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If y=x^x , prove that (d^2y)/(dx^2)-1/y(...

If `y=x^x ,` prove that `(d^2y)/(dx^2)-1/y((dy)/(dx))^2-y/x=0`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Find the position vector of a point which divides the join of points w...

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  2. Matrix A=[0 2b-2 3 1 3 3a3-1] is given to be symmetric, find values of...

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  3. If y=x^x , prove that (d^2y)/(dx^2)-1/y((dy)/(dx))^2-y/x=0

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  4. Show that the equation of normal at any point t on the curve x=3cost-c...

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  5. If A is a square matrix such that A^2=I , then find the simplified val...

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  6. Find the maximum value of |[1, 1, 1],[ 1, 1+sintheta,1],[ 1, 1, 1+cost...

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  7. Find the vector equation of a plane which is at a distance of 5 units ...

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  8. Find : int(sqrt(x))/(sqrt(a^3-x^3))dxdot

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  9. Find the intervals in which f(x) = sin 3x – Cos 3x, 0 < 0 < pi, is str...

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  10. Show that the altitude of the right circular cone of maximum volume th...

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  11. A and B throw a pair of dice alternately. A wins the game if he gets a...

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  12. Prove that |[yz-x^2,zx-y^2,xy-z^2],[zx-y^2,xy-z^2,yz-x^2],[xy-z^2,yz-x...

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  13. Using elementary transformations, find the inverse of the matrix A=(8 ...

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  14. Three persons A, B and C apply for a job of Manager in a Private Compa...

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  15. Solve for x : 2tan^(-1)(cosx)=tan^(-1)(2cos e cx)

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  16. int(-1)^2|x^3-x|dxdot

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  17. Find the particular solution of the differential equation (1-y^2)(1+lo...

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  18. Find the general solution of the following differential equation : (1...

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  19. Show that the vectors vec a , vec b and vec c are coplanar if vec a+...

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  20. Find the vector and Cartesian equations of the line through the point ...

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