Class 7 Important Questions for Maths - Algebraic Expressions ... - Free Printable

Let's solve each question step by step:

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Question 1:

An algebraic expression containing three terms is called a
(a) monomial
(b) binomial
(c) trinomial
(d) All of these

Solution:
- A monomial is an expression with one term.
- A binomial is an expression with two terms.
- A trinomial is an expression with three terms.

Since the question asks for an expression with three terms, the correct answer is:
Answer: (c) trinomial

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Question 2:

Number of terms in the expression \(3x^2y - 2y^2z - z^2x + 5\) is
(a) 2
(b) 3
(c) 4
(d) 5

Solution:
The given expression is:
\[ 3x^2y - 2y^2z - z^2x + 5 \]

Each term is separated by a plus or minus sign:
1. \(3x^2y\)
2. \(-2y^2z\)
3. \(-z^2x\)
4. \(5\)

There are 4 terms in total.

Answer: (c) 4

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Question 3:

The terms of expression \(4x^2 - 3xy\) are:
(a) \(4x^2\) and \(-3xy\)
(b) \(4x^2\) and \(3xy\)
(c) \(4x^2\) and \(-xy\)
(d) \(x^2\) and \(xy\)

Solution:
The given expression is:
\[ 4x^2 - 3xy \]

The terms are:
1. \(4x^2\)
2. \(-3xy\)

Answer: (a) \(4x^2\) and \(-3xy\)

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Question 4:

Factors of \(-5x^2 y^2 z\) are
(a) \(-5 \times x \times y \times z\)
(b) \(-5 \times x^2 \times y \times z\)
(c) \(-5 \times x \times x \times y \times y \times z\)
(d) \(-5 \times x \times y \times z^2\)

Solution:
The expression \(-5x^2 y^2 z\) can be factored as:
\[ -5 \times x \times x \times y \times y \times z \]

This is because:
- The coefficient is \(-5\).
- \(x^2\) means \(x \times x\).
- \(y^2\) means \(y \times y\).
- \(z\) remains as \(z\).

Thus, the factors are:
\[ -5 \times x \times x \times y \times y \times z \]

Answer: (c) \(-5 \times x \times x \times y \times y \times z\)

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Question 5:

Coefficient of \(x\) in \(-9xy^2z\) is
(a) \(9yz\)
(b) \(-9yz\)
(c) \(9y^2z\)
(d) \(-9y^2z\)

Solution:
The given expression is:
\[ -9xy^2z \]

To find the coefficient of \(x\), we treat \(x\) as the variable and consider the rest of the terms as the coefficient:
- The coefficient of \(x\) is \(-9y^2z\).

Answer: (d) \(-9y^2z\)

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Question 6:

Which of the following is a pair of like terms?
(a) \(-7xy^2z, -7x^2yz\)
(b) \(-10xyz^2, 3xyz^2\)
(c) \(3xyz, 3x^2y^2z^2\)
(d) \(4xyz^2, 4x^2yz\)

Solution:
Like terms are terms that have the same variables raised to the same powers.

- Option (a): \(-7xy^2z\) and \(-7x^2yz\) → Different powers of \(x\) and \(y\). Not like terms.
- Option (b): \(-10xyz^2\) and \(3xyz^2\) → Same variables with the same powers. Like terms.
- Option (c): \(3xyz\) and \(3x^2y^2z^2\) → Different powers of \(x\), \(y\), and \(z\). Not like terms.
- Option (d): \(4xyz^2\) and \(4x^2yz\) → Different powers of \(x\) and \(z\). Not like terms.

Answer: (b) \(-10xyz^2, 3xyz^2\)

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Question 7:

Identify the binomial out of the following:
(a) \(3x^2 + 5y - x^2y\)
(b) \(x^2y - 5y - x^2y\)
(c) \(xy + yz + zx\)
(d) \(3x^2 + 5y - xy^2\)

Solution:
A binomial is an expression with exactly two terms.

- Option (a): \(3x^2 + 5y - x^2y\) → Three terms. Not a binomial.
- Option (b): \(x^2y - 5y - x^2y\) → Simplifies to \(-5y\), which is one term. Not a binomial.
- Option (c): \(xy + yz + zx\) → Three terms. Not a binomial.
- Option (d): \(3x^2 + 5y - xy^2\) → Three terms. Not a binomial.

None of the options are binomials. However, if there is a typo or misinterpretation, recheck the options.

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Question 8:

The sum of \(x^4 - xy + 2y^2\) and \(-x^4 + xy + 2y^2\) is
(a) Monomial and polynomial in \(y\)
(b) Binomial and Polynomial
(c) Trinomial and polynomial
(d) Monomial and polynomial in \(x\)

Solution:
Add the two expressions:
\[ (x^4 - xy + 2y^2) + (-x^4 + xy + 2y^2) \]

Combine like terms:
- \(x^4\) and \(-x^4\) cancel out.
- \(-xy\) and \(+xy\) cancel out.
- \(2y^2 + 2y^2 = 4y^2\).

The result is:
\[ 4y^2 \]

This is a monomial and a polynomial in \(y\).

Answer: (a) Monomial and polynomial in \(y\)

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Question 9:

The subtraction of 5 times of \(y\) from \(x\) is
(a) \(5x - y\)
(b) \(y - 5x\)
(c) \(x - 5y\)
(d) \(5y - x\)

Solution:
Subtract 5 times \(y\) from \(x\):
\[ x - 5y \]

Answer: (c) \(x - 5y\)

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Question 10:

\(-b - 0\) is equal to
(a) \(-1 \times b\)
(b) \(1 - b - 0\)
(c) \(0 - (-1) \times b\)
(d) \(-b - 0 - 1\)

Solution:
Simplify \(-b - 0\):
\[ -b - 0 = -b \]

Option (a) \(-1 \times b\) is equivalent to \(-b\).

Answer: (a) \(-1 \times b\)

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Question 11:

The side length of the top of square table is \(x\). The expression for perimeter is:
(a) \(4 + x\)
(b) \(2x\)
(c) \(4x\)
(d) \(8x\)

Solution:
The perimeter of a square is given by:
\[ \text{Perimeter} = 4 \times \text{side length} \]

If the side length is \(x\), then:
\[ \text{Perimeter} = 4x \]

Answer: (c) \(4x\)

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Question 12:

The number of scarfs of length half metre that can be made from \(y\) metres of cloth is:
(a) \(2y\)
(b) \(\frac{y}{2}\)
(c) \(y + 2\)
(d) \(y + \frac{1}{2}\)

Solution:
If each scarf is of length \(0.5\) metres (or \(\frac{1}{2}\) metre), then the number of scarfs that can be made from \(y\) metres of cloth is:
\[ \text{Number of scarfs} = \frac{y}{0.5} = \frac{y}{\frac{1}{2}} = y \times 2 = 2y \]

Answer: (a) \(2y\)

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Question 13:

\(123x^2y - 138x^2y\) is a like term of:
(a) \(10xy\)
(b) \(-15xy\)
(c) \(-15x^2y\)
(d) \(10x^2y\)

Solution:
Simplify the given expression:
\[ 123x^2y - 138x^2y = (123 - 138)x^2y = -15x^2y \]

The like term is \(-15x^2y\).

Answer: (c) \(-15x^2y\)

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Question 14:

The value of \(3x^2 - 5x + 3\) when \(x = 1\) is
(a) 1
(b) 0
(c) \(-1\)
(d) 11

Solution:
Substitute \(x = 1\) into the expression:
\[ 3x^2 - 5x + 3 \]
\[ = 3(1)^2 - 5(1) + 3 \]
\[ = 3 \cdot 1 - 5 \cdot 1 + 3 \]
\[ = 3 - 5 + 3 \]
\[ = 1 \]

Answer: (a) 1

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Question 15:

The expression for the number of diagonals that we can make from one vertex of a \(n\)-sided polygon is:
(a) \(2n + 1\)
(b) \(n - 2\)
(c) \(5n + 2\)
(d) \(n - 3\)

Solution:
From one vertex of an \(n\)-sided polygon, you can draw diagonals to all other vertices except itself and its two adjacent vertices. Therefore, the number of diagonals is:
\[ n - 3 \]

Answer: (d) \(n - 3\)

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Question 16:

The length of a side of a square is given as \(2x + 3\). Which expression represents the perimeter of the square?
(a) \(2x + 16\)
(b) \(6x + 9\)
(c) \(8x + 3\)
(d) \(8x + 12\)

Solution:
The perimeter of a square is given by:
\[ \text{Perimeter} = 4 \times \text{side length} \]

If the side length is \(2x + 3\), then:
\[ \text{Perimeter} = 4(2x + 3) \]
\[ = 4 \cdot 2x + 4 \cdot 3 \]
\[ = 8x + 12 \]

Answer: (d) \(8x + 12\)

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Final Answers:

1. (c) trinomial
2. (c) 4
3. (a) \(4x^2\) and \(-3xy\)
4. (c) \(-5 \times x \times x \times y \times y \times z\)
5. (d) \(-9y^2z\)
6. (b) \(-10xyz^2, 3xyz^2\)
7. (No correct option provided; recheck.)
8. (a) Monomial and polynomial in \(y\)
9. (c) \(x - 5y\)
10. (a) \(-1 \times b\)
11. (c) \(4x\)
12. (a) \(2y\)
13. (c) \(-15x^2y\)
14. (a) 1
15. (d) \(n - 3\)
16. (d) \(8x + 12\)

Boxed Final Answer:
\[
\boxed{(c), (c), (a), (c), (d), (b), (\text{recheck}), (a), (c), (a), (c), (a), (c), (a), (d), (d)}
\]