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If p, q, r are in G.P. and the equation...

If p, q, r are in G.P. and the equations, `p x^2+2q x+r=0`and `dx^2+2e x+f=0`have a common root, then show that `d/p`,`e/q`,`f/r`are in A.P.

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To solve the problem step by step, we will follow the logical flow of the video transcript while ensuring clarity and coherence. ### Step 1: Understanding the Given Information We are given that \( p, q, r \) are in Geometric Progression (G.P.). This means that: \[ q^2 = pr \] ...
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NCERT ENGLISH-SEQUENCES AND SERIES-SOLVED EXAMPLES
  1. Let the sequence anbe defined as follows : a1=1,an=a(n-1)+2for ngeq2. ...

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  2. In an A.P. if m^(t h)term is n and the n^(t h)term is m, where m!=n, ...

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  3. The income of a person is Rs. 3, 00,000, m the first year and he rece...

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  4. Find the sum of first n terms of the following series:5+11+19+29+41+ ...

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  5. If A.M. and GM. of two positive numbers a and b are 10 and 8, respect...

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  6. How many terms of the G.P. 3, 3/2,3/4,dotdotdotare needed to give the...

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  7. Find the sum of first n terms and the sum of first 5 terms of the geo...

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  8. In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th t...

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  9. Which term of the G.P., 2, 8, 32, . . . up to n terms in 131072?

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  10. Insert three numbers between 1 and 256 so that the resulting sequence...

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  11. A person has 2 parents, 4 grandparents, 8 great grand parents, and so ...

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  12. Find the sum of the sequence 7, 77, 777, 7777, . . . to n terms.

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  13. The sum of first three terms of a G.P. is (13)/(12)and their product ...

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  14. If p, q, r are in G.P. and the equations, p x^2+2q x+r=0and dx^2+2e x...

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  15. If a, b, c are in G.P. and a^(1/x)=b^(1/y)=c^(1/z),prove that x, y, z...

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  16. If a, b, c, d and p are different real numbers such that (a^2+b^2+c^2...

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  17. Find the sum of n terms of the series whose nth term is: n(n+3)

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  18. If p^(t h),\ q^(t h),\ r^(t h)a n d\ s^(t h) terms of an A.P. are in G...

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  19. If the sum of n terms of an A.P. is n P +1/2n(n-1)Q ,where P and Q ar...

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  20. The sum of n terms of two arithmetic progressions are in the ratio (3n...

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