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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 4-PROBLEM
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  4. Find x and y if [[1,3],[2,-1]][[x],[y]] = [[4],[1]].

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  8. Let x Epsilon (2 π/4, π), y=| cos x | +| sin x | what is dy/dx ?

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  9. Write the least value of a for which the function f defined by f(x)=x^...

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  10. Evaluate:int x^2 dx/x*3 +1.

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  12. What is the projection of the line segment joining (1,3,-1) and (3,2,4...

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  13. If vec a=(2,-2,1), vec b =(2,3,6) and vec c =(-1,0,2) then what is the...

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  15. Check if the relation R on set of real numbers, defined as R = {(a,b) ...

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  16. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

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  17. If A+B+C = pi, prove that [[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,c...

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  18. If A=[[1,2,3],[3,-2,1],[4,2,1]]"show that"A^3-23A-40I=0

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  19. Show that (a+1) is a factor of abs([(a+1),2,3],[1,a+1,3],[3,-6,a+1])

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  20. Find the dy/dx when x = a[cos t + log tan (t//2)], y = a sin t

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