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Find the G.M. of n observations a, ar, a...

Find the G.M. of n observations `a, ar, `ar^2`,…………..ar^(n-1)`.

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Show that the products of the corresponding terms of the sequences a, ar, ar^2 ,…ar^(n – 1) and A, AR, "AR"^2, … "AR"^(n – 1) form a G.P, and find the common ratio.

A variable takes values, a, ar, ar^2 ,……….., ar^(n - 1) with equal frequencies. Find AM, GM and HM and hence show that (GM)^2 = A.M. xx H.M.

If the sum of the first n terms of the series a + ar + ar^(2) +…+ ar^(n-1) +… oo is (a)/(1-r) , then -

The sum of first n terms of the series a + ar + ar^(2) +…+ ar^(n-1) +… oo is -

Prove that by using the principle of mathematical induction for all n in N : a+ ar+ ar^(2)+ ..+ ar^(n-1)= (a(r^(n)-1))/(r-1)

The geometric mean of the first n terms of the G.P. a,ar,ar^2 ,….is

If a variable assumes n values a, ar,……… ar^(n - 1) (r < 1) with equal frequencies then verify that AH = G^2

The cor-ordinate of three consecutive verties of a parallelogram ar (3, -1, 2), (I, 2, -4) and (-1, 1, 2). Find the co-ordinate of 4th vertex.

The A.M. between m and n and the G.M. between a and b are each equal to (ma + nb)/(m+n) . Find m and n in terms of a and b.

For all ninNN , prove by principle of mathematical induction that, a+ar+ar^(2)+ . . . to n terms =a*(r^(n)-1)/(r-1)[rne1] .

UNITED BOOK HOUSE-Question Paper 2015-Exercise
  1. What are the tests proposed by Fisher for checking goodness of an inde...

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  2. What do you mean by purchasing power of money?

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  3. What is the effect of change of base and scale on central moments?

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  4. What are the differences between primary data and secondary data?

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  5. Distinguish between qualitative and quantitiative data.

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  6. Find the G.M. of n observations a, ar, ar^2,…………..ar^(n-1).

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  7. Write down the classical definition of probability.

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  8. Describe the different parts of table.

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  9. For three distinct positive numbers a, b, c with a + b + c = 1, show t...

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  10. For three values a, frac(a+b)(2) and b(> a) find the value of (Range)/...

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  11. State Lagrange's interpolation formula.

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  12. The first two moments of a distribution about the value 5 are 3 and 25...

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  13. In a certain distribution of the first three moments about the value 4...

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  14. State and prove Bayes Theorem of probability.

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  15. If the events E1, E2,………….En are independent and such that P(Ei^C) = i...

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  16. Define Laspeyre's and Paasche's price index formula.

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  17. Define Pearson's 2nd measure of Skewness (SK2). Show that -3 <SK<3

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  18. Two boxes contain balls as under: Box 1: 3 White and 2 Red balls Bo...

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  19. State and prove Bayes Theorem of probability.

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  20. Describe the different columns of a life table.

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