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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-Techno India Group Academia South Kolkata, Question Paper -Exercise
  1. If f(x) =e^(x + a) , g(x) = x^(b^2) and h(x) = e^(b^2 x), then find th...

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  2. If A.M. and coefficient of variation of x is 6 and 50% respectively, t...

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

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  4. If p, q, r be the roots of the equation x^3 + ax - b = 0, then the val...

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  5. Given 2 mutually exclusive events A and B such that P(A) = 0.45, P(B) ...

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  6. Two fair dice are thrown. If the sum of two nos. obtained is 8, then t...

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  7. For a positively skewed distribution, what is the relation between mea...

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  8. If the number of educated persons is 65% of the population, then in pi...

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  9. If the mean and median of a distribution is 5 and 6 respectively, then...

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  10. If 2u = 5x and the harmonic mean of x is 0.4, then find the harmonic m...

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  11. If P(A) = 2/3, P(B) = 1/2 and P(A uu B) = 3/4 then find the value of P...

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  12. If P(A) = 2/3, P(B) = 1/2 and P(A uu B) = 3/4 then find the value of P...

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  13. If P(A) = 2/7, P(B) = 6/11, what is the probability that at least one ...

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  14. What is the value of Sheppard's correction of moments for m4?

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  15. State anyone of the Pearson's measure of skewness.

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  16. State true or false : "Index number is a unit-free number".

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  17. If the standard deviation of the set of nos. 1, 2, 3,….,k is 2, then f...

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  18. If the A.M. and G.M. of two positive real nos. are 45 and 9 respective...

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  19. Show that the sum of deviations of a set of observations about their m...

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  20. In a group of 20 males and 5 females, 10 males and 3 females ae servic...

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