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A variable plane meets the coordinate ax...

A variable plane meets the coordinate axes at A, B, C and is at a constant distance d from origin. Prove that the locus of the centroid of the triangle ABC is ` frac[1][x^2]+frac[1][y^2]+frac[1][z^2]=frac[9][d^2]`

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MODERN PUBLICATION-TEST PAPER 2-PROBLEM
  1. Answer the following: What is the value of [[o,-h,-g],[h,o,-f],[g,f,...

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  2. Show that no two normals to a parabola are parallel.

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  3. Find the intervals where the following functions are (a) increasing an...

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  4. Find int (cos x /sin^(2) x + sin x ) dx

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  5. Evaluate : int(0) ^(pi/4) dx/cos x (cos x + sin x).

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  6. Find the differential equation whose general soltution is c1x^2+c2y=1 ...

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  7. Find the area of the region bounded by the curve y=6x-x^(2), the X-axi...

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  8. Prove the following by vector method. The parallelogram whose diagonal...

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  9. Prove that the two lines whose direction cosines are connected by the ...

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  10. A variable plane meets the coordinate axes at A, B, C and is at a cons...

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  11. Find the equation of the line through the point (3, -1, 2) and paralle...

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  12. If N denotes the set of all natural numbers and R be the relation on N...

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  13. If a, b and c are all positive real, then prove that minimum value of ...

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  14. Solve the following system of equations by the matrix inversion method...

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  15. Find the inverse of [(1,1,2),(0,1,2),(1,2,1)] using elementary operati...

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  16. Show that of all the rectangles inscribed in a given fixed circle, the...

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  17. Evaluate : int dx /cosx (5+3 cos x).

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  18. Find the area of the parallelogram whose diagonals are the vectors 3ha...

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  19. For an vector vec(r) = x hat(i) + y hat(j) + z hat(k), prove that vec(...

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  20. Find the equation of plane through the point (2,0,-3) and containing t...

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