## Arithmetic Mean - Advance

Dear Readers,

In mathematics and statistics, the arithmetic mean, or simply the mean or the average, is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results of an experiment or an observational study, or frequently a set of results from a survey.

Q1.  The sum of n arithmetic means between a and b, is

•   n(a+b)/2
•  n(a+b)
•  (n+1)(a+b)/2
•   (n+1)(a+b

n(a+b)/2

Q2.  Given that n A.M.'s are inserted between two sets of numbers a, 2b and 2a, b, where a, b are Rational numbers. Suppose further that mth mean between these sets of numbers is same, then the ratio a : b equals

•  n – m + 1 : m
•  n – m + 1 : n
•  n : n – m + 1
•  m : n – m + 1

m : n – m + 1

Q3.  Given two number a and b. Let A denote the single A.M. and S denote the sum of n A.M.'s between a and b, then S/A depends on

•   n, a, b
•  n,a
•  n,b
•   n

n

Q4.  The A.M. of series a+(a+d)+(a+2d)+.........+(a+nd) is

•   a+(n-1)d
•   a+nd
•  a+(n+1)d
•  None of these

a+nd

Q5. If 11 AM's are inserted between 28 and 10, then three mid terms of the series are

•  41/2, 9 , 35/2
•  20, 41/2, 43/2
•  20, 61/2, 62/3
•  None of these

41/2, 9 , 35/2

Q6.  If f(x+y,x-y)=xy , then the arithmetic mean of f(x,y) and f(y,x) is

•  x
•   y
•  0
•  1

0

Q7.  If A.M. of the roots of a quadratic equation is 8/5 and the A.M. of their reciprocals is 8/7 then the quadratic equation is

•   7x2+16x+5=0
•  7x2-16x+5=0
•  5x2-16x+7=0
•  5x2-8x+7=0

5x2-16x+7=0

Q8.  If A.M. of the numbers 51+x and51-x is 13 then the set of possible real values of x is

•  {5,1/5}
•   {1,-1}
•   0
•   None of these

{1,-1}

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