The differential equation of all straight lines touching the circ

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 Multiple Choice QuestionsMultiple Choice Questions

91.

The solution of the differential equation dydx = sinx + ytanx +y - 1 is

  • cscx +y + tanx + y = x +c

  • x + cscx + y = c

  • x + tanx + y = c

  • x + secx + y = c


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92.

The differential equation of all straight lines touching the circle x2 + y2 = a2 is

  • y - dydx2 = a21 + dydx2

  • y - xdydx2 = a21 + dydx2

  • y - xdydx = a21 + dydx

  • y - dydx = a21 - dydx


B.

y - xdydx2 = a21 + dydx2

The equation of straight line touching the circle x2 + y2 = a is

       xcosθ + ysinθ = a             ...(i)

On differentiating w.r.t. x, regarding θ as a constant

       cosθ + y'sinθ = 0             ...(ii)

From Eqs. (i) and (ii), we get

cosθ = ay'xy' - y and sinθ = - axy' - y cos2θ + sin2θ = 1 a2y'2 + a2xy' - y2 = 1 y - xdydx2 = a21 + dydx2


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93.

The differential equation dydx + y + 3 = 0 admits

  • infinite number of solutions

  • no solutions

  • a unique solution

  • many solutions


94.

Solution of the differential equation xdy - ydx - x2 + y2dx = 0

  • y - x2 + y2 = cx2

  • y + x2 + y2 = cx2

  • y + x2 + y2 = cy2

  • x - x2 + y2 = cy2


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95.

If xsinxydy = ysinyx - xdx and y1 = π2, then the value of cosyx is equal to :

  • x

  • 1x

  • logx

  • ex


96.

The differential equation of the system of all circles of radius r in the xy plane is :

  • 1 + dydx32 = r2d2ydx22

  • 1 + dydx32 = r2d2ydx23

  • 1 + dydx23 = r2d2ydx22

  • 1 + dydx23 = r2d2ydx23


97.

The general solution of the differential equation

d2ydx2 + 2dydx + y = 2e3x is given by

  • y = c1 + c2xex + e3x8

  • y = c1 + c2xe- x + e- 3x8

  • y = c1 + c2xe- x + e3x8

  • y = c1 + c2xex + e- 3x8


98.

The solution of the differential ydx + (x - y3)dy = 0 is:

  • xy = 13y3 + c

  • xy = y4 + c

  • y4 = 4xy + c

  • 4y = y3 + c


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99.

If the distances covered by a particle in time t is proportional to the cube root of its velocity, then the acceleration is

  • a constant

  •  s3

  •  1s3

  •  s5


100.

The solution of the differential equation dydx = yx + ϕyxϕ'yx is

  • yx = k

  • ϕyx = kx

  • yx = k

  • ϕyx = ky


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