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Q1. The number of non-negative rational numbers between -5 and 5 are _______ .

• 11
• 6
• 5
• indefinite

Solution

There are infinite rational numbers between any two rational numbers. Hence, the number of non-negative rational numbers between -5 and 5 is indefinite.

Q2. If a unit on the  number line is divided into 2 equal parts and let each part be called a smaller unit, then the distance between 2 and its reciprocal, in terms of smaller units is

• 1
• 2
• 3
• 4

Solution

Q3. In order to represent a rational number on a number line, _____ of the rational number tells the number of parts that should be considered when the first unit is divided into equal parts.

• denominator
• mean of numerator and denominator
• numerator
• half of numerator

Solution

Q4. When the equation 3x + 5 = 7 is solved, then we find that x is a/an

• Rational Number
• Integer
• Natural Number
• Whole Number

Solution

Q5. Multiplicative inverse of rational number(s) ______ is equal to the rational number themselves.

• zero
• 1 and -1
• 2
• -10

Solution

Q6. Which of the following is a rational number?

• 0
• 2
• -3
• All of above

Solution

A rational number is one which can be expressed as , where b≠0.

Q7. There are infinite rational numbers between any two given

• Natural numbers
• Whole numbers
• Integers
• All of the above

Solution

There are indefinite rational numbers between any two integers. And, Natural numbers and whole numbers are also integers. Therefore, there are infinite rational numbers between integers, natural numbers and whole numbers.

Q8. Reciprocal of any natural number lies between

• 0 and -1
• 0 and 1
• 1 and infinity
• 100 and 1000

Solution

A natural number is always equal to or greater than 1. The reciprocal of a number which is greater than 1 is always less than 1. Moreover, all natural numbers are positive and reciprocal of a positive number is always positive. Therefore, the reciprocal of any natural number lies between 0 and 1.

Q9. On a number line, 3.7 will lie

• in between 3.8 and 3.9
• to the left of 3
• in between 3.6 and 3.8
• to the left of 0

Solution

3.7 is greater than 3.6 and less than 3.8. Hence, on a number line, 3.7 will lie between 3.6 and 3.8

Q10. In the representation of rational numbers, the number line extends 

• idnefinitely on both sides of 0
• indefinitely to the right side of zero
• indefinitely to the right side of 1
• indefinitely to the left side of zero

Solution

Since, rational numbers include whole numbers, natural numbers and integers, representation of rational numbers on number lines extends indefinitely on both sides of 0.

Q11. Between any two consecutive integers there is definitely a ______ .

• natural number
• integer
• whole number
• rational number

Solution

There always exist a rational number between any two real numbers. Hence, between any two consecutive integers, there is definitely a rational number.

Q12. Which property is illustrated by the following statement? 150 × (-30 + 63) = 150 × -30 + 150 × 63

• Commutative property of integers
• Associative property of integers
• Distributive property of addition over multiplication
• Distributive property of multiplication over addition

Solution

For Integers, multiplication distributes over addition. Hence, 150 × (-30 +  63) = 150 × -30 +  150 × 63 which follows Distributive property of multiplication over addition.

Q13. (3 - 5)  is not a natural number. This shows that

• natural numbers are not closed under subtraction
• natural numbers are not commutative for subtraction
• natural numbers are not associative for subtraction
• subtraction is not defined for natural numbers

Solution

3 - 5 = -2 -2 is not a natural number. This shows that natural numbers are not closed under subtraction.

Q14. ______ are associative for rational numbers.

• Addition and subtraction
• Multiplication and division
• Addition and Multiplication
• Subtraction and division

Solution

Q15. While representing a whole number, the number line extends 

• indefinitely on both sides of zero
• indefinitely to the right side of zero
• indefinitely to the right side of 1
• indefinitely to the left side of 1

Solution

Whole numbers are 0, 1, 2, 3, ..... Hence, while representing whole numbers, the number line extends indefinitely to the right side of zero.

Q16. ______ is the only rational number which does not have a reciprocal.

• 1
• -1
• zero
• -100

Solution

The rational number that does not have a reciprocal is zero.

Q17. A rational number between -4 and -6 is

• 0
• -1
• -2
• -5

Solution

-5 lies between -4 and -6. Hence, it is a rational number between -4 and -6.

Q18. If a and b are two rational numbers such that a < 0 and b > 0, then, on the number line

• a lies to the left of 0 and b lies to the right of 0
• a lies to the right of 0 and b lies to the left of 0
• both lie to the left of 0
• both lie to the right of 0

Solution

Q19. Every integer is

• negative
• positive
• a whole number
• a rational number

Solution

Q20. While representing an integer, the number line extends 

• indefinitely on both sides of 0
• indefinitely to the right side of 0 only
• indefinitely to the right side of 1 only
• indefinitely to the left side of 0 only

Solution

Integers constitute both positive and negative numbers; hence the number line extends indefinitely on both sides of zero.

Q21. The solution to the equation x + 7 = 7 results in a/an

• natural number
• whole number
• integer
• both (b) and (c)

Solution

x + 7 = 7 gives x = 0.    0 is a whole number as well as an integer.

Q22. Rational numbers between 11 and 14 are

• 12 and 13
• 11 and 14
• 14 and 15
• 10 and 11

Solution

The numbers should be more than 11 and less than 14.

Q23. 0.0001 <...... <0.01

• 0.011
• 0.001
• 0.00001
• 0.1

Solution

The numbers should be more than 0.0001 and less than 0.01. 

Q24. Which of the following is the largest set of numbers?

• Natural numbers
• Whole numbers
• Integers
• Rational numbers

Solution

Since, Rational numbers include natural numbers, whole numbers and integers, it is the largest set of numbers.

Q25. Which is the bigger set?

• Natural numbers
• Rational numbers
• Integers
• Whole numbers

Solution

Rational numbers include integers, natural numbers and whole numbers. 

Q26. The product of a non-zero rational number and its additive inverse always lie

• on the left of 0.
• on the right of 0.
• at 1
• at 0

Solution

A non-zero rational number and its additive inverse have opposite signs. Therefore, on multiplying them, the product will always have a negative sign, since product of a positive and a negative number is negative. Also, we know that all negative rational numbers lie on the left side of 0. Thus, the product of a non-zero rational number and its additive inverse always lie on the left of 0.

Q27. Every terminating number can be represented as a ……….number. 

• Whole
• Natural
• Integer
• Rational

Solution

Every number can be represented as a rational number. 

Q28. The mean of 6 and 0.6 is

• 6.6
• 3.3
• 3
• None of the above

Solution

Mean = (6+0.6) ÷ 2=3.3

Q29. While representing natural numbers, the number line extends

• indefinitely on both sides of 0
• indefinitely to the right side of zero
• indefinitely to the right side of 1
• indefinitely to the left side of 1

Solution

Natural numbers are 1, 2, 3, ......... Hence, while representing natural numbers on the number line, the number line extends indefinitely to the right side of 1.

Q30. The solution of the equation x + 11 = 2 is

• an integer
• a whole number
• a natural number
• zero

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