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Prove that x^2-y^2=c(x^2+y^2)^2 is t...

Prove that `x^2-y^2=c(x^2+y^2)^2` is the general solution of differential equation `(x^3-3x""y^2)dx=(y^3-3x^2y)dy` , where c is a parameter.

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-XII Boards-All Questions
  1. Evaluate: int(2x)/((x^2+1)(x^2+2))dx

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  2. Evaluate: int0^pi(xsinx)/(1+cos^2x)\ dx

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  3. Prove that x^2-y^2=c(x^2+y^2)^2 is the general solution of differe...

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  4. Show that the function f(x) = x^3– 3x^2 + 6x – 100 is increasing on R

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  5. The x-coordinates of a point on t line joining the points Q(2,2,1)a...

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  6. The random variable X can the values 0, 1, 2, 3, Give P(X = 0) = P(X =...

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  7. A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be ...

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  8. Often it is taken that a truthful person commands, more respect in ...

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  9. Two tailors, A and B, earn 300 and 400 per day respectively. A can st...

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  10. Find : int (dx)/(5-8x-x^2)

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  11. Discuss the commutativity and associativity of binary operation * d...

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  12. If the sum of lengths of hypotenuse and a side of a right angled tri...

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  13. Using integration, find the area of region bounded by the triangle who...

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  14. If tan^-1 ((x-3)/(x-4))+tan^-1((x+3)/(x+4))=pi/4, find x

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  15. If x^y+y^x=a^b , then find dy/dx.

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  16. Evaluate : int0^pi(xtanx)/(secx+tanx)dx

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  17. Solve the differential equation: (1+x^2) dy/dx + y = tan^-1 x

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  18. Show that the points A, B, C with position vectors 2hati – hatj + hat...

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  19. Evaluate int0^(2pi) sin^2x cos^4x dx

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  20. Write the distance of a point P(a ,b ,c) from x-axis.

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