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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.

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)

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.

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

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.

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.

Which element of the following has the highest ionisation potential? Na, Cl, Si and Ar.

The element with the electronic configurations as [Ar] 3d^104s^24p^3 represents a

UNITED BOOK HOUSE-Model Test Set - 1-Exercise
  1. Give the forniula of Fisher’s index number ?

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  2. Distinguish between positive skewness and negative skewness.

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

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  4. Write the demerits of geometric mean?

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  5. Express the following probabilities in the probability. Statement : P(...

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  6. Express the following probabilities in the probability. Statement : P(...

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  7. Prove that if A^c and B^c are independent, then are A and B?

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  8. Write the classical definition of probability and state its limitation...

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  9. What is Ogive? What are its uses?

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  10. Describe the construction process of a questionnaire.

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  11. The lower and the upper quartiles of a disiribution are 14.6 and 25.2 ...

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  12. What is histogram? How does it differ from a bar diagram?

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  13. State and prove Remainder theorem.

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  14. Find a polynomial in x, of the second degree which vanishes when x = -...

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  15. State and prove Cauchy-Schwartz inequality.

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  16. Two unbiased dice are thrown. What is the probability that the sum of ...

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  17. If P(A)=a and P(B)=b, Show that P(A/B) lea/b.

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  18. A card is drawn from each of two well shuffled pack of cards. Find the...

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  19. Discuss about different sources of data on vital events.

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  20. Prove that Laspeyre’s and Paasche’s index numbers will be equal if the...

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