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A variable plane which remains at a constant distance p from the origin cuts the coordinate axes in A, B, C. The locus of the centroid of the tetrahedron OABC is `x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2)=(k)/(p^(2))x^(2)y^(2)z^(2),` then `root(5)(2k)` is

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`(2)`
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Integer Answer Type Questions)
  1. If the triangle ABC whose vertices are A(-1, 1, 1), B(1, -1, 1) and C(...

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  2. The equation of a plane which bisects the line joining (1, 5, 7) and (...

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  3. The shortest distance between origin and a point on the space curve ...

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  4. The plane 2x-2y+z+12=0 touches the surface x^2+y^2+z^2-2x-4y+2z-3=0 on...

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  5. If the centroid of tetrahedron OABC where A,B,C are given by (a,2,3),(...

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  6. If the circumcentre of the triangle whose vertices are (3, 2, -5), (-...

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  7. If overline(P1P2) is perpendicular to overline(P2P3), then the value o...

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  8. Let the equation of the plane containing line x-y-z-4=0=x+y+2z-4 and...

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  9. Let P(a, b, c) be any on the plane 3x+2y+z=7, then find the least valu...

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  10. The plane denoted by P1 : 4x+7y+4z+81=0 is rotated through a right ang...

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  11. The distance of the point P(-2, 3, -4) from the line (x+2)/(3)=(2y+3)/...

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  12. The position vectors of the four angular points of a tetrahedron OABC ...

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  13. Value of lambda do the planes x-y+z+1=0, lambdax+3y+2z-3=0, 3x+lambday...

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  14. If the lattice point P(x, y, z) , x, y, zgto and x, y, zinI with least...

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  15. If the line x=y=z intersect the line xsinA+ysinB+zsinC-2d^(2)=0=xsin(2...

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  16. The number of real values of k for which the lines (x)/(1)=(y-1)/(k)=(...

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  17. Let G(1), G(2) and G(3) be the centroid of the triangular faces OBC, O...

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  18. A variable plane which remains at a constant distance p from the origi...

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  19. If (l(1), m(1), n(1)) , (l(2), m(2), n(2)) are D.C's of two lines, th...

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  20. If the coordinates (x, y, z) of the point S which is equidistant from ...

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