AP 9th Maths Mock Test 2021 for Chapter-1 “Real Numbers” Online Practice Test

1. Which of the following decimal is terminating ?
2. Integers possess the following groups of numbers ______
3. When do we say that a number is a rational number ?
4. Which of the following are in case of rational numbers ?
5. Is there any integer exists between two successive integers ?
6. Is there any rational number exists between two successive rational numbers ?
7. The decimal expansion of rational numbers is in the form of
8. A number which cannot be written in the form of  \frac{p}{q} is called as
9. If x = 2 + \sqrt{3} then x+\frac{1}{x} =
10. If x^{2} + \frac{1}{ x^{2} } = 83 then x^{3} - \frac{1}{ x^{3} } =
11. If \frac{5 - \sqrt{3} }{2 + \sqrt{3} } = a + b \sqrt{3} then the value of 'a' and 'b' are
12. Which is an irrational number between \sqrt{2} and \sqrt{3} ?
13. The rational number for 0.\overline{5} is
14. If x= \sqrt{5} + 2 then the value of x - \frac{1}{x} is
15. Match the following
  1. 1.\overline{428577} ( ) p. \frac{35}{9}
  2. 0.\overline{36}         ( ) q. \frac{142}{45}
  3. 3.\overline{8}           ( ) r. \frac{10}{7}
  4. 3.12\overline{7}       ( ) s. \frac{4}{11}
 
16. Choose the correct option

17. Match the following
18. Match the following
19. If the product of two surds is a rational then each of two surds is called
20. R.F of \sqrt{108} is
21. R.F of \sqrt{75}  + \sqrt{32}  is
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
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} }
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
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}
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}
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}
28. If \frac{ \sqrt{3} + 1 }{2 - \sqrt{3} } = x + y\sqrt{3} then x , y are
29. Which of the following rational numbers change into a terminating decimal ?
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
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
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
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 }
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}
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
36. Which of these are not related ?
37. Covert the rational number \frac{3}{4} into decimal form
38. Covert the rational number\frac{5}{3} into decimal form
39. The digit which are present in the recurring part are called
40. The number of digits present in the recurring part is called
41. Period of \frac{7}{22}
42. Periodicity of \frac{1}{7}
43. Periodicity of \frac{13}{44} is
44. Period and periodicity of \frac{15}{7}
45. Find the correct statements
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
48. Which of the following is not related ?
49. If x^{x \sqrt{x} } = (x\sqrt{x})^{x} then value of x is
50. The value of \sqrt{3} is
51. The value of 2.44949 ... is
52. The value of \sqrt{7} is
53. Which of the following is rational ?
54. Which of the following is not irrational number ?
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)
56. Which of the following is not related ?
57. Name the above activity
58. The line segment \overline{OQ} denotes the length of
59. Which line segment denotes the length of \sqrt{3} ?
60. The line segment \overline{OS} denotes the length of
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
63. 7 can be expressed as
64. 10 can be expressed as
65. -4 can be expressed as
66. The rational number between 2 and 3
67. Which of the following are not a rational number between \frac{-3}{11} and \frac{8}{11} ?
68. Which of the following are non terminating recurring decimal ?
69. Express the following rational number \frac{243}{1000} into decimal number
70. Express the following rational number \frac{354}{500} into decimal number
71. Express the following rational number \frac{11}{9} into decimal number
72. Convert the following decimal number 0.36 into rational number
73. Convert the following decimal number 15.4 into rational number
74. Which of the following are terminating decimal ?
75. Which of the following are non terminating decimals ?
76. \sqrt{2} is
77. \sqrt{5} is not a rational number because
78. We say the rational number is non terminating when
79. Which of the following are irrational numbers ?
80. A number which cannot be written in the form of \frac{p}{q} where p and q are integers and q\neq0 is called
81. How many irrational numbers are there in between \frac{5}{7} and \frac{7}{9} ?
82. 2.236 is value of
83. Find the false statement ?
84. The rationalizing factor of the denominators of \frac{1}{2 \sqrt{3} } is
85. The rationalizing factor of the denominators of \frac{3}{ \sqrt{5} } is
86. The value of (16)^{ \frac{1}{2} }
87. Write the surd \sqrt[3]{9}
88. Write the surd \sqrt[5]{20}
89. Write the exponential form 5^{ \frac{1}{7} }
90. Write the exponential form 142^{ \frac{1}{2} }
91. Which of the following are not a irrational number ?
92. \pi is
93. Find the value of \frac{ \sqrt{10} - \sqrt{5} }{2 \sqrt{2} }.(\sqrt{3} = 1.732 , \sqrt{5} = 2.236)
94. Find the value of \frac{ \sqrt{10} - \sqrt{5} }{2 \sqrt{2} }.(\sqrt{2} = 1.414 , \sqrt{5} = 2.236)
95. ......... is a number or quantity that can not be expressed as ratio of two integers
96. \sqrt[n]{a} , here 'a' is
97. \sqrt[n]{a} , \sqrt[n]{} is
98. Which of the following are not a closed with rational numbers ?
99. If the product of two  irrational number is a rational number , then each of the two is the
100. The collection of all rational numbers and irrational numbers are

 

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