# Free Number Systems 01 Practice Test - 9th Grade

Choose the correct statements.

A.

1 is the smallest natural number

B.

1 is the smallest whole number

C.

-1 is the smallest negative integer

D.

0 is an integer

#### SOLUTION

Solution : A and D

Natural numbers are all the counting numbers starting from 1, i.e. {1, 2, 3, ...}
Therefore, statement: '1 is smallest natural number'; is correct.

Whole numbers are all counting numbers and zero, i.e. {0, 1, 2, 3, ...}
Therefore, statement: '1 is smallest whole number'; is wrong.

Integers include the set of natural numbers, their negatives and 0; i.e. {...-3, -2, -1, 0, 1, 2, 3, ...}. Thus, -1 is the greatest negative integer, not the smallest one.

0 is included among integers.
Hence, the statement is correct.

Find the hypotenuse of a right angled triangle whose perpendicular sides are 6 cm and 3 cm.

A.

4 cm

B.

3 cm

C.

2 cm

D.

1 cm

#### SOLUTION

Solution : B

Given: perpendicular sides of a right angled triangle are 6 and 3.

Using Pythagoras theorem,

Hypotenuse = 62+32

= 6+3

= 9  cm

=  3 cm

Find the value of (3+5)(35) .

A.

1

B. 2
C. 3
D. 4

#### SOLUTION

Solution : D

We know the identity:
a2b2=(a+b)(ab)

(3+5)(35)=(32(5)2=95=4

Hence, (3+5)(35)=4, which is a rational number.

23×32 is ___. (rational/irrational)

.

#### SOLUTION

Solution :

23×32=2×3×2×3=66
The presence of factor 6 makes the expression irrational.

From the options, choose the irrational numbers that lie between 4 and 9.

A.

36

B.

31

C.

17

D.

25

#### SOLUTION

Solution : B and C

6×6 = 36, a perfect square, hence 36 is not irrational .
Also 25 is the perfect square of 5, hence 25 is rational.

42=16 & 92=81, hence all the numbers between  16 and 81  lie between 4 and 9.

We can see that  17, 31   are irrational numbers  between 16 and 81, and they lie between 4 and 9.

Represent 0.45 as a rational number.

A.

45

B.

92

C.

54

D.

920

#### SOLUTION

Solution : D

To convert 0.45 into a fraction:
0.45=45100
[Multiplying 0.45 with 100100]

Dividing the numerator and the denominator by 5, we get
45100=920

0.45=920

Expand (79)3.

A.

343729

B.

729343

C.

4981

D.

8149

#### SOLUTION

Solution : A

(79)3=7×7×79×9×7(79)3=343729

If (1024)3=8x, then x is ________.

A.

5

B.

15

C.

10

D.

2

#### SOLUTION

Solution : A

Given:
(1024)3=8x

((210))3=8x.

(((25)2))3=8x.  {as (am)n=amn}

(25)3=(23)x

(23)5=(23)x

(8)5= (8)x

We know that, if an= am then, n=m.

Hence,
x=5

Which of the following fractions is equal to 157?

A.

(5+7)4

B.

(5+7)2

C.

(57)2

D.

(5+7)8

#### SOLUTION

Solution : B

Rationalizing the expression we get,
157=5+7(57)(5+7)

=5+7(5)2(7)2

=5+757
=(5+7)2

n2×n3=n6

A.

True

B.

False

#### SOLUTION

Solution : A

We know that na×nb=nab

So,n2×n3=n2×3=n6