Real Numbers

Q. Which rational numbers do points A and B represent in the given number line? (Assume that any two divisions between two integers in the given number line are equal.)

1. A=$\frac{1}{3}$, B=- $\frac{2}{3}$
2. A=$\frac{1}{4}$, B= -$\frac{5}{4}$
3. A=$\frac{1}{3}$, B= -$\frac{4}{3}$
4. A=$\frac{1}{3}$, B= -$\frac{2}{3}$

Q.

Find the smallest positive integer which when divided by 3 , 7, 11 leaves remainder 1, 6, 5 respectively

Q. There is only one rational number between $\frac{1}{5}$ and $\frac{3}{5}$.

1. False
2. True

Q.

During the summer months, one ice cream truck visits Dipanshu's neighbourhood every 4 days and another ice cream truck visits his neighbourhood every 5 days. If both trucks visited today, when is the next time both trucks will visit on the same day?

1. 10

2. 9

3. 20

4. 40

Q.

The greatest number among $\sqrt[3]{9},\sqrt[4]{11}$ and $\sqrt[6]{17}$ is

1. $\sqrt[3]{9}$

2. $\sqrt[4]{11}$

3. $\sqrt[6]{17}$

4. Cannot be determined.

Q. Every even and odd integers can be represented as ________ and ________

1. 3q and 3q+1
2. 2q and q+1
3. 2q and 2q+1
4. 3q and 3q+2

Q. Question 132
Find five rational numbers between 0 and 1.

Q. 3. Insert
(i) two rational numbers between 5/6 and 6/5
(ii)three rational numbers between 3/7 and 1/11

Q. Solve the following equation and verify your answer:

$\left(i\right)$ $\frac{2x-3}{3x+2}=-\frac{2}{3}$

Q. Find four rational number between 4 and 5. How many rational number lie between these two numbers.

Q. When a set of rational numbers is combined with a set of irrational numbers, it will result in which type of numbers?

1. Complex numbers
2. Whole numbers
3. Natural numbers
4. Real numbers

Q. Find three rational numbers between 2 / 3 and 3 /4

Q. Question 2
Represent $\frac{-2}{11},\frac{-5}{11},\frac{-9}{11}$ on the number line.

Q. Question 6
$m-\frac{m-1}{2}=1-\frac{m-2}{3}$

Q. is an irrational number.

1. $\pi$
2. 2526
3. 118

Q. Find five rational numbers between 2/3 and 4/5

Q. find. three rational number between 1/4 and 1/2 using the average method ?

Q. Every point on a number line represents

1. a natural number
2. a rational number
3. a unique real number
4. an irrational number

Q. The rational number between $\frac{2}{5}and\frac{3}{5}$ is

1. $\frac{62}{60}$
2. $\frac{13}{30}$
3. $\frac{31}{30}$

Q. What are rational numbers

Q. Write:
a) The rational number that does not have a reciprocal
b) The rational numbers that are equal to their reciprocals.
c) The rational number that is equal to its negative.

Q. Write each of the following in decimal form and say what kind of decimal expansion each has. (i) $\frac{5}{8}$ (ii) $\frac{7}{25}$ (iii) $\frac{3}{11}$ (iv)$\frac{5}{13}$ (v) $\frac{11}{24}$ (vi)$\frac{261}{400}$ (vii) $\frac{231}{625}$ (viii)$2\frac{5}{12}$

Q. There are infinitely many rational numbers between 5 and 7.

1. True
2. False

Q.

Which of the following rational numbers are equivalent to $\frac{9}{4}$?

1. $\frac{12}{3}$

2. $\frac{81}{25}$

3. $\frac{36}{16}$

4. $\frac{63}{28}$

Q.

While representing a whole number, the number line extends _______ .

1. Indefinitely to the left side of 1

2. Indefinitely on both sides of zero

3. Indefinitely to the right side of 1

4. Indefinitely to the right side of zero

Q. The addition of a rational number with an irrational number will result in which type of number?

1. Rational number.
2. Irrational number.
3. Real number.

Q. For $m^2>m^3$, $m$ is a ____ integer.

1. positive
2. negative
3. non-positive
4. non-negative

Q.

Find four rational numbers between $-1$ and $\frac{1}{2}$.

Q. how to find out the rational numbers between -5/6 and 13/3 also how to find out the rational number between -5/3, 13/3 and -7/8

Q. is an irrational number.

1. 118
2. $\pi$
3. 2526