Number Systems Test

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Number Systems Test - 25

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Weekly Quiz Competition

Question 1
1 / -0

Simplify and give reasons:
$$\cfrac { { 3 }^{ -2 } }{ 3 } \times \left( { 3 }^{ 0 }-{ 3 }^{ -1 } \right) $$

A
$$\cfrac{2}{81}$$

B
$$\cfrac{1}{81}$$

C
$$\cfrac{4}{81}$$

D
None of these

Solution
Question 2
1 / -0

Simplify and give reasons:
$$\left[ { \left( \cfrac { 3 }{ 2 } \right) }^{ -2 } \right] ^{ 2 }$$

A
$$\cfrac{16}{81}$$

B
$$\cfrac{6}{81}$$

C
$$\cfrac{16}{1}$$

D
None of these

Solution

we know that,

$$\because (a^m)^n=a^{mn}$$

so,

$$((\dfrac32)^{-2})^2=(\dfrac32)^{-4}$$
we also know

$$\because (\dfrac{a}{b})^{-m}=(\dfrac{b}{a})^m$$

$$=(\dfrac23)^4$$

$$=\dfrac{16}{81}$$
Question 3
1 / -0

Simplify:
$$\left[ { \left( \cfrac { 3 }{ 5 } \right) }^{ -2 }\div { \left( \cfrac { 4 }{ 5 } \right) }^{ -3 } \right] \times { { \left( \cfrac { 3 }{ 5 } \right) } }^{ -2 }$$

A
$$\cfrac{{4}^{3}\times 5}{{3}^{4}}$$

B
$$\cfrac{{3}^{3}\times 5}{{3}^{4}}$$

C
$$\cfrac{{6}^{3}\times 5}{{3}^{4}}$$

D
None of these

Solution
Question 4
1 / -0

Which irrational number is plotted on the number line in figure?

A
$$\pi$$

B
$$\sqrt{2}$$

C
$$\sqrt{3}$$

D
$$\sqrt{5}$$

Solution

According to the given figure,

the red dot is closer to $$1.75$$ and out of the options only $$\sqrt3$$ is only one near to $$1.75$$ .
The irrational number is plotted on the number line
$$\sqrt {3}=1.732$$.

Hence, option $$C$$ is correct.
Question 5
1 / -0

Classify the following numbers as rational or irrational: $$\displaystyle \frac{\sqrt{12}}{\sqrt{75}}$$.

A
Rational

B
Irrational

C
Can't be determined

D
None of these

Solution

$$\dfrac { \sqrt { 12 } }{ \sqrt { 75 } } =\dfrac { 2\sqrt { 3 } }{ 5\sqrt { 3 } } =\dfrac { 2 }{ 5 } $$, which is a rational number.
Hence, the correct answer will be option $$A$$.
Question 6
1 / -0

$$\displaystyle\frac{2}{\sqrt{2}}$$ is equal to:

A
$$2\sqrt{2}$$

B
$$\sqrt{2}$$

C
$$\displaystyle\frac{\sqrt{2}}{2}$$

D
$$2$$

Solution

To find $$\dfrac{2}{\sqrt2}$$,

Multiply numerator and denominator by $$\sqrt2$$, we get,

$$\dfrac{2}{\sqrt2}$$ $$=\dfrac{2 \times \sqrt2 }{\sqrt2 \times \sqrt2}$$

$$= \dfrac{2\sqrt2 }{2}$$ $$= \sqrt2$$

Hence, option $$B $$ is correct.
Question 7
1 / -0

Which one of the following is an irrational number?

A
$$\pi$$

B
$$\sqrt{9}$$

C
$$\displaystyle\frac{1}{4}$$

D
$$\displaystyle\frac{1}{5}$$

Solution

$$\textbf{Step 1: Simplifying the following options.}$$
$$\text{The numbers which are non-repeating and non-terminating are irrational numbers.}$$
$$\text{Option A : }\pi = 3.141... \text{ is an irrational number.}$$
$$\text{Option B : }\sqrt{9} = 3 \text{ is a rational number.}$$
$$\text{Option C : }\dfrac{1}{4} \text{ is a rational number.}$$
$$\text{Option D : }\dfrac{1}{5} \text{ is a rational number.}$$
$$\therefore \text{Option A : }\pi \text{ is an irrational number.}$$
$$\textbf{Hence, option A is the correct answer.}$$
Question 8
1 / -0

$$p^{0}$$ is equal to

A
$$0$$

B
$$1$$

C
$$-1$$

D
$$p$$

Solution

As we can see that $$p$$ is raised to power $$0$$. It means that there is no term of $$p$$.

So, $$p^{0}=1$$
Any real number when raised to the power $$0$$ gives $$1$$.
Question 9
1 / -0

Simplify the following using law of exponents.
$$2^{10}\times 2^4$$

A
$$2^{10}$$

B
$$2^{12}$$

C
$$2^{13}$$

D
$$2^{14}$$

Solution

we know that,

$$\because a^m \times a^n=a^{m+n}$$

so,
$$2^{10}\times 2^4$$

$$=2^{10+4}$$

$$=2^{14}$$
Question 10
1 / -0

Evaluate $$2^0+3^0$$

A
$$2$$

B
$$3$$

C
$$5$$

D
$$1$$

Solution

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Re-Attempt Weekly Quiz Competition

Number Systems Test - 25

Result

Number Systems Test - 25

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SHARING IS CARING

Question 1

$$\cfrac{2}{81}$$

$$\cfrac{1}{81}$$

$$\cfrac{4}{81}$$

None of these

Solution

Question 2

$$\cfrac{16}{81}$$

$$\cfrac{6}{81}$$

$$\cfrac{16}{1}$$

None of these

Solution

Question 3

$$\cfrac{{4}^{3}\times 5}{{3}^{4}}$$

$$\cfrac{{3}^{3}\times 5}{{3}^{4}}$$

$$\cfrac{{6}^{3}\times 5}{{3}^{4}}$$

None of these

Solution

Question 4

$$\pi$$

$$\sqrt{2}$$

$$\sqrt{3}$$

$$\sqrt{5}$$

Solution

Question 5

Rational

Irrational

Can't be determined

None of these

Solution

Question 6

$$2\sqrt{2}$$

$$\sqrt{2}$$

$$\displaystyle\frac{\sqrt{2}}{2}$$

$$2$$

Solution

Question 7

$$\pi$$

$$\sqrt{9}$$

$$\displaystyle\frac{1}{4}$$

$$\displaystyle\frac{1}{5}$$

Solution

Question 8

$$0$$

$$1$$

$$-1$$

$$p$$

Solution

Question 9

$$2^{10}$$

$$2^{12}$$

$$2^{13}$$

$$2^{14}$$

Solution

Question 10

$$2$$

$$3$$

$$5$$

$$1$$

Solution

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