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Find the slope of the tangent to the cur...

Find the slope of the tangent to the curve
x=2(t-sin t) and y = 2(1-cost) at t=`(pi)/(4)`

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MODERN PUBLICATION-SAMPLE PAPER 2013-EXERCISE
  1. Find the derivative of x^(sinx) w.r.t.x.

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  2. Differentiate sin^(-1) ((2X)/(1+X^(2))) with respect to cos^(-1) ((1-X...

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  3. Find the slope of the tangent to the curve x=2(t-sin t) and y = 2(1...

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  4. If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a

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  5. Find the extreme values of the function y = X + 1/x.

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  6. Find the intervals where the following functions are (a) increasing an...

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  7. Integrate : int (sin6x + sin4x) / (cos6x + cos4x) dx.

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  8. Evaluate the following integrals : int(dx)/(x[(logx)^(2)+25])

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  9. Integrate : int sin^(-1)xdx.

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  10. Evaluate int0^(pi/2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cos x))dx

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  11. solve , dy/dt = e^((2t)+(3y)).

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  12. solve , dy/dx + y = e^(-x).

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  13. Find the differential equation whose general solution is y = a cos x +...

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  14. If vec a = (2,-2,1), vec b = (2,3,6) and vec c = (-1,0,2),Find the mag...

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  15. Prove the following by vector method. An angle inscribed in a semi-cir...

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  16. Show that the points (3,-2,4)(1,1,1) and (-1,4,-1) are collinear.

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  17. Find the equation of a plane biscting the line segment joining (-1,4,3...

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  18. Find the value of r, if the line  (x-1)/(1) = (y+2)/(3) = (z-1)/(-1) =...

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  19. Find equation of the sphere if the line segment joining the Points (4,...

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  20. Maximise Z=50x(1)+60x(2) Subject to 2x(1)+3x(2)le6,x(1),x(2)ge0.

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