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If 27 abc> (a+b+c)^3 and 3a +4b +5c=12 ...

If `27 abc> (a+b+c)^3 and 3a +4b +5c=12` then `1/a^2+1/b^3+1/c^5=10`, where a, b, c are positive real numbers. Statement-2: For positive real numbers `A.M.>= G.M.`

A

Statement -1 is true, statement-2 is true and statement-2 is correct explanation for statement -1

B

Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1

C

Statement-1 is true, statement-2 is false

D

Statement-1 is false, statement-2 is true

Text Solution

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The correct Answer is:
D
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ALLEN-SEQUENCE AND PROGRESSION-Exercise O-2
  1. If for an A.P. a1,a2,a3,........,an,........a1+a3+a5=-12 and a1a2a3=8,...

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  2. If the sum of the first 11 terms of an arithmetical progression equals...

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  3. Let s(1), s(2), s(3).... and t(1), t(2), t(3).... are two arithmetic s...

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  4. If x in R , the numbers 5^(1+x) + 5^(1-x) , a/2 , 25^x + 25^(-x) form ...

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  5. Along a road lies an odd number of stones placed at intervals of 10m. ...

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  6. In an A.P. with first term 'a' and the common difference d(a, d!= 0), ...

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  7. Let an, n in N is an A.P with common difference d and all whose terms ...

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  8. Let a(1), a(2), a(3).... and b(1), b(2), b(3)... be arithmetic progres...

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  9. The arithmetic mean of the nine number in the given set {9,99,999, ......

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  10. If (1 + 3 + 5 + .... " upto n terms ")/(4 + 7 + 10 + ... " upto n term...

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  11. If a != 1 and l n a^(2) + (l n a^(2))^(2) + (l n a^(2))^(3) + ... = 3 ...

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  12. The sum of the first three terms of an increasing G.P. is 21 and the s...

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  13. a, b, c are distinct positive real in HP, then the value of the expres...

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  14. If sin(x-y),sinx,sin(x+y) are in H.P., then find the value of sinxsec(...

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  15. An H.M. is inserted between the number 1/3 and an unknown number. If w...

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  16. lf abcd=1 where a,b,c,d are positive reals then the minimum value of ...

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  17. If 27 abc> (a+b+c)^3 and 3a +4b +5c=12 then 1/a^2+1/b^3+1/c^5=10, wh...

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  18. If x = sum(n=0)^(oo) a^(n), y=sum(n=0)^(oo) b^(n), z = sum(n=0)^(oo) ...

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  19. IF S=1^2+3^2+5^2....99^2 then the value of the sum 2^2+4^2+6^2...100^2

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  20. For which positive integers n is the ratio, (sum+(k=1)^(n) k^(2))/(sum...

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