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All questions of Algebraic Expressions for Class 7 Exam

The number of terms in 4p2q − 3pq+ 5 is
  • a)
    3
  • b)
    7
  • c)
    5
  • d)
    1
Correct answer is option 'A'. Can you explain this answer?

Varun Kapoor answered
Number of terms means the total number of individual elements present in a statement.
We have 4p2q, 3pq2 and 5 separated by a plus or minus sign, so these three are our terms.

Which of the following pairs of terms is a pair of unlike terms?
  • a)
     -p2q2,12q2p2
  • b)
    -4yx2,-4xy2
  • c)
    41,100
  • d)
    qp2,13p2q
Correct answer is option 'B'. Can you explain this answer?

Varun Kapoor answered
The correct option is B −4yx2,−4xy2
  • −p2q2,12q2p2: terms contain same variables with equal exponents, so these are like terms.
  • −4yx2,−4xy2: As in −4yx2, x has exponent 2 & y has exponent 1 and in −4xy2 , y has exponent 2 & x has exponent 1. So both the terms have same variables but with different exponent. Hence −4yx2,−4xy2 are unlike terms.
  • 41, 100: terms do not contain any variable, so these are like terms.
  • qp2,13p2q: terms have same variables p and q with equal exponent 2 and 1 respectively. So, these are like terms.

What is the numerical coefficient of y2in the expression 2x2y - 15xy+ 7y
  • a)
    x
  • b)
    5
  • c)
    -15
  • d)
    15x
Correct answer is option 'C'. Can you explain this answer?

The numerical coefficient is the constant part of the term without the variables. In this case, the numerical coefficient of y2 is -15.

The coefficient of yin the expression y − y3+ y2is
  • a)
    -1
  • b)
    2
  • c)
    1
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Coefficient is the numerical number associated with the variable. So here we have (-1)y3. So the answer is -1.

The expression xyz is
  • a)
    binomial
  • b)
    monomial
  • c)
    trinomial
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Maitri Sarkar answered
Monomial: An algebraic expression which consists of one non-zero term only is called a monomial.Examples of 

Simplify the following: 7xy− y+ 7x2y − 5x2 − 3y2 + 4y2x  − 3y+ x2
  • a)
     11xy+ 7xy2 − 4x2 − 7y2
  • b)
     7xy2 − 11xy2  + 4x2 − 7y2
  • c)
     
     7x2y + 11xy2 − 4x2 − 7y2
  • d)
     11xy2 − 7xy2  + 4x2 − 7y2
Correct answer is option 'C'. Can you explain this answer?

To simplify the expression 7xy2 - y2 + 7x2y - 5x2 - 3y2 + 4y2x - 3y2 + x2, follow these steps:
7xy2 + 4y2x + 7x2y - 5x2 + x2 - 3y2 - y2 - 3y2
- For xy2: (7 + 4)xy2 = 11xy2
- For x2: (1 - 5)x2 = -4x2
- For y2: (-3 - 1 - 3)y2 = -7y2
11xy2 + 7x2y - 4x2 - 7y2
  • Rearrange the terms:
  • Combine like terms:
  • Final simplified expression:

When terms have the same algebraic factor, they are called __________.
  • a)
    like terms
  • b)
    expressions
  • c)
    unlike terms
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Vp Classes answered
- When terms have the same algebraic factor, they are called like terms.
- Like terms have identical variables raised to the same powers, but they may have different coefficients.
- For example, in the expression 3x2 + 5x - 2x2, the terms 3x2 and -2x2 are like terms.

A _________ can take various values.
  • a)
    variable
  • b)
    expression
  • c)
    term
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Subset Academy answered
- A variable is a symbol used to represent a quantity that can change or take on different values.
- In mathematics and programming, variables are placeholders for data that can vary.
- Examples include variables in algebra like  x or y, which can represent any number.
- Unlike constants, which have a fixed value, variables are designed to be flexible and adaptable to different situations.

The number of terms in the expression 1.2ab – 2.4 b + 3.6a is
  • a)
    4
  • b)
    3
  • c)
    2
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

The expression 1.2ab−2.4b+3.6aconsists of three terms:
  1. 1.2ab
  2. −2.4b
  3. 3.6a
Hence, the number of terms in this expression is 3.

From the following expressions 10pq, 7p, 8q, −p2q2, -7pq, -23, ab, 3a, b.The like terms are
  • a)
    7p, 8q
  • b)
    ab, 3a, b
  • c)
    10pq,-7pq
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Freak Artworks answered
Like terms are those that have the same variable(s) raised to the same power(s).
Here, 10pq and −7pq are like terms because they both contain pq with the same powers of p and q.

A taxi charges $27 per km and a fixed charge of $45. If the taxi is hired for z km, which of the following is an algebraic expression to find the total fare?
  • a)
    27z − 45
  • b)
    27z + 45
  • c)
    45z + 27
  • d)
    45z − 27
Correct answer is option 'B'. Can you explain this answer?

Rashi patil answered
Total Taxi Fare Calculation
To find the total fare for a taxi ride, we need to consider both the variable and fixed components of the fare.
Components of the Fare
- Fixed Charge: This is the base charge that applies regardless of the distance traveled. In this case, it is $45.
- Variable Charge: This charge depends on the distance traveled, which is $27 per kilometer.
Expression for Total Fare
To calculate the total fare when the taxi is hired for 'z' kilometers, we combine both the fixed and variable charges:
- Variable Charge for 'z' km: Since the taxi charges $27 for each kilometer, for 'z' kilometers, the charge would be 27z.
- Total Fare Calculation: The total fare is the sum of the fixed charge and the variable charge:
Total Fare = Fixed Charge + Variable Charge
Total Fare = 45 + 27z
This can be rearranged to:
Total Fare = 27z + 45
Therefore, the correct algebraic expression for the total fare is 27z + 45, which corresponds to option 'B'.
Why Other Options Are Incorrect
- Option A (27z - 45): This incorrectly subtracts the fixed charge from the variable charge.
- Option C (45z + 27): This suggests a charge of $45 for each kilometer, which is incorrect.
- Option D (45z - 27): This again incorrectly combines the charges and does not reflect the correct pricing structure.
Conclusion
Thus, the correct expression to calculate the total taxi fare for 'z' kilometers is 27z + 45.

Simplify the expression −3(x + y) +5(x − y)
  • a)
    2x − 8y
  • b)
    − 2x + 2y
  • c)
    8x − 8y
  • d)
    2x + 8y
Correct answer is option 'A'. Can you explain this answer?

Coachify answered
To simplify the expression −3(x + y) + 5(x − y), follow these steps:
  • Expand the expression:
  • −3(x + y) + 5(x − y)
  • Distribute the terms:
  • −3x − 3y + 5x − 5y
  • Combine like terms:
  • (−3x + 5x) + (−3y − 5y) = 2x − 8y
Thus, the simplified expression is 2x − 8y.

Sita is y years old this year. Her brother is twice as old as her. How old was her brother 2 years ago?
  • a)
    2y−2
  • b)
    2y−4
  • c)
    y−2
  • d)
    y−1
Correct answer is option 'B'. Can you explain this answer?

Praveen Kumar answered
Sita's current age = y years.
Her brother's current age = 2y (since he is twice as old as her).
Two years ago, her brother's age = 2y−2
Subtracting 2 from 2y:
2y−2−2 = 2y−4

What is the coefficient of x² in the expression 5x²yz?
  • a)
    5
  • b)
    y
  • c)
    z
  • d)
    5yz
Correct answer is option 'D'. Can you explain this answer?

Understanding the Expression
The expression given is 5x²yz. To find the coefficient of x², we need to isolate the term that contains x² and determine its coefficient.
Identifying the Coefficient
- The term "5x²yz" consists of:
- 5: This is the coefficient.
- : This is the variable part associated with the coefficient.
- y and z: These are additional variables but do not affect the coefficient of x².
Definition of Coefficient
- A coefficient is a numerical factor in a term of an algebraic expression.
- In this case, the coefficient of x² in the term 5x² is 5.
Considering Other Variables
- While y and z are present in the expression, they do not contribute to the coefficient of x². They are simply part of the term and do not alter the numerical coefficient.
Final Answer
Therefore, when asked for the coefficient of x² in the expression 5x²yz:
- The correct coefficient is 5 (which corresponds to the numerical factor before x²).
- However, since the answer choices include additional variables, the complete expression for the coefficient of x², considering y and z, would be represented as 5yz.
Conclusion
Thus, the correct answer is option D: 5yz, as it includes the coefficient (5) multiplied by the other variables (y and z).

The expression "twice the product of 3 and x" is the same as which of the following?
  • a)
    2 + (3x)
  • b)
    (2 + 3) x
  • c)
    2 (3x)
  • d)
    2 (3 + x)
Correct answer is option 'C'. Can you explain this answer?

The phrase “the product of 3 and x” means 3x.
“Twice” indicates that we multiply the product by 2.
Therefore, “twice the product of 3 and x” can be expressed as:
2(3x)

What is the value of the expression ax² + by² – cz when x = 1, y = -1, z = 2, a = -2, b = 1, and c = -2?
  • a)
    1
  • b)
    3
  • c)
    5
  • d)
    7
Correct answer is option 'B'. Can you explain this answer?

Praveen Kumar answered
The value of the expression ax² + by² - cz can be calculated by substituting the given values:
  • Let a = -2b = 1c = -2x = 1y = -1, and z = 2.
  • Calculate each term:
    • ax²:
      -2 * (1)² = -2
    • by²:
      1 * (-1)² = 1
    • cz:
      -2 * 2 = -4
  • Combine the results:
    -2 + 1 - (-4) = -2 + 1 + 4 = 3
Thus, the final value of the expression is 3.

What is the value of the expression ax + by + cz when x = 1, y = -1, z = 2, a = -2, b = 1, and c = -2?
  • a)
    -3
  • b)
    -5
  • c)
    -7
  • d)
    -9
Correct answer is option 'C'. Can you explain this answer?

Praveen Kumar answered
The value of the expression ax + by + cz can be calculated by substituting the given values:
  • Let x = 1y = -1z = 2a = -2b = 1, and c = -2.
  • Substituting these values into the expression:
  • ax = -2 * 1 = -2
  • by = 1 * (-1) = -1
  • cz = -2 * 2 = -4
Now, combine the results:
  • -2 + (-1) + (-4) = -2 - 1 - 4 = -7
Thus, the value of the expression is -7.

When a = 0, b = -1, find the value of 2a²b + 2ab² + ab.
  • a)
    0
  • b)
    1
  • c)
    -1
  • d)
    -0
Correct answer is option 'A'. Can you explain this answer?

To find the value of the expression:
We need to evaluate the expression 2a²b + 2ab² + ab with the values:
  • a = 0
  • b = -1
Substituting the values into the expression:
  • 2(0)²(-1) + 2(0)(-1)² + (0)(-1)
  • = 0 + 0 + 0
  • = 0
The final result is 0, which is the required value.

Chapter doubts & questions for Algebraic Expressions - Mathematics (Maths) Class 7 2025 is part of Class 7 exam preparation. The chapters have been prepared according to the Class 7 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 7 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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