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The total cost C(x) in Rupees, associated with the production of x units of an item is given by `C(x)=0. 005 x^3-0. 02 x^2+30 x+5000` . Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-XII Boards-All Questions
  1. Differentiate tan^(-1)((1+cosx)/sinx) with respect to x

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  2. Find the value of tan^(-1) sqrt3 - cot^(-1) (-sqrt3)

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  3. The total cost C(x) in Rupees, associated with the production of x ...

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  4. Integrate the functions (cos2x+2sin^2x)/(cos^2x)

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  5. Find the differential equation representing the family of curves y=ae^...

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  6. If the matrix A = [[0,a,-3],[2,0,-1],[b,1,0]] is skew symmetric, find ...

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  7. If theta is the angle between two vectors hati-2hatj+3hatk and 3hati-2...

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  8. Find the magnitude of each of the two vectors veca and vec b having th...

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  9. A black and a red dice are rolled. (a)   Find the conditional proba...

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  10. Using properties of determinants prove that |(1,1, 1+3x),(1+3y,1,1),(1...

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  11. Find (dy)/dx, if (x^2+y^2)^2=xy

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  12. If a * b, denoted the larger of 'a' and 'b' and if a o b = a*b + 3 , ...

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  13. If x=a(2theta-sin2theta) and y=a(1-cos2theta) find (dy)/(dx) when thet...

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  14. If y="sin"(sinx),"p r o v et h a t" (d^2y)/(dx^2)+tanx(dy)/(dx)+yco...

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  15. Prove that: 3sin^(-1)x=sin^(-1)(3x-4x^3), x in [-1/2,1/2]

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  16. Find the area of the region in the first quadrant enclosed by the x...

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  17. Find the equations of the tangent and the normal to the curve 16x^2+9y...

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  18. Find the intervals in which the function f(x)=x^4/4-x^3-5x^2+24x+12 is...

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  19. Evaluate : int(0)^(pi/4) (sinx+ cos x)/( 16 + 9sin2x)

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  20. Evaluate : int1^3 (x^2 + 3x + e^x) dx as the limit of the sum.

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