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If x=acos theta+bsin theta and y=a sin t...

If `x=acos theta+bsin theta` and `y=a sin theta-bcos theta`, then show that `y^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)+y=0`

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MODERN PUBLICATION-TEST PAPER 3-PROBLEM
  1. Differentiate with respect to x: y=3^(x^2)+tan^-1((cosx+sinx)/(cosx-si...

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  2. Find the dy/dx when cos x = sqrt ((1)/(1+t^2)), sin y = (2t)/(1+t^2)

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  3. Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...

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  4. Show that 2sinx+tanxge3x for all x epsilon(0,(pi)/(2)).

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  5. Evaluate : int (xe^x)/(x+1)^(2) dx

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  6. Evaluate the following integrals int(x^2)dx/((x^2+3)(x^2+2))

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  7. Solve : dy/dx + 1 = e^(x+y)

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  8. Solve : (x + 2y^3)dy/dx = y.

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  9. Find the equation of the plane passing through the points (2,1,3), (3,...

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  10. Find the image of the point (3,-2,1) in the plane x-y+3z=2.

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  11. Determine k such that a vector vec(r) is at right angles to each of th...

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  12. Find the foot of the perpendicular drawn from the point (5,7,3) to the...

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  13. Let f:XrightarrowY and g:YrightarrowZ. Prove that gof is bijective if ...

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  14. Find the product of matrices A and B, where A = [[-5,1,3],[7,1,-5],[1,...

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  15. Show that |{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}...

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  16. Find the inverse of the following matrices using elementary transforma...

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  17. If x=acos theta+bsin theta and y=a sin theta-bcos theta, then show tha...

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  18. Find the equation of the normal at a point on the curve x^(2) = 4y, wh...

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  19. Find the area of the smaller region bounded by the ellipse frac[x^2][a...

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  20. Prove analytically : The perpendicular bisector of the sides of a tria...

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