Tag: maths

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Questions Related to maths

Multiple choice maths repeated multiplication exponentiation index notation and products of prime factors powers

The greatest of the number 
$1,2^{1/2},3^{1/3},4^{1/4},5^{1/5}, 6^{1/6}, and \ 7^{1/7}$ is

  1. $2^1/2$
  2. $3^1/3$
  3. $7^1/7$
  4. $4^1/4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find the maximum of x^(1/x), consider the function f(x) = x^(1/x). Its derivative is f'(x) = x^(1/x) * (1 - ln(x)) / x^2. The maximum occurs at x = e (approx 2.718). Comparing values near e, 3^(1/3) is larger than 2^(1/2) and 4^(1/4).

Multiple choice maths repeated multiplication exponentiation index notation and products of prime factors powers

Find the value of $\displaystyle\frac{5^0+5^{-1}}{5^0-5^{-1}}-\left(\frac{8}{27}\right)^{\displaystyle\frac{1}{3}}-\left(\frac{36}{25}\right)^{-\displaystyle\frac{1}{3}}$

  1. 0
  2. $\displaystyle\frac{1}{2}$

  3. 1

  4. 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle\frac{\displaystyle1+\frac{1}{5}}{\displaystyle1-\frac{1}{5}}-\left[\left(\frac{2}{3}\right)^3\right]^{\displaystyle\frac{1}{3}}-\left[\left(\frac{6}{5}\right)^2\right]^{\displaystyle-\frac{1}{2}}=\frac{\displaystyle\frac{6}{5}}{\displaystyle\frac{4}{5}}-\left(\frac{2}{3}\right)^1-\left(\frac{6}{5}\right)^{-1}=\frac{6}{4}-\frac{2}{3}-\frac{5}{6}=\frac{18-8-10}{12}=0$

Multiple choice maths indices exponentiation index notation and products of prime factors powers

The approximate value of ${ \left{ { { \left( 3.92 \right)  }^{ 2 }\quad +3\left( 2.1 \right)  }^{ 4 } \right}  }^{ { 1 }/{ 6 } }$

  1. $2.0466$
  2. $2.755$
  3. $2.345$
  4. $0.242718$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

${(3.92^2+3(2.1^4)}^\dfrac{1}{6}$

 
$=(15.3664+3\times19.4481)^\dfrac{1}{6}$


$=(15.3664+58.3443)^\dfrac{1}{6}$

$=(73.7107)^\dfrac{1}{6}$

$=2.0476$

Multiple choice maths indices exponentiation index notation and products of prime factors powers

If $\displaystyle { 2 }^{ n }-{ 2 }^{ n-1 }=4$, then the value of $\displaystyle { n }^{ n }$ will be -

  1. 1
  2. $\displaystyle \frac { 3 }{ 2 } $

  3. 2

  4. 27
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle { 2 }^{ n }-{ 2 }^{ n-1 }=4$
$\displaystyle \therefore \quad { 2 }^{ n-1 }\left( 2-1 \right) =4$
$\displaystyle \therefore \quad { 2 }^{ n-1 }={ 2 }^{ 2 }$
$\displaystyle \therefore \quad n-1=2$
$\displaystyle \therefore \quad n=3$
$\displaystyle \therefore \quad { n }^{ n }={ 3 }^{ 3 }=27$

Multiple choice maths indices exponentiation index notation and products of prime factors powers

$\displaystyle \frac { { \left( 3.63 \right)  }^{ 2 }-{ \left( 2.37 \right)  }^{ 2 } }{ 3.63+2.37 } $ is simplified to -

  1. 6

  2. 1.36

  3. 2.26

  4. 1.26
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle \frac { { \left( 3.63 \right)  }^{ 2 }-{ \left( 2.37 \right)  }^{ 2 } }{ 3.63+2.37 } $
$\displaystyle =\frac { \left( 3.63+2.37 \right) \left( 3.63-2.37 \right)  }{ 3.63+2.37 } $
$\displaystyle =3.63-2.37$
$\displaystyle =1.26$

Multiple choice maths indices exponentiation index notation and products of prime factors powers

Simplest form of the Expression $\displaystyle { \left( { x }^{ 6 }.{ y }^{ { -5 }/{ 4 } } \right)  }^{ { -4 }/{ 3 } }$ will be-

  1. $\displaystyle { x }^{ -24 }y$
  2. $\displaystyle { x }^{ -8 }{ y }^{ { 5 }/{ 3 } }$
  3. $\displaystyle { x }^{ 8 }{ y }^{ { -5 }/{ 3 } }$
  4. $\displaystyle { x }^{ -8 }{ y }^{ { -5 }/{ 3 } }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle { \left( { x }^{ 6 }.{ y }^{ { -5 }/{ 4 } } \right)  }^{ { -4 }/{ 3 } }$
$\displaystyle ={ x }^{ -6\times { 4 }/{ 3 } }{ y }^{ \dfrac { -5 }{ 4 } \times -\dfrac { 4 }{ 3 }  }$
$\displaystyle ={ x }^{ -8 }{ y }^{ { 5 }/{ 3 } }$

Multiple choice maths rule of three direct proportion and inverse proportion types of proportions direct proportion

A man eats $200:g$ of rice a day and he has enough rice to last him for $35$ days. How long would the stock of rice last him if he were to eat $250:g$ rice a day.

  1. $\;42$
  2. $\;21$
  3. $\;28$
  4. $\;49$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Man eat $ 200$ g rice in a day then he  has $35\times 200=7000  g $ rice for  $35$  days
But if he eat  $250$  g rice in a day
Then $7000$  g rice is enough for $\dfrac{7000}{250}=28  \ days$