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If tan^(-1)(Y/X) = log (sqrt(X^2+Y^2)) ,...

If `tan^(-1)(Y/X)` = `log (sqrt(X^2+Y^2))` , prove that `(dy/dx)` = `((X+Y)/(X-Y))`

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-XII Boards-All Questions
  1. The vectors 3 hat i- hat j +2 hat k', 2 hat i+hat j + 3 hat k and hat ...

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  2. Find : int{(x^3 + 1)/(x^3-x)}dx

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  3. If tan^(-1)(Y/X) = log (sqrt(X^2+Y^2)) , prove that (dy/dx) = ((X+Y)/(...

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  4. Find the shortest distance between the lines vecr = 2hati - hatj + hat...

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  5. Find: int((tan^(3)x)/(cos^(3)x)) dx

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  6. Solve the following differential equation: (1+ e ^(y/x)) dy + e^(y...

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  7. Find f'(x) if f(x) = tan x^(tan x)

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  8. If y=e^(acos^(-1)x),-1lt=x<1, show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(d...

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  9. If f(x) = sqrt ((sec x -1)/(sec x + 1)) , find f'( pi /3)

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  10. The area of the triangle formed by the vertices O, A, and B, where vec...

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  11. If A = [(5, -1, 4), (2, 3, 5), (5, -2, 6)] , find A^(-1) and use it t...

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  12. The vectors 3hati - hatj +2hatk, 2hati+hatj+3hatk and hati+lambdahatj-...

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  13. A cottage industry manufactures pedestal lamps and wooden shades.Both ...

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  14. If x, y, z are different and Delta=|[x, x^2, 1+x^3],[y, y^2, 1+y^3],[...

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  15. Find the area of the triangle formed by O ,A ,B when vec O A= hat ...

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  16. Prove that tan^-1(1/4)+ tan^-1(2/9) = 1/2sin^-1(4/5)

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  17. Check whether the relation R in the set N of natural numbers given by ...

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  18. The function f(x) : (x-1)/(x( x^(2) -1)) is discontinuous at (a) exa...

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  19. The Integrating Factor of the differential equation x(dy)/(dx)-y=2x^2...

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  20. If I vec(a)I = 4 and -3 le lamda le 2,then Ilambda vec(a)I lies in ...

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