All in One Mathematics>Chapter 1 - Number Systems>Exam Practice>Q 58

EASY

9th CBSE

IMPORTANT

Earn 100

To judge the preparation of students of class IX on topic 'Number System', Mathematics teachers write two numbers on blackboard (as shown in figure).

He asks a question about the two members, which are following, then answer the question.
The decimal number $0.3 \bar{8}$ is the type of

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Important Questions on Number Systems

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 1 - Number Systems>Challengers*>Q 1

If

x = \frac{\sqrt{p + 2 q} + \sqrt{p - 2 q}}{\sqrt{p + 2 q} - \sqrt{p - 2 q}}

then

q x^{2} - p x + q

is equal to

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 1 - Number Systems>Challengers*>Q 2

If

a^{x} = b, b^{y} = c

and

x y z = 1

, then what is the value of

c^{z}

?

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 1 - Number Systems>Challengers*>Q 3

If

2^{m} + 2^{1 + m} = 96

, then find the minimum prime order pair for

m

which satisfy the given equation

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 1 - Number Systems>Challengers*>Q 4

For a positive integer

n

, define

d (n) =

nụmber of positive divisors of

n

. What is the value of

d [d (d (12))]

?

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 1 - Number Systems>Challengers*>Q 5

If

\sqrt{x} + \sqrt{x - \sqrt{1 - x}} = 1

, then

x

is equal to

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 1 - Number Systems>Challengers*>Q 6

If

x = {(4 + \sqrt{15})}^{1 / 3} + {(4 - \sqrt{15})}^{1 / 3}

, then

x^{3} - 3 x

is ecual to

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 1 - Number Systems>Challengers*>Q 7

If

a^{1 / 3} + b^{1 / 3} + c^{1 / 3} = 0

, then

(a + b + c)^{3}

is equal to

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 1 - Number Systems>Challengers*>Q 8

If

x = \frac{1}{2} (\sqrt{a} + \frac{1}{\sqrt{a}})

, then

\frac{\sqrt{x^{2}} - 1}{x - \sqrt{x^{2}} - 1}

is equal to