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Class 9

Explore popular questions from Number System for Class 9. This collection covers Number System previous year Class 9 questions hand picked by experienced teachers.

Number System

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Q 1. The value of {tex} 1 . \overline { 34 } + 4 . \overline { 12 } {/tex} is

A

{tex} \frac { 133 } { 99 } {/tex}

B

{tex} \frac { 371 } { 90 } {/tex}

C

{tex} \frac { 5169 } { 990 } {/tex}

{tex} \frac { 541 } { 99 } {/tex}

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Q 2. The rational number {tex} \frac { 0 } { 7 } {/tex}

A

has a positive numerator.

B

has a negative numerator.

C

has either a positive numerator or a negative numerator.

has neither a positive numerator nor a negative numerator.

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Q 3. The number {tex} ( \sqrt { x } + \sqrt { y } ) ( \sqrt { x } - \sqrt { y } ) {/tex} where {tex} x , y > 0 {/tex} is

rational

B

irrational

C

both

D

none

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Q 4. The rationalising factor of {tex} \sqrt [ 5 ] { a ^ { 2 } b ^ { 3 } c ^ { 4 } } {/tex} is :

{tex} \sqrt [ 5 ] { a ^ { 3 } b ^ { 2 } c } {/tex}

B

{tex} \sqrt [ 4 ] { a ^ { 3 } b ^ { 2 } c } {/tex}

C

{tex} \sqrt [ 3 ] { a ^ { 3 } b ^ { 2 } c } {/tex}

D

{tex} \sqrt { a ^ { 3 } b ^ { 2 } c } {/tex}

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Q 5. Which of the following is a pure surd?

A

{tex} 4 \sqrt { 3 } {/tex}

B

{tex} 3 \sqrt [ 3 ] { 5 } {/tex}

{tex} \sqrt { 12 } {/tex}

D

{tex} \frac { 3 } { 4 } \sqrt { 8 } {/tex}

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Q 6. {tex} \left( \frac { 1 + \sqrt { 2 } } { \sqrt { 5 } + \sqrt { 3 } } + \frac { 1 - \sqrt { 2 } } { \sqrt { 5 } - \sqrt { 3 } } \right) {/tex} simplifies to

A

{tex} \sqrt { 5 } + \sqrt { 6 } {/tex}

B

{tex} 2 \sqrt { 5 } + \sqrt { 6 } {/tex}

{tex} \sqrt { 5 } - \sqrt { 6 } {/tex}

D

{tex} 2 \sqrt { 5 } - 3 \sqrt { 6 } {/tex}

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Q 7. {tex} [ \sqrt [ 3 ] { 2 } \cdot \sqrt [ 2 ] { 2 } \cdot \sqrt [ 3 ] { 3 } \cdot \sqrt [ 2 ] { 3 } ] {/tex} is equal to

A

{tex} 6 ^ { 5 } {/tex}

{tex} 6 ^ { 5 / 6 } {/tex}

C

{tex} 6 {/tex}

D

None of these

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Q 8. {tex} \sqrt { 2 - \sqrt { 3 } } {/tex} is a surd.
Assertion: A irrational number whose radicand is a rational number is a surd.
Reason: If the radicand is irrational, it is not a surd.

A

Both Assertion and Reason are true and Reason is the correct explanation of 'Assertion'

Both Assertion and Reason are true and Reason is not the correct explanation of 'Assertion'

C

Assertion is true but Reason is false

D

Assertion is false but Reason is true

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Q 9. Match the following

Column I Column II
(A) {tex}\frac{2^n + 2^{n-1}}{2^{n+1}- 2^n}{/tex} (P) {tex}1{/tex}
(B) {tex}\frac{x^{a(b-c)}}{x^{b(a-c)}} ÷ (\frac{x^b}{x^a})^c{/tex} (Q) {tex}15{/tex}
(C) {tex}9^{3/2} - 3x5^0 - (\frac{1}{81})^{-1/2}{/tex} (R) {tex}\frac{3375}{512}{/tex}
(D) {tex}\frac{(25)^{3/2}× (243)^{3/5}} {(16)^{5/4}×(8)^{4/3}}{/tex} (S) {tex}\frac32{/tex}

{tex} ( \mathrm A ) - ( \mathrm S ) {/tex}

B

{tex} ( \mathrm { B } ) - ( \mathrm { R } ) {/tex}

C

{tex} ( \mathrm { C } ) -( \mathrm { P} ) {/tex}

D

{tex} ( \mathrm D ) - ( \mathrm Q ) {/tex}

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Q 10. Which one of the following is a rational number?

{tex} ( \sqrt { 2 } ) ^ { 2 } {/tex}

B

{tex} 2 \sqrt { 2 } {/tex}

C

{tex} ( 2 + \sqrt { 2 } ) ^ { 2 } {/tex}

D

{tex} \frac { \sqrt { 2 } } { 2 } {/tex}

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Q 11. Which of the following statements is true?

{tex} - \frac { 2 } { 3 } < \frac { 4 } { - 9 } < \frac { - 5 } { 12 } < \frac { 7 } { - 18 } {/tex}

B

{tex} \frac { 7 } { - 18 } < \frac { - 5 } { 12 } < \frac { 4 } { - 9 } < \frac { - 2 } { 3 } {/tex}

C

{tex} \frac { 4 } { - 9 } < \frac { 7 } { - 18 } < \frac { - 5 } { 12 } < \frac { - 2 } { 3 } {/tex}

D

{tex} \frac { - 5 } { 12 } < \frac { - 2 } { 3 } < \frac { 4 } { - 9 } < \frac { 7 } { - 18 } {/tex}

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Q 12. {tex} \pi {/tex} is

A

rational

irrational

C

imaginary

D

an integer

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Q 13. The value of :is

A

{tex} \frac { 40 } { 31 } {/tex}

B

{tex} \frac { 4 } { 9 } {/tex}

{tex} \frac { 1 } { 8 } {/tex}

D

{tex} \frac { 31 } { 40 } {/tex}

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Q 14. The value of:
{tex} \frac { a + \sqrt { a ^ { 2 } - b ^ { 2 } } } { \sqrt { a ^ { 2 } + b ^ { 2 } } + b } \div \frac { \sqrt { a ^ { 2 } + b ^ { 2 } } - b } { a - \sqrt { a ^ { 2 } - b ^ { 2 } } } {/tex}

A

{tex} \frac { a ^ { 2 } } { b ^ { 2 } } {/tex}

{tex} \frac { b ^ { 2 } } { a ^ { 2 } } {/tex}

C

{tex} \frac { a } { b } {/tex}

D

none

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Q 15. {tex} ( 16 ) ^ { 0.16 } \times ( 16 ) ^ { 0.04 } \times ( 2 ) ^ { 0.2 } {/tex} is equal to

A

1

2

C

4

D

16

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Q 16. {tex} 4 ^ { 3.5 }: 2 ^ { 5 } {/tex} is the same as

4:1

B

2:1

C

7:5

D

7:10

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Q 17. By how much does {tex} 5 \sqrt { 7 } - 2 \sqrt { 5 } {/tex} exceed {tex} 3 \sqrt { 7 } - 4 \sqrt { 5 } {/tex}

A

{tex} 5 ( \sqrt { 7 } + \sqrt { 5 } ) {/tex}

B

{tex} \sqrt { 7 } + \sqrt { 5 } {/tex}

{tex} 2 ( \sqrt { 7 } + \sqrt { 5 } ) {/tex}

D

{tex} 7 ( \sqrt { 2 } + \sqrt { 5 } ) {/tex}

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Q 18. The value of {tex} 4 \times 81 ^ { - 1 / 2 } \times \left( 81 ^ { 1 / 2 } + 81 ^ { 3 / 2 } \right) {/tex} is

A

{tex} 4 \left( 1 + 9 ^ { 2 } \right) {/tex}

B

{tex} 4 \times 81^{0} \left( 1 + 81 \right) {/tex}

C

{tex} \left( \frac { 81 ^ { 2 } x 4 } { 81 ^ { \frac { - 3 } { 2 } } } \right) {/tex}

Both A and B

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Q 19. Solve :-
{tex} \sqrt [ 3 ] { x ^ { 4 } y } \times \sqrt [ 3 ] { \frac { x ^ { 1 / 2 } } { y } } \times \sqrt [ 4 ] { \frac { 1 } { x ^ { 7 } } } {/tex}

{tex} \sqrt { \left( \frac { 1 } { x ^ { 1 / 2 } } \right) } {/tex}

B

{tex} \left( \frac { 1 } { x ^ { 2 } } \right) {/tex}

C

{tex} \{ \sqrt [ 3 ] { \left( \frac { 1 } { x } \right) ^ { - 8 } } \} ^ { - 3 / 2 } {/tex}

D

{tex} \left( x ^ { - 2 } \right) ^ { - 1 / 2 } {/tex}

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Q 20. Which of the following statements is/are true?

A

The sum or difference of a rational and an irrational number is always an irrational number

B

The product of two rational number is always a rational number

C

The product of two irrational number can be rational or irrational

All of the above

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Q 21. The simplified form of {tex} [ \sqrt { 7 + 4 \sqrt { 3 } } - \sqrt { 3 } ] {/tex} is

A

{tex}2{/tex}

B

{tex} \sqrt { 4 \times 3 ^ { 3 } \times 9 ^ { - 3 / 2 } } {/tex}

C

{tex} 4 ^ { 1 / 2 } \times 3 ^ { 3 / 2 } \times 9 ^ { - 3 / 4 } {/tex}

All of the above

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Q 22. The value of {tex} ( \sqrt { 72 } - \sqrt { 18 } ) \div \sqrt { 12 } {/tex} is equal to

A

Rational number

B

{tex} \sqrt { 6 } {/tex}

C

{tex} \sqrt { 7 } {/tex}

{tex} \frac { \sqrt { 6 } } { 2 } {/tex}

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Q 23. Match the following:

Column I Column II
(A) {tex}(5 + \sqrt 10)(5 - \sqrt 10){/tex} (P) Rational
(B) {tex}\frac{1}{\sqrt 7 - 2}{/tex} (Q) {tex}15{/tex}
(C) {tex}\sqrt 225{/tex} (R) Irrational
(D) {tex}(\sqrt 3 + \sqrt 7)^2{/tex} (S) {tex}\frac{\sqrt 7 + 2}{3}{/tex}

A

{tex} ( \mathrm { A } ) - ( \mathrm { R} ) {/tex}

B

{tex} ( \mathrm { B } ) - ( \mathrm { Q} ) {/tex}

C

{tex} ( \mathrm { C } ) - ( \mathrm { S } ) {/tex}

{tex} (\mathrm D ) - ( \mathrm R ) {/tex}

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Q 24. The value of {tex} \sqrt { 5 \sqrt { 5 \sqrt { 5 \sqrt { 5 } \ldots . . } } } {/tex} is

A

0

5

C

Cannot be determined

D

none