Tag: maths

Questions Related to maths

$(\dfrac{24}{4\times 12})^2$ = ?

maths square and square root perfect square or square number squares and triangles powers and roots

  1. $\dfrac{3}{4}$

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

  3. $\dfrac{5}{4}$

  4. $\dfrac{1}{3}$

Show answer
Correct Option: B
Explanation:

$4\times12$ $=$ $48$

$(\dfrac{24}{48})^2$=$(\dfrac{1}{2})^2$ 
$=$ $\dfrac{1}{4}$
Hence, Option B is correct.

$(\dfrac{30 \times 25}{60\times 5})^2$ = ?

maths square and square root perfect square or square number squares and triangles powers and roots

  1. $\dfrac{15}{4}$

  2. $\dfrac{25}{3}$

  3. $\dfrac{12}{4}$

  4. $\dfrac{25}{4}$

Show answer
Correct Option: D
Explanation:

$30\times25$ $=$ $750$

$60\times5$ $=$ $300$
$\dfrac{750}{300}$ $=$ $\dfrac{5}{2}$
$\dfrac{5}{2}$$\times$$\dfrac{5}{2}$ $=$ $\dfrac{25}{4}$
Hence, Option D is correct.

If a four-digit perfect square number is such that the number formed by the first two digits and the number formed by the last two digits are also perfect squares, identify the four digit number.

maths square and square root perfect square or square number squares and triangles powers and roots

  1. $6416$

  2. $3616$

  3. $1681$

  4. $1664$

Show answer
Correct Option: C
Explanation:

Four digit number $accd$

$ab$ is a perfect square
$cd$ is also a perfect square
Consider $6416$
$64$and$16$ are perfect square but $6416$ is not a perfect square.
Consider $3616$
$36$and$16$ are perfect square but $3616$ is not a perfect square.

Consider $1681$
$16$and$81$ are perfect square and $1681$ is a perfect square.

Consider $1664$
$16$and$64$ are perfect square but $1664$ is not a perfect square.
Hence, Option C is correct.


Determine the square for the rational number: $(\dfrac{16\times24}{48})$

maths square and square root perfect square or square number squares and triangles powers and roots

  1. $64$

  2. $16$

  3. $46$

  4. $48$

Show answer
Correct Option: A
Explanation:

$(\cfrac{16\times24}{48})^2$
On simplifying, we get

$(\cfrac{24}{3})^2$
$ = 8^2$
$= 64$

Determine the square for the rational number: $(\cfrac{5\times25}{50})$

maths square and square root perfect square or square number squares and triangles powers and roots

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

  2. $\dfrac{4}{25}$

  3. $\dfrac{5}{4}$

  4. $\dfrac{25}{4}$

Show answer
Correct Option: D
Explanation:

$(\cfrac{5\times25}{50})^2$
On simplifying, we get
$(\cfrac{5\times25}{50})^2 = (\cfrac{5}{2})^2$
= $\cfrac{25}{4}$

A rectangular veranda is of dimension $18$m $72$cm $\times 13$ m $20$ cm. Square tiles of the same dimensions are used to cover it. Find the least number of such tiles.

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

  1. $4290$

  2. $4540$

  3. $4620$

  4. $4230$

Show answer
Correct Option: A
Explanation:

The edge of rectangular veranda are $18\ m\ 72\ cm=1872\ cm$ and $13\ m\ 20\ cm=1320\ cm$.


On taking $HCF$ of $1872$ and $1320$, we get

$HCF=24$

Therefore,
No. of tiles required $=$ $\dfrac{Area\ of\ Veranda}{Area\ of\ tiles}$

                                  $=\dfrac{1872\times 1320}{24\times 24}$

                                  $=4290$

Hence, this is the answer.

What is the H.C.F. of two co-prime numbers ?

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

  1. $1$

  2. $0$

  3. $2$

  4. none of these

Show answer
Correct Option: A
Explanation:

The two numbers which have only 1 as their common factor are called co-primes.

For example, Factors of $ 5 $  are $ 1, 5 $
Factors of $ 3 $ are $ 1, 3 $

Common factors is $ 1 $.
$ => HCF = 1 $

The HCF of $256,442$ and $940$ is

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

  1. $2$

  2. $14$

  3. $142$

  4. none

Show answer
Correct Option: A
Explanation:

Prime factors of numbers are 

$256=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\ 442=2\times 13\times 17\ 940=2\times 2\times 5\times 47\ Hence,\quad HCF=2$
So, correct answer is option A. 

HCF of $x^2 -y^2$ and $x^3-y^3$ is

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

  1. $x-y$

  2. $x^3-y^3$

  3. $(x^2-y^2)$

  4. $(x+y)(x^2+xy+y^2)$

Show answer
Correct Option: A
Explanation:

Since, $x^2-y^2=(x+y)(x-y)$
$x^3-y^3=(x-y)(x^2+xy+y^2)$
$H.C.F.=(x-y)$
Option A is correct.

Determine the HCF of $a^2 - 25, a^2 -2a -35$ and $a^2+12a+35$

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

  1. (a-5)(a+7)

  2. (a+5)(a-7)

  3. (a-7)

  4. (a+5)

Show answer
Correct Option: D
Explanation:

Since, $a^2 - 25 = (a-5)(a+5) $
$ a^2 -2a -35 = a^2 -7a +5a -35 $
                         $= a(a-7)+5(a-7) $
                         $= (a+5)(a-7) $
and
$a^2+ 12a + 35 =a^2 +7a +5a +35 $
                          $=(a+7)(a+5) $
Clearly HCF of $a^2 - 25, a^2 -2a -35$ and $a^2+ 12a + 35$ i.e $ (a-5)(a+5), (a+5)(a-7)$ and $(a+7)(a+5)$ is $a+5$
Option D is correct.