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Published on: 23/08/2019
Number Systems
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Questions + Answers key
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1.
The value of \(\sqrt [ 4 ]{ \sqrt [ 3 ]{ { 2 }^{ 2 } } } \) is equal to:
\({ 2 }^{ -\frac { 1 }{ 6 } }\)
\({ 2 }^{ -6 }\)
\({ 2 }^{ \frac { 1 }{ 6 } }\)
\({ 2 }^{ 6 }\)
2.
The simplified value of \({ \left( 81 \right) }^{ -1/4 }\times \sqrt [ 4 ]{ 81 } \) is:
9
3
1
0
3.
Simplified value of \({ \left( 25 \right) }^{ \frac { 1 }{ 3 } }\times { \left( 5 \right) }^{ \frac { 1 }{ 3 } }\) is:
25
3
1
5
4.
If \({ x }^{ a/b }=1,\)then the value of a is
0
1
-1
None of these
5.
If b>0 and b2=a then \(\sqrt { a } \) is equal to:
-b
b
\(\sqrt { b } \)
b2
6.
Value of \(\frac { 1 }{ \sqrt { 18 } -\sqrt { 32 } } \) is equal to:
\(\sqrt { 2 } \)
\(-\sqrt { 2 } \)
\(\frac { 1 }{ \sqrt { 2 } } \)
\(-\frac { 1 }{ \sqrt { 2 } } \)
7.
\({ \left( \sqrt { 2 } +1/\sqrt { 2 } \right) }^{ 2 }\) is equal to:
\(4\sqrt { 2 } \)
9/2
\(4/\sqrt { 12 } \)
9
8.
\(\left( -2-\sqrt { 3 } \right) \left( -2+\sqrt { 3 } \right) \) when simplified is:
positive and irrational
positive and rational
negative and irrational
negative and rational
9.
\(\pi \) is:
a rational number
an integer
an irrational number
a whole number
10.
Which of the following numbers is an irrational number?
\(\sqrt { 23 } \)
\(\sqrt { 225 } \)
0.3796
\(7.\overline { 478 } \)
11.
\(5.3\overline { 7 } \) lies most accurately
between 5.37 and 5.38
between 5.3 and 5.4
between 5.377 and 3.378
between 5.3777 and 5.3778
12.
A number is an irrational if and only if its decimal representation is:
non-terminating
non-terminating and repeating
non terminating and non repeating
terminating
13.
The decimal form of 56/1000 is
0.56
0.056
0.0056
5.6
14.
A rational number lying between -3 and 3 is:
0
-4.3
-3.4
1.101 1001 10001...
15.
Every rational number is:
a natural number
an integer
a real number
a whole number
16.
Simplify: √72+√800-18.
17.
Write the equivalent of (a+√b)(a-√b).
18.
If b>0 and b2=a, then find the value of √a.
19.
Calculate the value of 4√28\(\div\)3√7.
20.
Simplify: (5 + √5)(5 - √5)
21.
Simplify the number (√2+√5)2
22.
Calculate the irrational number between 2 and 2.5.
23.
Find the decimal expansion of \(\frac{58}{1000}\)
24.
Write the simplest form of a rational number \(\frac{177}{413}\)
25.
Is \(\frac{\sqrt{98}}{\sqrt{2}}\) a rational number or not?
1.
(c)
\({ 2 }^{ \frac { 1 }{ 6 } }\)
2.
(c)
1
3.
(d)
5
4.
(a)
0
5.
(b)
b
6.
(d)
\(-\frac { 1 }{ \sqrt { 2 } } \)
7.
(b)
9/2
8.
(b)
positive and rational
9.
(c)
an irrational number
10.
(a)
\(\sqrt { 23 } \)
11.
(d)
between 5.3777 and 5.3778
12.
(c)
non terminating and non repeating
13.
(b)
0.056
14.
(a)
0
15.
(c)
a real number
16.
( )
√72 + √800-√18
=\(\sqrt{36\times2}+\sqrt{400\times2}-\sqrt{9\times2}\)
= 6√2 + 20√2 - 3√2 = 23√2
17.
( )
(a+√b)(a-√b)=(a)2-(√b)2=a2-b.
18.
( )
b2=a ⇒ √a=b.
19.
( )
4√28\(\div\)3√7 = 4 x 2√7\(\div\)3√7=\(\frac{8}{3}\)
20.
( )
(5 + √5)(5 - √5) = {52 - (√5)2}
= {25 - 5}
= 20
21.
( )
(√2 + √5)2 = (√2)2 + (√5)2+ 2 x √2 x √5
= 2 + 5 + 2√10
= 7 + 2√10 (Irrational number)
22.
( )
Since, √5=2.236
Hence, the irrational number between 2 and 2.5 is √5.
23.
( )
\(\frac{58}{1000}\)= 0.058 (Decimal point is shifted three places to the left)
24.
( )
\(\frac{177}{413}\)= \(\frac{59\times3}{59\times7}=\frac{3}{7}\)
25.
( )
\(\frac{\sqrt{98}}{\sqrt{2}}\)=\(\frac{\sqrt{98}}{\sqrt{2}}\) = √49 = 7
So, it is a rational number.
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CBSE 9th Standard CBSE Subjects
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