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This mock test of Test: Algebraic Expressions - 3 for Class 7 helps you for every Class 7 entrance exam.
This contains 20 Multiple Choice Questions for Class 7 Test: Algebraic Expressions - 3 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If x+y = 5, y+z = 7and z+x = 12, what is the value of x+y+z?

Solution:

⇒ x+y+z = 12

2 (x + y + z) = 24

QUESTION: 2

How many auxiliary formulae can be formed from the expression in the box?

Solution:

3 formulae with the three unknowns can be formed from the given expression.

QUESTION: 3

What is the difference between 3a + 2b and −2a − 5b?

Solution:

(3a + 2b) − (−2a − 5b)

= 3a + 2b + 2a + 5b = 5a + 7b

QUESTION: 4

The length and breadth of a rectangular plot are I and b. Two rectangular paths each of width W run inside the plot one parallel to the length and the other parallel to the breadth. What is the total area of the paths?

Solution:

Area of the path along length = l×w

Area of the path along breadth = l×w

The common area of the paths = w^{2}

∴ Total area of the path = lw+lw−w^{2} = (l+b−w)w

QUESTION: 5

In a two digit number, the units digit is x and tens digit is (x+3). What is the sum of the digits in the number?

Solution:

Sum of units digit (x) and tens digit (x + 3) is x + x + 3 = 2x+3.

QUESTION: 6

A and B are polynomials and each is the additive inverse of the other. What does it mean?

Solution:

QUESTION: 7

When a certain number, 'm' is divided by 5 and added to 8, the result is equal to thrice the number subtracted from 4. What is the value of 'm?

Solution:

QUESTION: 8

5 added to thrice a number is equal to 12 added to twice the number. What is the number?

Solution:

QUESTION: 9

In the figure given what is the perimeter, in cm, of the triangle?

Solution:

QUESTION: 10

If , find the value of x.

Solution:

⇒ C(x−b) = x−a

⇒ x =

QUESTION: 11

Match the following.

Solution:

QUESTION: 12

Which of the following is true?

Solution:

QUESTION: 13

If x = 3, a = (−1) and b= (−2), what is the value of 2−6x + 4a−3b?

Solution:

QUESTION: 14

For what value of 'm' is 9 − 5m = (−1)?

Solution:

QUESTION: 15

Simplify x^{2}y^{3 }−1.5x^{2}y^{3}+1.4x^{2}y^{3}.

Solution:

QUESTION: 16

What is the value of(a^{3}−2a^{2}+4a−5)−(−a^{3}−8a+2a^{2}+5)?

Solution:

a^{3}−2a^{2 }+ 4a − 5 −(−a^{3 }− 8a + 2a^{2}+5)=a^{3 }− 2a^{2 }+ 4a − 5 + a^{3 }+ 8a - 2a^{2}-5

=2a^{3 }− 4a^{2 }+ 12a − 10

QUESTION: 17

By how much is x^{4}−4x^{2}y^{2}+y^{4 }less than x^{4}+8x^{2}y^{2}+y^{4}?

Solution:

x^{4}+8x^{2}y^{2}+y^{4}-(x^{4}-4x^{2}y^{2}+y^{4})=x^{4}+8x^{2}y^{2}+y^{4}-x^{4}+4x^{2}y^{2}-y^{4}

=12x^{2}y^{2}

QUESTION: 18

What is the sum of ; and a^{2}+b^{3}+c^{3}?

Solution:

+ (a^{2 }+ b^{3 }+ c^{3})

QUESTION: 19

Match the following.

Solution:

Substitute the given values in the expressions and evaluate.

a^{3}−b^{3 }= 3^{3}−2^{3 }= 9−8 =1

z^{3}−3 (z−10) =10^{3}−3(10−10)

=10^{3 }− 0 =1000

x^{2}+2x+1 = (−1)^{2 }+ 2(1)+1

= 1−2+1 = 0

QUESTION: 20

Simplify the following expression.x(y−z)−y(z−x)−z(x−y)

Solution:

x(y−z) − y(z−x) − z(x−y)

= xy − xz − yz + xy − zx + yz

= 2xy − 2zx = 2x(y−z)

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