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If x,y,z are in HP, then show that log(x...

If x,y,z are in HP, then show that log(x+z)+log(x+z-2y)=2 log (x-z)

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VMC MODULES ENGLISH-SEQUENCE AND SERIES -JEE MAIN & Advance ( ARCHIVE)
  1. If A1,A2 be two A.M.\'s G1,G2 be the two G.M.\'s and H1,H2 be the two ...

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  2. Let a(1), a(2)...be positive real numbers in geometric progression. Fo...

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  3. If x,y,z are in HP, then show that log(x+z)+log(x+z-2y)=2 log (x-z)

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  4. about to only mathematics

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  5. If a >0,b >0 and c >0 prove that (1984, 2M) (a+b+c)(1/a+1/b+1/c)geq9

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  6. If the sum of first n terms of an A P is c n^2, then the sum of square...

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  7. Let Sn=sum(k=1)^(4n)(-1)(k(k+1))/2k^2dot Then Sn can take value (s) 10...

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  8. Let f(x)=ax^2 + bx+c whose roots are alpha and beta , a ne 0 and tr...

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  9. Let a, b, c be in an AP and a^2, b^2, c^2 be in GP. If a < b < c and a...

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  10. Let alphaa n dbeta be the roots of x^2-x+p=0a n dgammaa n ddelta be th...

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  11. Three positive numbers form an increasing GP. If the middle terms in t...

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  12. If (10)^9+2(11)^2(10)^7 +….+10 (11)^9 = k(10)^9

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  13. The sum of first 20 terms of the sequence 0.7 ,0.77 , 0.777 …., is

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  14. An infinite G.P. has first term as a and sum 5, then a belongs to a) |...

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  15. Consider an infinite geometric series with first term a and common rat...

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  16. Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+............

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  17. Let S(1),S(2),"…." be squares such that for each n ge 1, the length o...

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  18. Let a1,a2,a3,... be in harmonic progression with a1=5a n da(20)=25. Th...

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  19. Let the positive numbers a ,b ,ca d nd be in the A.P. Then a b c ,a b ...

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  20. If m is the A.M of two distict real numbers l and n (l, n gt 1)and G1,...

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