RS Aggarwal & V Aggarwal - Mathematics

Book: RS Aggarwal & V Aggarwal - Mathematics

Chapter: 1. Real Number

Subject: Mathematics - Class 9th

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

Chapter Exercises

Exercise 1A
Exercise 1B
Exercise 1C
Exercise 1D
Exercise 1E
Exercise 1F
CCE Questions
Formative Assessment (Unit Test)

Exercise 1A

1

What are rational numbers? Give ten examples of rational numbers.
2

Represent each of the following rational numbers on the number line:

(i) 5 (ii) -3


(iii) (iv) (v) 1.3


(vi) -2.4 (vii)

3

Find a rational number lying between

(i) (ii)


(iii) 1.3 and 1.4 (iv) 0.75 and 1.2


(v) (vi)

4

Find three rational numbers lying between.
5

Find five rational numbers lying between

6

Insert six rational numbers between 3 and 4.
7

Insert 16 rational numbers between 2.1 and 2.2.

Exercise 1B

1

Without actual division, find which of the following rationals are terminating decimals.

(i) (ii) (iii)


(iv) (v)

2

Convert each of the following into a decimal.

(i) (ii) (iii)


(iv) (v)

3

Express each of the following as a fraction as a fraction in simplest form.

(i) (ii) (iii)


(iv) (v) (vi)


(vii) (viii)

4

Write, whether the given statement is true or false. Give reasons.

(i) Every natural number is a whole number.


(ii) Every whole number is a natural number.


(iii) Every integer is a rational number.


(iv) Every rational number is a whole number.


(v) Every terminating decimal is a rational number.


(vi) Every repeating decimal is a rational number.


(vii) 0 is a rational number.

Exercise 1C

1

What are irrational numbers? How do they differ from rational numbers? Give examples.
2

Classify the following numbers as rational or irrational. Give reasons to support your answer.

(i) (ii) (iii)


(iv) (v) (vi)


(vii) (viii) (ix) 1.232332333…


(x) 3.040040004… (xi) 3.2576


(xii) 2.3565656… (xiii)(xiv)
3

Represent and on the real line.
4

Represent and on the real line.
5

Giving reason in each case, show that each of the following numbers is irrational.

(i) (ii) (iii)


(iv) (v) (vi)

6

State in each case, whether the given statement is true or false.

(i) The sum of two rational numbers is rational.


(ii) The sum of two irrational numbers is irrational.


(iii) The product of two rational numbers is rational.


(iv) The product of two irrational numbers is irrational.


(v)The sum of a rational number and an irrational number is irrational.


(vi) The product of a nonzero rational number and an irrational number is a rational number.


(vii)Every real number is rational.


(viii) Every real number is either rational or irrational.


(ix) is irrational and is rational.

Exercise 1D

1

Add:

(i)


(ii)


(iii)

2

Multiply:

(i) (ii)


(iii) (iv)


(v) (vi)

3

Divide:

(i) (ii)


(iii)

4

Simplify:

(i)


(ii)


(iii)


(iv)


(v) (vi)

5

Represent geometrically on the number line.
6

Represent geometrically on the number line.
7

Mention the closure property, associative law, commutative law, existence of identity, existence of inverse of each real number for each of the operations

(i) addition (ii) multiplication on real numbers.

Exercise 1E

1

Rationalise the denominator of each of the following :
2

Rationalise the denominator of each of the following :
3

Rationalise the denominator of each of the following :
4

Rationalise the denominator of each of the following :
5

Rationalise the denominator of each of the following :
6

Rationalise the denominator of each of the following :
7

Rationalise the denominator of each of the following :
8

Rationalise the denominator of each of the following :
9

Rationalise the denominator of each of the following :
10

Find the values of a and b in each of the following.
11

Find the values of a and b in each of the following.
12

Find the values of a and b in each of the following.
13

Find the values of a and b in each of the following.
14

Simplify:

15

Simplify:

16

If find the value of

17

If find the value of

18

Show that

Exercise 1F

1

Simplify:

(i) (ii) (iii)

2

Simplify:

(i) (ii) (iii)

3

Simplify:

(i) (ii) (iii)

4

Simplify:

(i) (ii) (iii)

5

Evaluate:

(i)

6

Evaluate:
7

Evaluate:

CCE Questions

1

Which of the following is an irrational number?
2

Which of the following is an irrational number?
3

Which of the following is an irrational number?
4

Which of the following is a rational number?
5

Every rational number is
6

Between any two rational numbers there
7

The decimal representation of a rational number is
8

The decimal representation of an irrational number is
9

Decimal expansion of is:
10

The product of two irrational number is
11

Which of the following is a true statement?
12

Which of the following is a true statement?
13

A rational number between is
14

15

16

17

18

19

20

21

22

23

24

25

(625)0.16 × (625)0.09 = ? 
26

27

The simplest form of

28

The simplest form of

19

The simplest form of

30

28. The simplest form of is
31

An irrational number between 5 and 6 is
32

An irrational number between

33

An irrational number between

34

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.


Assertion (A)



Reason (R)



The rational numbers between and are:



A rational number between two rational numbers p and q is


35

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.


Assertion (A)



Reason (R)



is irrational number.



Square root of a positive integer which is not a perfect square is an irrational number.
36

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.


Assertion (A)



Reason (R)



e is an irrational number.



is an irrational number.
37

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.


Assertion (A)



Reason (R)



is an irrational number.



The sum of a rational number and an irrational number is an irrational number.
38

Match the following columns:


Column I



Column II



A.


B.


C. The length of period of


D. If then



(p) 14


(q) 6


(r) a rational number


(s) an irrational number



The correct answer is:


(a)-……., (b)-……., (c)-……., (d)-…….,
39

Match the following columns:


Column I



Column II



A.


B. then x = ……. ,


C. then


D.



(p) 4


(q)


(r)


(s) 3



The correct answer is:


(a)-……., (b)-……., (c)-……., (d)-…….,
40

Give an example of two irrational numbers whose sum as well as the product is rational.
41

If x is rational and y is irrational, then show that (x + y) is always irrational.
42

Is the product of a rational and an irrational number always irrational?

Give an example.
43

Given an example of a number x such that x2 is an irrational number and x4 is a rational number.
44

The number expressed as a vulgar fraction is
45

if find the value of

46

If find the values of a and b.
47

If find the values of a and b.
48

If find the values of a and b.
49

If find the values of a and b.
50

If and find

51

If show that the value of is 3.
52

if show that

53

if show that

54

if show that

55

if show that

Formative Assessment (Unit Test)

1

Find two rational numbers lying between

2

Find four rational numbers between

3

Write four irrational numbers between 0.1 and 0.2.
4

Express in its simplest form.
5

Express as a pure surd.
6

Divide

7

Express as a rational number in the form where p and q are integers and

8

If find the values of a and b.
9

The simplest form of is
10

Which of the following is irrational?
11

Between two rational numbers
12

Decimal representation of an irrational number is
13

If

14

Rationalize the denominator of

15

Simplify:

16

Find the smallest of the numbers

17

Match the following columns:


Column I



Column II



A.


B.


C.


D.



(p) a rational number


(q) an irrational number


(r)


(s)



The correct answer is:


(a)-……., (b)-……., (c)-……., (d)-…….,
18

If and find the value of

19

If find the value of

20

Prove that