Objective Type Questions: Introduction to Algebra

# Objective Type Questions: Introduction to Algebra | Mathematics (Maths) Class 6 PDF Download

``` Page 1

Objective Type Questions                                                  PAGE: 8.13
Mark the correct alternative in each of the following:

1. 5 more than twice a number x is written as
(a) 5 + x + 2
(b) 2x + 5
(c) 2x - 5
(d) 5x + 2
Solution:

The option (b) is correct answer.
5 more than twice a number x is written as 2x + 5.

2. The quotient of x by 2 is added to 5 is written as
(a) x/2 + 5
(b) 2/x+5
(c) (x+2)/ 5
(d) x/ (2+5)
Solution:

The option (a) is correct answer.
The quotient of x by 2 is added to 5 is written as x/2 + 5.

3. The quotient of x by 3 is multiplied by y is written as
(a) x/3y
(b) 3x/y
(c) 3y/x
(d) xy/3
Solution:

The option (d) is correct answer.
It can be written as
x/3 × y = xy/3

4. 9 taken away from the sum of x and y is
(a) x + y - 9
(b) 9 - (x+y)
(c) x+y/ 9
(d) 9/ x+y
Solution:

The option (a) is correct answer.
9 taken away from the sum of x and y is x + y – 9.

5. The quotient of x by y added to the product of x and y is written as
(a) x/y + xy
(b) y/x + xy
(c) xy+x/ y
(d) xy+y/ x
Page 2

Objective Type Questions                                                  PAGE: 8.13
Mark the correct alternative in each of the following:

1. 5 more than twice a number x is written as
(a) 5 + x + 2
(b) 2x + 5
(c) 2x - 5
(d) 5x + 2
Solution:

The option (b) is correct answer.
5 more than twice a number x is written as 2x + 5.

2. The quotient of x by 2 is added to 5 is written as
(a) x/2 + 5
(b) 2/x+5
(c) (x+2)/ 5
(d) x/ (2+5)
Solution:

The option (a) is correct answer.
The quotient of x by 2 is added to 5 is written as x/2 + 5.

3. The quotient of x by 3 is multiplied by y is written as
(a) x/3y
(b) 3x/y
(c) 3y/x
(d) xy/3
Solution:

The option (d) is correct answer.
It can be written as
x/3 × y = xy/3

4. 9 taken away from the sum of x and y is
(a) x + y - 9
(b) 9 - (x+y)
(c) x+y/ 9
(d) 9/ x+y
Solution:

The option (a) is correct answer.
9 taken away from the sum of x and y is x + y – 9.

5. The quotient of x by y added to the product of x and y is written as
(a) x/y + xy
(b) y/x + xy
(c) xy+x/ y
(d) xy+y/ x

Solution:
The option (a) is correct answer.
The quotient of x by y added to the product of x and y is written as x/y + xy.

6. a
2
b
3
× 2ab
2
is equal to
(a) 2a
3
b
4

(b) 2a
3
b
5

(c) 2ab
(d) a
3
b
5

Solution:

The option (b) is correct answer.
It can be written as
a
2
b
3
× 2ab
2
= 2a
2
× a × b
3
× b
2
= 2a
3
b
5
.

7. 4a
2
b
3
× 3ab
2
× 5a
3
b is equal to
(a) 60a
3
b
5

(b) 60a
6
b
5

(c) 60a
6
b
6

(d) a
6
b
6

Solution:

The option (c) is correct answer.
It can be written as
4a
2
b
3
× 3ab
2
× 5a
3
b = 4 × 3 × 5 × a
2
× a × a
3
× b
3
× b
2
× b = 60a
6
b
6

8. If 2x
2
y and 3xy
2
denote the length and breadth of a rectangle, then its area is
(a) 6xy
(b) 6x
2
y
2

(c) 6x
3
y
3

(d) x
3
y
3

Solution:

The option (c) is correct answer.
We know that area of a rectangle = length × breadth
By substituting the values
Area = 2x
2
y × 3xy
2
= 6x
3
y
3

9. In a room there are x
2
rows of chairs and each two contains 2x
2
chairs. The total number of chairs in the
room is
(a) 2x
3

(b) 2x
4

(c) x
4

(d) x
4
/2
Solution:

The option (b) is correct answer.
We know that
Total number of chairs in the room = Number of rows × Number of chairs
By substituting the values
Page 3

Objective Type Questions                                                  PAGE: 8.13
Mark the correct alternative in each of the following:

1. 5 more than twice a number x is written as
(a) 5 + x + 2
(b) 2x + 5
(c) 2x - 5
(d) 5x + 2
Solution:

The option (b) is correct answer.
5 more than twice a number x is written as 2x + 5.

2. The quotient of x by 2 is added to 5 is written as
(a) x/2 + 5
(b) 2/x+5
(c) (x+2)/ 5
(d) x/ (2+5)
Solution:

The option (a) is correct answer.
The quotient of x by 2 is added to 5 is written as x/2 + 5.

3. The quotient of x by 3 is multiplied by y is written as
(a) x/3y
(b) 3x/y
(c) 3y/x
(d) xy/3
Solution:

The option (d) is correct answer.
It can be written as
x/3 × y = xy/3

4. 9 taken away from the sum of x and y is
(a) x + y - 9
(b) 9 - (x+y)
(c) x+y/ 9
(d) 9/ x+y
Solution:

The option (a) is correct answer.
9 taken away from the sum of x and y is x + y – 9.

5. The quotient of x by y added to the product of x and y is written as
(a) x/y + xy
(b) y/x + xy
(c) xy+x/ y
(d) xy+y/ x

Solution:
The option (a) is correct answer.
The quotient of x by y added to the product of x and y is written as x/y + xy.

6. a
2
b
3
× 2ab
2
is equal to
(a) 2a
3
b
4

(b) 2a
3
b
5

(c) 2ab
(d) a
3
b
5

Solution:

The option (b) is correct answer.
It can be written as
a
2
b
3
× 2ab
2
= 2a
2
× a × b
3
× b
2
= 2a
3
b
5
.

7. 4a
2
b
3
× 3ab
2
× 5a
3
b is equal to
(a) 60a
3
b
5

(b) 60a
6
b
5

(c) 60a
6
b
6

(d) a
6
b
6

Solution:

The option (c) is correct answer.
It can be written as
4a
2
b
3
× 3ab
2
× 5a
3
b = 4 × 3 × 5 × a
2
× a × a
3
× b
3
× b
2
× b = 60a
6
b
6

8. If 2x
2
y and 3xy
2
denote the length and breadth of a rectangle, then its area is
(a) 6xy
(b) 6x
2
y
2

(c) 6x
3
y
3

(d) x
3
y
3

Solution:

The option (c) is correct answer.
We know that area of a rectangle = length × breadth
By substituting the values
Area = 2x
2
y × 3xy
2
= 6x
3
y
3

9. In a room there are x
2
rows of chairs and each two contains 2x
2
chairs. The total number of chairs in the
room is
(a) 2x
3

(b) 2x
4

(c) x
4

(d) x
4
/2
Solution:

The option (b) is correct answer.
We know that
Total number of chairs in the room = Number of rows × Number of chairs
By substituting the values

Total number of chairs in the room = x
2
× 2x
2
= 2x
4

10. a
3
× 2a
2
b × 3ab
5
is equal to
(a) a
6
b
6
(b) 23a
6
b
6
(c) 6a
6
b
6
(d) None of these
Solution:
The option (c) is correct answer.
It can be written as
a
3
× 2a
2
b × 3ab
5
= 2 × 3 × a
3
× a
2
× a × b × b
5
= 6a
6
b
6

```

## Mathematics (Maths) Class 6

94 videos|347 docs|54 tests

## FAQs on Objective Type Questions: Introduction to Algebra - Mathematics (Maths) Class 6

 1. What is algebra?
Ans. Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. It involves solving equations, simplifying expressions, and understanding the relationship between numbers and variables.
 2. What are the basic operations in algebra?
Ans. The basic operations in algebra are addition, subtraction, multiplication, and division. These operations are used to perform calculations with variables and numbers.
 3. How is algebra used in real life?
Ans. Algebra is used in various real-life situations such as calculating expenses, determining profit and loss, solving problems involving distance, speed, and time, and analyzing data through graphs and equations. It is also used in fields like engineering, finance, and science.
 4. What are variables in algebra?
Ans. Variables are symbols or letters used to represent unknown quantities or values in algebraic expressions and equations. They are used to generalize mathematical relationships and solve problems by assigning values to the variables.
 5. How can I improve my algebra skills?
Ans. To improve your algebra skills, practice regularly by solving a variety of algebraic problems. Understand the concepts and rules of algebra, seek help from teachers or online resources when needed, and apply algebra in real-life scenarios to enhance your problem-solving abilities.

## Mathematics (Maths) Class 6

94 videos|347 docs|54 tests

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