Tag: maths

Questions Related to maths

$\frac{1}{3}(-2p+6q-9r)-\frac{1}{6}(-4p -18q +24r) = $

maths use of brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $-\frac{4}{3}p$

  2. 5q

  3. -7r

  4. 5q-7r

Show answer
Correct Option: D
Explanation:

$\frac{1}{3}(-2p+6q-9r)-\frac{1}{6}(-4p -18q +24r) = \frac{1}{3}(-2p+6q-9r)-\frac{1}{3}(-2p -9q +12r) $
$=\frac{1}{3} [\left (-2p+6q-9r)-(-2p -9q +12r) \right]$
$=\frac{1}{3} (-2p + 6q - 9r + 2p + 9q -12r)$
$=\frac{1}{3} (15q - 21r)$
$=(5q - 7r)$

$ \frac{3}{4}(a+y) \left [ y + a - \frac{1}{3} \left ( y + a -\frac{1}{4}(a+y) \right )\right ]$

maths use of brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $(a+y)^{2}$

  2. $\frac{3a}{16}$

  3. $\frac{9}{16}(a+y)^{2}$

  4. 1

Show answer
Correct Option: C
Explanation:

$ \frac{3}{4}(a+y) \left [ y + a - \frac{1}{3} \left ( y + a -\frac{1}{4}(a+y) \right )\right ]$
= $ \frac{3}{4}(a+y) \left [ y + a - \frac{1}{3} \left (\frac{3}{4}(a+y) \right) \right ]$
= $ \frac{3}{4}(a+y) \left [ y + a - \frac{1}{4}(a+y)\right ]$
= $ \frac{3}{4}(a+y) \left [ \frac{3}{4}(a+y)\right ]$
= $ \frac{9}{16}(a+y)^2$

$-84\times 29+365=$?

maths place value, ordering and rounding order operations and algebra using brackets in algebraic expressions order of operations

  1. $2436$

  2. $2801$

  3. $-2801$

  4. $-2071$

  5. None of these

Show answer
Correct Option: D
Explanation:

Given Exp. $=-84\times (30-1)+365$
$=-(84\times 30)+84+365$
$=-2520+449$
$=-2071$

In a class, there are 18 boys who are over 160 em tall. If these constitute three-fourths of the boys and the total number of boys is two-third of the total number of students in the class, what is the number of girls in the class?

maths place value, ordering and rounding order operations and algebra using brackets in algebraic expressions order of operations

  1. 6

  2. 12

  3. 18

  4. 24

Show answer
Correct Option: B
Explanation:

Total number of boys $\displaystyle=18\div\frac{3}{4}=24$

Total number of students $\displaystyle=24\times\frac{3}{2}=36$

$\therefore$ Number of girls $=36-24=12$

$35+15\times 1.5=$?

maths place value, ordering and rounding order operations and algebra using brackets in algebraic expressions order of operations

  1. $85$

  2. $51.5$

  3. $57.5$

  4. $5.25$

  5. None of these

Show answer
Correct Option: C
Explanation:

Given Exp.$=35+15\times \cfrac{3}{2}=35+\cfrac{45}{2}=35+22.5=57.5$

$(800\div 64)\times (1296\div 36)=$?

maths place value, ordering and rounding order operations and algebra using brackets in algebraic expressions order of operations

  1. $420$

  2. $460$

  3. $500$

  4. $540$

  5. None of these

Show answer
Correct Option: E
Explanation:

Given Exp. $=\cfrac { 800 }{ 64 } \times \cfrac { 1296 }{ 36 } =450$

$9+\cfrac { 3 }{ 4 } +7+\cfrac { 2 }{ 17 } -\left( 9+\cfrac { 1 }{ 15 }  \right) =$?

maths place value, ordering and rounding order operations and algebra using brackets in algebraic expressions order of operations

  1. $7+\cfrac { 719 }{ 1020 } $

  2. $9+\cfrac { 817 }{ 1020 } $

  3. $9+\cfrac { 719 }{ 1020 } $

  4. $7+\cfrac { 817 }{ 1020 } $

  5. None of these

Show answer
Correct Option: D
Explanation:

Given the sum $=9+\cfrac { 3 }{ 4 } +7+\cfrac { 2 }{ 17 } -\left( 9+\cfrac { 1 }{ 15 }  \right) $
$=(9+7-9)+\left( \cfrac { 3 }{ 4 } +\cfrac { 2 }{ 17 } -\cfrac { 1 }{ 15 }  \right) $
$=7+\cfrac { 765+120-68 }{ 1020 } $
$=7+\cfrac { 817 }{ 1020 } $

${\rm{1}}\,{\rm{g/c}}{{\rm{m}}^{\rm{3}}}$ is equal to____________.

maths how much does it weigh? define weight and units of weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. ${\rm{1}}\,{\rm{kg/c}}{{\rm{m}}^{\rm{3}}}$

  2. ${\rm{1}}{{\rm{0}}^3}\,{\rm{kg/}}{{\rm{m}}^{\rm{3}}}$

  3. ${\rm{1}}{{\rm{0}}^{ - 2}}\,{\rm{kg/c}}{{\rm{m}}^{\rm{3}}}$

  4. ${\rm{1}}{{\rm{0}}^{ - 3}}\,{\rm{kg/c}}{{\rm{m}}^{\rm{3}}}$

Show answer
Correct Option: D
Explanation:

We have,

$1\ g/cm^3$

Since,
$1000\ g=1\ kg$
$1\ g=10^{-3} \ kg$

So,

$1\ g/cm^3 =10^{-3}\ kg/cm^3$

Hence, this is the answer.

A spherical bowl  with diameter  $24$ m. How much it weigh  (approx. in kg)  (if $1$ gm $= 1$ cubic cm).

maths how much does it weigh? define weight and units of weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $7216473.6 kg$

  2. $216473.6 kg$

  3. $721473.6 kg$

  4. None of these

Show answer
Correct Option: A

Weight of $1$ mango is $250$ gms. Then identify the weight of $16$ mangos. (Write your answer in kilograms)

maths how much does it weigh? define weight and units of weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: D
Explanation:
the weight of $1$ mango $=250 $  $gram$

weight of $16$ mangoes $=250 \times 16 = 4000$  $gram$

We know that

$1$  $kg =1000$  $gram$

$1$  $gram =\dfrac1{1000}$  $kg$

Given That, we have to convert $4000$  $gram$  to   $kg$

$4000$  $gm =\dfrac{1}{1000} \times 4000$  $kg$

                    $ =\dfrac{4000}{1000} $  $kg$

                   $=4$  $kg$

So, option $D$ is correct