If the solution of the differential equation xdydx +&nb

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 Multiple Choice QuestionsMultiple Choice Questions

11.

If f''(0) = k, k  0, then the value of limx0 2f(x) - 3f(2x) +f(4x)x2 is

  • k

  • 2k

  • 3k

  • 4k


12.

If  y = emsin- 1x then 1 - x2d2ydx2 - xdydx - ky = 0, where k is equal to

  • m2

  • 2

  • - 1

  • - m2


13.

Solution of x + y2dydx = a2 ( 'a' being a constant) is

  • x + ya = tany + Ca, C is an arbitrary

  • xy = atanCx, C is an arbitrary

  • xa = tanyC, C is an arbitrary

  • xy = tan(x + C), C is an arbitrary


14.

The integrating factor of the first order differential equation

x2x2 - 1dydx + xx2 + 1y = x2 - 1 is

  • ex

  • x - 1x

  • x + 1x

  • 1x2


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15.

Let a and B be the roots of x2 + x + 1 = 0. If n be a positive integer, then αn + βn is

  • 2cos23

  • 2sin23

  • 2cos3

  • 2sin3


16.

For real x, the greatest value of x2 + 2x + 42x2 + 4x + 9 is

  • 1

  • - 1

  • 12

  • 14


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17.

If the solution of the differential equation xdydx + y = xex be xy = exϕ(x) + C, then ϕx is equal to

  • x + 1

  • x - 1

  • 1 - x

  • x


B.

x - 1

Given,

xdydx + y = xex

 dydx + yx = ex   ...(i)

On comparing Eq. (i) by dydx + Py = Q, we get

P = 1x and Q = ex

IF = e1xdx

    = elogx

Hence, solution of differential equation,

y . x = xexdx + C

 xy = xex - exdx + C

 xy = xex - ex + C

 xy = exx - 1 + C   ...(ii)

 xy = exϕx + C  as given  ...(iii)

On comparing Eqs. (ii) and (iii), we get

ϕx = x - 1


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18.

The order of the differential equation of all parabolas whose axis of symmetry along X-axis is

  • 2

  • 3

  • 1

  • None of these


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19.

General solution of ydydx + by2 = acosx, 0 < x < 1 is

  • y2 = 2a2bsinx + cosx + ce- 2bx

  • 4b2 + 1y2 = 2asinx + 2bcosx + ce- 2bx

  • 4b2 + 1y2 = 2asinx + 2bcosx + ce2bx

  • y2 = 2a2bsinx + cosx + ce- 2bx


20.

The integrating factor of the differential equation

1 + x2dydx + y = etan-1x is

  • tan-1x

  • 1 + x2

  • etan-1x

  • loge1 + x2


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