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NUMBER SYSTEMS
1. The decimal expansion of the number is
2
a. A finite decimal
b. 1.414121
c. Non-terminating recurring
d. Non-terminating non recurring
2. Which of the following is an irrational number?
a. 3.14 b. 3.141414….. C. 3.14444…… d. 3.141141114….
3. The simplest form of
0 . 5 4
a. b. c. d. None of these
49
90
6
11
4
7
4.
1
3 + 2
π‘’π‘žπ‘’π‘Žπ‘™π‘ 
a. b. c. d.
3 βˆ’ 2
4
3 + 2 3 βˆ’ 2
3 βˆ’ 2
5
5. Which of the following is an irrational number?
a. b. c. 0.3796 d. 7.478478
23 225
6. The number obtained on rationalising the denominator of
1
7 βˆ’ 2
𝑖𝑠
a. b. c. d.
7 + 2
3
7 βˆ’ 2
3
7 + 2
5
7 + 2
45
7. Every rational number is
a. A natural number
b. An integer
c. A real number
d. A whole number
8. Every rational number is
a. A natural number b) A real number c) An integer d) A whole
number
9. Between two rational numbers :-
a. There is no rational number
b. There is exactly one rational number
c. There are infinitely many rational numbers
d. There are only rational numbers and no irrational numbers
10. The simplest form of is :-
0 . 12 3
a. b. c. d. None of these
41
330
37
100
41
333
11. A rational number between
2 π‘Žπ‘›π‘‘ 3 𝑖𝑠
a. b. c. 1.5 d. 1.8
2 + 3
2
2 βˆ’ 3
2
12. Decimal representation of a rational number cannot be :-
a. Terminating b. Non-terminating c, Non-terminating non-repeating
d. Non-terminating
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13. Can we write 0 in the form of ?
𝑝
π‘ž
a. Yes b. No c. Cannot be explained d. None of the above
14.
𝐼𝑓 π‘₯ = 3 βˆ’ 2 3 , π‘‘β„Žπ‘’π‘› π‘‘β„Žπ‘’ π‘£π‘Žπ‘™π‘’π‘’ π‘œπ‘“ π‘₯
2
βˆ’
1
π‘₯
2
𝑖𝑠 :
a. b. c. 38 d. 34
24 2 βˆ’ 24 2
15.
9 𝑖𝑠 π‘Ž
a. Rational number
b. An irrational number
c. Neither rational number nor irrational
d. None of the above
16. The value of is 2 3 + 3
a. b. c. d.
2 6 26 3 3 4 6
17. 𝐹𝑖𝑛𝑑 𝑓𝑖𝑣𝑒 π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘™ π‘›π‘’π‘šπ‘π‘’π‘Ÿπ‘  𝑏𝑒𝑑𝑀𝑒𝑒𝑛
1
6
π‘Žπ‘›π‘‘
1
3
.
18.
𝐼𝑓 π‘Ž = 2 + 3 , 𝑓𝑖𝑛𝑑 π‘‘β„Žπ‘’ π‘£π‘Žπ‘™π‘’π‘’ π‘œπ‘“ π‘Ž βˆ’
1
π‘Ž
19.
𝐼𝑓 π‘₯
2
+
1
π‘₯
2
= 119 , 𝑓𝑖𝑛𝑑 π‘‘β„Žπ‘’ π‘£π‘Žπ‘™π‘’π‘’ π‘œπ‘“ π‘₯ +
1
π‘₯
20.
𝐹𝑖𝑛𝑑 π‘‘β„Žπ‘’ π‘£π‘Žπ‘™π‘’π‘’π‘  π‘œπ‘“ π‘Ž π‘Žπ‘›π‘‘ 𝑏 :
7 + 5
7 βˆ’ 5
βˆ’
7 βˆ’ 5
7 + 5
= π‘Ž +
7
11
5 𝑏 .
21.
𝐼𝑓 π‘Ž =
1
7 βˆ’ 4 3
, 𝑏 =
1
7 + 4 3
, π‘‘β„Žπ‘’π‘› 𝑓𝑖𝑛𝑑 π‘‘β„Žπ‘’ π‘£π‘Žπ‘™π‘’π‘’π‘  π‘œπ‘“ :
a.
π‘Ž
2
+ 𝑏
2
b.
π‘Ž
3
+ 𝑏
3
22. Every rational number is
a. A rational number
b. A whole number
c. An integer
d. A real number
23. The product of irrational number is
a. Always irrational
b. Always rational
c. Always an integer
d. Sometimes irrational and sometimes rational
24.
𝐸π‘₯π‘π‘Ÿπ‘’π‘ π‘  7 . 5 π‘œπ‘› π‘Ž π‘›π‘’π‘šπ‘π‘’π‘Ÿ 𝑙𝑖𝑛𝑒 .
25. Express 0.53333333…….. in the form of .
𝑝
π‘ž
26.
𝐹𝑖𝑛𝑑 π‘‘π‘€π‘œ π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘™ π‘›π‘’π‘šπ‘π‘’π‘Ÿπ‘  𝑏𝑒𝑑𝑀𝑒𝑒𝑛
3
4
π‘Žπ‘›π‘‘
2
5
.
27.
𝐸π‘₯π‘π‘Ÿπ‘’π‘ π‘  0 . 4 7 𝑖𝑛 π‘‘β„Žπ‘’ π‘“π‘œπ‘Ÿπ‘š π‘œπ‘“
𝑝
π‘ž
, π‘€β„Žπ‘’π‘Ÿπ‘’ 𝑝 π‘Žπ‘›π‘‘ π‘ž π‘Žπ‘Ÿπ‘’ π‘–π‘›π‘‘π‘’π‘”π‘’π‘Ÿπ‘  π‘Žπ‘›π‘‘ π‘ž β‰  0 .
28.
𝐼𝑓 𝑝 =
3 βˆ’ 5
3 + 5
π‘Žπ‘›π‘‘ π‘ž =
3 + 5
3 βˆ’ 5
, 𝑓𝑖𝑛𝑑 π‘‘β„Žπ‘’ π‘£π‘Žπ‘™π‘’π‘’ π‘œπ‘“ 𝑝
2
+ π‘ž
2
+ 2 π‘π‘ž
29. Find the values of a and b if
7 + 3 5
3 + 5
βˆ’
7 βˆ’ 3 5
3 βˆ’ 5
= π‘Ž + 5 𝑏
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30. Two classmates Piyush and Sanjeet simplified two different expressions during the
revision hour and explained to each other three simplifications. Piyush explained
simplification of
2
5 + 3
𝑏𝑦 π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘™π‘–π‘§π‘–π‘›π‘” π‘‘β„Žπ‘’ π‘‘π‘’π‘›π‘œπ‘šπ‘–π‘›π‘Žπ‘‘π‘œπ‘Ÿ π‘Žπ‘›π‘‘ π‘†π‘Žπ‘›π‘—π‘’π‘’π‘‘ 𝑒π‘₯π‘π‘™π‘Žπ‘–π‘›π‘’π‘‘
simplification of by using the identity (a+b)(a-b). Answer the
2 + 3
( )
2 βˆ’ 3
( )
following question:-
a. What is the rationalizing factor of ?
5 + 3
( )
b. Add
3 3 + 7 2
( )
π‘Žπ‘›π‘‘ 5 3 βˆ’ 2 2
( )
c.
πΈπ‘£π‘Žπ‘™π‘’π‘Žπ‘‘π‘’ 72 + 800 βˆ’ 18
d.
π‘…π‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘™π‘–π‘§π‘’
2 + 3
2 βˆ’ 3
31. Show how can be represented on the number line.
5
32.
π‘…π‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘™π‘–π‘§π‘’ π‘‘β„Žπ‘’ π‘‘π‘’π‘›π‘œπ‘šπ‘–π‘›π‘Žπ‘‘π‘œπ‘Ÿ :
1
2 + 3
.
33. Represent the number line.
9 . 5 π‘œπ‘›
34. Express in the form of , where p and q are integers and .
0 . 001
𝑝
π‘ž
π‘ž β‰  0
35. ASSERTION : Every integer is a rational number.
REASON: Every integer is expressed in the form of so it is a rational number.
π‘š
𝑙
a. Both assertion (A) and reason (R) are true and (R) is the correct explanation of
assertion (A).
b. Both assertion (A) and reason (R) are true and (R) is not the correct explanation
of assertion (A).
c. Assertion (A) is true but reason (R) is false.
d. Assertion (A) is false but reason (R) is true.
36. Assertion (A): Rational number lying between 1 and 2 is .
3
2
Reason (R): Rational number lying between two rational numbers x and y is
π‘₯ + 𝑦 ( )
2
a. Both assertion (A) and reason (R) are true and (R) is the correct explanation of
assertion (A).
b. Both assertion (A) and reason (R) are true and (R) is not the correct explanation
of assertion (A).
c. Assertion (A) is true but reason (R) is false.
d. Assertion (A) is false but reason (R) is true.
37. Are the square roots of all positive integers irrational ? If not, give an example of the
square root of a number that is a rational number.
38. Find the decimal expansion of , and .
10
3
7
8
1
7
39. Express 2.454545…. as a rational number in the form of , where p and q are integers.
𝑝
π‘ž
40. Write in the form of decimal and say what kind of decimal expansion?
41
8
41. If find the value of without actually doing the long division.
1
7
= 0 . 142857 ,
12
7
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42. Find 5 rational numbers between
5
7
π‘Žπ‘›π‘‘
6
7
.
43. Express , where p and q are integers but q is not equal to zero.
0 . 2 35 𝑖𝑛 π‘‘β„Žπ‘’ π‘“π‘œπ‘Ÿπ‘š π‘œπ‘“
𝑝
π‘ž
44. Represent on the number line.
5
45. Find 5 rational numbers between 3 and 7.
46. Find the value of β€˜a’ and β€˜b’ in the following question:
2 + 3
3 2 βˆ’ 2 3
= π‘Ž βˆ’ 𝑏 6
47. Represent on the real number line.
3
48. Simplify:
7 3
10 + 3
βˆ’
2 5
6 + 3
βˆ’
3 2
15 + 3 2
49. To judge the preparation of students class 9 on topic β€œNumber System β€œ mathematics
teachers write two numbers on black board, and asks some questions about the
members, which are following , then answer the question:
a. Write the decimal form of
2
11
i. 0.81 ii. 0.18 iii. 0.17 iv. 0.71
b. Write the .
𝑝
π‘ž
π‘“π‘œπ‘Ÿπ‘š π‘œπ‘“ 0 . 38
i. ii. iii. iv.
5
18
7
18
11
18
1
18
c. Write the decimal expansion of
2
11
i. Non terminating
ii. Terminating
iii. Non-terminating repeating
iv. Non-terminating non-repeating
d. If
𝑝
π‘ž
π‘“π‘œπ‘Ÿπ‘š π‘œπ‘“ 0 . 38 𝑖𝑠
π‘š
𝑛
, π‘‘β„Žπ‘’π‘› π‘£π‘Žπ‘™π‘’π‘’ π‘œπ‘“ ( π‘š + 𝑛 ) 𝑖𝑠
i. 25 ii. 11 iii. 29 iv. 23
50. Two classmates Raju and Anil simplified two different expressions during the revision
hour and explained to each other their simplification. Raju explains simplification of
by rationalizing the denominator and ANil explains simplification of
2
5 + 3
by using the identity. Answer the following questions:
2 + 3
( )
2 βˆ’ 3
( )
a. What is the conjugate of
5 + 3
b. By rationalizing the denominator what answer Raju should get?
c. ANil applied which identity to solve ?
2 + 3
( )
2 βˆ’ 3
( )
d. Give one example of addition of two irrational numbers equal to rational
numbers.