Tag: real number

Quizzes (6) Questions (132)

Questions Related to real number

Multiple choice maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

When the HCF of $468$ and $222$ is written in the form of  $ 468 x + 222y$ then the value of $ x$ and $y$ is 

  1. $x =-9 \ and \ y =19$
  2. $x =9 \ and \ y = -19$
  3. $x =9\ and \ y = 19$
  4. $x =-9 \ and \ y =- 19$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

HCF of $468$ and $222$
$468 = \left(222 \times 2\right) + 24$
$222 = \left(24\times\ 9\right) + 6$
$24 = \left(6\times\ 4\right) + 0$
$\therefore HCF = 6$

$6 = 222 - \left(24\times\ 9\right)$
$ = 222 - \left[\left(468 -222 \times 2\right) \times\ 9\right]  $ [where $468 = 222 \times 2 + 24$]
$ = 222 - \left[468 \times 9 -222 \times 2 \times 9\right]$
$= 222 - \left(468 \times9\right) - \left(222\times 18\right)$
$ = 222 + \left(222 \times 18\right) - \left(468 \times9\right)$
$= 222\left[1 + 18\right]-  468 \times 9$
$= 222 \times19-  468 \times 9$
$  = 468 \times -9 + 222\times 19$
$\therefore x=-9$ and $y=19$.

Multiple choice maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

The HCF of $136 ,170 \ and \ 255$ is 

  1. $13$
  2. $15$
  3. $17$
  4. $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

136)170(1

  -    136
-------------------
          34)136(4
                136
----------------------------
                 0</div>

34)255(7
   -  238
-------------------
        17)34(2
             34
------------------------
              0

Multiple choice maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

The H.C.F. of two expressions is x and their L.C.M is $ \displaystyle x^{3}-9x  $  IF one of the expression is $ \displaystyle x^{2}+3x  $  then,the other expression is 

  1. $ \displaystyle x^{2}-3x $
  2. $ \displaystyle x^{3}-3x $
  3. $ \displaystyle x^{2}+9x $
  4. $ \displaystyle x^{2}-9x $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let two expressions $p(x)$ and $q(x)$ then

$p(x)\times q(x)=L.C.M.\ \times\ H.C.F.$

Since $p(x)=x^2+3x$
$(x^2+3x)\times q(x)=(x^3-9x) \times\ x$
$(x^2+3x)\times q(x)=(x^2-3x) \times\ (x^2+3x)$

$q(x)=(x^2-3x)$
Hence, this is the required solution.

Multiple choice maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

The H.C.F. of the numbers $16.5, 0.90$ and $15$ is

  1. $16.5$
  2. $0.90$
  3. $15$
  4. $0.3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$1650 = 2\times 3\times 5^{2}\times 11$
$90 = 2\times 3^{2} \times 5^{1}$
$1500 = 2^{2} \times 3^{1} \times 5^{3}$
H.C.F. of $1650, 90$ and $1500$ is $2\times 3\times 5 = 30$

Therefore, H.C.F. of $16.5, 0.90$ and $15$ is $0.30$.
So, option D is correct.