Tag: maths

Questions Related to maths

Find AM of multiple of $3$  from natural numbers $1$ to $100$.

maths average arithmetic mean of ap introduction to averages means

  1. $48$

  2. $51$

  3. $36$

  4. $57$

Show answer
Correct Option: B
Explanation:

First term $=3$

Last term $=99$
$\therefore A.M.=\dfrac{3+99}{2}=51$

The  arithmatic mean of $4,6,8$ is

maths average arithmetic mean of ap introduction to averages means

  1. $4$

  2. $6$

  3. $8$

  4. $4.5$

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Correct Option: B
Explanation:

$\Rightarrow$  First adding numbers $4,\, 6$ and $8$ = $4+6+8=18$

$\Rightarrow$   We have number of terms 3
$\Rightarrow$   $Arithemetic\, mean=\dfrac{S}{N}=\dfrac{18}{3}=6$

Find AM of  $ 3$  digit even numbers between $1$  to $500$.

maths average arithmetic mean of ap introduction to averages means

  1. $200$

  2. $400$

  3. $300$

  4. $150$

Show answer
Correct Option: C
Explanation:

First term $=100$

Last term $=500$
$\therefore A.M.=\cfrac{100+500}{2}=300$

Find AM of divisors of $100$.

maths average arithmetic mean of ap introduction to averages means

  1. $24$

  2. $25.5$

  3. $24.11$

  4. $21.9$

Show answer
Correct Option: C
Explanation:

Divisors of 100 are:

$1, 2, 4, 5, 10, 20, 25, 50, 100$
$\therefore n=9$
$\therefore S=1+2+4+5+10+20+25+50+100=217$
$\therefore A.M.=\dfrac{S}{n}=\dfrac{217}{9}=24.11$

If the nth term of AP is $2n+5$. Then find the  AM of first $38$  terms.

maths average arithmetic mean of ap introduction to averages means

  1. $99$

  2. $98$

  3. $100$

  4. $44$

Show answer
Correct Option: D
Explanation:
Given:
$t _{n}=2n+5$
First term $=2\times 1+5=7$
Last term $=2\times 38+5=81$
$\therefore A.M.=\dfrac{7+81}{2}=44$

The AM of  multiple of $5$ from numbers $1$ to $500$ is

maths average arithmetic mean of ap introduction to averages means

  1. $250$

  2. $\dfrac{500}{2}$

  3. $\dfrac{505}{2}$

  4. $252.5$

Show answer
Correct Option: D
Explanation:

First term $=5$

Last term $=500$
$\therefore A.M.=\dfrac{5+500}{2}=252.5$

The  Sum of three numbers in AP is $75$, and product of extremities is $609$. The numbrs and AM of 1st two numbers is 

maths average arithmetic mean of ap introduction to averages means

  1. ${21,25,29}$, AM $= 23$

  2. ${13,17,21}$, AM $= 22$

  3. ${21,25,29}$, AM $= 25$

  4. ${21,22,29}$, AM $= 23$

Show answer
Correct Option: A
Explanation:

Let the numbers in A.P.  be (a-d), a, (a+d)

$\therefore (a-d)+a+(a+d)=75$
$\Rightarrow a=25$
Also, $(a-d)(a+d)=609$
$\Rightarrow a^{2}-d^{2}=609$
$\Rightarrow 25^{2}-d^{2}=609$
$\therefore d=\pm4$
The numbers are {21,25,29} or {29,25,21}
According to option, we take {21,25,29}
A.M. of 1st two numbers $=\dfrac{21+25}{2}=23$

If the Arithmetic mean of $8, 6, 4, x, 3, 6, 0$ is $4$; then the value of $x =$

maths average arithmetic mean of ap introduction to averages means

  1. $7$

  2. $6$

  3. $1$

  4. $4$

Show answer
Correct Option: C
Explanation:

Arithmetic mean $= \cfrac{\text{sum of all observations}}{\text{no. of observations}}$

$\Rightarrow 4=\cfrac { 8+6+4+x+3+6+0 }{ 7 } \ \Rightarrow 28=27+x\ \Rightarrow x=1$

Arithmetic mean of $2$ and $8$ is

maths average arithmetic mean of ap introduction to averages means

  1. $5$

  2. $10$

  3. $16$

  4. $3.2$

Show answer
Correct Option: A
Explanation:

Arithmetic mean of $a$ and $b$ is $\dfrac{a+b}{2}$

$\therefore$ arithmetic mean of 2 and 8 is $\dfrac{2+8}{2}=\dfrac{10}{2}=5$
Hence, option $A$ is correct.

State the following statement is True or False
Arithmetic mean of first five natural numbers is $3$.

maths average arithmetic mean of ap introduction to averages means

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

First five natural numbers are $1 ,2 , 3 ,4, 5$

arithmetic mean = $\dfrac { sum\quad of\quad numbers }{ count\quad of\quad numbers } $
$ = \dfrac{1 + 2 + 3 + 4  + 5 }{ 5} $
$=\dfrac { 15 }{ 5 } =3$
Arithmetic mean of first five natural number is 3.
Hence the given statement is true.