Linear Equations in One Variable MCQs

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When displayed on a graph, a linear equation is an equation between two variables that results in a straight line and is a mathematical expression that can be written in the manner

a₁x₁+a₂x₂+…………+a_nx_n+b=0

where the variables (or unknowns) are x₁, x₂, ……..., x_n and the coefficients (typically actual numbers) are b, a₁, a₂, …….an which should never be zero.

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Question 1. The standard form of a linear equation in one variable x is

ax + b = 0
ax² + bx + c = 0
ax³ + bx² + cx + d = 0
ax⁴ + bx³ + cx²+ dx + e = 0.

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Answer: (a)

Explanation: a single variable linear equation is always of the form

ax + b = 0

Question 2. Which of the following is not a linear equation in one variable?

33
33(x+y)
33x
33y

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Answer: (b)

Explanation: In (b) i.e., 33(x+y), contains two variables x and y.

Question 3. The solution of 2x-3=7 is:

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Answer: (a)

Explanation: 2x-3=7

2x=7+3

=10

x=10/2

= 5

Question 4. The solution of 2y + 9 = 4 is:

9/2
4/9
-4/9
-5/2

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Answer: (d)

Explanation: 2y+9 = 4

2y = 4-9 = -5

y=-5/2

Question 5. The solution of y/5 = 10 is:

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Answer: (c)

Explanation: y/5 = 10

y = 5×10 = 50

Question 6. What should be added to -7/3 to get 3/7?

21/58
58/21
47/21
50/21

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Answer: (b)

Explanation: Let the number be x

-7/3+x = 3/7

x=3/7+7/3 = (9+49)/21 = 58/21

Question 7. The perimeter of a rectangle is 20cm. If the length of the rectangle is 6cm, then its breadth will be:

4 cm
6 cm
10 cm
14 cm

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Answer: (a)

Explanation: Perimeter of rectangle = 2(Length + Breadth)

20 = 2(6+x)

6+x = 20/2

6+x = 10

x = 10-6

x=4 cm

Question 8. The age of the father is three times the age of the son. If the age of the son is 15 years old, then the age of the father is:

50 years
55 years
40 years
45 years

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Answer: (d)

Explanation: Let age of the father is x

Given: x = 3 × (age of son) = 3 × (15) = 45 years

Question 9. The difference between the two whole numbers is 66. The ratio of the two numbers is 2: 5. The two numbers are:

60 and 6
100 and 33
110 and 44
99 and 33

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Answer: (c)

Explanation: Let the two numbers be 2x and 5x since they are in the ratio of 2:5.

The difference between 5x and 2x = 66

5x – 2x = 66

3x = 66

x = 22

Hence, 2x = 2(22) = 44 and 5x = 5(22) = 110.

Question 10. Three consecutive integers add up to 51. The integers are:

16,17,18
15,16,17
17,18,19
18,19,20

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Answer: (a)

Explanation: Let the three consecutive integers be x, x+1, x+2

x+(x+1)+(x+2) = 51

3x+3 = 51

3x = 51 – 3

x = 48/3 = 16

x+1 = 16+1=17

x+2 = x+2 = 18

Question 11. The solution for 3m = 5m – (8/5) is:

8/5
4/5
5/4
4/3

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Answer: (b)

Explanation: 3m = 5m – (8/5)

8/5 = 5m – 3m

2m = 8/5

m = 8/10 = 4/5

Question 12. What is the value of x if x + 9 = 12?

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Answer: (b)

Explanation: x + 9 = 12

X = 12 – 9

X = 3

Question 13. If a number is divided by 8 it gives 6 as the value. Find the number.

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Answer: (c)

Explanation: Let X be the number

X/8 = 6

X = 8 x 6 = 48

Question 14. Solve 2x + 9 = 4.

X = 6
X = -5/2
X = -3/2
X = -9/2

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Answer: (b)

Explanation: 2x + 9 = 4

2x = 4 – 9

2x = -5

x = -5/2

Question 15. Find the value of x if 2x + 10 = 76.

33
7.6
66
32

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Answer: (a)

Explanation: 2x + 10 = 76

2x = 76 – 10

2x = 66

x = 66/2

x = 33

Question 16. The perimeter of a rectangle is 40 cm. If its width is 10 cm, then find the length.

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Answer: (a)

Explanation: Perimeter of a rectangle = 40 cm

Width = 10 cm

Let the length be x.

Perimeter of rectangle = 2(length + width)

40 = 2 (x + 10)

40/2 = x + 10

20 = x + 10

x = 20 – 10 = 10

Thus, the length is also 10 cm.

Hence, we can say, that the given rectangle is a square, with all its sides equal.

Question 17. If x is an even number, then the next even number is:

x+1
x+2
x+3
x+4

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Answer: (b)

Explanation: If x = 2, then x + 2 = 2 + 2 = 4

Question 18. The difference between the two numbers is 30. If the bigger number is x, then what is the smaller number?

x – 30
30 – x
30x
None of these

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Answer: (a)

Explanation: x – small number = 30

Small number = x – 30

Question 19. When a number is added to itself, it becomes 24. What is the number?

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Answer: (c)

Explanation: Let the number be x.

x + x = 24

2x = 24

x = 24/2

x = 12

Question 20. Present ages of Akansha and Anubhav are in the ratio of 5/7. Four years from now the ratio of their ages will be 7/9. Find the present age of Akansha.

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Answer: (b)

Explanation: Let the present age of Akansha and Anubhav be 5x and 7x years respectively.

After four years their ages will be 5x+4, 7x+4

The ratio of their ages after 4 years will be

5x+4/7x+4 = 7/9

By cross multiplication

9(5x+4)=7(7x+4)

45x+36=49x+28

(49-45)x=36-28

4x=8

x=2

Therefore, Akansha’s age is 5x i.e., 5*2 = 10 years.

Question 21. Simplify the following linear equation:
4(m-4) = 5(2m-5)

3/2
5/2
9/2
7/1

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Answer: (a)

Explanation: 4(m-4) = 5(2m-5)

4m-16=10m-25

6m=9

m=3/2

Question 22. Solve: 3b=5b – 8/5

4/5
6/5
3/5
9/5

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Answer: (a)

Explanation: 3b=5b – 8/5

2b=8/5

b=4/5

Question 23. Solve 3y+6/5=27/5-y

2/5
21/4
27/8
21/20

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Answer: (d) 21/20

Explanation: 3y+6/5=27/5-y

3y+y=27/5-6/5

4y=21/5

y=21/20

Question 24. The ratio of boys and girls in the class is 9:5, the number of boys is 12 more than the number of girls. What is the strength of the class?

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Answer: (c)42

Explanation: let the number of boys and girls in the class be 9x and 5x respectively.

According to the question 9x+12=5x

4x=12

X=3

The total strength of class=no. of boys + no. of girls

=9x+5x

=14x

=14*3

=42

Question 25. 3/4 part of a number is 5 more than its 2/3 parts. This statement in the form of an equation is

2/3 x – 3/4 x=5
2/3 x – 5 =3/4 x
3/4 x = 2/3 x + 5
3/4 x – 5 = –2/3 x

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Answer: (c)

Explanation: Let's represent the unknown number as x. The statement "3/4 part of a number is 5 more than its 2/3 parts" can be translated into the equation:

¾ x = 2/3 x + 5

In this equation:

3/4x represents 3/4 part of the number,
2/3x represents 2/3 parts of the number, and
5 is the additional amount.

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Linear Equations in One Variable MCQs

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CBSE X Related Questions

1.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

2.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

3.
Use graphical method to solve the system of linear equations : $x = -3$ and $5x - 2y = -5$.

4.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

5.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

6.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

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Linear Equations in One Variable MCQs

Related Links

CBSE X Related Questions

1.Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

2.An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

3.Use graphical method to solve the system of linear equations : $x = -3$ and $5x - 2y = -5$.

4.Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

5.A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

6.The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

2.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

3.
Use graphical method to solve the system of linear equations : $x = -3$ and $5x - 2y = -5$.

4.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

5.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

6.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.