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All questions of Fundamental Concepts of Algebra for Class 6 Exam
What type of expression is 4x²y + 2 - 3x?- a)Binomial
- b)Polynomial
- c)Monomial
- d)Trinomial
Correct answer is option 'D'. Can you explain this answer?
What type of expression is 4x²y + 2 - 3x?
a)
Binomial
b)
Polynomial
c)
Monomial
d)
Trinomial
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Prasad Kulkarni answered |
Understanding the Expression: 4x²y + 2 - 3x
To classify the expression 4x²y + 2 - 3x, it is essential to understand the definitions of different types of algebraic expressions.
What is a Monomial?
- A monomial consists of a single term. For example, 5x or 3y².
What is a Binomial?
- A binomial contains two terms. For example, 2x + 3 or 4y - 5.
What is a Trinomial?
- A trinomial consists of three distinct terms. For example, x² + 2x + 1.
What is a Polynomial?
- A polynomial is a general term that includes monomials, binomials, and trinomials. It consists of one or more terms combined by addition or subtraction.
Analyzing the Expression
1. The expression 4x²y + 2 - 3x has three separate terms:
- 4x²y (first term)
- 2 (second term)
- -3x (third term)
2. Since there are three distinct terms in the expression, it qualifies as a trinomial.
Conclusion
Thus, the correct classification for the expression 4x²y + 2 - 3x is option 'D', which is trinomial. Understanding these classifications helps in identifying and working with algebraic expressions more effectively.
To classify the expression 4x²y + 2 - 3x, it is essential to understand the definitions of different types of algebraic expressions.
What is a Monomial?
- A monomial consists of a single term. For example, 5x or 3y².
What is a Binomial?
- A binomial contains two terms. For example, 2x + 3 or 4y - 5.
What is a Trinomial?
- A trinomial consists of three distinct terms. For example, x² + 2x + 1.
What is a Polynomial?
- A polynomial is a general term that includes monomials, binomials, and trinomials. It consists of one or more terms combined by addition or subtraction.
Analyzing the Expression
1. The expression 4x²y + 2 - 3x has three separate terms:
- 4x²y (first term)
- 2 (second term)
- -3x (third term)
2. Since there are three distinct terms in the expression, it qualifies as a trinomial.
Conclusion
Thus, the correct classification for the expression 4x²y + 2 - 3x is option 'D', which is trinomial. Understanding these classifications helps in identifying and working with algebraic expressions more effectively.
What is a monomial?- a)An expression with at least two variables
- b)An expression with two terms
- c)An expression with three terms
- d)An expression with one term
Correct answer is option 'D'. Can you explain this answer?
What is a monomial?
a)
An expression with at least two variables
b)
An expression with two terms
c)
An expression with three terms
d)
An expression with one term
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EduRev Class 6 answered |
A monomial is defined as an algebraic expression that contains exactly one non-zero term. Examples include x, 3y, and 5ab.
What is the degree of the polynomial 3x²y + 4x - 7?- a)3
- b)2
- c)4
- d)1
Correct answer is option 'B'. Can you explain this answer?
What is the degree of the polynomial 3x²y + 4x - 7?
a)
3
b)
2
c)
4
d)
1
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Get Idea answered |
The degree of a polynomial is determined by the highest power of the variable. In this case, the term 3x²y has the highest power (2), so the degree is 2.
What does the term "coefficient" refer to in algebra?- a)The numerical factor of a term
- b)The total number of terms in an expression
- c)The degree of a term
- d)The variable part of an expression
Correct answer is option 'A'. Can you explain this answer?
What does the term "coefficient" refer to in algebra?
a)
The numerical factor of a term
b)
The total number of terms in an expression
c)
The degree of a term
d)
The variable part of an expression
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Get Idea answered |
The coefficient is the numerical factor that multiplies the variable(s) in a term. For example, in 4x, the coefficient is 4.
What is the rule for combining like terms?- a)Divide the coefficients and keep the variable part.
- b)Multiply the coefficients and add the variables.
- c)Add the numerical coefficients and keep the variable part the same.
- d)Change the variable part to match.
Correct answer is option 'C'. Can you explain this answer?
What is the rule for combining like terms?
a)
Divide the coefficients and keep the variable part.
b)
Multiply the coefficients and add the variables.
c)
Add the numerical coefficients and keep the variable part the same.
d)
Change the variable part to match.
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EduRev Class 6 answered |
To combine like terms, you add their numerical coefficients while keeping the variable part the same. This helps simplify expressions effectively.
What is the highest degree of the polynomial 2x³y - x² + 4y²?- a)4
- b)1
- c)2
- d)3
Correct answer is option 'D'. Can you explain this answer?
What is the highest degree of the polynomial 2x³y - x² + 4y²?
a)
4
b)
1
c)
2
d)
3
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Get Idea answered |
The highest degree of the polynomial 2x³y - x² + 4y² is 3, which comes from the term 2x³y. The degree indicates the term with the largest exponent of the variable.
What is the area of a rectangle if its length is l and breadth is b?- a)l × b
- b)l - b
- c)l + b
- d)2(l + b)
Correct answer is option 'A'. Can you explain this answer?
What is the area of a rectangle if its length is l and breadth is b?
a)
l × b
b)
l - b
c)
l + b
d)
2(l + b)
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EduRev Class 6 answered |
The area of a rectangle is found by multiplying its length (l) by its breadth (b), resulting in the formula Area = l × b. This formula is fundamental in geometry and helps in various practical situations.
Which of these is an example of an unlike term?- a)2y and 3y
- b)-7xy and 7xy
- c)4x² and 4xy
- d)5x and 3x
Correct answer is option 'C'. Can you explain this answer?
Which of these is an example of an unlike term?
a)
2y and 3y
b)
-7xy and 7xy
c)
4x² and 4xy
d)
5x and 3x
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EduRev Class 6 answered |
4x² and 4xy are unlike terms because they have different literal factors (x² vs. xy). Recognizing like and unlike terms is essential for simplifying expressions.
If n represents the number of triangles, how many matchsticks are needed to form n triangles?- a)3n
- b)n + 3
- c)3n - 1
- d)2n
Correct answer is option 'A'. Can you explain this answer?
If n represents the number of triangles, how many matchsticks are needed to form n triangles?
a)
3n
b)
n + 3
c)
3n - 1
d)
2n
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Get Idea answered |
The formula for the number of matchsticks needed to form n triangles is 3n. This helps in understanding how to generalize patterns.
Which of the following statements is true about a binomial?- a)It cannot contain variables.
- b)It has one non-zero term.
- c)It has three non-zero terms.
- d)It has two non-zero terms.
Correct answer is option 'D'. Can you explain this answer?
Which of the following statements is true about a binomial?
a)
It cannot contain variables.
b)
It has one non-zero term.
c)
It has three non-zero terms.
d)
It has two non-zero terms.
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EduRev Class 6 answered |
A binomial is defined as an algebraic expression that consists of exactly two non-zero terms. This concept is foundational in algebra for simplifying expressions.
What is the term for a letter or symbol in algebra whose value can change?- a)Variable
- b)Coefficient
- c)Constant
- d)Term
Correct answer is option 'A'. Can you explain this answer?
What is the term for a letter or symbol in algebra whose value can change?
a)
Variable
b)
Coefficient
c)
Constant
d)
Term
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A variable is a symbol (like x, y, or z) that can take on different values. In contrast, a constant has a fixed value. Understanding the distinction between constants and variables is essential for solving algebraic expressions.
Which of the following is an example of a constant?- a)3x
- b)-5
- c)y
- d)2a
Correct answer is option 'B'. Can you explain this answer?
Which of the following is an example of a constant?
a)
3x
b)
-5
c)
y
d)
2a
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EduRev Class 6 answered |
A constant is a number that does not change. For example, -5 is a constant, while 3x and 2a are variables because they include letters that can vary in value.
What is an algebraic expression?- a)A formula without numbers
- b)A combination of constants and variables
- c)A constant only
- d)A single number
Correct answer is option 'B'. Can you explain this answer?
What is an algebraic expression?
a)
A formula without numbers
b)
A combination of constants and variables
c)
A constant only
d)
A single number
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Get Idea answered |
An algebraic expression is a combination of constants, variables, and arithmetic operations. It can include multiple terms and is used to represent mathematical relationships.
What distinguishes like terms from unlike terms?- a)They have the same literal factors with the same powers.
- b)They have different numerical factors.
- c)They have the same numerical factors.
- d)They have the same coefficients.
Correct answer is option 'A'. Can you explain this answer?
What distinguishes like terms from unlike terms?
a)
They have the same literal factors with the same powers.
b)
They have different numerical factors.
c)
They have the same numerical factors.
d)
They have the same coefficients.
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Get Idea answered |
Like terms share the same literal factors raised to the same powers, while unlike terms differ in either their literal factors or the powers of those factors.
If n represents the number of squares, what is the formula for the number of matchsticks needed to form n squares?- a)n + 3
- b)2n + 1
- c)3n + 1
- d)4n
Correct answer is option 'C'. Can you explain this answer?
If n represents the number of squares, what is the formula for the number of matchsticks needed to form n squares?
a)
n + 3
b)
2n + 1
c)
3n + 1
d)
4n
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Get Idea answered |
The formula for the number of matchsticks needed to form n squares is 3n + 1. This shows how algebra can help us derive general rules from patterns.
Which of these is NOT a polynomial?- a)3x + 2
- b)5x²
- c)4/x
- d)7y - 3
Correct answer is option 'C'. Can you explain this answer?
Which of these is NOT a polynomial?
a)
3x + 2
b)
5x²
c)
4/x
d)
7y - 3
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EduRev Class 6 answered |
The expression 4/x is not a polynomial because it includes a variable in the denominator, which is not allowed in polynomials. Polynomials consist only of non-negative integer powers of variables.
In the expression 5xy, what is the numerical factor?- a)None of the above
- b)5
- c)xy
- d)y
Correct answer is option 'B'. Can you explain this answer?
In the expression 5xy, what is the numerical factor?
a)
None of the above
b)
5
c)
xy
d)
y
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Get Idea answered |
The numerical factor in the term 5xy is 5. The numerical part is the coefficient, while the letters (x and y) are the variables.
In the expression 2x² - 3xy + 5, which term is a constant?- a)-3xy
- b)5
- c)All are constants
- d)2x²
Correct answer is option 'B'. Can you explain this answer?
In the expression 2x² - 3xy + 5, which term is a constant?
a)
-3xy
b)
5
c)
All are constants
d)
2x²
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Get Idea answered |
The term 5 is the constant in the expression because it does not contain any variables. Understanding constants is vital for evaluating expressions.
What is the perimeter formula for a square with side length l?- a)6l
- b)l + l
- c)2l
- d)4l
Correct answer is option 'D'. Can you explain this answer?
What is the perimeter formula for a square with side length l?
a)
6l
b)
l + l
c)
2l
d)
4l
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EduRev Class 6 answered |
The perimeter of a square is calculated as 4 times the side length (4l). Understanding this formula is crucial for solving problems related to geometric figures.
If the formula for the total length of the edges of a cube is 12l, what does l represent?- a)The volume of the cube
- b)The length of one edge
- c)The perimeter of one face
- d)The area of one face
Correct answer is option 'C'. Can you explain this answer?
If the formula for the total length of the edges of a cube is 12l, what does l represent?
a)
The volume of the cube
b)
The length of one edge
c)
The perimeter of one face
d)
The area of one face
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EduRev Class 6 answered |
In the formula 12l, l represents the length of one edge of the cube. This formula helps us find the total length of all 12 edges based on the length of a single edge.
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Mathematics Class 6 ICSE
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