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If m, n are positive quantities, prove t...

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

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. If a,b,c gt 0 show that (bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)le(a+b+c)/2.

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  2. Show that a^2(1+b^2)+b^2(1+c^2)+c^2(1+a^2)ge6abc.

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

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  4. Prove that ((bc+ac+ab)/(a+b+c))^(a+b+c)ge(b)^a(c)^b(a)^c [where a,b,c ...

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  5. If log2,log(2^n-1) and log(2^n+3) are in A.P. then n =

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  6. If the ratiio of the sum of n terms ofd two AP's is (3n+1):(2n+3) then...

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  7. If a1,a2,a3,.......an are in AP where a1 gt 0foralli then the value of...

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  8. Given p no. of A.P. each of which consists of an n terms. If their fir...

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  9. Answer the following question based on above passage: The coefficient...

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  10. If a,b,c ,d and p are distinct real number such that (a^2+b^2+c^2)p^2-...

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  11. Suppose a,b,c are in A.P and a^2,b^2,c^2 are in G.P. If a lt b lt c an...

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  12. The value of 4^(1/3).4^(1/9).4^(1/27)....infty is.

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  13. If the sum of an infinite GP is 20 and sum of their square is 100 then...

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  14. If S=1+a+a^2+....... t o infty , then a=

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  15. If 4a^2+9b^2+16c^2=2(3ab+6bc+4ca) where a,b,c are non zero real number...

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  16. If a,b,c in AP and x=sum(n=0)^inftya^n,y=sum(n-0)^inftyb^n,z=sum(n-0)^...

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  17. If a,b,c are in G.P., then the equations ax^2+2bx+c =0 and dx^2+2ex+f ...

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  18. If the product of n positive number is unity, then their sum is

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  19. If x1gt0,i=1,2.....50 and x1+x2+.....x50=50 then the minimum value of ...

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  20. If a,b,c,d are positive real number such that a+b+c+d=2 , then M=(a+b)...

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