Tag: introduction to averages

Questions Related to introduction to averages

In a Maths test the average score of the $10$ girls in a class is $15$ and the average score of the $15$ boys is $10$. The average score of the class in the test is 

maths average arithmetic mean of ap introduction to averages means

  1. $12$

  2. $12.5$

  3. $13$

  4. $12.75$`

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Correct Option: A

Mean deviation of first $7$ natural no. about their A.M. is?

maths average arithmetic mean of ap introduction to averages means

  1. $2$

  2. $\sqrt{2}$

  3. $\dfrac{12}{7}$

  4. $0$

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Correct Option: A

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