This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Applications of Linear Equation (Just Solving the Equations)”.

1. What should be added to twice the rational number \(\frac{13}{3}\) to get \(\frac{13}{6}\)?

a) \(\frac{-13}{4}\)

b) \(\frac{-13}{2}\)

c) \(\frac{13}{2}\)

d) \(\frac{13}{4}\)

View Answer

Explanation: Twice the rational number is (2) × \(\frac{13}{3} = \frac{26}{3}\)

Let x be added to \(\frac{26}{3}\),

x + \(\frac{26}{3} = \frac{13}{6}\)

x = \(\frac{13}{6} – \frac{26}{3}\)

x = \(\frac{13}{6} – \frac{52}{6}\)

x = \(\frac{-39}{6}\)

x = \(\frac{-13}{2}\).

2. Perimeter of a square is 48 m. What is the length of one side?

a) 12 m

b) 192 m

c) 13 m

d) 14 m

View Answer

Explanation: Formula for perimeter is square,

Perimeter = 4 × (Length of one side)

48 = 4 × (Length of one side)13

Dividing throughout by 4 we get,

Length of one side = 12.

3. At Tanay’s birth, he was 34 years younger than his father. What will be his age after 20 years?

a) 20

b) 54

c) 0

d) 14

View Answer

Explanation: At birth Tanay’s age would be 0, at that time difference in ages was 34 years.

As the time passes Tanay and his father’s age increases but the difference remains same.

Hence, Tanay’s age would be

i.e. Age at his birth + 20 years

i.e. 0 + 20 years

i.e. 20 years.

4. If a side of a regular hexagon is 20 cm then what will be the perimeter of that regular hexagon?

a) 120 cm

b) 120 m

c) 60 cm

d) 60 m

View Answer

Explanation: A regular hexagon has six equal sides.

Perimeter of a regular hexagon = 6 × (Side of the hexagon)

Perimeter of a regular hexagon = 6 × (20)

Perimeter of a regular hexagon = 120 cm.

5. Sum of two distinct numbers is positive then which of the following statements is correct?

a) Both numbers are equal and negative

b) Greater one positive and smaller one negative

c) Both positive

d) Both negative

View Answer

Explanation: Here we are given that there are two distinct numbers, so the option stating equal and negative is ruled out. The second information we have is the sum is negative, so if the greater number is positive than the sum is positive and hence the option which states greater one positive and smaller one negative also is ruled out. Now we have two options left they are both positive or negative. We know that sum two positive number is positive. So the option left is both negative which is the correct options.

6. There are two parties in an election the ratio of their votes is 2:3. The total number of voters who took part in that election are 1200. How many votes did the winning party get?

a) 480

b) 600

c) 1200

d) 720

View Answer

Explanation: Let the common ratio be x.

∴ 2x + 3x = 1200

∴ 5x = 1200

∴ x = 240

The party which gets higher number of votes wins the election so, the party which has 3x votes is the winning party.

Number of votes = 3x

= 3 × 240

= 720.

7. If circumference of a circle is 6.28 cm then what is the radius of the circle?

a) 2 cm

b) 1 cm

c) 4 cm

d) 3 cm

View Answer

Explanation: Circumference of a circle = 2 × π × Radius

6.28 = 2 × 3.14 × Radius

Radius = 1.

8. The degree of linear equation in one variable is _______

a) 1

b) 2

c) 3

d) 4

View Answer

Explanation: Degree is the highest power of any equation.

In any linear equation the highest power is 1

Hence the degree of linear equation in one variable is 1.

9. The process of shifting any constant or variable in an equation from one side to other is ___________

a) assosiativity

b) distributivity

c) commutativity

d) transposition

View Answer

Explanation: This is the property used while we solve equations. In this property when we take a component of equation from LHS to RHS or vice versa the signs change, the change of signs is in order to balance the equation.

10. Linear equation in one variable has ________ number of solution/s.

a) one

b) one and only one

c) two

d) infinite

View Answer

Explanation: The number of solution of any equation depends on the degree of the equation (degree is the highest power of the equation. Example x

^{2}+x-2=0 here the degree of the equation is 2 as the highest power in this equation is 2). Since the linear equation in one variable has it’s degree as 1 always, therefore the answer would be ‘one and only one solution’. The option ‘one’ is not accurate and hence one should select ‘one and only one’.

**Sanfoundry Global Education & Learning Series – Mathematics – Class 8**.

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