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If xy=e^(x-y), prove that (dy)/(dx)=(y(x...

If `xy=e^(x-y)`, prove that `(dy)/(dx)=(y(x-1))/(x(y+1))`.

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XII BOARDS PREVIOUS YEAR-QUESTION PAPER 2023-Question
  1. Assertions (A) :The line vecr=vec(a1)+lamda vec (b1) and vecr=vec(a2)+...

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  2. Assertions (A): All trigonometric functions have their inverses over t...

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  3. If xy=e^(x-y), prove that (dy)/(dx)=(y(x-1))/(x(y+1)).

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  4. Find the domain of y=sin^-1(x^2-4)

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  5. Evaluate : cos^-1[cos(-(7pi)/(3))]

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  6. If the projection of the vector hati+hatj+hatk on the vector p hati+ha...

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  7. Find the point on the curve y^2=8x for which the abscissa and ordinate...

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  8. Find the vector equation of the line passing the point (2,1,3) and per...

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  9. The equation of a line are 5x-3=15y+7=3-10z. Write the direction cosin...

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  10. Find int(2)/((1-x)(1+x^2))dx

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  11. Evaluate int(1/3)^1 (x-x^3)^(1/3)/x^4dx

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  12. Evaluate : int1^3 {abs(x-1)+abs(x-2)}dx

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  13. Maximize Z = 5x + 3y subject to the constraints: 3x + 5y le 15, 5x + 2...

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  14. From a lot of 30 bulbs which include 6 defective bulbs, a sample of 2 ...

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  15. Find the particular solution of the differential equation (dy)/(dx)=(...

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  16. Find the general solution of the differential equation e^xtanydx+(1-...

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  17. Evaluate: int(pi/4)^(pi/2)e^(2x)((1-sin2x)/(1-cos2x))dx

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  18. Evaluate: int(-2)^2 x^2/(1+5^x)dx

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  19. Find the image of the point (2,-1,5) in the line (x-11)/10=(y+2)/-4=(z...

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  20. Vertices B and C of Delta ABC lie along the line (x+2)/2=(y-1)/1=(z-0)...

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