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If 4a^2+9b^2+16c^2=2(3ab+6bc+4ca) where ...

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

A

A.P

B

G.P.

C

H.P.

D

none of these

Text Solution

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The correct Answer is:
C
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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. If the sum of an infinite GP is 20 and sum of their square is 100 then...

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

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

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  4. 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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  5. 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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  6. If the product of n positive number is unity, then their sum is

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

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

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  9. If a1,a2,.....an are positive real number whose product is a fixed num...

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  10. The greatest value x^2y^3 is, where xgt0 and ygt0 are connected by the...

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  11. Let S=8/5+16/65+......128/(2^18+1) then

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  12. The sum of the infinite terms of the series 5/(3^2. 7^2)+9/(7^2. 11^2)...

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  13. The sum to infinity of the series 1+2/3+6/3^2+10/3^3+14/3^4+....

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  14. The sum to n terms of the series 1+2(1+1/n)+3(1+1/n)^2+....... is give...

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  15. For absx lt1 the value of 1+3x+6x^2+10x^3+.....t o infty is

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  16. If pth, qth, and rth term of an AP are equal to corresponding terms of...

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  17. If a,b,c are positive real number, then the least value of (a+b+c)(1/a...

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  18. An infinite GP has first term x and sum 5, then x belongs to

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  19. 2^(1/4),2^(2/8),2^(3/16),2^(4/32)......infty is equal to

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  20. Let alpha , beta be the roots of x^2-x+p=0 and gamma,delta be the root...

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