Let y = y(x) be the solution of the differential equation,2 

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 Multiple Choice QuestionsMultiple Choice Questions

391.

The differential equation corresponding to the family of circles inthe plane touching the Y-axis at the origin, is

  • dydx = y2 - x22xy

  • dydx = 2xyx2 + y2

  • dydx = x2 - y22xy

  • dydx = y2 + x22xy


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392.

Let y = y(x) be the solution of the differential equation,

2 + sinxy + 1 . dydx = - cosx, y > 0, y0 = 1. If yπ = aand dydx at x = π is b, then the ordered pair a, b = ?

  • 2, 32

  • (1, - 1)

  • (2, 1)

  • (1, 1)


D.

(1, 1)

dy1 + y =  - cosx2 + sinxdxlog1 + y = - log2 + sinx +logc1 + y2 + sinx = c4 1 = c  c = 41 + y = 42 + sinx  y = 42 + sinx - 1yπ = 2 - 1 = 1 = adydx =  - 42 + sinx2 . cosx = 1 at x = π  b = 1a b = 1, 1


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393.

The equation of the normal to the curve y = (1 + x)2y + cos2(sin – 1(x)) at x = 0 is :

  • y = 4x + 2

  • y + 4x = 2

  • x + 4y = 8

  • 2y + x = 4


394.

If a curve y = f(x), passing through the point (1,2), is the solution of the differential equation, 2x2dy = 2xy + y2dx, then f12 is equal to

  • 11 - loge2

  • 1 + loge2

  • 11 + loge2

  •  - 11 + loge2


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 Multiple Choice QuestionsShort Answer Type

395.

If y =k = 16 cos-135coskx - 45sinkx then dydx at x = 0 is


 Multiple Choice QuestionsMultiple Choice Questions

396.

The equation of curve satisfying differential equation 1 + y2ex + 1dy = exy2dx and also passes through the point 0, 1 is

  • y2 + 1 = y1 + ex2

  • y2 - 1 = ylog1 + ex2

  • y + 1 = ylog1 + ex2

  • 2y2 +1 = ylog1 + ex2


397.

If y2 + logcos2x = y then

  • y''0 = 2

  • y'0 + y''0 = 1

  • y'0  + y''0 = 3

  • None of these


398.

If x3dy + xydx = x2dy + 2ydx; y2 = e and x > 1, then y4 = ?

  • e2

  • 12 + e

  • 32e

  • 32 + e


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399.

If the sum of the series 20 + 1935 + 1915 + 1845 + ... upto nth term is 488 andthe nth term is negative

  • nth term is - 425

  • n = 41

  • nth term is - 4

  • n = 60


400.

If the surface area of a cube is increasing at a rate of 3.6 cm2/sec, retaining its shape; then the rate of change of its volume (in cm3/sec.), when the length of a side of the cube is 10 cm, is

  • 20

  • 10

  • 18

  • 9


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