AP 9th Maths Mock Test 2023 for Chapter-1 "Real Numbers" Online Practice Test

1. Which of the following decimal is terminating ?

$\frac{3}{11}$

$\frac{11}{6}$

$\frac{15}{7}$

$\frac{11}{16}$

2. Integers possess the following groups of numbers ______

Negative numbers

Zero

Positive numbers

All

3. When do we say that a number is a rational number ?

Number is in the form of $\frac{p}{q}$

q $\neq$ 0

Number is in the form of $\frac{p}{q}$ and q $\neq$ 0

Number is in the form of $\frac{p}{q}$ and p $\neq$ 0

4. Which of the following are in case of rational numbers ?

These are also called Quotient numbers

Rational numbers are denoted by 'Q'

These are in the form of $\frac{p}{q}$

All

5. Is there any integer exists between two successive integers ?

Positive integer exists

Negative integer exists

Zero

No integer exists

6. Is there any rational number exists between two successive rational numbers ?

1 rational number exists

Infinite number of rational number exists

0 rational number exists

None

7. The decimal expansion of rational numbers is in the form of

Terminating decimal

Non-terminating recurring decimal

Either Terminating or non-terminating recurring decimal

Remains in the form of a fraction

8. A number which cannot be written in the form of $\frac{p}{q}$ is called as

Rational numbers

Irrational numbers

Integers

Whole number

9. If x = 2 + $\sqrt{3}$ then x+ $\frac{1}{x}$ =

2 $\sqrt{3}$

10. If $x^{2} + \frac{1}{ x^{2} }$ = 83 then $x^{3} - \frac{1}{ x^{3} }$ =

702

256

756

729

11. If $\frac{5 - \sqrt{3} }{2 + \sqrt{3} } = a + b \sqrt{3}$ then the value of 'a' and 'b' are

-13 , -7

13 , 7

13 , -7

-13 , 7

12. Which is an irrational number between $\sqrt{2}$ and $\sqrt{3}$ ?

$2^{ \frac{1}{2} }$

$3^{ \frac{1}{4} }$

$6^{ \frac{1}{4} }$

$6^{ \frac{1}{8} }$

13. The rational number for 0. $\overline{5}$ is

$\frac{9}{5}$

$\frac{5}{10}$

$\frac{5}{9}$

$\frac{10}{5}$

14. If x= $\sqrt{5}$ + 2 then the value of x - $\frac{1}{x}$ is

2 $\sqrt{5}$

$\sqrt{5}$

15. Match the following

1. $\overline{428577}$ ( ) p. $\frac{35}{9}$
0. $\overline{36}$ ( ) q. $\frac{142}{45}$
3. $\overline{8}$ ( ) r. $\frac{10}{7}$
3.12 $\overline{7}$ ( ) s. $\frac{4}{11}$

1-s , 2-r , 3-q , 4-p

1-p , 2-s , 3-r , 4-q

1-q , 2-p , 3-r , 4-s

1-r , 2-s , 3-q , 4-p

16. Choose the correct option

1-p , 2-r , 3-q , 4-s

1-q , 2-s , 3-p , 4-r

1-r , 2-p , 3-q , 4-s

1-s , 2-q , 3-p , 4-r

17. Match the following

1-R , 2-S , 3-P , 4-Q

1-Q , 2-R , 3-P , 4-S

1-S , 2-P , 3-Q , 4-R

1-R , 2-P , 3-S , 4-Q

18. Match the following

1-Q , 2-S , 3-R , 4-P

1-Q , 2-R , 3-P , 4-S

1-Q , 2-P , 3-R , 4-S

1-S , 2-P , 3-R , 4-Q

19. If the product of two surds is a rational then each of two surds is called

Rationalizing factor of surd

Rationalizing factor of other

Multiplicative factor

None

20. R.F of $\sqrt{108}$ is

$\sqrt{2}$

$\sqrt{3}$

$\sqrt{27}$

$\sqrt{108}$

21. R.F of $\sqrt{75}$ + $\sqrt{32}$ is

5 $\sqrt{3}$ + 4 $\sqrt{2}$

3 $\sqrt{5}$ + 2 $\sqrt{3}$

5 $\sqrt{3}$ - 4 $\sqrt{2}$

-5 $\sqrt{3}$ - 4 $\sqrt{2}$

22. Which of the following statements are correct ?

i . $( x^{-1} + y^{-1} )^{-1}$ expression is equal to $\frac{xy}{x + y}$
ii. If x = 2 + $\sqrt{3}$ then the value of $x^{2} + \frac{1}{ x^{2} }$ = 14
iii. If $16^{ \frac{3}{2} }$ = x then the value of x = 64

i , ii , iii

i , ii

ii , iii

i , iii

23. Statement I : If x = $\frac{5 + \sqrt{3} }{ \sqrt{8} }$ , y = $\frac{5 - \sqrt{3} }{ \sqrt{32} }$ then $\sqrt{xy}$ is $\frac{ \sqrt{22} }{4}$
Statement II : $\frac{ 4^{-3} \times a^{-5} \times b^{-4} }{4^{-5} \times a^{-6} \times b^{3} }$ = $\frac{16 a}{ b^{7} }$

Statement I is true and Statement II is false

Statement II is true and Statement I is false

Both Statements are true

Both statements are false

24. Statement I : If x = $\sqrt{3} + 1$ then x + $\frac{1}{x}$ = $\frac{3 \sqrt{3} + 1}{2}$
Statement II : If $\sqrt{108}$ = k $\sqrt{3}$ then k = 4

Statement I is true and Statement II is false

Statement II is true and Statement I is false

Both are true

Both are false

25. Arrange the steps to find three rational numbers between $\frac{3}{5}$ and $\frac{2}{3}$

a : 3 + 1 = 4 and both are rational numbers multiply with $\frac{4}{4}$
b : $\frac{3}{5}$ = $\frac{3}{5} \times\frac{3}{3}$ = $\frac{9}{15}$ ; $\frac{2}{3}$ = $\frac{2}{3} \times\frac{5}{5}$ = $\frac{10}{15}$
c : L.C.M of 5 and 3 is 15
d : $\frac{3}{5}$ < $\frac{37}{60}$ < $\frac{38}{60}$ < $\frac{39}{60}$ < $\frac{2}{3}$

a , b , c , d

a , c , d , b

c , a , b , d

c , b , a , d

26. Arrange the steps to find $(46656)^{ \frac{-1}{6} }$

a : $[ (2 \times 3)^{6}^{ \frac{-1}{6} }]$
b : $6^{-1}$
c : $(2^{6} \times 3^{6})^{ \frac{-1}{6} }$
d : $\frac{1}{6}$

a , b , c , d

c , b , a , d

c , a , b , d

d , c , b , a

27. Arrange the steps to rationalize the denominator of $\frac{ \sqrt{6} }{ \sqrt{3} - \sqrt{2} }$
a : $\frac{ \sqrt{6} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{\sqrt{3} + \sqrt{2}}$
b : $\frac{ \sqrt{6} \times \sqrt{3} + \sqrt{6} \times \sqrt{2}}{3 - 2}$
c : The r.F of denominator is $\sqrt{3}$ + $\sqrt{2}$
d : $\sqrt{18}$ + $\sqrt{12}$ = 3 $\sqrt{2}$ + 2 $\sqrt{3}$

a , b , c , d

a , c , d , b

c , d , b , a

c , a , b , d

28. If $\frac{ \sqrt{3} + 1 }{2 - \sqrt{3} }$ = x + y $\sqrt{3}$ then x , y are

3 , 5

5 , 3

3 , 4

3 , 6

29. Which of the following rational numbers change into a terminating decimal ?

$\frac{7}{12}$

$\frac{5}{44}$

$\frac{13}{125}$

$\frac{2}{9}$

30. Assertion A : An irrational number between 3 and 4 is 2 $\sqrt{3}$
Reason R : If 'a' and 'b' are rational numbers then $\sqrt{ab}$ is an irrational number

A is correct , R is false

R is correct , A is false

Both are false

Both are true

31. Assertion A : $\sqrt{36}$ + $\sqrt{24}$ ; $\sqrt{49}$ - $\sqrt{87}$ ; 3 $\times \sqrt{6}$ are irrational numbers
Reason R : If 'q' is rational and 's' is irrational then q + s , q - s , qs (s $\neq$ 0 ) are rational numbers

A is correct , R is incorrect

R is correct , A is incorrect

Both A and R are correct but R is not correct explanation of A

Both A and R are correct but R correct explanation of A

32. Assertion A : The sum , difference , quotients and products of irrational numbers need nit be irrational numbers
Reason R : So irrational numbers are not closed with respect to addition , subtraction , multiplication , division

A is true and R is false

R is true and A is false

Both A and R are correct but R is correct explanation of A

Both A and R are correct but R is not correct explanation of A

33. Assertion A : The value of $\frac{1}{3 + \sqrt{2} }$ = $\frac{3 + \sqrt{2}}{7}$
Reason R : To rationalise the denominator of $\frac{1}{\sqrt{a} + b}$ , we multiply it by $\frac{ \sqrt{a} -b}{ \sqrt{a} -b }$

A is true and R is false

A is false and R is true

Both A and R are correct but R is not correct explanation of A

Both A and R are correct and R is correct explanation of A

34. Assertion : The rationalizing factor of a given irrational number is not unique
Reason R : The R.F s of $\sqrt{8}$ are $\sqrt{2}$ and $\sqrt{8}$

A is correct , R is not correct

R is correct , A is not correct

Both A and R are correct

Both A and R are false

35. Statement I : If A = 0.414141.......... , B = 0.414114111............. A is rational and B is irrational
Statement II : A rational number can be expressed as a terminating or non terminating recurring decimal

Statement I is true

Statement II is true

Both are correct

None

36. Which of these are not related ?

1.232323

0.123123

5.15161718

3,125612561256

37. Covert the rational number $\frac{3}{4}$ into decimal form

0.5

0.25

0.75

1.5

38. Covert the rational number $\frac{5}{3}$ into decimal form

1. $\overline{6}$

1. $\overline{7}$

1.6

1.7

39. The digit which are present in the recurring part are called

Periodicity

Period

Terminating

All

40. The number of digits present in the recurring part is called

Period

Periodicity

Terminating

None

41. Period of $\frac{7}{22}$

42. Periodicity of $\frac{1}{7}$

142856

43. Periodicity of $\frac{13}{44}$ is

0.2954

2954

44. Period and periodicity of $\frac{15}{7}$

6 , 142857

6 , 132857

6 , 142857

None

45. Find the correct statements

All real numbers are rational numbers

If A is rational and B is irrational then A+B is irrational

The rationalizing factor of $\frac{1}{a + b \sqrt{x} }$ is a - b $\sqrt{x}$

If A is rational and B is irrational then A+B is irrational and The rationalizing factor of $\frac{1}{a + b \sqrt{x} }$ is a - b $\sqrt{x}$

46. Find the odd one

a. All complex numbers are called imaginary numbers
b. All real numbers can be complex numbers
c. In 0.3 $\overline{75}$ the period is 75
d. $\sqrt{a}$ + $\sqrt{b}\neq\sqrt{a+b}$

47. P : $\sqrt[n]{ \sqrt[m]{( a^{p} )^{q}} }$ = $\sqrt[mn]{ a^{pq} }$
Q : The value of $\frac{ ( x^{a+b})^{2}.( x^{b+c})^{2}.( x^{c+a})^{2} }{ (x^{a} . x^{b} . x^{c})^{4} }$ = 1

P is true and Q is false

Q is true and P is false

Both are true

Both are fasle

48. Which of the following is not related ?

$\sqrt{6.25}$

$\sqrt{1.44}$

$\sqrt{4.25}$

$\sqrt{4.41}$

49. If $x^{x \sqrt{x} }$ = $(x\sqrt{x})^{x}$ then value of x is

$\frac{9}{4}$

$\frac{4}{9}$

$\frac{2}{9}$

$\frac{3}{2}$

50. The value of $\sqrt{3}$ is

1.414213

1.7320508

1.84070

2.43607

51. The value of 2.44949 ... is

$\sqrt{2}$

$\sqrt{3}$

$\sqrt{6}$

$\sqrt{7}$

52. The value of $\sqrt{7}$ is

2.4494

2.6457

2.23606

None

53. Which of the following is rational ?

$\sqrt{2}$

$\sqrt{3}$

$\sqrt{4}$

$\sqrt{5}$

54. Which of the following is not irrational number ?

$\sqrt{4}$

$\sqrt{9}$

$\sqrt{1}$

$\sqrt{6}$

55. Arrange the steps to represent $\sqrt{2}$ on number line
a. Take the measure of $\sqrt{2}$ drawn online number from Q and are intersecting the number line . "A" represents $\sqrt{2}$
b. Start with point 'O' and drawn a line segment $\overline{OP}$ of 1 unit length , on number line
c. Join OQ( $\overline{OQ}$ = $\sqrt{2}$ )
d. Draw a line segment $\overline{PQ}$ perpendicular to $\overline{OP}$ of unit length (where OP = PQ = 1)

a , b , c , d

b , d , a , c

b , d , c , a

d , c , b , a

56. Which of the following is not related ?

$\frac{2}{3}$

$\frac{3}{2}$

$\frac{5}{2}$

$\frac{7}{2}$

57. Name the above activity

Cube root spiral

Square root spiral

Both

None

58. The line segment $\overline{OQ}$ denotes the length of

$\sqrt{2}$

$\sqrt{3}$

$\sqrt{4}$

$\sqrt{1}$

59. Which line segment denotes the length of $\sqrt{3}$ ?

$\overline{OP}$

$\overline{OQ}$

$\overline{OR}$

$\overline{OS}$

60. The line segment $\overline{OS}$ denotes the length of

$\sqrt{2}$

$\sqrt{3}$

$\sqrt{4}$

All

61. The length of line segment $\overline{OS}$ denotes the value of number line is

62. The value of $\sqrt{3}$ on number line lies between

0 and 1

1 and 2

2 and 3

None

63. 7 can be expressed as

$\frac{7}{1}$

$\frac{14}{2}$

$\frac{21}{3}$

All

64. 10 can be expressed as

$\frac{10}{1}$

$\frac{20}{2}$

$\frac{30}{3}$

All

65. -4 can be expressed as

$\frac{-4}{1}$

$\frac{-8}{2}$

$\frac{-12}{3}$

All

66. The rational number between 2 and 3

$\frac{13}{6}$

$\frac{14}{6}$

$\frac{15}{6}$

All

67. Which of the following are not a rational number between $\frac{-3}{11}$ and $\frac{8}{11}$ ?

$\frac{6}{11}$

$\frac{7}{11}$

$\frac{-2}{11}$

$\frac{7}{12}$

68. Which of the following are non terminating recurring decimal ?

$\frac{1}{17}$

$\frac{1}{19}$

Both

None

69. Express the following rational number $\frac{243}{1000}$ into decimal number

0.243

0.123

0.242

1.345

70. Express the following rational number $\frac{354}{500}$ into decimal number

0.876

0.965

0.708

0.235

71. Express the following rational number $\frac{11}{9}$ into decimal number

1.2

1.3

1. $\overline{2}$

1. $\overline{3}$

72. Convert the following decimal number 0.36 into rational number

$\frac{8}{25}$

$\frac{7}{25}$

$\frac{5}{25}$

$\frac{9}{25}$

73. Convert the following decimal number 15.4 into rational number

$\frac{77}{5}$

$\frac{76}{25}$

$\frac{8}{5}$

$\frac{87}{25}$

74. Which of the following are terminating decimal ?

$\frac{3}{25}$

$\frac{13}{20}$

Both

$\frac{11}{18}$

75. Which of the following are non terminating decimals ?

$\frac{11}{18}$

$\frac{41}{42}$

Both

None

76. $\sqrt{2}$ is

Rational number

Terminating decimal

Non terminating decimal

None

77. $\sqrt{5}$ is not a rational number because

We can't written this in $\frac{p}{q}$

It is not an integer

Both

None

78. We say the rational number is non terminating when

The numerators are multiple of 5

The denominators have prime numbers

The denominators have prime numbers other than 2 and 5

None

79. Which of the following are irrational numbers ?

30.232342345 and 7.484848..

30.232342345 and $\sqrt{27}$

All

None

80. A number which cannot be written in the form of $\frac{p}{q}$ where p and q are integers and q $\neq$ 0 is called

Rational number

Irrational number

Both

None

81. How many irrational numbers are there in between $\frac{5}{7}$ and $\frac{7}{9}$ ?

Infinitely

82. 2.236 is value of

$\sqrt{3}$

$\sqrt{5}$

$\sqrt{7}$

$\sqrt{9}$

83. Find the false statement ?

Every irrational number is a real number

Every rational number is real number

Every real number is need not to be a rational number

All real numbers are irrational

84. The rationalizing factor of the denominators of $\frac{1}{2 \sqrt{3} }$ is

$\sqrt{5}$

$\sqrt{7}$

$\sqrt{9}$

$\sqrt{3}$

85. The rationalizing factor of the denominators of $\frac{3}{ \sqrt{5} }$ is

$\sqrt{3}$

$\sqrt{7}$

$\sqrt{5}$

$\sqrt{2}$

86. The value of $(16)^{ \frac{1}{2} }$

87. Write the surd $\sqrt[3]{9}$

$9^{ \frac{1}{3} }$

$20^{ \frac{1}{5} }$

$9^{ \frac{1}{2} }$

$5^{ \frac{1}{3} }$

88. Write the surd $\sqrt[5]{20}$

$20^{ \frac{1}{5} }$

$19^{ \frac{1}{5} }$

$19^{ \frac{1}{17} }$

$20^{ \frac{1}{15} }$

89. Write the exponential form $5^{ \frac{1}{7} }$

$\sqrt[6]{20}$

$\sqrt[5]{17}$

$\sqrt[5]{25}$

$\sqrt[7]{5}$

90. Write the exponential form $142^{ \frac{1}{2} }$

$\sqrt[1]{20}$

$\sqrt[6]{290}$

$\sqrt[4]{240}$

$\sqrt[1]{142}$

91. Which of the following are not a irrational number ?

5 - $\sqrt{3}$

$\sqrt{3}$ + $\sqrt{2}$

$( \sqrt{2} - 2)^{2}$

$\frac{2 \sqrt{7} }{7 \sqrt{7} }$

92. $\pi$ is

Rational number

Irrational number

Either rational number or irrational number

We can't say

93. Find the value of $\frac{ \sqrt{10} - \sqrt{5} }{2 \sqrt{2} }$ .( $\sqrt{3}$ = 1.732 , $\sqrt{5}$ = 2.236)

0.325

0.346

0.328

1.328

94. Find the value of $\frac{ \sqrt{10} - \sqrt{5} }{2 \sqrt{2} }$ .( $\sqrt{2}$ = 1.414 , $\sqrt{5}$ = 2.236)

0.325

0.346

0.328

1.328

95. ......... is a number or quantity that can not be expressed as ratio of two integers

Terminating decimal

Non terminating decimal

Recurring decimal

Surd

96. $\sqrt[n]{a}$ , here 'a' is

Radicand

Radical sign

Surd

None

97. $\sqrt[n]{a}$ , $\sqrt[n]{}$ is

Radicand

Surd

Radical sign

None

98. Which of the following are not a closed with rational numbers ?

Addition

Subtraction

Division

Multiplication

99. If the product of two irrational number is a rational number , then each of the two is the

Surd

Radicand

Rationalizing factor

Recurring factor

100. The collection of all rational numbers and irrational numbers are

Terminating decimal

Non terminating decimal

Surd

Real numbers

AP 9th Maths Mock Test 2023 for Chapter-1 “Real Numbers” Online Practice Test

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