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

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

  1. $\sqrt{17}-\sqrt{12}$
  2. $\sqrt{11}-\sqrt{6}$

  3. Both are equal

  4. Cannot comare
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

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

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

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

  1. $\dfrac{1}{5}$
  2. $\dfrac{2}{9}$
  3. $\dfrac{2}{5}$
  4. $\dfrac{1}{8}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

Which of the following is/are correct?

  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
Reveal answer Fill a bubble to check yourself
A,B,D Correct answer
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.

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

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

  1. $1$ and $1$
  2. $1$ and $2$
  3. $2$ and $0$
  4. $-1$ and $-1$
Reveal answer Fill a bubble to check yourself
A Correct answer
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).
Multiple choice maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

Use ______________ to represent an irrational number on number line.

  1. Isosceles-angle theorem

  2. Scalene angle theorem

  3. Right-angled theorem

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

$D$ 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 ?

  1. $99$
  2. $18$
  3. $125$
  4. $75$
Reveal answer Fill a bubble to check yourself
A Correct answer
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$.$

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

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

  1. $\sqrt{3},-\sqrt{3}$
  2. $\sqrt{5,}-\sqrt{5}$
  3. $4\sqrt{3},-2\sqrt{3}$

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
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.