The differential equation of all circles touching the axis of y a

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

221.

The order and power of differential equation

d2ydx2 + 7dydx + ydx = sinx is

  • 1, 3

  • 3, 1

  • 1, 2

  • 2, 1


222.

The solution of differential equation xcos2ydx = ycos2xdx is

  • xtanx - ytany - logsecx/secy = c

  • ytanx - xtanx - logsecx.secy = c

  • xtanx - ytany + logsecx.secy = c

  • None of the above


223.

Differential equation of those circles which passes through origin and their centres lie on y-axis will be

  • x2 - y2dydx +2xy = 0

  • x2 - y2dydx =2xy

  • x2 - y2dydx =xy

  • x2 - y2dydx +xy = 0


Advertisement

224.

The differential equation of all circles touching the axis of y at origin and centre on the x-axis is given by

  • xydydx - x2 + y2 = 0

  • 2xydydx - x2 - y2 = 0

  • x2 + y2dydx - 2xy = 0

  • None of these


D.

None of these

Let the required equation of circle be

            x2 + y2 - 2gx = 0

On differentiating w.r.t. x, we get

          2x + 2ydydx - 2g = 0 ydydx + x - x2 + y22x = 0      from Eq. (i)      2xydydx + x2 - y2 = 0

Hence, option(d) None of these is correct.


Advertisement
Advertisement
225.

The solution of the differential equation

e- 2x - yxdxdy = 1 is given by

  • e2x = 2x + c

  • ye- 2x = x + c

  • y = x

  • None of these


226.

The solution of the differential equation

dydx = 1 - y21 - x2 is

  • sin-1y - sin-1x = c

  • sin-1y + sin-1x = c

  • sin-1xy = 2

  • None of these


227.

The solution of differential equation (1 + x)ydx + (1 - y)x dy = 0 is

  • logexy + x - y = c

  • logexy + x + y = c

  • logexy - x + y = c

  • logexy - x + y = c


228.

The differential equation of all circles which passes through the origin and whose centre lies on y-axis is

  • x2 - y2dydx - 2xy = 0

  • x2 - y2dydx + 2xy = 0

  • x2 - y2dydx - xy = 0

  • x2 - y2dydx + xy = 0


Advertisement
229.

The general solution of y2dx + (x2 - xy + y2)dy = 0 is

  • tan-1xy + logy + c = 0

  • 2tan-1xy + logx + c = 0

  • logy + x2 + y2 + logy + c = 0

  • sinh-1xy + logy + c = 0


230.

The solution of the equation d2ydx2 = e- 2x is

  • y = 14e- 2x + cx2 +d

  • y = 14e- 2x + cx +d

  • y = 14e- 2x + cx2 +d

  • y = 14e- 2x + cx3 +d


Advertisement