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Solve the following differential equatio...

Solve the following differential equation: `[(e^(-2\ sqrt(x)))/(sqrt(x))-y/(sqrt(x))](dx)/(dy)=1,\ x\ !=0`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Using matrix method, solve the following system of equations: 2/x+...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. If the radius of a sphere is measured as 9 cm with an error of 0.03...

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  15. Prove that y=(4sintheta)/((2+costheta))-theta is an increasing func...

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  16. Evaluate: int(sinx+cosx)/(9+16sin2x)\ dx

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  17. Show that the total surface area of a closed cuboid with square bas...

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  18. Show that the height of the cylinder of maximum volume that can be ...

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  19. If y=log\ [x+sqrt(x^2+1)] , prove that (x^2+1)(d^2\ y)/(dx^2)+x(dy)/(d...

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  20. Prove that: d/(dx)[x/2\ sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a)]=sqrt(a^2-...

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