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

If p, q, r are in G.P and the equation `px^2+2qx+r=0` and `dx^2+2ex+f=0` have a common root, then show that d/p, e/q, f/r are in AP.

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UNITED BOOK HOUSE-TECHNO INDIA GROUP ACADEMIA,SOUTH KOLKATA.-EXERCISE
  1. If x+iy=2/(3+costheta+isintheta),show that 2x^2+2y^2=3x-1

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  2. find the co-efficient of (2r+4)th and (r-2)th terms in the expansion o...

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  3. If p, q, r are in G.P and the equation px^2+2qx+r=0 and dx^2+2ex+f=0 h...

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  4. Show that the points (a,0),(0,b)and (3a,-2b)are collinear.Also find th...

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  5. Find the distance between the parallel lines 4x-3y+5=0 and 4x-3y+7=0.

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  6. Find the equation of a circle through origin which cuts of intercepts ...

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  7. Find the value of the limit lim(nrarroo)(1^2+2^2+...+n^2)/n^3

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  8. If y=sqrt((1-x)/(1+x)),prove that (1-x^2)dy/dx+y=0

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  9. If x^2is an odd number then x is also odd number,justify the validity ...

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  10. If x and y are odd integers, then xy is also an odd integer r examine ...

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  11. In single throw of two dice,the probality of obtaning 'a total of 8' i...

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  12. Find S.D from the following data:

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  13. Solve :sqrt3cosx-sinx=1

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  14. Prove that, cos20^@cos40^@cos60^@cos80^@=1/16

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  15. Exhibit graphically the solution sets of the following system of linea...

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  16. Solve :3x^2+8ix+3=0

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  17. Find the sum of n terms of the series 1/2.5+1/5.8+1/8.11…to n terms.

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  18. There are 10 points in a plane of which 4 are collinear, Find the numb...

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  19. There are 10 points in a plane of which 4 are collinear, find the numb...

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  20. The directrix of a parabola is x+y+4=0and vertex is at (-1,-1).Find th...

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