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If y=e^a\ sin^((-1x))\ ,\ -1\ lt=x\ lt=1...

If `y=e^a\ sin^((-1_x))\ ,\ -1\ lt=x\ lt=1,` then show that `(1-x^2)\ (d^2\ y)/(dx^2)-\ x(dy)/(dx)-\ a^2y=0`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. If y=cos^(-1)((3x+4\ sqrt(1-x^2))/5),\ "f i n d"(dy)/(dx)

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  2. Evaluate the following: int1^2(5x^2)/(x^2+4x+3)\ dx

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  3. If y=e^a\ sin^((-1x))\ ,\ -1\ lt=x\ lt=1, then show that (1-x^2)...

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  4. Find the coordinates of the foot of the perpendicular and the perpe...

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  5. A bag contains 4 balls. Two balls are drawn at random, and are foun...

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  6. One kind of cake requires 300g of flour and 15g of fat, another kin...

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  7. If the length of three sides of a trapezium other than the base is ...

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  8. Using matrix method, solve the following system of equations: 2/x+...

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  9. Using elementary transformations, find the inverse of the matrix [[1...

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  10. Solve the following differential equation: [(e^(-2\ sqrt(x)))/(sqrt(x)...

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  11. Solve the following differential equation: 3e^xtany\ dx+(2-e^x)sec^2y\...

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  12. Using properties of determinants, prove that |[a, a+b, a+b+c],[2a,3...

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  13. Write the direction cosines of a line parallel to z-axis.

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  14. If f(x)=(4x+3)/(6x-4) ,\ x\ !=2/3, show that fof(x)=x for all x!=2/3do...

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  15. Evaluate: int(cos2x-cos2alpha)/(cosx-cosalpha)\ dxdot

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  16. Evaluate : int(1-x^2)/(x(1-2x))\ dxdot

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  17. Evaluate: inte^x\ ((sin4x-4)/(1-cos4x))\ dx

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  18. Evaluate: int(x+2)/(sqrt(x^2+2x+3))dx

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  19. Differentiate x^(xcosx)+(x^2+1)/(x^2-1)\ wdotrdottdotx

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  20. If x=a\ (theta-sintheta),\ y=a\ (1+costheta),\ \ \ find (d^2\ y)/(dx^...

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