We provide number systems practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on number systems skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of number systems Questions

Question No | Questions | Class |
---|---|---|

1 | Simplify and express with positive zponents ( left[left(frac{mathbf{9}}{mathbf{1 1}}right)^{-mathbf{3}} timesleft(frac{mathbf{9}}{mathbf{1 1}}right)^{-mathbf{7}}right] div ) ( left(frac{9}{11}right)^{-3} ) | 9 |

2 | Which of the following is a rational number? ( mathbf{A} cdot 3^{29 / 27} .3^{27 / 29} ) B ( cdot sqrt[6]{left(3^{50 / 51} .3^{52 / 51}right)^{3}} ) ( mathbf{c} cdot 3^{15 / 6}-3^{7 / 8} ) D. ( sqrt[15]{left(3^{3}right)^{1 / 5}} ) | 9 |

3 | Represent on number line ( frac{1}{6} ) | 9 |

4 | Classify the result as rational or irrationals. ( (3+sqrt{23})-sqrt{23} ) A. Rational number B. Irrational number c. Data Insufficient D. None of the above | 9 |

5 | Draw the number line and represent the following rational number on it: ( frac{-5}{8} ) | 9 |

6 | Which of the following statements is true? A ( cdot frac{-5}{8} ) lies to the left of 0 on the number line B. ( frac{3}{7} ) lies to the right of 0 on the number line. C the rational numbers ( frac{1}{3} ) and ( frac{-7}{3} ) are on opposite sides of 0 on the number line D. All the above | 9 |

7 | Is zero a rational number? Can you write it in the form ( frac{p}{q}, ) where ( p ) and ( q ) are integers and ( boldsymbol{q} neq mathbf{0} ? ) | 9 |

8 | Find: (i) ( 9^{frac{3}{2}} ) (ii) ( 32^{frac{2}{5}} ) (iii) ( 16^{frac{3}{4}} ) (iv) ( 125^{frac{-1}{3}} ) | 9 |

9 | A rational number ( frac{-2}{3} ) A. Lies to the left side of 0 on the number line. B. Lies to the right side of 0 on the number line. C. Is not possible to represent on the number line. D. None of these. | 9 |

10 | State True or False. A rational number can always be written in what as a fraction ( frac{a}{b}, ) where a and b are not integers ( (boldsymbol{b} neq mathbf{0}) ) A. True B. False | 9 |

11 | Is zero a rational number? Justify | 9 |

12 | Express ( 0 . overline{38} ) as a rational number in simplest form. | 9 |

13 | n exponential form ( 729=3^{a}, ) what is the value of ( a ? ) | 9 |

14 | Mark the following rational numbers on number line. ( frac{-8}{3} ) | 9 |

15 | Rewrite the following rational numbers in the simplest form: ( frac{25}{45} ) | 9 |

16 | By what number should ( left(frac{-2}{3}right)^{-3} ) be divided so that the quotient may be ( left(frac{4}{27}right)^{-2} ) | 9 |

17 | 52. Arranging the following in de- scending order, we get 44, 12, 93, 45 (1) 14 > 45>2 > 3 (2) 15 > 14 > 3 > V2 (3) V2 > 3 > 4 > 45 (4) 03 > 45 > 34 > 2 | 9 |

18 | Find the value of ( (27)^{-frac{2}{3}}+ ) ( left(left(2^{-frac{2}{3}}right)^{-frac{5}{3}}right)^{-frac{9}{10}} ) A ( cdot frac{1}{9} ) B. ( frac{2}{9} ) c. ( frac{11}{18} ) ( D ) | 9 |

19 | The number of rational numbers between two given rational numbers is A . Infinite B. Finite c. Two D. one | 9 |

20 | ( left[5left{left(frac{1}{8}right)^{frac{-1}{3}}+left(frac{1}{27}right)^{frac{-1}{3}}right}right]^{frac{1}{2}} ) ( mathbf{A} cdot 5 ) B. ( sqrt{13} ) ( mathbf{c} .25 ) D. 13 | 9 |

21 | If ( 10^{4 x}=625 ) then find the value of ( 10^{-x} ) | 9 |

22 | Evaluate: ( frac{1}{(216)^{frac{-2}{3}}} div frac{1}{(27)^{frac{-4}{3}}} ) is equal to ( frac{4}{m} ) value of ( m ) is | 9 |

23 | Solve and find the value of ( x ) ( mathbf{2}^{boldsymbol{x}-mathbf{5}}=mathbf{2 5 6} ) | 9 |

24 | Is this a negative rational number? ( frac{-2}{-9} ) | 9 |

25 | 52. Arranging the following in de- scending order, we get 34, 12, 93, 45 (1) 4 > 45 > 2> 93 (2) 45 > 4> 93> (3) V2> 93 > 34 > 45 (4) 93 > 45 > 34 > | 9 |

26 | If ( boldsymbol{x}=mathbf{3} ) and ( boldsymbol{y}=-mathbf{2}, ) the value of ( boldsymbol{x}^{boldsymbol{x}}+ ) ( boldsymbol{y}^{boldsymbol{y}} ? ) A . 27 B. 9 c. 8 D. none of the above | 9 |

27 | ( left(frac{1}{64}right)^{0}+(64)^{frac{-1}{2}}+(32)^{frac{4}{5}}-(32)^{frac{-4}{5}} ) is equal to A ( cdot_{16} frac{1}{8} ) в. ( 17 frac{1}{8} ) c. ( _{17} frac{1}{16} ) D. ( -17 frac{1}{16} ) | 9 |

28 | The number 0 is not the reciprocal of any number. A. True B. False c. Ambiguous. D. None | 9 |

29 | The values of ( A ) and ( B ) represented on the number line are begin{tabular}{cccccccccc} hline & & & & & & & & & \ ( frac{-6}{1} ) & ( frac{-5}{1} ) & ( frac{-4}{1} ) & ( frac{-3}{mathrm{A}} ) & ( frac{-2}{1} ) & ( frac{-1}{1} ) & ( frac{0}{1} ) & ( frac{1}{mathrm{B}} ) & ( frac{2}{1} ) & ( frac{3}{1} ) end{tabular} A . 1,1 B. -1,1 ( c cdot 1,-1 ) D. -1,-1 | 9 |

30 | Fill in the blank: The quotient when a rational number is divided by its additive inverse is | 9 |

31 | Solve : ( left(14 x^{3} times 2 x^{4} times 8 x^{8}right) div 7 x^{3} ) | 9 |

32 | Find the value of ( left(x^{3} times x^{7}right) div x^{12} ) for ( x= ) (-2) | 9 |

33 | Given: ( left(frac{1}{2^{3}}right)^{2}=frac{1}{2^{m}} . ) The value of ( m ) is | 9 |

34 | Are the following statements true or false? Given reasons for your answer. Every rational number is a whole number. A. True B. False | 9 |

35 | Solve ( left[left(frac{-2}{3}right)^{4} timesleft(frac{-2}{3}right)^{2} divleft(frac{4}{9}right)^{3}right] ) | 9 |

36 | Express each of the following exponential expressions as a rational number. ( left(frac{2}{3}right)^{(-1)}+left(frac{3}{2}right)^{(-2)} ) | 9 |

37 | There exists …….. number of rational numbers between ( frac{2}{5} ) and ( frac{4}{5} ) A. 0 B. 1 c. 5 D. infinite | 9 |

38 | Rationalising the denominator of ( frac{5}{sqrt{3}-sqrt{5}} ) is – A ( cdotleft(frac{5}{2}(sqrt{3}+sqrt{5})right. ) B ( cdotleft(-frac{5}{2}(sqrt{3}+sqrt{5})right. ) c. ( left(frac{5}{2}(sqrt{3}-sqrt{5})right. ) D ( cdotleft(-frac{5}{2}(sqrt{3}-sqrt{5})right. ) | 9 |

39 | Simplify: ( 2^{2} times frac{3^{2}}{2^{-2}} times 3^{-1} ) | 9 |

40 | State, whether the following number is rational, If rational then enter 1 and if false then | 9 |

41 | There are ………… rational numbers between two rational numbers. A . infinite B. two c. one D. none of these | 9 |

42 | Is ( frac{mathbf{6 3}}{mathbf{9 0}} ) a terminating rational number? Justify. | 9 |

43 | Simplify the following using laws of exponents. ( left(3^{2}right) timesleft(3^{2}right)^{4} ) | 9 |

44 | Mark the following rational numbers on the number line. ( frac{3}{2} ) | 9 |

45 | Find any two rational numbers between ( frac{-1}{2} ) and ( frac{-2}{3} ) | 9 |

46 | ( frac{5}{7}+frac{4}{7}-frac{3}{7} ) is equal to A ( cdot frac{3}{7} ) B. ( frac{5}{7} ) ( c cdot frac{6}{7} ) D. ( frac{12}{7} ) | 9 |

47 | Find 9 rational numbers between 2 and 3 ( mathbf{A} cdot 2<2.1<2.2<3.3<2.4<ldots<2.9<3 ) B . ( 2<4.1<2.2<2.3<2.4<ldots<2.9<3 ) c. ( 2<2.1<2.2<2.3<2.4<ldots<2.9<3 ) D. ( 2<2.1<2.2<2.3<2.4<ldots<0.9<3 ) | 9 |

48 | ( sqrt{9} ) is a rational number. It is equal to A . 4.5 B. 3 ( c cdot 27 ) D. 18 | 9 |

49 | Find the value of ( x ) if ( 2^{4} times 2^{5}=left(2^{3}right)^{x} ) | 9 |

50 | Find the value of i) ( 2^{6} ) ii) ( 9^{3} ) iii) ( 11^{2} ) | 9 |

51 | Find the value of ( m ) for which ( 5^{m} div ) ( 5^{-3}=5^{5} ) | 9 |

52 | Find the five rational numbers between ( frac{1}{6} ) and ( frac{1}{3} ) | 9 |

53 | Find whether the following statement are true or false. In a rational number of the form ( frac{boldsymbol{p}}{boldsymbol{q}}, boldsymbol{q} ) must be a non zero integer. A. True B. False | 9 |

54 | Find two rational and two irrational number between 2 and 5 | 9 |

55 | Convert in ( frac{boldsymbol{p}}{boldsymbol{q}} ) form: (i) ( 0 . overline{47} ) (ii) ( 0 . overline{001} ) (iii) ( 0 . overline{9} ) (iv) ( 2.3 overline{5} ) | 9 |

56 | Represent ( -frac{7}{5} ) on no line | 9 |

57 | ( 4^{3.5}: 2^{5} ) is the same as | 9 |

58 | The rational number lying between the numbers ( frac{1}{3} ) and ( frac{3}{4} ) are A. ( frac{97}{300}, frac{299}{500} ) в. ( frac{99}{300}, frac{301}{400} ) c. ( frac{95}{300}, frac{301}{400} ) D. ( frac{117}{300}, frac{287}{400} ) | 9 |

59 | Find the value of following ( (625)^{frac{-3}{4}} ) | 9 |

60 | If ( 2^{x}-2^{x-1}=4, ) then what is the value of ( 2^{x}+2^{x-1} ? ) A . 8 B. 12 c. 10 D. 16 | 9 |

61 | Assertion 2 is a rational number. Reason The square roots of all positive integers are irrationals. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 9 |

62 | Find the 12 rational number between -1 and ( 2 ? ) | 9 |

63 | Which of the following number lines represents only natural numbers? ( A ) ( begin{array}{lllllllllll}nwarrow & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \ 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10end{array} ) B. ( c ) D. ( frac{1}{10} frac{2}{10} frac{3}{10} frac{4}{10} frac{5}{10} frac{6}{10} frac{7}{10} frac{8}{10} frac{9}{10} frac{10}{10} ) | 9 |

64 | Write 5 rational number between ( frac{2}{5} ) and ( frac{3}{5}, ) having the same denominators | 9 |

65 | Find the value of ( x ) for which ( left(frac{4}{9}right)^{x} times ) ( left(frac{4}{9}right)^{-7}=left(frac{4}{9}right)^{2 x+1} ) | 9 |

66 | The value of ( (-3)^{0}-(-3)^{3}- ) ( (-3)^{-1}+(-3)^{4}-(-3)^{-2} ) is A ( cdot_{109} frac{2}{9} ) в. ( _{109} frac{9}{2} ) ( c .109 ) D. None of these | 9 |

67 | Find two rational numbers between ( frac{-3}{4} ) and ( frac{1}{2} ) | 9 |

68 | Which of the following are not rational? This question has multiple correct options A ( cdot frac{2}{sqrt{3}} ) B. ( sqrt{16} ) ( c . pi ) D. ( 2+sqrt{25} ) | 9 |

69 | If ( 25^{x+1}=frac{125}{5^{x}}: ) then the value of ( x ) is 1 ( bar{m} ) Value of ( m ) is A .2 B. 4 ( c cdot 3 ) D. none of the above | 9 |

70 | Classify the following number as rational or irrational – (i) ( 2-sqrt{5} ) (ii) ( (3+sqrt{23})-sqrt{23} ) (iii) ( frac{2 sqrt{7}}{7 sqrt{7}} ) (iv) ( frac{1}{sqrt{2}} ) (v) ( 2 pi ) | 9 |

71 | Find 4 rational numbers between ( frac{1}{6} ) and ( frac{3}{8} ) | 9 |

72 | Represent on number line ( frac{3}{7} ) | 9 |

73 | State True or False. The five rational numbers between ( frac{3}{5} ) and ( frac{4}{5} ) are ( frac{19}{30}, frac{20}{30}, frac{21}{30}, frac{22}{30}, frac{23}{30} ) A. True B. False | 9 |

74 | The value of ( left(8^{-25}-8^{-26}right) ) is A ( cdot 7 times 8^{-25} ) В. ( 7 times 8^{-26} ) c. ( 8 times 8^{-26} ) D. None of these | 9 |

75 | Represent on number line ( frac{mathbf{3}}{mathbf{4}} ) | 9 |

76 | Insert three rational numbers between ( frac{2}{3} ) and ( frac{3}{5} ) | 9 |

77 | Simplify ( frac{1}{177} cdot 11 frac{1}{17} ) | 9 |

78 | ff ( 4^{x+3}=112+8 times 4^{x} ); find the value of ( (18 x)^{3 x} ) | 9 |

79 | If ( sqrt{sqrt{mathbf{2 5 0 0}}+sqrt{mathbf{9 6 1}}}=(x)^{2}, ) then ( boldsymbol{x} ) equals ( mathbf{A} cdot 81 ) в. c. 6561 ( D ) | 9 |

80 | A rational number can be expressed as a terminating decimal if the denominator has factors: ( A cdot 2 ) or 5 в. 2,3 от 5 c. 3 or 5 D. None of these | 9 |

81 | Mark the following rational numbers on the number line. ( frac{1}{2} ) | 9 |

82 | State true or false: ( left(frac{2}{3}right)^{4} divleft(frac{2}{3}right)^{6}=left(frac{2}{3}right)^{2} ) A. True B. False c. Ambiuous D. Data insufficient | 9 |

83 | Simpify and express following as a rational number: ( left(frac{3}{4}right)^{2} timesleft(frac{-1}{2}right)^{5} times 2^{3} ) | 9 |

84 | Draw the number line and represent the following rational numbers on it: ( frac{-5}{8} ) | 9 |

85 | Following are the five rational numbers which are smaller than ( 2 Rightarrow ) ( 1, frac{1}{2}, 0,-1, frac{-1}{2} ) If true then enter 1 and if false then enter ( mathbf{0} ) | 9 |

86 | The product of ( x^{1 / 2} cdot x^{1 / 4} cdot x^{1 / 8} dots infty ) equals ( mathbf{A} cdot mathbf{0} ) B. c. ( x ) ( D cdot infty ) | 9 |

87 | Write a rational number between 7 and 87 | 9 |

88 | Which of the following rational number lies between ( frac{4}{9} ) and ( frac{4}{5} ? ) A. -1 в. ( frac{28}{45} ) c. 0 ( D ) | 9 |

89 | How many rational numbers are there between ( -frac{3}{2} ) and 0 with denominator as 1? | 9 |

90 | Draw the number line and represent the following rational numbers on it: ( frac{3}{4} ) | 9 |

91 | ( f(-4)^{-2} ) is ( frac{1}{m}, ) then the value of ( m ) is | 9 |

92 | Which of the following numbers lies between ( 2 frac{1}{7} ) and ( 3 frac{1}{7} ? ) A ( frac{37}{7} ) B. ( frac{14}{7} ) ( c cdot frac{37}{14} ) D. 2 | 9 |

93 | ( frac{3^{x} times 3}{3^{2 x-2}}=9^{-2}, ) find ( x ) | 9 |

94 | Draw number lines and locate the points on them: ( frac{2}{5}, frac{3}{5}, frac{8}{5}, frac{4}{5} ) | 9 |

95 | If we divide a positive integer by another positive integer, what is the resulting number? A. Always a natural number B. Always an integer c. A rational number D. An irrational number | 9 |

96 | ( f frac{4 a b^{2}left(-5 a b^{3}right)}{10 a^{2} b^{2}}=-K b^{3} ) then value of ( boldsymbol{K} ) is | 9 |

97 | ( frac{2^{n+4}-2 times 2^{n}}{2 times 2^{n+3}}+2^{-3}=? ) ( mathbf{A} cdot mathbf{1} ) B. 2 ( c cdot frac{1}{2} ) D. | 9 |

98 | Simplify. ( frac{25 times t^{-4}}{5^{-3} times 10 times t^{-8}}(t neq 0) ) is ( frac{m t^{4}}{2} ) The value of ( m ) is | 9 |

99 | Represent on number line ( frac{2}{3} ) | 9 |

100 | Simplify and give reasons: ( (-2)^{7} ) ( mathbf{A} cdot-128 ) в. 128 ( c cdot-28 ) D. None of these | 9 |

101 | 54. Among the following num- bers 512, 34, 45, 73 the least one is : (1) C12 (2) 44 (3) 45 (4) 13 | 9 |

102 | Find whether the following statements are true or false. ( pi ) is an irrational number. A. True B. False | 9 |

103 | Write ( frac{120 m^{2} n^{-3}}{60 m^{5} n^{-2}} ) in simplest form using only positive exponents. Assume that ( m neq 0 ) and ( n neq 0 ) A ( cdot frac{2 n}{m^{3}} ) в. ( frac{2}{m^{3} n} ) c. ( frac{2 m^{3}}{n} ) D. ( frac{1}{2 m^{3} n} ) | 9 |

104 | Find the value of ( x ) if ( x^{3}=left(frac{6}{5}right)^{-3} x ) ( left(frac{6}{5}right)^{6} ) | 9 |

105 | Which are two rational number between ( frac{6}{5} ) and ( frac{7}{5} ) | 9 |

106 | Write three rational numbers that lie between the two given numbers. ( frac{7}{9},-frac{5}{9} ) | 9 |

107 | Zero is a rational number. if true then enter 1 and if false then enter 0 | 9 |

108 | Which of the following rational numbers is in the standard form? A ( -frac{8}{-36} ) в. ( frac{-7}{56} ) c. ( frac{3}{-4} ) D. None | 9 |

109 | Find five rational numbers between ( frac{2}{3} ) and ( frac{mathbf{3}}{mathbf{5}} ) | 9 |

110 | If ( sqrt{9^{x}}=sqrt[3]{9^{2}}, ) then ( x= ) A ( cdot frac{2}{3} ) B. ( frac{4}{3} ) ( c cdot frac{1}{3} ) D. | 9 |

111 | Mark the following rational numbers on the number line. ( frac{10}{3} ) | 9 |

112 | The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational and of the from ( frac{p}{q}, ) what can you say about the prime factors of ( q ? ) ¡) 43.123456789 | 9 |

113 | Which of the following statement is true about a rational number ( frac{-2}{3} ? ) A . It lies to the left side of ( ^{prime} 0^{prime} ) on the number line B. It lies to the right side of ‘ ( 0^{prime} ) on the number line c. It is not possible to represent on the number line. D. It cannot be determined on which side the number lies | 9 |

114 | Find the value of ( m ) for which (i) ( 5^{m} div 5^{-3}=5^{5} ) (ii) ( 4^{m}=64 ) (iii) ( 8^{m-3}=1 ) (iv) ( left(a^{3}right)^{m}=a^{9} ) (v) ( left(5^{m}right)^{2} times(25)^{3} times 125^{2}=1 ) ( (mathrm{vi}) 2^{m}=(8)^{frac{1}{3}} divleft(2^{3}right)^{2 / 3} ) | 9 |

115 | Zero can be written in the form of ( frac{boldsymbol{p}}{boldsymbol{q}} ) where p and q are integers and ( mathrm{q} neq 0 ? ) If above statement is true then enter 1 and if false then enter 0 | 9 |

116 | Find the value of: (i) ( left(3^{0}+4^{-1}right) times 2^{2} ) (ii) ( left(2^{-1} times 4^{-1}right) div 2^{-2} ) (iii) ( left(frac{1}{2}right)^{-2}+left(frac{1}{3}right)^{-2}+left(frac{1}{4}right)^{-2} ) (iv) ( left(3^{-1}+4^{-1}+5^{-1}right)^{0} ) ( (v)left[left(frac{-2}{3}right)^{-2}right]^{2} ) ( (v i) 7^{-20}-7^{-21} ) | 9 |

117 | The exponential form of 512 is ( 2^{k} ) then value of ( k ) is | 9 |

118 | Out of the following numbers, which cannot be represented on a number line? ( mathbf{0}, frac{mathbf{5}}{6}, 1, frac{2}{4} ) ( mathbf{A} cdot mathbf{0} ) в. ( frac{5}{6} ) c. 1 D. None of these | 9 |

119 | By expressing the following in the form ( frac{p}{q}, ) where ( p ) and ( q ) are integers and ( q neq ) ( mathbf{0} ) 0.2 is equal to ( frac{1}{m}, ) Find the value of ( m ) | 9 |

120 | Identify the rational numbers represented by ( mathrm{B}, mathrm{C} ) and ( mathrm{D} ) if ( mathrm{AB}=mathrm{CD}=mathrm{DE} ) as drawn on the number line. [ begin{array}{|c|c|c|} hline E D & C & A \ hline-2 & 0 & 2 \ hline end{array} ] A. 0,-1,-2 в. [ frac{-1}{2},-1, frac{-3}{2} ] c. [ frac{1}{2}, 1, frac{3}{2} ] D. [ frac{-1}{4},-1, frac{-5}{2} ] | 9 |

121 | List five rational numbers between: ( frac{-4}{5} ) and ( frac{-2}{3} ) | 9 |

122 | ( frac{1}{text { The vaue of } 13} frac{1}{5} .17^{frac{1}{5}}-(221)^{frac{1}{5}} ) is | 9 |

123 | Give four rational numbers equivalent to: ( frac{mathbf{5}}{-3} ) | 9 |

124 | State whether the following statement is true or false. The rational numbers are whole numbers, fractions, mixed numbers, and decimals, together with their negative images. A. True B. False | 9 |

125 | Find the value of ( x ) in the number line. [ begin{array}{ccc} 1 & 1 & 1 & 1 \ 0 & sqrt{x} & 6 end{array} ] | 9 |

126 | If ( a b c=1, ) then ( frac{1}{1+a+b^{-1}}+ ) ( frac{1}{1+b+c^{-1}}+frac{1}{1+c+a^{-1}} ) is equal to ( A ) B. 0 ( c ) D. – 5 | 9 |

127 | Mark the following rational numbers on the number line. ( frac{3}{4} ) | 9 |

128 | Does the following pairs represent the same rational number: ( frac{-7}{21} ) and ( frac{3}{9} ) | 9 |

129 | Explain the density of rational numbers with examples. | 9 |

130 | Simplify and give reasons: ( (-3)^{-4} ) ( ^{A} cdot frac{1}{81} ) в. ( frac{-1}{81} ) c. ( frac{3}{81} ) D. None of these | 9 |

131 | The rational number lying exactly in between the numbers ( frac{1}{5} ) and ( frac{1}{3} ) is A ( cdot frac{1}{2} ) в. c. ( frac{2}{15} ) D. ( frac{4}{15} ) E. ( frac{8}{15} ) | 9 |

132 | If ( frac{mathbf{9}^{n} times mathbf{3}^{5} times(mathbf{2 7})^{mathbf{3}}}{mathbf{3} times(mathbf{8 1})^{4}}=mathbf{2 7}, ) then the value of ( n ) is ( mathbf{A} cdot mathbf{0} ) B . 2 ( c cdot 3 ) D. | 9 |

133 | Solve ( 17^{2} cdot 17^{-5} ) | 9 |

134 | Find any two rational numbers ( frac{1}{4} ) and ( frac{3}{4} ) | 9 |

135 | Rational numbers on the number line represented by ( boldsymbol{A}, boldsymbol{E} ) and ( boldsymbol{H} ) ( operatorname{are} boldsymbol{A}=frac{mathbf{1}}{mathbf{1 0}}, boldsymbol{E}=frac{mathbf{5}}{mathbf{1 0}}, boldsymbol{H}=frac{mathbf{8}}{mathbf{1 0}} . ) Are the values correct? A. Yes B. No c. cannot be determined D. None | 9 |

136 | Rewrite the following rational numbers in the simplest form: ( frac{-44}{72} ) | 9 |

137 | 13. 2 4 .5 6 1546-56-28 + 2 =? 1 11 (2) – 5 (3) 3 + 2 (4),3-5 | 9 |

138 | Is this a negative rational number? ( frac{6}{11} ) | 9 |

139 | Evaluate: ( [sqrt[3]{sqrt[6]{5^{9}}}]^{4}[sqrt[6]{sqrt[3]{5^{9}}}]^{4} ) ( A cdot 5^{2} ) в. ( 5^{4} ) ( c cdot 5^{8} ) D. ( 5^{12} ) | 9 |

140 | ( (-3)^{-2}=frac{1}{k} ) then value of ( k ) is | 9 |

141 | Find the nine rational numbers between 0 and 1 A. ( 0.1,0.2,0.3, ldots, 0.9 ) в. ( 1.1,0.2,10.3, ldots, 0.9 ) c. ( 0.1,0.2,0.3, ldots, 20.9 ) D. ( 0.1,0.2,10.3, ldots, 0.9 ) | 9 |

142 | State whether the statement is true/false. 8 can be written as a rational number with any integer as denominator. A. True B. False | 9 |

143 | State whether the following number is rational, If rational then enter 1 and if false then | 9 |

144 | Is this a negative rational number? ( frac{-2}{3} ) | 9 |

145 | Which of the following numbers are rational? ( mathbf{A} cdot mathbf{1} ) B. – 6 ( c cdot_{3} frac{1}{2} ) D. All above are rationa | 9 |

146 | State true or false: Rational number from following real numbers ( -8.0, sqrt{5}, frac{5}{7},-sqrt{18}, sqrt{32}, 4.28, pi, 3, frac{8}{15} ) ( operatorname{are}-8.0 . frac{5}{7}, 4.28,3, frac{8}{15}, 0.075 ) A. True B. False | 9 |

147 | The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational or not. If they are rational, and of them ( frac{p}{q}, ) what can you say about the prime factors of ( q ) ( ? ) ¡) 43.123456789 ¡i) 0.120120012000120000…. iii) ( 43 . overline{123456789} ) | 9 |

148 | Evaluate ( (sqrt{3}+sqrt{2})^{6}-(sqrt{3}+sqrt{2})^{6} ? ) | 9 |

149 | State whether the following number is rational, If rational then enter 1 and if false then enter 0 ( (2+sqrt{2})^{2} ) | 9 |

150 | Fill in the blanks so as to make the statement true: Two rational numbers with different | 9 |

151 | All rational numbers are real numbers. A . True B. False | 9 |

152 | List five rational numbers between: ¡) -1 and 0 ii) -2 and -1 | 9 |

153 | Express in the simplest form. ( sqrt{frac{mathbf{1 7 5}}{mathbf{2 7}}} ) A. ( -frac{5}{3} sqrt{frac{7}{3}} ) в. ( frac{5}{3} sqrt{frac{7}{3}} ) c. ( frac{5}{3} sqrt{frac{1}{3}} ) D. Not possible | 9 |

154 | Between two rational numbers, there exists- A. No rational number B. Only one rational number c. Infinite numbers of rational numbers D. No irrational number | 9 |

155 | Solved: ( 65536=4^{n-1} ) | 9 |

156 | Find four rational numbers between ( frac{3}{5} ) and ( frac{4}{5} ) | 9 |

157 | Simplify: ( frac{8^{-1} times 5^{3}}{2^{-4}} ) | 9 |

158 | Evaluate : ( left(frac{5}{3}right)^{x} cdotleft(frac{9}{25}right)^{x^{2}+2 x-11}= ) ( left(frac{5}{3}right)^{9} ) | 9 |

159 | ( sqrt[3]{frac{54}{250}} ) equals: A ( cdot frac{9}{25} ) B. ( frac{3}{5} ) c. ( frac{27}{125} ) D. ( frac{sqrt[3]{2}}{5} ) | 9 |

160 | Find the value of the following: ( left(frac{3}{8}right)^{5} timesleft(frac{3}{8}right)^{4} divleft(frac{3}{8}right)^{9} ) | 9 |

161 | Prove that ( frac{left(boldsymbol{a}^{boldsymbol{p}+boldsymbol{q}}right)^{2}left(boldsymbol{a}^{boldsymbol{q}+boldsymbol{r}}right)^{2}left(boldsymbol{a}^{boldsymbol{r}+boldsymbol{p}}right)^{mathbf{2}}}{left(boldsymbol{a}^{boldsymbol{p}} cdot boldsymbol{a}^{boldsymbol{q}} boldsymbol{a}^{boldsymbol{r}}right)^{boldsymbol{4}}}=mathbf{1} ) | 9 |

162 | Write five rational numbers greater than -2 | 9 |

163 | Given ( 2^{-3} times(-7)^{-3}=-frac{1}{m} ) Value of ( m ) is | 9 |

164 | On the real number line below, numbers increase in value from left to right. If ( B>0, ) then the value of ( A ) must be: A. Negative B. Positive c. Less than ( B ) D. Greater than ( B ) E. Between 0 and ( B ) | 9 |

165 | Solve: ( x^{11} div x^{15} ) | 9 |

166 | Write the rational numbers which are smaller than 2 | 9 |

167 | 5 is a rational number. It can be written as A ( cdot frac{5}{1} ) B. ( frac{1}{5} ) ( c cdot frac{5}{5} ) D. ( frac{5}{25} ) | 9 |

168 | The rational number, which equals the number 2.357 with recurring decimal is (1983 – 1 Mark) (a) 2355 (b) 2379 (c) 2355 1001 (0) 907 (C) 000 (d) none of these | 9 |

169 | Simplification of ( left(frac{3}{5}right)^{3} timesleft(frac{15}{2}right)^{3} ) is ( frac{729}{8} ) A. True B. False | 9 |

170 | State where ( (sqrt{6}+sqrt{9}) ) is rational or not | 9 |

171 | The points ( P, Q, R, S, T, U, A ) and ( B ) on the number line are such that ( boldsymbol{T} boldsymbol{R}= ) ( boldsymbol{R S}=boldsymbol{S U} ) and ( boldsymbol{A P}=boldsymbol{P Q}=boldsymbol{Q B} . ) Name the rational numbers represented by ( boldsymbol{P}, boldsymbol{Q}, boldsymbol{R}, boldsymbol{S} ) | 9 |

172 | State true or false: If ( a^{x}=b, b^{y}=c ) and ( c^{z}=a, ) then ( x y z= ) 1 A. True B. False | 9 |

173 | Simplify: ( 3^{0}+2^{-2} ) | 9 |

174 | If ( 3^{n-2}=frac{1}{81}, n= ) A . B. ( c cdot 2 ) D. – E. -4 | 9 |

175 | Find ( boldsymbol{a}^{3} ) if ( left(frac{2}{mathbf{7}}right)^{boldsymbol{a}}=left(frac{mathbf{1 6}}{mathbf{2 1}}right)^{-mathbf{5}} timesleft(frac{mathbf{3}}{mathbf{8}}right)^{-5} ) | 9 |

176 | State the following statement is True or False The reciprocal of 0 lie on the real line. | 9 |

177 | Write the following rational numbers in ascending order: ( frac{-3}{7}, frac{-3}{2}, frac{-3}{4} ) | 9 |

178 | Which number is represented by ( A ), in the following number line? A . 13 в. ( frac{6}{13} ) c. 6 D. ( frac{0}{13} ) | 9 |

179 | 68. If p-S and q = 3. then p + q- pq will be equal to 43 | 9 |

180 | What can you say about the prime factorisations of the denominators of the following rationals: (i) 43.123456789 (ii) ( 43 . overline{123456789} ) (iii) ( mathbf{2 7} mathbf{.} overline{mathbf{1 4 2} mathbf{8 5 7}} ) (iv) 0.120120012000120000 | 9 |

181 | Represented ( frac{-3}{4} & frac{1}{8} ) on the number line | 9 |

182 | Find the rational numbers ( a ) and ( b ) ( frac{sqrt{5}+sqrt{3}}{sqrt{5}-sqrt{3}}=a-sqrt{15} b ) | 9 |

183 | Express in terms of bases to the power of exponenets ( 8.9^{2} ) | 9 |

184 | Simplify:( 2 times(9)^{frac{3}{2}} times(9)^{frac{-1}{2}} ) | 9 |

185 | State true or false: If ( 4^{2 x}=frac{1}{32}, ) then the value of ( x ) is ( -frac{5}{4} ) A. True B. False | 9 |

186 | State whether true or false. ( frac{5}{11} ) is an irrational number. A. True B. False | 9 |

187 | 01 Lese. 12 The expression 3+ 55+25 is equal to (1980) (2) 1- √5 + √2 + √10 (6) 1+ √5 + √2-10 o 1+ √5 – √2 + √10 (d) 1- √5-√2+ To at the correct alternative in each ofthef.11 | 9 |

188 | Represent the following rational numbers on the number line: ( frac{-8}{5} ; frac{3}{8} ; frac{2}{7} ; frac{12}{5} ; frac{45}{13} ) | 9 |

189 | Find the product. ( left(a^{2}right)left(2 a^{22}right)left(4 a^{26}right) ) ( mathbf{A} cdot 8 a^{40} ) B. ( 8 a^{50} ) ( c cdot 8 a^{30} ) D. ( 8^{20} ) | 9 |

190 | f ( 2^{x+1}=3^{1-x} ) then find the value of ( x ) | 9 |

191 | Simplify : ( frac{left(2^{4}right)^{2} times 7^{3}}{8^{2} times 7} ) | 9 |

192 | If ( x ) is so small that ( x^{3} ) and higher powers of ( x ) may be neglected, then ( frac{(1+x)^{3 / 2}-left(1+frac{1}{2} xright)^{3}}{(1-x)^{1 / 2}} ) may be approximated as A ( cdot frac{x}{2}-frac{3}{8} x^{2} ) B. ( -frac{3}{8} x^{2} ) c. ( _{3 x+frac{3}{8} x^{2}} ) D. ( 1-frac{3}{8} x^{2} ) | 9 |

193 | Simplify: ( left(-frac{4}{5}right)^{4} ) | 9 |

194 | Find the factor which will rationalise: ( 2+sqrt[4]{7} ) | 9 |

195 | Solve: ( 2^{2 x+1}=8 ) | 9 |

196 | Simplify: ( frac{left(3^{3}right)^{-2} timesleft(2^{2}right)^{-3}}{left(2^{4}right)^{-2} times 3^{-4} times 4^{-2}} ) | 9 |

197 | What fraction lies exactly halfway between ( frac{2}{3} ) and ( frac{3}{4} ? ) A ( cdot frac{3}{5} ) в. ( frac{5}{6} ) c. ( frac{7}{12} ) D. ( frac{9}{16} ) E ( frac{17}{24} ) | 9 |

198 | List five rational numbers between: ( frac{1}{2} ) and ( frac{2}{3} ) | 9 |

199 | Find six rational number between ( frac{1}{2} ) and ( frac{2}{3} ) | 9 |

200 | Which of the following is a rational number ( (s) ? ) A ( cdot frac{-2}{9} ) B. ( frac{4}{-7} ) ( c cdot frac{-3}{17} ) D. All the three given numbers | 9 |

201 | Simplify the following using laws of exponents. ( left(frac{3}{5}right)^{4} timesleft(frac{3}{5}right)^{3} timesleft(frac{3}{5}right)^{8} ) | 9 |

202 | Choose the rational number which does not lie between rational numbers ( -frac{2}{5} ) and ( -frac{1}{5} ) ( A cdot-frac{1}{4} ) B. ( -frac{3}{10} ) c. ( frac{3}{10} ) D. ( -frac{7}{20} ) | 9 |

203 | Find the value of ( x ) for which ( left(frac{3}{4}right)^{6} timesleft(frac{16}{9}right)^{5}=left(frac{4}{3}right)^{x+2} ) | 9 |

204 | Which of the following numbers lies between ( frac{-5}{2} ) and ( frac{3}{4} ? ) A . B. 0 c. -3 D. 3 | 9 |

205 | Insert three rational of number between ( frac{3}{7} ) and ( frac{4}{7} ) | 9 |

206 | Evaluate:- ( left(frac{2}{7}right)^{2} timesleft(frac{7}{2}right)^{-3} divleft{left(frac{7}{5}right)^{-2}right}^{-4} ) | 9 |

207 | Find one rational number between the following pairs of rational numbers (i) ( frac{4}{3} ) and ( frac{2}{5} ) (ii) ( frac{-2}{7} ) and ( frac{5}{6} ) (iii) ( frac{5}{11} ) and ( frac{7}{8} ) (iv) ( frac{7}{4} ) and ( frac{8}{3} ) | 9 |

208 | State true or false: Every rational number is a whole number. A. True B. False | 9 |

209 | Is zero a rational number? Can you write it in the form ( frac{p}{q}, ) where ( p ) and ( q ) are integers and ( boldsymbol{q} neq mathbf{0} ? ) A. True B. False | 9 |

210 | Can we represent every decimal number in the form of ( frac{p}{q} ) or not? Explain it. | 9 |

211 | Write any two rational numbers which are between 2.3 and 2.4 | 9 |

212 | Write a rational number between ( sqrt{2} ) and ( sqrt{mathbf{3}} ) A ( cdot frac{3}{2} ) B. ( frac{4}{2} ) ( c cdot frac{5}{2} ) D. 5 | 9 |

213 | There are – m. rational numbers between two given rational numbers. A . 2 B. 5 c. none D. infinite | 9 |

214 | are rational numbers between ( -frac{3}{4} ) and ( frac{1}{2} ) A ( cdot frac{-7}{16}, frac{-1}{8}, frac{9}{16} ) в. ( frac{-15}{16}, frac{-1}{8}, frac{3}{16} ) c. ( frac{-7}{16}, frac{-1}{8}, frac{3}{16} ) D. none of the above | 9 |

215 | A rational number ( -2 / 3 ) A. Lies to the left side of 0 on the number line. B. Lies to the right side of 0 on the number line. C. It is not possible to represent on the number line. D. Cannot be determined on which side the number lies. | 9 |

216 | Find the following product. ( operatorname{str} times 7 r^{2} s^{2} ) | 9 |

217 | Find any ten rational numbers between ( frac{-5}{6} ) and ( frac{5}{8} ) | 9 |

218 | ( left(frac{-1}{2}right)^{2}=frac{1}{2^{m}} ) | 9 |

219 | 57. A rational number between is (1) 2 colo vs OTCO (2) | 9 |

220 | Express each of the following exponential expressions as a rational number. ( left(frac{2}{5}right)^{(-3)} ) | 9 |

221 | Show that ( 7-sqrt{5} ) is irrational given that ( sqrt{5} ) is irrational. | 9 |

222 | Simplify the following: ( left(frac{1}{4}right)^{-2}-3(8)^{2 / 3}(4)^{0}+left(frac{9}{16}right)^{frac{-1}{2}} ) | 9 |

223 | Are ( frac{-1}{2} ) and ( frac{-3}{6} ) represented by the same point on the number line? | 9 |

224 | If ( left(a b^{-1}right)^{2 x-1}=left(b a^{-1}right)^{x-2}, ) then what is the value of ( x ? ) ( mathbf{A} cdot mathbf{1} ) B . 2 ( c .3 ) D. | 9 |

225 | 55. The difference of 5.76 and 2.3 (1) 2.54 (3) 3.46 (2) 3.73 (4) 3.43 | 9 |

226 | ( left[(13)^{2}+sqrt[3]{1728}-sqrt{441}right] div 4^{2} times 15^{3} ) equals A ( cdot frac{2}{675} ) B. 33750 ( c cdot frac{2}{45} ) D. 485 | 9 |

227 | The rational number lies between ( frac{3}{7} ) and ( frac{2}{3} ) is A ( cdot frac{2}{5} ) B. ( frac{4}{7} ) ( c cdot frac{3}{7} ) D. | 9 |

228 | Express ( 1 . overline{32}+0 . overline{35} ) in the form of ( frac{p}{q} ) where ( p ) and ( q ) are integers and ( q neq 0 ) Find ( p+q ) | 9 |

229 | State whether true or false. ( frac{2}{7} ) is an irrational number. A. True B. False | 9 |

230 | ( (64)^{frac{-2}{3}} timesleft(frac{1}{4}right)^{-3} ) equals to ( A cdot 4 ) B. ( c ) D. 16 | 9 |

231 | Given: ( boldsymbol{x}, boldsymbol{y} ) and ( boldsymbol{z} ) are integers and ( mathbf{3}^{x+5}=mathbf{2 7}^{y+1}, ) then ( boldsymbol{x} ) is even A. True B. False | 9 |

232 | The rational number of the form ( frac{p}{q}, q neq ) ( 0, p ) and ( q ) are positive integers, which represents ( 0.1 overline{34} ) i.e., ( (0.1343434 ldots . .) ) is A ( cdot frac{134}{999} ) в. ( frac{134}{990} ) c. ( frac{133}{999} ) D. ( frac{133}{990} ) | 9 |

233 | The value of ( left[2-3(2-3)^{-1}right]^{-1} ) is A ( cdot frac{-1}{5} ) B. c. -5 D. 5 | 9 |

234 | Find whether the following statement is true or false: Equivalent rational numbers of a positive rational numbers are all positive. A. True B. False | 9 |

235 | If we divide a positive integer by another positive integer, what is the resulting number? A. It is always a natural number B. It is always an integer c. It is a rational number D. It is an irrational number | 9 |

236 | Find three rational numbers between 5 and -2 | 9 |

237 | Apply laws of exponents and simplify. ( left(3^{0} times 2^{5}right)+5^{0} ) | 9 |

238 | Ten rational numbers between ( frac{-2}{5} ) and ( frac{1}{2} ) ( operatorname{are} frac{-7}{20}, frac{-6}{20}, frac{-5}{20}, frac{-4}{20}, frac{-3}{20}, frac{-2}{20}, frac{-1}{20}, 0 ldots, frac{1}{20}, frac{2}{20} ) If true then enter 1 and if false then enter ( mathbf{0} ) | 9 |

239 | Write 0,7,10,-4 in ( frac{p}{q} ) form | 9 |

240 | The sum of two rational numbers is ( frac{-2}{3} ) If one of them is ( frac{-8}{15}, ) find the other. | 9 |

241 | If ( 2=10^{m} ) and ( 3=10^{n} ) then find the value of 0.15 A ( cdot 10^{n-m-1} ) B . ( 10^{n-m+1} ) c. ( 10^{n-m-2} ) D. ( 10^{n-m}-m ) | 9 |

242 | Represent these number on number line: ( frac{7}{8}, frac{-5}{3} ) | 9 |

243 | Evaluate ( 3 times(9)^{5 / 2} times(9)^{-1 / 2} ) | 9 |

244 | State whether the statement is True or False. ( (boldsymbol{m}+boldsymbol{n})^{-1}left(boldsymbol{m}^{-1}+boldsymbol{n}^{-1}right)=(boldsymbol{m} boldsymbol{n})^{-1} ) A. True B. False | 9 |

245 | Find the value of ‘ ( n ) ‘ in the following: ( left(frac{2}{3}right)^{3} timesleft(frac{2}{3}right)^{5}=left(frac{2}{3}right)^{n-2} ) | 9 |

246 | Solve:3 ( x+8>2 ) when ( x ) is an real number. | 9 |

247 | If ( boldsymbol{x}=mathbf{2} ) and ( boldsymbol{y}=mathbf{3}, ) then find the value of ( left[frac{1}{x^{x}}+frac{1}{y^{y}}right] ) A ( cdot frac{-31}{108} ) в. ( frac{31}{108} ) c. ( frac{125}{171} ) D. ( frac{153}{222} ) | 9 |

248 | Does the following pairs represent the same rational number: ( frac{-16}{20} ) and ( frac{20}{-25} ) | 9 |

249 | 53. The value of 32 43 13+V6 T6+T2 T3+ Te is (1) 4 (2) 0 (3) 2 0 (4) 3 76 | 9 |

250 | 67. If x= + va and y = = = 1 then value of x +1 be 1 y +1 Will | 9 |

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