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Algebraic Expression can be defined as an expression that consists of variables and constants in which a variable can take any value. It means that if the variable values are changed, then the expression value can change. Algebraic Identities are described as equality that is true for all the values of the variables.
Algebraic Identities are referred to as algebraic equations which are valid for all values of variables in them. They are very useful in the factorization of polynomials. In simpler terms, we can say that algebraic identities help in the computation of algebraic expressions and solving different polynomials. The Multiple Choice Questions for Algebraic Expression and Identities are provided below so that the students can utilise these solutions to help them better understand the concept.
Read More: Algebra and Its Branches
Ques 1. An algebraic expression that contains two terms, each of which is a monomial is called:
- Monomial
- Binomial
- Polynomial
- None of the above
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Ans. (b) Binomial
Explanation: A polynomial with only one pair of terms is called a binomial. A sum or difference between two monomials makes a binomial. For example, (3x+5) is a binomial. They are also called binomial expressions.
Ques 2. The algebraic expression 8a + 6b – 9c is a
- Monomial
- Binomial
- Trinomial
- None of the above
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Ans. (c) Trinomial
Explanation: The given algebraic expression contains three terms, 8a, 6b, and 9c, hence it is a trinomial. We must know that a trinomial is an algebraic expression with three terms.
Read More: Algebra Formula
Ques 3. A polynomial has the following number of terms:
- One
- Two
- Four
- None of the above
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Ans. (d) None of the above
Explanation: Any (finite) number of terms can be found in a polynomial. A polynomial can have one or more than one term, for example, 5x² + 4y – 6z +9 is a polynomial.
Ques 4. In which of the following, the two expressions are unlike terms?
- 5x and 77xy
- 6y² and 16y
- 8t and 25z²
- All of the above
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Ans. (d) All of the above
Explanation: Unlike terms are the algebraic terms that do not have the same literal coefficients (variables) and cannot be raised to the same power. In the above question, all the options have different literal coefficients, hence the correct option is all of the above.
Ques 5. The value of a² + a + 2b, when a= 1, b= –1
- 4
- 7
- 0
- –1
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Ans. (c) 0
Explanation: a= 1, b= –1
Putting the value of a and b in the given expression, we get
a² + a +2b
or, (1)² + 1 + 2×(–1)
or, 1 + 1 –2
= 0.
Hence the correct option is C
Ques 6. How many terms are there in the expression 7x² + 5x + 6y – 3xy + 8y²?
- 1
- 5
- 6
- None of the above
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Ans. (b) 5
Explanation: In the given algebraic expression, there are 5 terms – 7x², 5x, 6y, 3xy, 8y². Hence, the correct option is (b)
Ques 7. The numerical coefficient in the term 7a²b³ is
- 7
- 8
- 2
- 3
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Ans. (a) 7
Explanation: A numerical coefficient is any constant term (number) in front of one or more variables in an algebraic expression. In the above question, 7 is the constant term multiplied by a²b³. Hence, the correct option is (a).
Ques 8. Which one is the like terms in the following options?
- 3xy, 7yx
- ab, 6b
- –7, 7z
- 6z², 12y²
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Ans. (a) 3xy, 7yx
Explanation: Like terms are the algebraic terms that have the same literal coefficients (variables) and are raised to the same power. In the above question, option A has the same literal coefficient i.e. xy, thus, the correct option is (a).
Read More: Like and Unlike Algebraic Terms & Examples
Ques 9. The number of like terms in ¼a²bc, a²cba², a²bca², –24ba²c is
- 4
- 6
- 7
- None of the above
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Ans. (a) 4
Explanation: All the terms in the question have the same literal coefficient a²bc, hence the correct option is (a).
Ques 10. The coefficient of x²y in 62apqrx²y is
- Pq
- 62apqr
- 8x
- pqra
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Ans. (b) 62apqr
Explanation: The terms in the expression 62apqrx²y except x²y is 62apqr. Hence, the correct option is (b)
Ques 11. If we add, 7xy + 8yz – 6zx, 4yz + 2zx – 7y and –9xz + 5x – 2xy, then the answer is:
- 5xy + 9yz +3zx + 5x – 4y
- 5xy +53yz +3zx – 5x – 4y
- 5xy + 12yz –13zx + 5x –7y
- 5xy + 10yz +3zx + 5x – 6y
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Ans. (c) 5xy + 12yz –13zx + 5x –7y
Explanation: Given, 7xy + 8yz – 6zx, 4yz + 2zx – 7y and –9xz + 5x – 2xy
To add, combine the like terms together.
(7xy – 2xy) + (8yz + 4yz) + (2zx – 6zx – 9xz) –7y +5x
= 5xy + 12yz – 13zx + 5x –7y
Hence, the correct option is ©.
Ques 12. If we subtract 4a – 7ab + 2b + 10 from 14a – 9ab + 5b – 3, then the answer is:
- 8a+2ab+2b+15
- 10a–2ab+3b–13
- 10a–2ab+3b–15
- 8a–2ab–2b–15
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Ans. (b) 10a–2ab+3b–13
Explanation: (14a – 9ab + 5b – 3) – (4a – 7ab + 2b + 10)
= 14a – 9ab + 5b – 3 – 4a + 7ab –2b–10
= (14 – 4)a – (9 – 7)ab + (5 – 2)b – 3 – 10
= 10a – 2ab + 3b – 13
Hence, the correct option is (b)
Read More: Algebraic Operations on Complex Numbers
Ques 13. If we multiply 8ab and (–12a³b²c), then we get:
- 96a²b²c
- 96a³bc²
- –96a4b³c
- –96a³b³c
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Ans. © –96a4b³c
Explanation: 8ab × (–12a³b²c)
= 8 × a × b × (–12) × a × a × a × b × b × c
= –96 × a4 × b³ × c
= –96a4b³c
Hence, the correct option is (c)
Ques 14. The area of a rectangle whose length and breadth are 6y and 9y² respectively is:
- 12y³
- 45y³
- 54y³
- 54y²
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Ans. (c) 54y³
Explanation: Given, length= 6y and breadth= 9y²
Area of rectangle = length × breadth
= 6y × 9y²
= 54y³.
Hence, the correct option is (c)
Ques 15. The sum of 5x², -7x², 13x², 11x² and -5x² is
- 2x²
- 6x²
- 9x²
- 17x²
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Ans. (d) 17x²
Explanation: Given terms are: 5x², -7x², 13x², 11x² and -5x²
Adding all the terms, we get
5x² – 7x² + 13x² +11x² –5x²
or, 17x².
Hence, the correct option is (d).
Ques 16. The perimeter of a rectangle with length 2l²m² and breadth 3l²m² is
- 6l³m³
- 10l²m²
- 2l³m
- 10l²m³
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Ans. (b) 10l²m²
Explanation: Perimeter of a rectangle = 2 (length + breadth)
= 2 (2l²m² + 3l²m²)
= 2 × 5l²m²
= 10l²m²
Hence, the correct option is (b)
Ques 17. The volume of a cube of side 6xyz² is
- 36xyz²
- 216x³y³z³
- 26xyz²
- 216x³y³z6
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Ans. (d) 216x³y³z6
Explanation: Volume of a cube = (side)³
= 6xyz² × 6xyz² × 6xyz²
= 216 x × x × x × y × y × y × z² × z² × z²
= 216x³y³z6
Hence, the correct option is (d)
Ques 18. The value of (b – c)(b + c) + (c – a)(c + a) + (a – b) (a + b) is:
- b + c + a
- b² + c² + a²
- b² + ca + ab
- 0
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Ans. (d) 0
Explanation: Given, (b – c)(b + c) + (c – a)(c + a) + (a – b) (a + b)
= b² – c² + c² – a² + a² – b² [By algebraic identity: a2 – b2 = (a + b) (a – b)]
= 0
Hence, the correct option is (d)
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