Tag: maths

Questions Related to maths

Which one of the following is not true?

maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

  1. $\sqrt{2}$ is an irrational number

  2. $\sqrt{17}$ is a irrational number

  3. $0.10110011100011110...$ is an irrational number

  4. $\sqrt[4]{16}$ is an irrational number

Show answer
Correct Option: D
Explanation:

$2^{4} =16$


$\because \sqrt[4]{16} = 2$, which is a rational number.

The greater number between $\sqrt{17}-\sqrt{12}$ and $\sqrt{11}-\sqrt{6}$ is ____.

maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

  1. $\sqrt{17}-\sqrt{12}$

  2. $\sqrt{11}-\sqrt{6}$

  3. Both are equal

  4. Cannot comare

Show answer
Correct Option: B
Explanation:

$\sqrt{17}=4.12\ \sqrt {12}=3.46\ \therefore\sqrt{17}-\sqrt{12}=0.66$

$\sqrt{11}=3.32\ \sqrt6=2.45\ \therefore\sqrt{11}-\sqrt6=0.87$

$\sqrt{11}-\sqrt6>\sqrt{17}-\sqrt{12}$

The value of $0.\overline{2}$ in the form $\frac{p}{q}$ , where p and q are integers and $q\ne 0$ is :

maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

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

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

  3. $\dfrac{2}{5}$

  4. $\dfrac{1}{8}$

Show answer
Correct Option: B
Explanation:

$Let\quad x=.222....\ On\quad multiplying\quad by\quad 10\quad on\quad both\quad sides\quad \ 10x=2.222....\ On\quad subtracting\quad both\quad equations\quad \ 9x=2\ x=\dfrac { 2 }{ 9 } $

Hence,correct answer is option B.

Which of the following is/are correct?

maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

  1. Every integer is a rational number.

  2. The sum of a rational number and an irrational number is an irrational number.

  3. Every real number is rational.

  4. Every point on the number line is associated with a real number

Show answer
Correct Option: A,B,D
Explanation:

Yes every integer can be represented in the form of $p/q$ where q is 1 for integers, so every integer is a rational number.
The sum of rational and irrational numbers is always irrational.
No, every real number is not rational. Real numbers are classified as rational numbers and irrational numbers.
Any number on the number line is a real number because that number can be either rational or irrational. Rational and irrational numbers together form real numbers.

To represent a rational number $\sqrt{2}$ on number line, take sides of right triangle as:

maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

  1. $1$ and $1$

  2. $1$ and $2$

  3. $2$ and $0$

  4. $-1$ and $-1$

Show answer
Correct Option: A
Explanation:
Notice that $\sqrt{2}= \sqrt{(1^2 + 1^2)}$. So, we can form a length of $\sqrt{2}$ units using two mutually perpendicular sides of length $1$ unit each. (Since, $1,1,\sqrt{2}$ form sides of a right angled triangle by Pythagoras theorem).

Use ______________ to represent an irrational number on number line.

maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

  1. Isosceles-angle theorem

  2. Scalene angle theorem

  3. Right-angled theorem

  4. None of the above

Show answer
Correct Option: C
Explanation:
Using the Pythagoras Theorem, we can represent some irrational numbers, which are surds, on a number line.
Since it involves Pythagoras Theorem, we get to use Right Angle Theorem.

Hence, to represent an irrational number, we generally use right angled theorem.

$D$ is a real number with non terminating digits $a _1$ and $a _2$ after the decimal point. Let $D = 0, a _1 a _2 a _1 a _2 ........ $  with $a _1 & a _2$ both not zero which of the following when multiplied by $D$ will necessarily give an integer ?

maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

  1. $99$

  2. $18$

  3. $125$

  4. $75$

Show answer
Correct Option: A
Explanation:

its straight question
give $D=0.abababab$ $(say - 1)$ 
Multiply both sides by $100$ $i.e.$ 
$100D = ab.abababab$ $(say - 2)$
now subtract $1$ from $2 .$ That gives
$99D = ab => D = ab/99$ hence it should be multiplied by $99k$ to get an integer ab$.$

The number $5\sqrt{34}$ lies between

maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

  1. $29$ and $30$

  2. $30$ and $31$

  3. $31$ and $32$

  4. $32$ and $33$

Show answer
Correct Option: A
Explanation:
$5\sqrt {34}\ \le \ 5\sqrt {36} \ = \ 5\times 6=30$
less than $30$
i.e., $=29$ to $30$


Can $\sqrt { 3 } -3$ be represented on the number line. 

maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Yes, 


Number line consists of all real numbers i.e., Both rational and Irrational Numbers

Since $\sqrt 3-3$ is a real number It can be represented on number line 

Give an example of two irrational numbers whose difference is an irrational number.

maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

  1. $\sqrt{3},-\sqrt{3}$

  2. $\sqrt{5,}-\sqrt{5}$

  3. $4\sqrt{3},-2\sqrt{3}$

  4. None of the above

Show answer
Correct Option: C
Explanation:

$4\sqrt{3},2\sqrt{3}$ are the irrational numbers and thier difference,


$4\sqrt{3}-2\sqrt{3}=2\sqrt 3$ is also an irrational number.