2.5 is 

(a) √11
(b) √5
(c) √22.5
(d) √12.5

20. The decimal representation of the rational number is

(a) Always terminating
(b) Either terminating or repeating
(c) Either terminating or non-repeating
(d) Neither terminating nor repeating

Answer: 

1. Answer: (c) 17/4, 18/4, 19/4

Explanation: There are several rational numbers between 4 and 5.

The numbers are between 16/4 and 20/4.

Therefore, the answer is c, that is, 17/4, 18/4, 19/4

2. Answer: (b) Infinitely many rational numbers

3. Answer: (c) Always an irrational number

4. Answer: (d) Non-terminating and non-recurring

5. Answer: (c) 1.5

6. Answer: (a) Yes

Explanation: 0 is a rational number and hence it can be written in the form of p/q.

Example: 0/4 = 0

7. Answer: (b) 13/4, 14/4, 15/4

Explanation: There are many rational numbers between 3 and 4

To find 3 rational numbers, we need to multiply and divide both the numbers by 3+1 = 4

Hence, 3 x (4/4) = 12/4 and 4 x (4/4) = 16/4

Thus, three rational numbers between 12/4 and 16/4 are 13/4, 14/4 and 15/4.

8. Answer: (d) Real number

9. Answer: (a) A rational

Explanation: √9 = 3

Hence, √9 is a rational number.

10. Answer: (c) √12

Explanation: √12 cannot be simplified to a rational number.

11. Answer: (b) 7√6

Explanation: 3√6 + 4√6 = (3+4)√6 = 7√6

12. Answer: (a)

Explanation: √6 x √27 = √(6 x27) = √(2x3x3x3x3) = 3×3√2 = 9√2

13. Answer: (c) x⁶/x³

Explanation: x⁶/x³ = x^6-3 = x³  

14. Answer: (a) 9√5

15. Answer: (a) √23

Explanation: √23 = 4.79583152331…

Since the decimal expansion of the number is non-terminating non-recurring. Hence, it is an irrational number.

16. Answer: (d) 0.4014001400014…

Explanation: 0.4014001400014…is an irrational number as it is non-terminating and non-repeating.

17. Answer: (c) 3√3

Explanation: 2√3+√3 = (2+1)√3= 3√3.

18. Answer: (b) 0/4

Explanation: 0/4 is a rational number that is equal to 0. Whereas π and √3 are irrational numbers and 4/0 is meaningless.

19. Answer: (b) √5

Explanation: The irrational number between 2 and 2.5 is √5 because the approximate value of √5 is 2. 23606…

20. Answer: (b) Either terminating or repeating

Explanation: As per the definition of rational number, its decimal representation is either terminating or repeating.

Click here to practice more MCQ questions from Chapter Number system Class 9 Maths

a) Cusec: A unit of flow equal to 1 cubic foot per second. 

1 Cusec = 0.028316 cubic feet per second = 28.316 litre per second. 

Cusec is the unit to measure the liquids in large numbers quantity.

b) TMC: TMC is the unit to measure the water in large quantity. 

TMC means Thousand Million Cubic feet. 

1 TMC = 0.28316000000 litre 

= 28.316 billion litre 

= 2831.6 crores litre

c) Metric tonne: Metric tonne is the unit of weight. 

Metric tonne = 1000 kg = 10 quintals 

We should use this unit in measuring crops, paddy, dall, etc.

d) Kilometer: Kilometre is the unit of length. 

1 kilometer = 1000 meters. 

We should use this unit is measuring distance between villages, towns, cities,…. etc.

1,00,005

We have to find a 6 digit natural number ending with 5. Thus, we first fill the unit's position with 5. We now have 5 more places to fill. The position of Lakh in the number i.e the left-most blank must be smallest to create the smallest number. If we assign 0 to that position the number becomes 5 digit. The smallest number after 0 is 1 thus, we assign 1 to that position. 1 _ _ _ _ 5 

Now we can fill the remaining positions with 0 Thus the smallest 6 digit natural number ending with 5 is 1,00,005.

(C) 50

Let us assume the number be x.

From the question it is given that, number is added to 25 = x + 25

The same number is subtracted to from 25 = 25 – x

Then, the sum of the resulting numbers is = (x + 25) + (25 – x)

= x + 25 + 25 – x

= 50 + x – x

= 50 + 0

= 50

(C) 7 + 8 × 9 = (7 + 8) × (7 + 9)

Consider the left hand side = 7 + 8 × 9

= 7 + (8 × 9)

= 7 + 72

= 79

Now, consider the right hand side = (7 + 8) × (7 + 9)

= 15 × 16

= 240

By comparing LHS and RHS

LHS ≠ RHS

79 ≠ 240

10001 x 0 = 0

False.

Zero (0) is the identity for addition of whole numbers.

Consider any whole number i.e. 8.

Then, 8 + 0 = 8

(B) Zero is the identity for multiplication of whole numbers.

Example:- 1 × 0 = 0

(iv) (-6) x (+5)

(i) -20 + (10) = -10 

(ii) 60 – 30 = 30 

(iii) 10 + 20 = 30 

(iv) (-6) x (+5) = – 30

1001 x 2002 =1001 x (1001 + 1001)

(iii) distributive

True.

Consider any whole number i.e. 6.

6 × 1 = 6

2395 × 6195 = 6195 × 2395

We know that if a and b are two whole numbers then by commutative property,  

a × b= b × a

So, 2395 × 6195 = 6195 × 2395

Multiplication is distributive over addition for whole numbers.

Division of a whole number by ZERO is not defined.

Addition, Multiplication

If a and b are two whole numbers, 

Addition of a and b is a + b which is again a whole number, therefore whole numbers are closed under addition. 

Multiplication of a and b is (a x b) which is again a whole number, therefore whole numbers are closed under multiplication.

False.

For example:-

2 + 3 = 5

2 × 3 = 6

From the above example, we can say that sum of two whole numbers is not always less than their product.

True.

Consider the two odd numbers 2 and 5.

Then, sum = 2 + 5 = 7 it is an odd number.

Now, difference = 2 – 5 = 3 it also an odd number.

True.

Co-prime number is a set of numbers or integers which have only 1 as their common factor i.e. their highest common factor (HCF) will be 1. Co-prime numbers are also known as relatively prime or mutually prime numbers. It is important that there should be two numbers in order to form co-primes.

(A) 2

Prime factors of,

75 = 3 × 5 × 5

60 = 2 × 2 × 3 × 5

105 = 3 × 5 × 7

So, common prime factors in the given three numbers are 3 and 5.

Therefore, the number of common prime factors of 75, 60, 105 is 2.

(A) 8, 10

First of all, both the numbers are even.

Then, common factor of both numbers is 2 other than 1.

Therefore, 8 and 10 are not coprime.

(C) 22222222

To check the divisibility of a number by 11, the rule is, find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is either 0 or divisible by 11, then the number is divisible by 11.

So, 2 – 2 + 2 – 2 + 2 – 2 + 2 – 2 = 0

Therefore, 22222222 is divisible by 11.

Number of votes secured by the winner = 1,32,356 

Number of votes secured by the rival = 42,246 

Number of more votes secured by the winner = 1,32,356 – 42,246 = 90,110 

Majority of the winner = 90,110 votes.