If y'' - 3y' + 2y = 0 where y(0) = 1, y'(0) = 0, then the value o

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 Multiple Choice QuestionsMultiple Choice Questions

41.

Let fx = tan-1x. Then, f'(x) + f''(x) is 0, when x is equal to

  • 0

  • 1

  • i

  • - i


42.

If y = tan-11 + x2x, then y'(1) is equal to

  • 1/4

  • 1/2

  • - 1/4

  • - 1/2


 Multiple Choice QuestionsShort Answer Type

43.

If dydx + 1 - y21 - x2 = 0 prove that, x1 - y2 + y1 - x2 = A where A is constant.


44.

If f(a) = 2, f'(a) = 1, g(a) = - 1 and g'(a) = 2, find the value of limxagafa - gafxx - a


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 Multiple Choice QuestionsMultiple Choice Questions

45.

If the displacement, velocity and acceleration of a particle at time t be x, v and f respectively, then which one is true ?

  • f = v3d2tdx2

  • f = - v3d2tdx2

  • f = v2d2tdx2

  • f = - v2d2tdx2


46.

The displacement x of a particle at time t is given by x = At2 + Bt + C where A, B, C are constants and v is velocity of a particle, then the value of 4Ax - v2 is

  • 4AC + B2

  • 4AC - B2

  • 2AC - B2

  • 2AC + B2


47.

The displacement of a particle at time t is x,  where x = t4 - kt3. If the velocity of the particle at time t = 2 is minimum, then 

  • k = 4

  • k = - 4

  • k = 8

  • k = - 8


48.

The general solution of the differential equation

100d2ydx2 - 20dydx + y = 0 is

  • y = (c1 + c2x)ex

  • y = (c1 + c2x)ex

  • y = c1 + c2xex10

  • y = c1ex + c2e- x


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49.

If y'' - 3y' + 2y = 0 where y(0) = 1, y'(0) = 0, then the value of y at x = log(2) is

  • 1

  • - 1

  • 2

  • 0


D.

0

d2ydx2 - 3dydx + 2y = 0

The corrosponding equation is m2 - 3m + 2 = 0

 General solution of given equation is,

y = Aex + Be2x

y' = Aex + 2Be2x

At x = 0, y = 1  A + B = 1

and x = 0, y' = 0  A + 2B = 0

Solving these equation A = 2, B = 1

 y = 2ex - e2xAt x = log(2), y = 0


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50.

The degree of the differential equation x = 1 + dydx + 12!dydx2 + 13!dydx3 + ...

  • 3

  • 2

  • 1

  • not defined


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