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Class 8

Explore popular questions from Algebraic Expressions and Identities for Class 8. This collection covers Algebraic Expressions and Identities previous year Class 8 questions hand picked by experienced teachers.

Algebraic Expressions and Identities

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Q 1. The coefficient of {tex}\mathrm{ x ^ { 0 }} {/tex} in {tex} \mathrm{3 x ^ { 3 } - 4 x ^ { 2 } + 7 x - 2 }{/tex} is :

A

7

B

2

{tex} - 2 {/tex}

D

0

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Q 2. The number of like terms in {tex} 4 \mathrm { x } ^ { 2 } \mathrm { y } - 6 \mathrm { xy } ^ { 2 } + 3 \mathrm { x } ^ { 2 } \mathrm { y } - 2 \mathrm { yx } + 7 \mathrm { xyz } {/tex} is :

2

B

3

C

4

D

None

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Q 3. The value of expression {tex}\mathrm{4 a ^ { 2 } b - 2 a b ^ { 2 } + 7 a b - 3} {/tex} at {tex}\mathrm{ a = - 1 , b = 2 }{/tex} is

A

{tex} - 27 {/tex}

B

{tex} 1{/tex}

C

{tex} 27 {/tex}

{tex} - 1 {/tex}

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Q 4. The sum of {tex}\mathrm{- 2 a - b + 3 c - d }{/tex} and {tex}\mathrm{2 a + 4 b + 6 c} {/tex} is

A

Monomial

Binomial

C

Trinomial

D

Polynomial with 4 terms

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Q 5. The product of {tex}\mathrm - 7 \mathrm { x } ^ { 2 } \mathrm { yz } , - 13 \mathrm { y } ^ { 2 } {/tex} and {tex} \mathrm { yz } {/tex} is :

A

{tex} 91 \mathrm { xy } ^ { 4 } \mathrm { z } ^ { 2 } {/tex}

B

{tex} 91{/tex} {tex} \mathrm { xy } ^ { 2 } {/tex}

{tex} 91{/tex} {tex}\mathrm{ x ^ { 2 } y ^ { 4 } z ^ { 2 }}{/tex}

D

{tex} - 91{/tex} {tex}\mathrm{ x ^ { 2 } y z ^ { 2 }} {/tex}

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Q 6. The product of {tex} - 7 \mathrm { xy } {/tex} and {tex} \mathrm { x } ^ { 2 } - 4 \mathrm { y } ^ { 2 } {/tex} is

A

{tex} 7{/tex} {tex}\mathrm{x ^ { 2 } y ^ { 2 } - 28 x y ^ { 3 }} {/tex}

{tex}\mathrm{ - 7 x ^ { 3 } y + 28 x y ^ { 3 }} {/tex}

C

{tex}\mathrm{ - 7 x ^ { 2 } y + 28 x ^ { 2 } y ^ { 2 }} {/tex}

D

{tex} \mathrm{- 7 x ^ { 3 } - 28 x y ^ { 3 }} {/tex}

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Q 7. The value of the expression {tex}\mathrm{ 4 x y \left( x ^ { 2 } - y ^ { 2 } \right)} {/tex} at {tex}\mathrm{ x = - 1} {/tex} and {tex}\mathrm{ y = - 1} {/tex} is

A

{tex} 4 {/tex}

B

{tex} - 1 {/tex}

C

{tex} - 4 {/tex}

{tex} 0{/tex}

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Q 8. On simplifying {tex} 3 \mathrm { ab } \left( \mathrm { a } ^ { 2 } - \mathrm { b } ^ { 2 } \right) - 3 \mathrm { b } \left( \mathrm { a } ^ { 3 } - \mathrm { ab } ^ { 2 } + 4 \mathrm { ab } \right) , {/tex} we get

{tex}\mathrm{ - 12 a b ^ { 2 } }{/tex}

B

{tex}\mathrm{0 }{/tex}

C

{tex}\mathrm{ 12 a ^ { 2 } b} {/tex}

D

{tex}\mathrm{ 3 a ^ { 2 } b ^ { 2 }} {/tex}

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Q 9. The value of the expression {tex} \mathrm{3 x y \left( x ^ { 2 } - x y + y ^ { 2 } \right) }{/tex} at {tex}\mathrm{ x = 1 , y = - 1} {/tex} is

A

{tex} - 3 {/tex}

{tex} - 9 {/tex}

C

{tex}3{/tex}

D

{tex}1{/tex}

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Q 10. On simplifying {tex} 4 \mathrm { pq } \left( \mathrm { p } ^ { 2 } + \mathrm { q } ^ { 2 } \right) - 4 \mathrm { pq } \left( \mathrm { p } ^ { 2 } - \mathrm { q } ^ { 2 } \right) , {/tex} we get

A

{tex} \mathrm{0} {/tex}

B

{tex} \mathrm{8 p ^ { 3 } q} {/tex}

{tex}\mathrm{ 8 p q ^ { 3 }} {/tex}

D

{tex} \mathrm{- 8 p q ^ { 3 }} {/tex}

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Q 11. The number of terms in the product of {tex}\mathrm{ ( x - 4 )} {/tex} and {tex}\mathrm{ \left( x ^ { 2 } - 7 x + 12 \right) }{/tex} is

4

B

6

C

5

D

2

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Q 12. The area of a rectangle is length {tex} \times {/tex} breadth. If the length is {tex}\mathrm{ ( x + 3 ) }{/tex} units and breadth is {tex}\mathrm{( y - 3 ) }{/tex} units the area is :

A

{tex} \mathrm{x y - 3 y + 3 x - 9} {/tex}

{tex}\mathrm{ x y + 3 y - 3 x - 9 }{/tex}

C

{tex}\mathrm{ x y + 3 y + 3 x - 9} {/tex}

D

{tex}\mathrm{ x y - 3 y - 3 x - 9 }{/tex}

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Q 13. The volume of a box is given by the formula length {tex} \times {/tex} breadth {tex} \times {/tex} height. If the length is {tex}\mathrm{4x}{/tex} units, breath is {tex}\mathrm{ 3 y ^ { 2 }} {/tex} units and height is {tex}\mathrm {2 x ^ { 2 } y} {/tex} units the volume is:

A

{tex}\mathrm{ 12 x ^ { 2 } y ^ { 2 } }{/tex}

B

{tex}\mathrm{ 24 x y ^ { 3 } }{/tex}

C

{tex} \mathrm{24 x ^ { 3 } y ^ { 2 } }{/tex}

{tex} \mathrm{24 x ^ { 3 } y ^ { 3 }} {/tex}

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Q 14. The middle term in the expression {tex}\mathrm{ ( 2 y - 3 z ) ^ { 2 }} {/tex} is

A

{tex} 12 \mathrm { yz } {/tex}

B

{tex} \mathrm{- 6 y z }{/tex}

{tex}\mathrm{ - 12 y z} {/tex}

D

{tex}\mathrm{ 6 y z }{/tex}

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Q 15. The vlaue of {tex} \mathrm{13.1 ^ { 2 } - 6.9 ^ { 2 } }{/tex} is

124

B

12.4

C

1.24

D

1124

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Q 16. The degree of {tex} 4 \mathrm { x } ^ { 2 } \mathrm { y } + \mathrm { x } ^ { 2 } - 2 \mathrm { y } ^ { 2 } {/tex} is

A

2

3

C

4

D

- 2

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Q 17. What must be added to {tex}\mathrm{ 2 x ^ { 2 } - 3 x - 8} {/tex} to get {tex}\mathrm{ 3 x ^ { 2 } + x + 6 ? }{/tex}

{tex}\mathrm{ x ^ { 2 } + 4 x + 14 }{/tex}

B

{tex} \mathrm{- x ^ { 2 } - 4 x - 14} {/tex}

C

{tex}\mathrm{ 5 x ^ { 2 } - 2 x - 2} {/tex}

D

{tex}\mathrm{ x ^ { 2 } - x - 2} {/tex}

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Q 18. What must be subtracted from {tex}\mathrm{ x ^ { 3 } + 3 x - 9} {/tex} to get {tex} \mathrm{3 x ^ { 3 } + x ^ { 2 } + 3 ? }{/tex}

A

{tex}\mathrm{ 4 x ^ { 3 } + 4 x ^ { 2 } - 6 }{/tex}

B

{tex}\mathrm {4 x ^ { 3 } + x ^ { 2 } + 3 x - 6} {/tex}

{tex} \mathrm{- 2 x ^ { 3 } - x ^ { 2 } + 3 x - 12} {/tex}

D

{tex} \mathrm{2 x ^ { 3 } - x ^ { 2 } - 3 x + 12} {/tex}

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Q 19. If {tex}\mathrm{ a = b = 2 , }{/tex} then the value of {tex}\mathrm{ ( a - b ) \left( a ^ { 2 } + a b - b ^ { 2 } \right) }{/tex} will be

A

2

0

C

1

D

48

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Q 20. {tex}\mathrm{ \frac { 2 } { 3 } x y \times \frac { 3 } { 4 } x z }{/tex} is

A

{tex}\mathrm{ \frac { 1 } { 12 } x ^ { 2 } y }{/tex}

B

{tex}\mathrm{ \frac { 1 } { 2 } x y z }{/tex}

{tex}\mathrm{ \frac { 1 } { 2 } x ^ { 2 } y z} {/tex}

D

{tex}\mathrm{ \frac { 1 } { 4 } x ^ { 2 } y} {/tex}

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Q 21. {tex}\mathrm{ ( - 3 a b ) \times \left( - 2 a ^ { 2 } b \right)} {/tex} is

A

{tex} \mathrm{- 6 a b ^ { 2 } }{/tex}

{tex} \mathrm{6 a ^ { 3 } b ^ { 2 } }{/tex}

C

{tex}\mathrm{ 6 a ^ { 3} b^{3 } }{/tex}

D

{tex} \mathrm{- 6 a ^ { 2 } b ^ { 2 }} {/tex}

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Q 22. {tex}\mathrm{ 25 x ^ { 8 } y ^ { 9 } z ^ { 5 } \times ( - 2 x y z ) ^ { 2 }} {/tex} is

A

{tex} \mathrm{50 x ^ { 9 } y ^ { 10 } z ^ { 6 }} {/tex}

{tex} \mathrm{100 x ^ { 10 } y ^ { 11 } z ^ { 7 }} {/tex}

C

{tex} \mathrm{ - 100 x ^ { 10 } y ^ { 11 } z ^ { 7 }} {/tex}

D

{tex} \mathrm{ - 50 x ^ { 9 } y ^ { 10 } z ^ { 6 }} {/tex}

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Q 23. The true statement is

A

{tex} \mathrm{3 x = 3 + x} {/tex}

B

{tex} \mathrm{ 2 ( x + 5 ) = 2 x + 5} {/tex}

{tex} \mathrm{ 4 \left( x ^ { 2 } - 3 \right) = 4 x ^ { 2 } - 12 }{/tex}

D

{tex} \mathrm{ x \times ( - 5 ) = x - 5} {/tex}

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Q 24. {tex} \mathrm{ ( 3 x - 4 ) ( 2 x + 7 )} {/tex} is

A

{tex} \mathrm{6 x ^ { 2 } + 3 x - 28} {/tex}

{tex} \mathrm{6 x ^ { 2 } + 13 x - 28} {/tex}

C

{tex} \mathrm{ 6 x ^ { 2 } + 29 x - 28} {/tex}

D

{tex} \mathrm{ 6 x ^ { 2 } - 29 x - 28 }{/tex}