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Find del/(dely)((delz)/(delx)) if z=x^(y...

Find `del/(dely)((delz)/(delx)) if z=x^(y) + y^(x)`

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MODERN PUBLICATION-SAMPLE PAPER 2012-EXERCISE
  1. Prove that , if y=logtan((pi)/(4)+(x)/(2)) , then (dy)/(dx)=secx

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  2. Differentiate with resi to x : Y = 2^(x^2) + tan^(-1)((cosx-sinx)/(cos...

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  3. Find del/(dely)((delz)/(delx)) if z=x^(y) + y^(x)

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  4. Evaluate lim(x to π/2) log(x-π/2)/tan x

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  5. Find the equation of tangent to the curve x=y^2-2 at the points where ...

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  6. Integrate int(-3//5)^(3//5)[2x+1]dx

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  7. Find the area of the region bounded by the curve y=6x-x^(2), the X-axi...

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  8. Solve y^(2)+x^(2)dy/dx=xydy/dx.

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  9. Solve(x log x )dy/dx+y=2 log x.

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  10. Find a vector vec(b) such that vec(a) xx vec(b) = vec(c) and vec(a).ve...

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  11. Prove by vector method that in a Delta ABC, c^(2) = a^(2) + b^(2) - 2a...

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  12. Find the co-ordinates of the point where the perpendicular from the or...

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  13. Solve for x, |{:(15-2x,11,10),(11-3x,17,16),(7-x,14,13):}|=0

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  14. If A=[{:(-1,3,5),(1,-3,-5),(-1,3,5):}], then find A^(3)-A^(2).

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  15. Find the value of the term free from X in the expansion of (3/2(x^(2))...

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  16. A and B are two events. If P(A) = (3)/(8), P(B) = (1)/(2) and P(A nn B...

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  17. If A and B are independent events,show that A^c and B^c are independ...

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  18. Find dy/dx y = cot^(-1)(lncosec^(-1)x)

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  19. Evaluate the following integrals int(12sinx-2cosx+3)/(sinx+cosx)dx

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  20. int0^pi(xdx)/(1+sinx)

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