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If a ,\ b\ c are in G.P., prove that the...

If `a ,\ b\ c` are in G.P., prove that the following are also in G.P.: `a^2, b^2, c^2`

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If a ,\ b\ c are in G.P., prove that the following are also in G.P.: a^3, b^3, c^3

If a ,b ,c are in A.P., then prove that the following are also in A.P. a^2(b+c),b^2(c+a),c^2(a+b)

If a,b,c are in A.P. prove that the following are also in A.P. a^(2)(b+c) , b^(2) (c+a) , c^(2)(a+b)

If a, b, c, d are in G. P., show that the following are also in G. P. b^(2)c^(2), c^(3)a^(2),a^(2)b^(2)

If a ,b ,c ,d are in G.P., prove that a+b,b+c ,c+d are also in G.P.

If a ,\ b ,\ c are in G.P. prove that loga ,\ logb ,\ logc are in A.P.

If a, b, c are in G.P. show that the are also in G.P. a^(2),b^(2),c^(2)

If a^2,b^2,c^2 are in A.P., then prove that the following are also in A.P. Prove 1/(b+c),1/(c+a),1/(a+b)

If a, b, c, d are in G. P., show that they are also in G. P. a^(2)+b^(2),b^(2) +c^(2), c^(2)+d^(2)

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RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. The sum of three numbers which are consecutive terms of an A.P. is 21....

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  2. The sum of three numbers in G.P. is 56. If we subtract 1,7,21 from the...

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  3. If a ,\ b\ c are in G.P., prove that the following are also in G.P.: a...

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  4. If a ,\ b\ c are in G.P., prove that the following are also in G.P.: a...

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  5. If a, b, c are in G. P., prove that a^2+ b^2, ab + bc, b^2 +c^2 are al...

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  6. If (a-b),\ (b-c),(c-a) are in G.P. then prove that (a+b+c)^2=3(a b+b c...

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  7. If the 4th, 10th and 16th terms of a G.P. are x, y, and z  respect...

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  8. 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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  9. If the pth, qth, rth, and sth terms of an A.P. are in G.P., t hen p-q ...

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  10. 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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  11. 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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  12. 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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  13. Find two numbers whose arithmetic mean is 34 and the geometric mean is...

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

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

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

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

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

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

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

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