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If p^(t h),\ q^(t h),\ a n d\ r^(t h) te...

If `p^(t h),\ q^(t h),\ a n d\ r^(t h)` terms of an A.P. and G.P. are both `a ,\ b\ a n d\ c` respectively show that `a^(b-c)b^(c-a)c^(a-b)=1.`

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RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. If a ,\ b ,\ c are in A.P. b ,\ c ,\ d are in G.P. and 1/c ,1/d ,1/e a...

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  2. If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d ...

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  3. If p^(t h),\ q^(t h),\ a n d\ r^(t h) terms of an A.P. and G.P. are bo...

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  4. Find two numbers whose arithmetic mean is 34 and the geometric mean is...

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  5. If A.M. and G.M. between two numbers is in the ratio m : n then prove...

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  6. a,b,c are positive real numbers forming a G.P. ILf ax^2+2bx+c=0and ...

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  7. Q. If a, b,c and d are distinct positive no. in AP. then (A) ad lt ...

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  8. Insert 6 geometric means between 27 and 1/(81)dot

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  9. Insert 5 geometric means between 16 and 1/4dot

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  10. Insert 5 geometric means between (32)/9a n d(81)/2dot

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  11. Find the geometric means of the following pairs of number: 2 and 8.

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  12. Find the geometric means of the following pairs of number: a^3b\ a n d...

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  13. Find the geometric means of the following pairs of number: -8\ a n d-2...

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  14. If a is the G.M. of 2\ a n d1/4, find adot

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  15. Find the two numbers whose A.M. is 25 and GM is 20.

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  16. If A and G are respectively arithmetic and geometric mean between posi...

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  17. The sum of two numbers is 6 times their geometric means, show that nu...

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  18. If A.M. and GM. of roots of a quadratic equation are 8 and 5, respe...

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  19. If AM and GM of two positive numbers a\ a n d\ b are 10 and 8 respecti...

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  20. If the fifth term of a G.P. is 2, then write the product of its 9 t...

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