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For a set of positive quantities, Prove ...

For a set of positive quantities, Prove that `A.M. ge GM ge H.M.`.

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For a set of an positive quantities prove that AM ge GM ge HM .

If a and b are two positive numbers, then prove that A.M. ge G.M. ge H.M.

If m, n are positive quantities, prove that ((mn+1)/(m+1))^(m+1)gen^m .

If x, y, z are positive quantities, prove that frac(x^3 + y^3)(x + y) + frac(y^3 + z^3)(y + z) + frac(z^3 + x^3)(z + x) ge xy + yz + zx

If the values of a variable are in G.P, then prove that A.M., G.M., H.M. of the values are also in G.P.

If A is the A.M. and G is the G.M. of two unequal positive real numbers p and q, prove that A gt G and |G| gt (G^(2))/(A)

State the condition when A.M. = G.M. = H.M.

If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A pm sqrt((A+G )(A−G )) .

Statement I : If the arithmetic mean of two numbers is (5)/(2) , geometric mean of the numbers is 2, then the harmonic mean will be (8)/(5) . Statement II : For a group of positive numbers (G.M.)^(2) = (A.M.) xx (H.M.)

Assuming a.m. ge g.m is true for 8 and 16 positive observation show that a.m ge g.m for 11 positive observation.

UNITED BOOK HOUSE-Model Test Set - 6-Exercise
  1. What do you mean by ETC?

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  2. Find the standard deviation of first n even positive integers.

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  3. Find the probability of getting a difference of score as ‘3’ when two ...

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  4. P (A cup B) = 0.6, P(A cap B) = 0.2 Determine, P(A^c) + P(B^C).

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  5. If P(A^C cup B^c)=5/6, P(A) = 1/2 , P(B^C) = 2/3 are the events A and...

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  6. Find the formula of combined geomtric mean.

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  7. State and prove Cauchy-Schwartz inequality.

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  8. Prove that,1/(x+y-z)+1/(z+x-y)+1/(y+z-x) > 9/(x+y+z) where x, y and z ...

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  9. State Newton’s forward interpolation formula. Derive the first two ter...

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  10. Find /\^3f(2) from the following values of f(x) : f(2) = 9, f(4)=63, f...

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  11. In respect to a finite sample space define, with example Disjoint even...

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  12. In respect to a finite sample space define, with example Equally likel...

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

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  14. If the letters of the word ‘RAMESH’ are arranged at random, what is th...

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  15. Define price index number and state its uses.

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  16. Show that criide death rate can be expressed as weighted arithmetic me...

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  17. For a set of positive quantities, Prove that A.M. ge GM ge H.M..

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  18. State and Prove the Bayes theorem of probability.

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  19. Discuss different problems in the construction of price index number.

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  20. Decribe the structure of a life table.

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