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Class 9

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

Polynomials

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Q 1. Factors of {tex} x ^ { 3 } + x ^ { 2 } + x + 1 {/tex}

A

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

B

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

C

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

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

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Q 2. The value of {tex} ( x - a ) ^ { 3 } + ( x - b ) ^ { 3 } + ( x - c ) ^ { 3 } - 3 ( x - a ) ( x - b ) ( x - c ) {/tex} when {tex} a + b + c = 3 x {/tex}

A

3

B

2

C

1

0

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Q 3. If {tex} \mathrm x + \mathrm {\frac { 1 } { x }} = \mathrm{a + b} {/tex} and {tex} \mathrm {x - \frac { 1 } { x }} = \mathrm{a - b} {/tex} then

{tex} \mathrm{a b} = 1 {/tex}

B

{tex} \mathrm a = \mathrm b {/tex}

C

{tex} \mathrm { ab } = 2 {/tex}

D

{tex} \mathrm{a + b} = 0 {/tex}

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Q 4. If {tex} x ^ { 1 / 3 } + y ^ { 1 / 3 } + z ^ { 1 / 3 } = 0 , {/tex} then

A

{tex} x ^ { 3 } + y ^ { 3 } + z ^ { 3 } = 0 {/tex}

B

{tex} x + y + z = 27 x y z {/tex}

{tex} ( x + y + z ) ^ { 3 } = 27 x y z {/tex}

D

{tex} x ^ { 3 } + y ^ { 3 } + z ^ { 3 } = 27 x y z {/tex}

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Q 5. Factorize: {tex} a ^ { 2 x } - b ^ { 2 x } {/tex}

{tex} \left( a ^ { x } + b ^ { x } \right) \left( a ^ { x } - b ^ { x } \right) {/tex}

B

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

C

{tex} \left( a ^ { x } + b ^ { x } \right) \left( a ^ { 2 } - b ^ { 2 } \right) {/tex}

D

{tex} \left( a ^ { x } + b ^ { x } \right) \left( a ^ { 2 } + b ^ { 2 } \right) {/tex}

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Q 6. {tex} 3 y - 5 x y + 7 x y ^ { 2 } {/tex} is a trinomial
Assertion: The number of terms in given polynomial is 3
Reason: A polynomial having two nonzero terms is called a binomial

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 7. {tex} 3 \sqrt { y } + 4 {/tex} is not a polynomial
Assertion: Given term does not contain integral power of y
Reason: An algebric expression having only non negative integral power of y is called a polynomial

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

B

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 8. If {tex} x - \frac { 1 } { x } = 9 , {/tex} then value of {tex} x ^ { 2 } + \frac { 1 } { x ^ { 2 } } {/tex} is

83

B

79

C

11

D

7

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Q 9. The value of {tex} \frac { ( 119 ) ^ { 2 } + ( 119 ) ( 111 ) + ( 111 ) ^ { 2 } } { ( 119 ) ^ { 3 } - ( 111 ) ^ { 3 } } {/tex}

A

{tex} 8{/tex}

{tex} 1 / 8 {/tex}

C

{tex} 230{/tex}

D

{tex} 1 / 230 {/tex}

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Q 10. If {tex} a + b + c = 2 s {/tex} then the value of {tex} ( s - a ) ^ { 2 } + ( s - b ) ^ { 2 } + ( s - c ) ^ { 2 } {/tex} will be

A

{tex} s ^ { 2 } + a ^ { 2 } + b ^ { 2 } + c ^ { 2 } {/tex}

{tex} a ^ { 2 } + b ^ { 2 } + c ^ { 2 } - s ^ { 2 } {/tex}

C

{tex} s ^ { 2 } - a ^ { 2 } - b ^ { 2 } - c ^ { 2 } {/tex}

D

{tex} 4 s ^ { 2 } - a ^ { 2 } - b ^ { 2 } - c ^ { 2 } {/tex}

Explanation

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Q 11. The value of {tex} \left( 2 x - \frac { y } { 3 } \right) ^ { 3 } {/tex} is

A

{tex} 4 x ^ { 2 } ( 2 x + y ) - y ^ { 3 } \left( \frac { 1 } { 27 } + \frac { 2 x } { 3 } \right) {/tex}

{tex} \left( 2 x - \frac { y } { 3 } \right) \left( 4 x ^ { 2 } + \frac { y ^ { 2 } } { 9 } - \frac { 4 x y } { 3 } \right) {/tex}

C

{tex} \left( 2 x - \frac { y } { 3 } \right) \left( 4 x ^ { 2 } + \frac { y ^ { 2 } } { 9 } + \frac { 4 x ^ { 2 } y ^ { 2 } } { 9 } \right) {/tex}

D

{tex} 8 x ^ { 5 } - \frac { y ^ { 3 } } { 27 } - 3x y \left( 3 x - \frac { y } { 3 } \right) {/tex}

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Q 12. If {tex} x + y + z = 0 , {/tex} then {tex} \frac { x ^ { 2 } } { y z } + \frac { y ^ { 2 } } { x z } + \frac { z ^ { 2 } } { x y } {/tex} is

A

{tex} 3 x ^ { 2 } y ^ { 2 } z ^ { 2 } {/tex}

B

{tex} 3 {/tex}

C

{tex} x ^ { o } + y ^ { o } + z ^ { o } {/tex}

Both B and C

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Q 13. If {tex} \left( x ^ { 2 } - 1 \right) {/tex} is a factor of {tex} a x ^ { 4 } + b x ^ { 3 } + c x ^ { 2 } + d x + e , {/tex} then which of the following is correct?

A

{tex} a + c + e = b + d {/tex}

B

{tex} a + c + e = 0 {/tex}

C

{tex} a + b + c + d + e = 0 {/tex}

All of the above

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Q 14. If {tex} p = 2 ^ { 2 / 3 } + 2 ^ { 1 / 3 } {/tex} then

A

{tex} p ^ { 3 } - 6 p + 6 = 0 {/tex}

B

{tex} p ^ { 3 } - 3 p - 6 = 0 {/tex}

{tex} p ^ { 3 } = 6 p + 6 {/tex}

D

{tex} p ^ { 3 } - 6 p = 6 {/tex}

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Q 15. Match the following

Column I Column II
(A) {tex} x^2 - x - 2{/tex} (P) {tex} x = 1{/tex}
(B) {tex} 5x - 4x^2 + 6{/tex} (Q) {tex} x = -1{/tex}
(C) {tex} 3x^4 - 4x^3 - 3x + 4{/tex} (R) {tex} x = 2{/tex}
(D) {tex}x^3 + 1{/tex} (S) {tex} x = -2{/tex}

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

B

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

C

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

D

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

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Q 16. Match the following

Column I Column II
(A) {tex} x^3 + 6x^2 + 11x + 6{/tex} (P) {tex}(x + 1){/tex}
(B) {tex}x^3 + 13x^2 + 32x + 20{/tex} (Q) {tex}(x + 2){/tex}
(C) {tex}2x^3 - x^2 - 2x + 1{/tex} (R) {tex}(x + 3){/tex}
(D) {tex}x^3 - 10x^2 - 53x - 42{/tex} (S) {tex}(x - 1){/tex}

{tex} ( \mathrm { A } ) - ( \mathrm { P } , \mathrm { Q } , \mathrm { R } ) {/tex}

B

{tex} ( \mathrm { B } ) - ( \mathrm { S } , \mathrm { P } ) {/tex}

C

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

D

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

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Q 17. Match the following

Column I Column II
(A) {tex}(x + 1)^2{/tex} (P) Quadratic
(B) {tex}x(x + 5) = -x(3-x) + 7{/tex} (Q) Linear
(C) {tex}x(x + y - z) - xy{/tex} (R) Binomial
(D) {tex}(\sqrt {2x^2} - 1)^2 - 3\sqrt{2x^2}{/tex} (S) Monomial

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

B

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

C

{tex} ( \mathrm { C } ) - ( \mathrm { Q } , \mathrm { R } ) {/tex}

D

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

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Q 18. {tex} x^n+y^n {/tex} is divisible by {tex}x+y{/tex} if

n is an odd integer

B

n is an even integer

C

n is rational number

D

n is irrational number