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A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is `1/x^2+1/y^2+1/z^2=1/p^2`.

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-XII Boards-All Questions
  1. If x^my^n = (x + y)^(m+n), prove that (d^2y)/(dx^2)=0.

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  2. Find the area enclosed between the parabola 4y=3x^2 and the straight l...

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  3. A variable plane which remains at a constant distance 3p from the orig...

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  4. Evaluate : int0^(3/2)|xsin pi x| dx

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  5. Determine the value of k for which the following function is continuou...

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  6. Find the distance between the planes 2x – y + 2z = 5 and 5x – 2.5y + ...

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  7. Using properties of determinants, prove that |(a^2+2a, 2a+1,1), (2a+1,...

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  8. Find the area bounded by the circle x^2 + y^2 = 16 and the line sqrt3y...

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  9. Using properties of determinants, prove that |(a^2+2a, 2a+1,1), (2a+1,...

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  10. Find the area bounded by the circle x^2 + y^2 = 16 and the line sqrt3y...

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  11. Find the vector equation of line passing through the point (1,2,-4)...

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  12. If |A| = 3 and A^-1 = [(3 -1), (-5/3 2/3)] then write the adj A.

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  13. For what value of k is the function f(x) = { k|x|/x, x<0; 3, x>=0 con...

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  14. Show that the function f given by f(x)=tan^(-1)(sinx+cosx), x" ">" "0 ...

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  15. Find the matrix X so that X[[1, 2, 3],[ 4 ,5, 6]]= [[-7,-8,-9],[2,4,6]...

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  16. If y=e^(tan^-1x), prove that (1+x^2)y2+(2x-1)y1=0

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  17. Find int e^(2x) sin (3x + 1) dx

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  18. Given =[(2,-3),(-4, 7)] , compute A^(-1) and show that 2A^(-1)=9I-A .

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  19. Differentiate tan^(-1)((1+cosx)/sinx) with respect to x

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  20. Find the value of tan^(-1) sqrt3 - cot^(-1) (-sqrt3)

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