Free Mathematics Notes for 9th Class

1. The number that can be expressed in the form of \frac{p}{q} \ where \ p \ and \ q are integers and q \neq 0 is called _______ numbers.
O Rational
O Irrational
O Imaginary
O None of these
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2. A rational in the form of \frac{p}{q} where \ p \ and q are _______
O Imaginary
O Complex
O Integers
O All of them
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3. A rational in the form of \frac{p}{q} where q _______ 0.
O Equal
O Not equal
O Both a and b
O None of these
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4. The word Rational is derived from _______
O Ratio
O Not Ratio
O lota
O All of them
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5. The rules of rational number for p \ and \ q are _______.
O \frac{p}{q}
O Integers
O q \neq 0
O All of them
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6. Rational number is denoted by _______.
O Q
O Q^{\prime}
O Both a and b
O None of these
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7. Irrational number is denoted by _______
O Q
O Q^{\prime}
O Both a and b
O None of these
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8. The word irrational means_______
O Ratio
O Not Ratio
O lota
O None of these
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9. Irrational numbers consist of all the numbers which are_______
O Rational
O Not rational
O lota
O None of these
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10. 1\frac{3}{4} is_______
O Rational
O Irrational
O Complex
O None of these
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11. \sqrt{3} is_______
O Rational
O Irrational
O Complex
O None of these
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12. \pi is_______
O Rational
O Irrational
O Complex
O None of these
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13. R is the symbol of _______ number.
O Rational
O Irrational
O Real
O Both a & b
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14. The union of rational and irrational numbers is the set of _______ numbers.
O Complex
O lota
O Prime
O Real
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15. Q \cup Q^{\prime}= _______
O i
O Prime
O R
O N
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16. All the numbers on the number line are _______ numbers.
O i
O Complex
O Real
O None of these
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17. All the numbers on the number line are _______ numbers.
O Rational
O Irrationa|
O Real
O All of them
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18. -17 is _______ numbers.
O Whole
O Natural
O Integers
O All of them
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19. A whole number is a number that does not contain_______
O Decimal
O Negative
O Fraction
O All of them
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20. All terminating and repeating decimals are_______
O Rational
O Irrational
O Complex
O All of them
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21. _______ decimals are Rational numbers.
O Terminating
O Repeating
O Both a & b
O None of these
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22. \frac{3}{8}=0.375 is _______ decimal.
O Terminating
O Repeating
O Both a & b
O None of these
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23. \frac{2}{15}=0.133 \ldots is _______ decimal
O Terminating
O Repeating
O Both a & b
O None of these
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24. 0.1 \overline{3} is _______ decimal
O Terminating
O Repeating
O Both a & b
O None of these
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25. Bar over the digit means that this digit is_______
O Terminated
O Repeated
O Both a & b
O None of these
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26. A decimal which is non-terminating and non-repeating is called _______ numbers.
O Rational
O Irrational
O Complex
O All of them
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27. The number line help in visualizing the set of _______ numbers.
O Complex
O Imaginary
O Real
O None of these
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28. For every real number there is a _______ on the line.
O Point
O Line
O Both a & b
O None of these
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29. The number associated with a point on the line is called the of _______ that point.
O Coordinate
O Zero
O Both a & b
O None of these
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30. The point on the number line is called the _______ of the number.
O Coordinate
O Zero
O Graph
O None of these
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31. The numbers to the right of “0” on a number line are called _______ numbers.
O Positive
O Negative
O Complex
O None of these
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32. The numbers to the left of “O” on a number line are called _______ numbers.
O Positive
O Negative
O Complex
O None of these
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33. 0 is _______
O Positive integers
O Negative integers
O Neither positive nor negative
O Not an integer
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34. Repeating decimals are called _______ decimals.
O Recurring
O Non-Recurring
O Both a & b
O None of these
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35. Non-Repeating decimals are called _______ decimals.
O Recurring
O Non-Recurring
O Botha \& b
O None of these
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36. \frac{5}{27}=0.185185185 \dots is called _______ recurring decimals.
O Terminating
O Non-Terminating
O Both a & b
O None of these
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37. \frac{5}{7} is _______ number.
O Rational
O Irrational
O Imaginary
O None of these
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38. \sqrt{36} is _______ .
O Rational
O Whole
O Natural
O All of them
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39. \frac{14}{3} is _______ number.
O Rational
O Whole
O Both a & b
O Irrational
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1. The set of Real number is the union of two ________ sets.
O Zero
O New
O Disjoint
O None of these
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2. Q \cap Q^{\prime}= ________ ]
O Q
O Q^{\prime}
O \emptyset
O All of them
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3. The sum of two real number is also a real number is called ________ property w.r.t Addition.
O Closure
O Commutative
O Associative
O None of these
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4 . The ________ of two real number is also a real number is called closure property.
O Product
O Commutative
O Associative
O None of these
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5. Example of closure property:
O 7+9=16
O 7 \times 9=63
O Both a & b
O None of these
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6. Commutative property w.r.t addition is ________
O a+b=b+c
O a+c=b+c
O a+b+c=a+b
O a+b=b+c
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7. Commutative property w.r.t multiplication is ________
O a b=b c
O a c=b c
O a b c=a b
O a b=b c
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8. Commutative property is ________
O a+b=b+a
O a b=b a
O Both a & b
O None of these
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9. Associative property w.rt Addition is ________
O a(bc)=(ab)c
O a+(b+c)=(a+b)+c
O Both a & b
O None of these
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10. Zero is called ________
O Additive identity
O Additive inverse
O Both a & b
O None of these
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11. a+0=0+a=a is
O Additive identity
O Additive inverse
O Both a & b
O None of these
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12. The product of real number and zero is________
O a
O That number
O Imaginary
O Zero
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13. 1 is called ________ w.r.t multiplication.
O Multiplicative identity
O Imaginary
O Multiplicative inverse
O None of these
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14. a \times 1=1 \times a=a is ________ property. O Multiplicative identityg>
O Imaginary
O Multiplicative inverse
O None of these
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Answer: Multiplicative identity
Explanation:
1 is called Multiplicative identity because multiplying “1” to a number does not change that number.

15. The product of 1 and a number is________
O 10
O Zero
O That number
O None of these
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Answer: That number
Explanation:
1 is called Multiplicative identity because multiplying “1” to any number does not change that number.

16. The sum of two numbers is zero (0) is called________
O Additive identity
O Additive inverse
O Both a & b
O None of these
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Answer: Additive inverse
Explanation:
Definition of Additive inverse

17. If a+a^{\prime}=a^{\prime}+a=0 \ then \ a^{\prime} is called ________ of a .
O Additive identity
O Additive inverse
O Both a & b
O None of these
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Answer: Additive inverse
Explanation:
When a real number and its opposite, the result will always be 0.

18. If a+(-a)=-a+a=0 \ then \ -a is called of ________ a .
O Additive identity
O Additive inverse
O Both a & b
O None of these
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Answer: Additive inverse
Explanation:
When a real number and its opposite, the result will always be 0.

19. The product of two numbers is 1 is called________
O Multiplicative identity
O Imaginary
O Multiplicative inverse
O None of these
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Answer: Multiplicative inverse
Explanation:
When a real number is multiplied by its inverse or reciprocal, the result will always be 1.

20. If a \cdot a^{-1}=a^{-1} \cdot a=1 \ then \ a^{-1} is called ________ of a .
O Multiplicative identity
O Imaginary
O Multiplicative inverse
O None of these
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Answer: Multiplicative inverse
Explanation:
When the Product of two numbers is “1” then it is said to be Multiplicative inverse.

21 If a \cdot \frac{1}{a}=\frac{1}{a}, a=1 \ then \ \frac{1}{a} is called of ________ a .
O Multiplicative identity
O Imaginary
O Multiplicative inverse
O None of these
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Answer: Multiplicative inverse
Explanation:
When the Product of two numbers is “1” then it is said to be Multiplicative inverse.

22. Distributive Property of Multiplication over Addition is ________
O a(b+c)=ab+ac
O (b+c)a=ba+ca
O Both a & b
O None of these
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Answer: Both a & b
Explanation:
Both a & b showed the Distributive Property of Multiplication over Addition

23. If a=a , then it is ________ property.
O Transitive
O Symmetric
O Reflexive
O None of these
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Answer: Reflexive
Explanation:
Every number is equal to itself is known as Reflexive property.

24. If a=b , then also b=a , it is ________ property.
O Transitive
O Symmetric
O Reflexive
O None of these
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Answer: Symmetric
Explanation:
By interchanging the sides of an equation doesn’t effect the result is known as symmetric Prperty.

25. If a=b \ and \ b=c then a=c , it is ________ property.
O Transitive
O Symmetric
O Reflexive
O None of these
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Answer: Transitive
Explanation:
If a equal to b under a rule and b equal to c under the same rules then  a equal to  c is known as transitive property.

26. If y=x^2 \ then \ also \ x^2=y , it is ________ property.
O Transitive
O Symmetric
O Reflexive
O None of these
Show Answer

Answer: Symmetric
Explanation:
By interchanging the sides of an equation doesn’t effect the result is known as symmetric Prperty.

27. I x+y=z \ and \ z=a+b then x+y=a+b , it is ________ property.
O Transitive
O Symmetric
O Reflexive
O None of these
Show Answer

Answer: Transitive
Explanation:
If a equal to b under a rule and b equal to c under the same rules then  a equal to  c is known as transitive property.

28. If 3=3 , then it is ________ property. O Transitive>
O Symmetric
O Reflexive
O None of these
Show Answer

Answer: Reflexive
Explanation:
Every number is equal to itself is known as Reflexive property.

29. If a=b , then also a+c=b+c , it is ________ property of equality. O Ad>ditive
O Multiplicative
O Both a & b
O None of these
Show Answer

Answer: Additive
Explanation:
If we add the same number or expression on both sides of an equation, the equation does not change which means both the sides remain equal.

30. If a=b then also ac=bc , it is ________ property of equality.
O Additive
O Multiplicative
O Both a & b
O None of these
Show Answer

Answer: Multiplicative
Explanation:
If we Multiply the same number or expression on both sides of an equation, the equation does not change which means both the sides remain equal.

31. If a+c=b+c then a=b , it is Cancellation property w.r.t ________
O Addition
O Multiplication
O Both a & b
O None of these
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Answer: Addition
Explanation:
In this, cancelled the non-zero common factor from both side of the equation by Adding or Subtraction.

32. If ac=bc then a=b , it is Cancellation property w.r.t ________
O Addition
O Multiplication
O Both a & b
O None of these
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Answer: Multiplication
Explanation:
In this, cancelled the non-zero common factor from both side of the equation by Multiplication or Divison.

33. Trichotomy property is used for ________ two numbers.
O Increasing
O Decreasing
O Comparing
O Equating
Show Answer

Answer: Comparing
Explanation:
See MCQs No. 34

34. Trichotomy property must be true for ________
O a=b
O a>b
O a < b
O All of them
Show Answer

Answer: All of them
Explanation:
Trichotomy property is used for compare two numbers.

35. Trichotomy property must be true for________
O 5=5
O 3 < 5
O Both a & b
O None of these
Show Answer

Answer: Both a & b
Explanation:
Trichotomy property is used for compare two numbers.

36. If a > b and b>c then a > c , it is ________ property of inequality.
O Additive
O Multiplicative
O Transitive
O All of them
Show Answer

Answer: Transitive
Explanation:
If a greater than b under a rule and b greater than c under the same rule then  a greater than  c is known as transitive property of inequlity.

37. If a < b & b < c then a < c, it is ________ property. O Additive>
O Multiplicative
O Transitive
O All of them
Show Answer

Answer: Transitive
Explanation:
If a less than b under a rule and b less than c under the same rule then  a less than  c is known as transitive property of inequlity.

38. If a > b then a+c > b+c , it is ________ property of inequlity.
O Additive
O Multiplicative
O Transitive
O All of them
Show Answer

Answer: Additive
Explanation:
If we add the same number or expression on both sides of an inequality, but the result will remain the same. i.e. left side is greater than right side.

39. If a < b then a+c < b+c , it is ________ property.
O Additive
O Multiplicative
O Transitive
O All of them
Show Answer

Answer: Additive
Explanation:
If we add the same number or expression on both sides of an inequality, but the result will remain the same. i.e. left side is less than right side.

40. If x > 5 then ________
O x \times 2 > 5 \times 2
O x \times 2 < 5 \times 2
O Both a & b
O None of these
Show Answer

Answer: x \times 2 > 5 \times 2
Explanation:
If we multiply the same number or expression on both sides of an inequality, but the result will remain the same. i.e. left side is greater than right side.
Note:
The number should be positive.

41. If x>5 then ________
O x \times -2 > 5 \times -2
O x \times -2 < 5 \times -2
O Both a & b
O None of these
Show Answer

Answer: x \times -2 < 5 \times -2
Explanation:
If we multiply the same Negative number to both sides of an inequality, the result will changed. i.e. left side becomes less than right side.

42. For c > 0 and a < b then Multiplicative property ________
O ac < bc
O ac > bc
O Both a & b
O None of these
Show Answer

Answer: ac < bc
Explanation:
If we multiply the same Positive number to both sides of an inequality, the result will remain same. i.e. left side is less than right side.

43. For c < 0 and a < b then Multiplicative property ________
O ac < bc
O ac > bc
O Both a & b
O None of these
Show Answer

Answer: ac > bc
Explanation:
If we multiply the same Negative number to both sides of an inequality, the result will changed. i.e. left side becomes greaer than right side.

44. For c < 0 and a > b then Multiplicative property ________
O ac < bc
O ac > bc
O Both a & b
O None of these
Show Answer

Answer: ac < bc
Explanation:
If we multiply the same Negative number to both sides of an inequality, the result will changed. i.e. left side becomes less than right side.