Tag: maths

Questions Related to maths

The ratio of sum of n arithmetic means between two given numbers to that of single arithmetic mean between them id

maths average arithmetic mean of ap introduction to averages means

  1. n : 1

  2. n$^2$ : 1

  3. 1 : 1

  4. $\sqrt{n}$ : 1

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Correct Option: A

If $\cfrac {a^n+b^n}{a^{n-1}+b^{n-1}}$ is the AM between a and b, then the value of n is 

maths average arithmetic mean of ap introduction to averages means

  1. 0

  2. 1

  3. -1

  4. none of these

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Correct Option: A
Explanation:

The A.M. of a and b is $\dfrac{a+b}{2}$.


Therefore, $\dfrac{a^{n+1}+b^{n+1}}{a^n+b^n}$ will be the A.M. of a and b, if 

$\dfrac{a^{n+1}+b^{n+1}}{a^n+b^n}=\dfrac{a+b}{2}$

$\Rightarrow 2(a^{n+1}+b^{n+1})=(a^n+b^n)(a+b)$

$\Rightarrow 2a^{n+1}+2b^{n+1}=a^{n+1}+a^nb+b^na+b^{n+1}$

$\Rightarrow a^{n+1}+b^{n+1}=a^nb+b^na$

$\Rightarrow a^n(a-b)=b^n(a-b)$

$\Rightarrow a^n=b^n$

$\Rightarrow \dfrac{a^n}{b^n}=1$

$\Rightarrow (\dfrac{a}{b})^n=1$

$\Rightarrow (\dfrac{a}{b})^n=(\dfrac{a}{b})^0$

$\Rightarrow n=0$

Find the average of the following set of scores $253,124,255,534,836,375,101,443,760$

maths average arithmetic mean of ap introduction to averages means

  1. $427$

  2. $413$

  3. $141$

  4. $409$

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Correct Option: A

The average age of $30$ girls. is $13\ yr$. The average of first $18$ girls is $15\ yr$. Find out the average age of remaining $12$ girls? 

maths average arithmetic mean of ap introduction to averages means

  1. $12\ yr$

  2. $10\ yr$

  3. $16\ yr$

  4. $10.5\ yr$

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Correct Option: A

A student bought $4$ books for $Rs.120$ from one book shop and $6$ books for $Rs.150$ from another. The average price (in  rupees), he paid per book was:

maths average arithmetic mean of ap introduction to averages means

  1. $27$

  2. $27.50$

  3. $135$

  4. $138$

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Correct Option: A

Let $(1-2x+3x^{2})^{10}=a _{0}+a _{1}x+a _{2}x^{2}+....+a _{n}x^{n},a _{n}\neq 0$, then the arithmetic mean of $a _{0},a _{1},a _{2},....a _{n}$ is

maths average arithmetic mean of ap introduction to averages means

  1. $\dfrac{1024}{11}$

  2. $\dfrac{512}{7}$

  3. $\dfrac{512}{11}$

  4. $\dfrac{1024}{21}$

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Correct Option: A

If $a,b,c,d,e,f$ are $A.M.s$ between $2$ and $12$ then $a+b+c+d+e+f$ is equal to

maths average arithmetic mean of ap introduction to averages means

  1. $14$

  2. $42$

  3. $84$

  4. $None\ of\ these$

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Correct Option: A

The average height of 25 boys is 1.4 m. When 5 boys leave the group, then the average height increases by 0.15 m. What is the average height of the 5 boys who leave?

maths average arithmetic mean of ap introduction to averages means

  1. 0.8 m

  2. 0.9 m

  3. 0.95 m

  4. 1.05 m

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Correct Option: A

The average age of 36 student in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years?

maths average arithmetic mean of ap introduction to averages means

  1. 31

  2. 36

  3. 51

  4. Cannot be determined

  5. None of these

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Correct Option: A

The sum of first $n$ natural numbers is given by the expression $(2n^{2}+3n)$. The mean of the given numbers is 

maths average arithmetic mean of ap introduction to averages means

  1. $\left(\dfrac{2}{n}+3\right)$

  2. $\left(2+\dfrac{3}{n}\right)$

  3. $(2+3n)$

  4. $(2n+3)$

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Correct Option: A