**CBSE Class 8 Maths – MCQ and Online Tests – Unit 2 – Linear Equations in One Variable**

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**CBSE Class 8 Maths – MCQ and Online Tests – Unit 2 – Linear Equations in One Variable**

Question 1.

The root of the equation x – 8 = 2 is

(a) 2

(b) 8

(c) 6

(d) 10.

## Answer

Answer: (d)

Hint:

x – 8 = 2 ? x = 2 + 8 = 10.

Question 2.

If two angles are complementary and one angle is 10° greater than the other, then the smaller angle of the two is

(a) 40°

(b) 50°

(c) 90°

(d) 180°.

## Answer

Answer: (a)

Hint:

x° = (90° – x°) + 10°

? 2x° = 100° ? x° = 50°

? 90° – x° = 40°.

Question 3.

The root of the equation 3x + 8 = 14 is

(a) 1

(b) 2

(c) -1

(d) \(\frac{1}{2}\)

## Answer

Answer: (b)

Hint:

3x + 8 = 14 ? 3x = 14 – 8 = 6

? x = \(\frac{6}{3}\) = 2.

Question 4.

The root of the equation 2y = 5(3 + y) is

(a) 5

(b) \(\frac{1}{5}\)

(c) -5

(d) –\(\frac{1}{5}\)

## Answer

Answer: (c)

Hint:

2y = 5 (3 + y) ? 2y = 15 + 5y

? 5y – 2y = -15

? 3y = -15 ? y = –\(\frac{15}{3}\) = -5

Question 5.

The statement ‘on adding 10 in a number, the number becomes 20’ in the form of an equation is

(a) x – 10 = 20

(b) x + 10 = 20

(c) 10x = 20

(d) \(\frac{x}{10}\) = 20.

## Answer

Answer: (b)

Hint:

Let the number be x.

Question 6.

If 9 is added to a number, it becomes 25. This statement in the form of an equation is

(a) x + 9 = 25

(b) x – 9 = 25

(c) 9x = 25

(d) \(\frac{x}{9}\) = 25.

## Answer

Answer: (a)

Hint:

Let the number be x.

Question 7.

If 15 is subtracted from a number, it becomes -5. This statement in the form of an equation is

(a) x + 15 = -5

(b) x – 15 = 5

(c) x + 15 = 5

(d) x – 15 = -5.

## Answer

Answer: (d)

Hint:

Let the number be x.

Question 8.

Seven times a number is 42. This statement in the form of an equation is

(a) x + 7 = 42

(b) 7x = 42

(c) \(\frac{x}{7}\) = 42

(d) x – 7 = 42.

## Answer

Answer: (b)

Hint:

Let the number be x.

Question 9.

A number when divided by 5 gives 6. This statement in the form of an equation is

(a) x – 5 = 6

(b) x + 5 = 6

(c) \(\frac{x}{5}\) = 6

(d) 5x = 6.

## Answer

Answer: (c)

Hint:

Let the number be x.

Question 10.

A number when subtracted from 40 results into 15. This statement in the form of an equation is

(a) 40 – x = 15

(b) x – 40 = 15

(c) 40 + x = 15

(d) 40x = 15.

## Answer

Answer: (a)

Hint:

Let the number be x.

Question 11.

If 6 is added to 3 times of a number, it becomes 15. This statement in the form of an equation is

(a) 3x + 6 = 15

(b) 3x – 6 = 15

(c) 3x + 15 = 6

(d) \(\frac{3x}{6}\) = 15.

## Answer

Answer: (a)

Hint:

Let the number be x.

Question 12.

On subtracting 30 from two times a number, we get 56. This statement in the form of an equation is

(a) 2x – 30 = 56

(b) 2x + 30 = 56

(c) 30 – 2x = 56

(d) \(\frac{30}{2x}\) = 56.

## Answer

Answer: (a)

Hint:

Let the number be x.

Question 13.

The root of the equation z + 4 = -8 is

(a) 3

(b) -32

(c) 12

(d) 4.

## Answer

Answer: (b)

Hint:

z + 4 = -8 ? \(\frac{z}{4}\) = -8

? z = 4 (-8) = -32.

Question 14.

The root of the equation 3x = \(\frac{20}{7}\) – x is

(a) 10

(b) \(\frac{20}{21}\)

(c) –\(\frac{5}{7}\)

(d) \(\frac{5}{7}\)

## Answer

Answer: (d)

Hint:

3x = \(\frac{20}{7}\) – x ? 3x + x = \(\frac{20}{7}\)

? 4x = \(\frac{20}{7}\) ? x = \(\frac{20}{7×4}\) = \(\frac{5}{7}\)

Question 15.

The root of the equation 2x + 3 = 2(x – 4) is

(a) 2

(b) 4

(c) 0

(d) does not exist.

## Answer

Answer: (d)

Hint:

2x + 3 = 2 (x – 4)

? 2x + 3 = 2x – 8

? 3 = -8 which is impossible.

Question 16.

x is an odd number. The largest odd number preceding x is

(a) x – 1

(b) x – 2

(c) x – 3

(d) x – 4.

## Answer

Answer: (b)

Question 17.

The difference of two numbers is 21. The larger number is x. The smaller number is

(a) 21 + x

(b) 21 – x

(c) x – 21

(d) -x – 21.

## Answer

Answer: (c)

Hint:

x – smaller number = 21

? smaller number = x – 21

Question 18.

In a two digit number, the unit’s digit is x and the ten’s digit is y. Then, the number is

(a) 10y + x

(b) 10x + y

(c) 10y – x

(d) 10x – y.

## Answer

Answer: (a)

Hint:

Required number

= 10 × y + 1 × x = 10y + x.

Question 19.

When 9 is added to two times a number, we get 67. The number is

(a) 25

(b) 27

(c) 29

(d) 31.

## Answer

Answer: (c)

Hint:

2x + 9 = 67 ? x = 29.

Question 20.

The root of the equation –\(\frac{5}{4x}\) = 15 is

(a) \(\frac{1}{12}\)

(b) –\(\frac{1}{12}\)

(c) \(\frac{1}{20}\)

(d) –\(\frac{1}{20}\)

## Answer

Answer: (b)

Hint:

–\(\frac{5}{4x}\) = 15 ? x = –\(\frac{5}{4×15}\) = –\(\frac{1}{12}\)

Question 21.

The value of x in \(\frac{3}{4}\) x = 7 – x is

(a) 4

(b) 3

(c) \(\frac{7}{3}\)

(d) 7.

## Answer

Answer: (a)

Hint:

\(\frac{3}{4}\) x = 7 – x ? \(\frac{3}{4}\) x + x = 7

? \(\frac{7}{4}\) x = 7 ? x = 4

Question 22.

\(\frac{3}{4}\) part of a number is 5 more than its \(\frac{2}{3}\) part. This statement in the form of an equation is

(a) \(\frac{2}{3}\) x – \(\frac{3}{4}\) x= 5

(5) \(\frac{2}{3}\) x – 5 =\(\frac{3}{4}\) x

(c) \(\frac{3}{4}\) x = \(\frac{2}{3}\) x + 5

(d) \(\frac{3}{4}\) x – 5 = –\(\frac{2}{3}\) x

## Answer

Answer: (c)

Hint:

Let the number be x²

Question 23.

The value of x in –\(\frac{2}{3}\) = 2x is 3

(a) \(\frac{1}{3}\)

(b) –\(\frac{1}{3}\)

(c) 3

(d) – 3.

## Answer

Answer: (b)

Hint:

–\(\frac{2}{3}\) = 2x ? x = –\(\frac{1}{3}\)

Question 24.

The root of the equation 5x – 8 = 7 is

(a) 1

(b) 2

(c) 3

(d) -3.

## Answer

Answer: (c)

Hint:

5x – 8 = 7 ? 5x = 8 + 7 = 15

? x = \(\frac{15}{5}\) = 3.

Question 25.

The root of the equation x + 3 = 5 is

(a) 1

(b) 2

(0 -1

(d) -2.

## Answer

Answer: (b)

Hint:

x + 3 = 5 ? x = 5 – 3 = 2.

Question 26.

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

(a) ax + b = 0

(b) ax² + bx + c = 0

(c) ax³ + bx² + cx + d = 0

(d) ax^{4} + bx³ + cx² + dx + e = 0.

## Answer

Answer: (a)

Question 27.

Of the following, the linear equation in one variable x, is

(a) \(\frac{4}{x}\) = \(\frac{x}{4}\)

(b) \(\frac{1}{x}\) + \(\frac{1}{x-1}\) = 1

(c) \(\frac{x}{2}\) + \(\frac{x}{3}\) + \(\frac{1}{4}\)

(d) x² + 2x + 3 = 0.

## Answer

Answer: (c)

Question 28.

The degree of the equation x² – 2x + 1 = x² – 3 is

(a) 1

(b) 2

(c) 0

(d) 3.

## Answer

Answer: (a)

Hint:

x² – 2x + 1 = x² – 3 ? 2x = 4

Question 29.

If two angles are supplementary and one angle is double the other, then the larger angle is

(a) 60°

(b) 90°

(c) 120°

(d) 180°.

## Answer

Answer: (c)

Hint:

x° + 2x° = 180° ? 3x° = 180°

? x° = 60° ? 2x° = 120°

Question 30.

Twice a number is as much greater than 30 as the three times of the number less than 60. The number is

(a) 6

(b) 9

(c) 12

(d) 18.

## Answer

Answer: (d)

Hint:

2x – 30 = 60 – 3x ? 5x = 90

? x = 18.

Question 31.

One number is greater than the other number by 3. The sum of two numbers is 23. The two numbers are

(a) 13, 10

(b) 14, 9

(c) 12, 11

(d) 15, 8.

## Answer

Answer: (a)

Hint:

(x + 3) + x = 23 ? 2x = 20

? x = 10 ? x + 3 = 13

Question 32.

The root of the equation \(\frac{y}{3}\) – 7 = 11 is

(a) 54

(b) -54

(c) 18

(d) -18

## Answer

Answer: (a)

Hint:

\(\frac{y}{3}\) – 7 = 11 ? \(\frac{y}{3}\) = 7 + 11 = 18

? y = 3 × 18 = 54

Question 33.

The root of the equation 14 – x = 8 is

(a) 2

(b) 4

(c) 6

(d) 8.

## Answer

Answer: (c)

Hint:

14 – x = 8 ? x = 14 – 8 = 6

Question 34.

The root of the equation \(\frac{5x}{3}\) = 30 is

(a) 9

(b) 12

(c) 15

(d) 18

## Answer

Answer: (d)

Hint:

\(\frac{5x}{3}\) = 30 ? 5x = 3 × 30 = 90

? x = \(\frac{90}{5}\) = 18

Question 35.

The root of the equation 3y + 4 = 5y – 4 is

(a) 1

(b) 2

(c) 3

(d) 4.

## Answer

Answer: (d)

Hint:

3y + 4 = 5y – 4 ? 5y – 3y = 4 + 4

? 2y = 8 ? y = \(\frac{8}{2}\) = 4

Question 36.

The root of the equation \(\frac{7x}{3}\) = 3 is

(a) \(\frac{5x}{3}\)

(b) \(\frac{5x}{3}\)

(c) 3

(d) 7

## Answer

Answer: (a)

Hint:

\(\frac{7}{x}\) = 3 ? 3x = 7 ? x = \(\frac{7}{3}\)

Question 37.

The root of the equation 3x + 4 = 13 is

(a) 1

(b) 2

(c) 3

(d) 4.

## Answer

Answer: (c)

Hint:

3x + 4 = 13 ? 3x = 13 – 4 = 9

? x = \(\frac{9}{3}\) = 3

Question 38.

The root of the equation 9z – 15 = 9 – 3z is

(a) 1

(b) 2

(c) 3

(d) 4.

## Answer

Answer: (b)

Hint:

9z – 15 = 9 – 3z ? 9z + 3z = 9 + 15

? 12x = 24 ? z = \(\frac{24}{12}\) = 2

Question 39.

The root of the equation \(\frac{4x}{7}\) – 12 = 0 is

(a) 7

(b) 14

(c) 21

(d) -21

## Answer

Answer: (c)

Hint:

\(\frac{4x}{7}\) – 12 = 0 ? \(\frac{4x}{7}\) = 12

? 4x = 7 × 12 = 84

? x = \(\frac{84}{4}\) = 21

Question 40.

The root of the equation 3x = \(\frac{20}{7}\) – x is

(a) \(\frac{7}{5}\)

(b) \(\frac{5}{7}\)

(c) –\(\frac{7}{5}\)

(d) –\(\frac{5}{7}\)

## Answer

Answer: (b)

Hint:

3x = \(\frac{20}{7}\) – x ? 3x + x = \(\frac{20}{7}\)

? 4x = \(\frac{20}{7}\) ? x = \(\frac{20}{7×4}\) = \(\frac{5}{7}\)

Question 41.

The root of the equation 2y = 5 (7 – y ) is

(a) 5

(b) -5

(c) 3

(d) -3.

## Answer

Answer: (a)

Hint:

2y = 5(7 – y) ? 2y = 35 – 5y

? 2y + 5y = 35

? 7y = 35 ? y = \(\frac{35}{7}\) = 5

Question 42.

The root of the equation

(2x – 1) + (x – 1) = x + 2 is

(a) 1

(b) 2

(c) -1

(d) -2.

## Answer

Answer: (b)

Hint:

(2x – 1) + (x – 1) = x + 2

? 2x = 4 ? x = \(\frac{4}{2}\) = 2.

Question 43.

The root of the equation

13x – 14 = 9x + 10 is

(a) 1

(b) 2

(c) 3

(d) 6.

## Answer

Answer: (d)

Hint:

13x – 14 = 9x + 10 ? 13x – 9x = 10 + 14

? 4x = 24 ? x = \(\frac{24}{4}\) = 6

Question 44.

The root of the equation

11x – 5 – x + 6 = 2x + 17 is

(a) 1

(b) 2

(c) 3

(d) 4.

## Answer

Answer: (b)

Hint:

11x – 5 – x + 6 = 2x + 17

? 8x = 16 ? x = 2.

Question 45.

The root of the equation \(\frac{2}{3}\) y = \(\frac{5}{12}\) is

(a) \(\frac{8}{5}\)

(b) \(\frac{5}{8}\)

(c) 5

(d) 8

## Answer

Answer: (b)

Hint:

\(\frac{2}{3}\) y = \(\frac{5}{12}\)

? y = \(\frac{5}{12}\) × \(\frac{3}{2}\) = \(\frac{5}{8}\)

Question 46.

The root of the equation 7 (x – 1) = 21 is

(a) 1

(b) 2

(c) 3

(d) 4.

## Answer

Answer: (d)

Hint:

7 (x – 1) = 21 ? x – 1 = \(\frac{21}{7}\) = 3

? x = 4.

Question 47.

The root of the equation \(\frac{3}{2}\) x = – 27 is

(a) 6

(b) 12

(c) 18

(d) -18

## Answer

Answer: (d)

Hint:

\(\frac{5}{12}\) x = -27 ? x = –\(\frac{27×2}{3}\) = -18.

Question 48.

The solution of the equation \(\frac{5}{x}\) = 2 is

(a) 10

(b) \(\frac{2}{5}\)

(c) \(\frac{5}{2}\)

(d) \(\frac{1}{10}\)

## Answer

Answer: (c)

Hint:

\(\frac{5}{x}\) = 2

? 2x = 5 ? x = \(\frac{5}{2}\)

Question 49.

The largest number of the three consecutive numbers is x + 1. Then, the smallest number is

(a) x + 2

(b) x + 1

(c) x

(d) x – 1.

## Answer

Answer: (d)

Hint:

x – 1, x, x + 1

Question 50.

If x is an even number then the consecutive even number is

(a) x + 1

(b) x + 2

(c) 2x

(d) x – 1.

## Answer

Answer: (b)

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