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If a,b,c are in G.P. are log(c) a , log ...

If a,b,c are in G.P. are `log_(c) a , log _(b) c, log_(a) b` are in A.P. , prove that the common difference of the A.P. is `(3)/(2)`.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
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  2. If there be m quantities in a G.P. whose common ratio is r and S(m)den...

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  3. If a,b,c are in G.P. are log(c) a , log (b) c, log(a) b are in A.P. , ...

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  4. Find the sum to n terms of the following series. 5+555+55555+...

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  5. If x in RR, solve the inequation (5x+8)/(4-x) lt2

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  6. The population of a twon at the beginning of a year is N and the figur...

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  7. Examine the validity of the following statement: If a and b ar odd i...

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  8. Show that the total number of permutations of n diferent things not mo...

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  9. A and B stand in a line with 10 other people. In how many of the perm...

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  10. Find the number of permutations of the letters x,x,x,y,y,y,z,w taken 5...

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  11. A bag contains 50 tickets 1,2,3,...50 of which 5 are drawn at random a...

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  12. In n gt 7 prove that ""^(n-1)C(3)+""^(n-1)C(4) gt ""^(n)C(3)

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  13. If (""^(n)C(r-1))/(a)=(""^(n)C(r))/(b)=(""^(n)C(r))/(c) prove that n=(...

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  14. A,B and C have respectively 4,3 and 2 differrent books. In how many d...

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  15. Find the modulus and ampltidue of the complex in numberz=(-2-i2 sqrt(3...

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  16. Find the amplitude of z=1+i "tan" (3pi)/(5)

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  17. Find the modulus and amplitude of z="sin" (6pi)/(5)+I (1+"cos" (6pi)...

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  18. There are m A.P. Whose common differences are 1,2,3,.. M respectively...

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  19. If S(1),S(2),S(3),...S(m) be the sum of first n terms of n A.P. Whose...

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  20. Show that the sum of the numbers in the n th bracket of the series (1)...

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