The differential equation of the family of circles passing throug

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 Multiple Choice QuestionsMultiple Choice Questions

251.

The differential equation of the family of straight lines whose slope is equal to y-intercept is

  • x + 1dydx - y = 0

  • x + 1dydx + y = 0

  • dydx = x - 1y - 1

  • dydx = x + 1y + 1


252.

The order and degree of the differential equation 1 + dydx513 = d2ydx2 are respectively

  • 1, 5

  • 2, 1

  • 2, 5

  • 2, 3


253.

The differential equation ydydx + x = c represents

  • a family of hyperbolas

  • a family of circles whose centres are on the y-axis

  • a family of parabolas

  • a family of circles whose centres are on the x-axis


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254.

The differential equation of the family of circles passing through the orign and having their centres on the x-axis is

  • y2 = x2 +2xydydx

  • y2 = x2 -2xydydx

  • x2 = y2 +xydydx

  • x2 = y2 +3xydydx


A.

y2 = x2 +2xydydx

The system of circles passing through origin and centre lies on x-axis is

x2 + y2 - 2hx = 0            ...(i)

On differentiating w.r.t. x, we get                    2x +2ydydx - 2h = 0 2x + 2ydydx - x2 + y2x = 0    from Eq. (i)              x2 - y2 +2xydydx = 0                      y2 = x2 +2xydydx


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255.

A population grows at the rate of 10% of the population per year. How long does it take for the population to double?

  • 20log(2) yr

  • 10log(2)yr

  • 5log(2) yr

  • None of the above


256.

The order and degree of the differential equation y = dpdxx = a2p2 +b2, where p = dydx (here a and b are arbitrary constants) respectively are

  • 2, 2

  • 1, 1

  • 1, 2

  • 2, 1


257.

The general solution of the differential equation 2xdydx - y = 3 is a family of

  • hyperbolas

  • parabolas

  • straight lines

  • circles


258.

If m and n are degree and order of 1 + y1223 = y2, then the value of m + nm - n is

  • 3

  • 4

  • 5

  • 2


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259.

The general solution of dydx2 = 1 - x2 - y2 + x2y2 is

  • 2sin-1y = x1 - x2 + sin-1x + C

  • cos-1y = xcos-1x + C

  • sin-1y =12sin-1x + C

  • 2sin-1y = x1 - y2 + C


260.

Solution of edy/dx = x when x = 1 and y = 0 is

  • y = x(log(x - 1) + 4

  • y = x(log(x) - 1) + 3

  • y = x(log(x) + 1) + 1

  • y = x(log(x) - 1) + 1


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