Distance between Points on a Number Line

Q.

Every point on a number line represents:

1. A unique real number

2. A natural number

3. A rational

4. none of these

Q.

An irrational number is marked on the number line (C) as shown in fig. Then the value of C is ___.

1. $\sqrt{7}$

2. $\sqrt{5}$

3. $\sqrt{2}$

4. $\sqrt{3}$

Q.

Which of the following lies between $\frac{25}{4}$ and $\frac{22}{3}?$

1. $\frac{13}{2}$
2. $\frac{15}{2}$
3. $\frac{17}{2}$
4. $8$

Q.

Question 1 (ii)
State whether the following statement is true or false. Justify your answer.

Every point on the number line is of the form $\sqrt{m}$, where m is a natural number.

Q. State whether the following statements are true or false. Justify your answers.
(i) Every irrational number is a real number.
(ii) Every point on the number line is of the form $\sqrt{m}$, where $m$ is a natural number.
(iii) Every real number is an irrational number.

Q.

Write the following sets of numbers in the set-builder and tabular forms, and represent them on the number line.

Integers greater than$-4$ and less than $1$

Q.

On the number line $\sqrt{17}$ lies between

1. 2 and 3

2. 4 and 5

3. 5 and 6

4. 16 and 18

Q. How to represent irrational number on number line?

Q.

If the following numbers are represented on a number line, which number will be the rightmost?
5.6, -3, 0.5, 3

1. 3

2. 0.5

3. -3

4. 5.6

Q.

The midpoint of the points 1 and -5 on the number line is

1. -3

2. -2

3. -1

4. 0

Q. Insert three rational number between $\frac{7}{3}$ and $\frac{3}{4}$.

Q.

The distance between the points $-2\frac{1}{2}$ and $-5\frac{1}{4}$ on the number line is

1. $\frac{15}{4}$ units

2. $\frac{13}{4}$ units

3. $\frac{11}{4}$ units

4. $\frac{9}{4}$ units

Q.

Question 7(d)

In the following pair of numbers, state which whole number is on the left of the other number on the number line? Also write them with the appropriate sign (>, <) between them.
9830415, 10023001

Q.

The distance between the points $4\frac{1}{2}$ and $3\frac{1}{4}$ on the number line is

1. $1\frac{1}{4}$ units

2. $2\frac{1}{4}$ units

3. $2\frac{1}{3}$ units

4. $1\frac{1}{2}$ units

Q.

An irrational number is marked on the number line (C) as shown in fig. Then the value of C is ___.

1. $\sqrt{2}$

2. $\sqrt{5}$

3. $\sqrt{3}$

4. $\sqrt{7}$

Q.

The midpoint of 5 and 8 is:

1. 6

2. 7

3. 6.5

4. any number between 6 and 7

Q.

Which of the following numbers lie
$\text{between}\frac{3}{4}\text{and}\frac{7}{4}?$

1. 5.0

2. 3.0

3. 2.5

4. 1.25

Q.

Which of the following numbers are:

$\left\{7,\frac{3}{2},-\frac{9}{5},-8,0,2,\frac{1}{4}\right\}$

1. natural numbers?
2. whole numbers?
3. integers?
4. rational numbers

Q. Insert three rational number between $\frac{4}{3}$ and $\frac{1}{4}$.

[ 2 Marks ]

Q.

Two points A & B are marked on the number line as shown in figure. A = -7 and distance between them is 10 units. The point B is

1. -3

2. 3

3. -17

4. 17

Q.

How many natural numbers are there
$\text{between}\frac{3}{10}\text{and}\frac{7}{10}$?

1. 0

2. 1

3. 2

4. 3

Q.

Two points A & B are marked on the number line as shown in fig with A = -2 & B = -5

The distance between them is

1. 3 units

2. -3 units

3. -7 units

4. 7 units

Q.

Distance between $-\sqrt{2}$ and $-\sqrt{3}$ is

1. 0.32

2. 0.23

3. 0.4

4. 0.2

Q.

The midpoint of the pair of points $-\sqrt{2}$ and $-\sqrt{3}$ on the number line is

1. $\frac{(\sqrt{2}+\sqrt{3})}{2}$

2. $\frac{-(\sqrt{2}+\sqrt{3})}{2}$

3. $\frac{-(\sqrt{2}-\sqrt{3})}{2}$

4. $\frac{(\sqrt{2}-\sqrt{3})}{2}$

Q.

Write all integers between:

$-3\mathrm{and}0$

Q.

An irrational number is plotted (c) on the number line as shown in the figure. Then the value of C is

1. $\sqrt{7}$

2. $\sqrt{5}$

3. $\sqrt{3}$

4. $\sqrt{2}$

Q.

Vicky walked 15 metres towards North, took a left turn and walked 20 metres, and again took a left turn and walked 15 metres and stopped walking. Towards which direction was he facing when he stopped walking?

1. East
2. West
3. South
4. North

Q.

Two points P & Q are marked on the number line as shown in figure with P = -8 & Q = -15

The distance between them is

1. 5 units

2. 8 units

3. 7 units

4. 15 units

Q.

An irrational number is plotted (c) on the number line as shown in the figure. Then the value of C is

1. $\sqrt{7}$

2. $\sqrt{5}$

3. $\sqrt{3}$

4. $\sqrt{2}$

Q.

On the number line $\sqrt{17}$ lies between

1. 16 and 18

2. 2 and 3

3. 4 and 5

4. 5 and 6