Number Systems Test

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Number Systems Test - 24

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Weekly Quiz Competition

Question 1
1 / -0

Irrational number is defined as

A
a real number that cannot be made by dividing two integers.

B
a real number that can be made by dividing two integer.

C
a number that can be made derived after multiplying two integers.

D
a real number that can be written as whole number.

Solution

An irrational is any real number that cannot be expressed as a ratio of integers.
Therefore, $$A$$ is the correct answer.
Question 2
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A terminating decimal has a ............ number of terms after the decimal point.

A
zero

B
infinite

C
finite

D
none of the above

Solution

A terminating decimal is a decimal that ends after a finite number of steps. Hence, is a decimal with a finite number of digits.
Therefore, $$C$$ is the correct answer.
Question 3
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There exists ....... number of rational numbers between $$\dfrac {2}{5}$$ and $$\dfrac {4}{5}.$$

A
$$0$$

B
$$1$$

C
$$5$$

D
infinite

Solution

There exists infinite number of rational numbers between any two rational numbers. i.e. in this case between $$\dfrac {2}{5}$$ and $$\dfrac {4}{5}$$.
Question 4
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If the quotient is terminating decimal, the division is complete only when ...............

A
we get the remainder $$1$$

B
we get the remainder zero

C
we get the remainder as the repeated numbers

D
All of the above

Solution

Any division is complete and terminates only when we get the remainder zero.

e.g. $$\dfrac 2 {10}=0.2$$

we can see the remainder becomes zero in this division.

Therefore, $$B$$ is the correct answer.
Question 5
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Which of the following rational numbers lies between $$0$$ and $$-1$$?

A
$$0$$

B
$$-1$$

C
$$\dfrac {-1}{4}$$

D
$$\dfrac {1}{4}$$

Solution

Clearly, $$0$$ and $$-1$$ cannot lie between $$0$$ and $$-1$$.
Also,
$$0=\dfrac{0}{4}$$ and $$-1=\dfrac{-4}{4}$$
We can clearly see that $$\dfrac {-1}{4}$$ lies between $$0$$ and $$-1$$.
Question 6
1 / -0

Which of the following is an irrational number?

A
$$\dfrac{11}{2}$$

B
$$\sqrt{16}$$

C
$$\sqrt{9}$$

D
$$\sqrt{11}$$

Solution

An irrational is any real number that cannot be expressed as a ratio of integers.
Option $$A$$ is a rational number.
Option $$B$$ and $$C$$ are $$\sqrt{16}$$ and $$\sqrt{9}$$, i.e. $$4$$ and $$3$$ respectively.
$$D$$ cannot be expressed as a ratio of integers.
$$D$$ is the correct answer.
Question 7
1 / -0

Which of the following rational numbers lies between $$\dfrac {3}{2}$$ and $$4$$ ?

A
$$\dfrac {1}{2}$$

B
$$3$$

C
$$\dfrac {8}{2}$$

D
$$\dfrac {9}{2}$$

Solution

We have to find a rational number between $$\dfrac {3}{2}$$ and $$4$$. The L.C.M. of the denominators of both numbers is $$2$$.
$$\therefore \dfrac {3}{2} = \dfrac {3}{2}$$ and $$4\times \dfrac {2}{2} = \dfrac {8}{2}$$.
$$\therefore$$ From the above given options, only $$\dfrac {6}{2}$$
i.e. $$=3$$ lies between $$\dfrac {3}{2}$$ and $$4$$.
Question 8
1 / -0

$$5$$ is a rational number. It can be written as ..........

A
$$\dfrac {5}{1}$$

B
$$\dfrac {1}{5}$$

C
$$\dfrac {5}{5}$$

D
$$\dfrac {5}{25}$$

Solution

Rational numbers are defined as all the numbers of the form $$\dfrac {p}{q}$$ where $$q\neq 0$$.

$$5$$ being a natural number can be written as $$\dfrac {5}{1}$$. A natural number is a rational number.
Therefore, $$A$$ is the correct answer.
Question 9
1 / -0

Given that $$2^h\times 2^3 = 2^9$$, find the value of h.

A
$$3$$

B
$$6$$

C
$$8$$

D
$$12$$

Solution

$$2^{h}\times 2^{3}=2^{9}$$
$$\Rightarrow 2^{h+3}=2^{9}$$
$$\Rightarrow h+3=9$$
$$\Rightarrow \boxed{h=6}$$
Question 10
1 / -0

$$\pi = 3.14159265358979........$$ is an

A
rational number

B
whole number

C
irrational number

D
all of the above

Solution

$$\pi = 3.14159265358979........$$ is a non-terminating and non-repeating irrational number.
Hence, option $$C$$ is correct.

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Re-Attempt Weekly Quiz Competition

Number Systems Test - 24

Result

Number Systems Test - 24

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SHARING IS CARING

Question 1

a real number that cannot be made by dividing two integers.

a real number that can be made by dividing two integer.

a number that can be made derived after multiplying two integers.

a real number that can be written as whole number.

Solution

Question 2

zero

infinite

finite

none of the above

Solution

Question 3

$$0$$

$$1$$

$$5$$

infinite

Solution

Question 4

we get the remainder $$1$$

we get the remainder zero

we get the remainder as the repeated numbers

All of the above

Solution

Question 5

$$0$$

$$-1$$

$$\dfrac {-1}{4}$$

$$\dfrac {1}{4}$$

Solution

Question 6

$$\dfrac{11}{2}$$

$$\sqrt{16}$$

$$\sqrt{9}$$

$$\sqrt{11}$$

Solution

Question 7

$$\dfrac {1}{2}$$

$$3$$

$$\dfrac {8}{2}$$

$$\dfrac {9}{2}$$

Solution

Question 8

$$\dfrac {5}{1}$$

$$\dfrac {1}{5}$$

$$\dfrac {5}{5}$$

$$\dfrac {5}{25}$$

Solution

Question 9

$$3$$

$$6$$

$$8$$

$$12$$

Solution

Question 10

rational number

whole number

irrational number

all of the above

Solution

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