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If n be a positive integer greater than 1, prove that `(frac(n+1)(2))^n > n`

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UNITED BOOK HOUSE-Hare School, Question Paper -Exercise
  1. State and prove that Cauchy-Schwarz inequality.

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  2. If a, b, c be three unequal sides of a triangle show that frac(1)(b+c-...

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  3. If n be a positive integer greater than 1, prove that (frac(n+1)(2))^n...

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  4. If a, b, c one positive numbers satisfying 4ab + 6bc + 8ca = 9 find th...

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  5. Distinguish between attribute and variable.

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  6. Find the arithmetic mean and median for first n natural numbers.

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  7. Find the AM of 5, 55, 555,…………….upto n times.

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  8. If P(A) = 1/2, P(B) = 2/3 then prove that 1/6 le P(A nn B) le 1/2

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  9. If 9 biscuits of different types be distributed among 3 children, find...

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  10. Show that overset(n)underset(i=1)sum (xi - A)^2 is minimum when A = ba...

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  11. If y = (x-a)/b, then prove that Sy = frac(Sx)(|b|)

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  12. Prove that P(A uu B) = P(A) + P(B) - P(A nn B)

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  13. The variance of 1, 2,…………..n is 24. Find n.

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  14. For 10 values of X, it is given that sumu = 4 and sum u^2 = 144, where...

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  15. Two groups of 15 and 22 values have variances 9 and 16 respectively. I...

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

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  17. Prove that 1/n overset(n)underset(E1)sum |xi - A| attains, minimum whe...

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  18. Let x be a variable assuming the values 1, 2,……….k and let F1 = n, F2,...

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  19. |x-2| le 6 implies that

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  20. When it comes to comparing different segments among themselves and als...

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