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Prove that: d/(dx)[x/2\ sqrt(a^2-x^2)+(...

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

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Show that the height of the cylinder of maximum volume that can be ...

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

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  4. Find the vector equation of the plane which contains the line of in...

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  5. Find the coordinates of the point, where the line (x-2)/3=(y+1)/4=(z-2...

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  6. Show that the function f(x)=2x-|x| is continuous but not differenti...

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  7. Differentiate tan^(-1)((sqrt(1+x^2-1))/x) with respect to tan^(-1)x...

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  8. Let A = R × R and * be the binary operation on A defined by (a, b) ...

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  9. Consider f: R rarr [-5,oo) given by f(x)=9x^2+6x-5 . Show that f is...

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  10. Evaluate: int(pi/6)^(pi/3)(dx)/(1+sqrt(tanx))

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  11. Find the vector equation of the line passing through the point (1,2...

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  12. Find the area of the region bounded by the parabola y=x^2 and y=|x| .

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  13. Find the particular solution of the differential equation(tan^(-1)y-x)...

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  14. Using elementary transformations, find the inverse of the matrix : [...

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  15. If vec a= hat a= hat i-\ hat j+7 hat k and vec b=5 hat j-\ hat j+l...

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  16. Use product [[1,-1, 2],[ 0, 2,-3],[ 3,-2, 4]] [[-2, 0, 1],[ 9, 2,-3],[...

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  17. Find the angle between the line (x+1)/2=(3y+5)/9=(3-z)/(-6) and the ...

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  18. Solve the following differential equation: cos^2x(dy)/(dx)+y=tanx

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  19. Solve the following differential equation: e^xtany\ dx+(1-e^x)sec^2y...

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  20. Find the value of a for which the function f defined by f9x)={asinpi/...

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