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If a,b,c be three distinct positive numb...

If a,b,c be three distinct positive numbers, each different from 1 such that `("log"_ba"log"_ca-"log"_aa)+("log"_ab"log"_cb-"log"_b b)+("log"_ac"log"_bc-"log"_c c)=0`, then prove that abc=1

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UNITED BOOK HOUSE-Model Test Set - 7-Exercise
  1. The mean and standard deviation for two values x1 and x2 (x1 < x2) of ...

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  2. Three points x, y and z are taken at random on a line segment. What is...

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  3. If events A and B are independent, then so are A^c and B?

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  4. What do you mean by statistical independence of events?

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  5. Find the arithmetic mean of 7, 77, 777.upto p^(th) term.

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  6. If y = a + bx and Mo is the mode of x, then show that the mode of y mu...

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  7. Show that the arithmetic mean of the square root of x cannot be greate...

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  8. If x > 0, y >0, z > 0 and x +y + z = 1, prove that (1+x)(1+y)(1+z)ge 8...

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  9. If a,b,c be three distinct positive numbers, each different from 1 suc...

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  10. Give f(x) = a + b(x - 10) + c(x - 1)(x - 2), f(1) = 7, f(2) = 17 and f...

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  11. Derive Lagrange's interpolation formula.

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  12. If P(A) = 1/2, P(B) = 1/3, and P(A^c cap B^c) = 5/12, find P(AIB) and...

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  13. Eight students are arranged in a row. Find the probability that two gi...

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  14. If the prices of all items in a place have increased by 145 times in c...

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  15. Study the effect of change of origin and scale on mean deviation and q...

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  16. The mean deviation of the series 3, 4, 5, 6, 7 about the median is

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  17. The standard deviation of the first n odd positive integers is sqrt85 ...

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  18. State and prove Cauchy-Schwartz inequality.

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  19. Why meiosis is considered as reductional division?

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  20. Give the forniula of Fisher’s index number ?

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