The differential equation representing the family of curves given

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

121.

The general solution of the differential equation dydx = eyex + e- x + 2x is

  • e- y = ex + e- x + x2 + C

  • e- y = e- x - ex - x2 + C

  • e- y = - e- x - ex - x2 + C

  • ey = e- x + ex + x2 + C


122.

The order and degree of the differential equation d2ydx313 = 2d2ydx2 + cos2x3 are, respectively

  • 3 and 1

  • 3 and 3

  • 1 and 3

  • 3 and 2


Advertisement

123.

The differential equation representing the family of curves given by y = ae3x + b, where a and b are arbitrary constants, is

  • d2ydx2 + 3dydx - 2y = 0

  • d2ydx2 - 3dydx = 0

  • d2ydx2 - 3dydx - 2y = 0

  • d2ydx2 + 3dydx = 0


D.

d2ydx2 + 3dydx = 0

Given differential equation is

y = ae- 3x + b                 ...(i)

On differentiating w.r.t. x, we get
dydx = - 3ae- 3x + 0        ...(ii)

Again, differentiating, we get

       d2ydx2 = 9ae- 3x       d2ydx2 = 3- dydx         from Eq. (ii) d2ydx2 + 3dydx = 0


Advertisement
124.

An integrating factor of the differential equation xdy - ydx + x2exdx = 0 is

  • 1x

  • log1 + x2

  • 1 + x2

  • x


Advertisement
125.

The solution of the differential equation xdydx = y1 + logx is

  • y = log(x) + C

  • y = C1 + logx

  • y = Cx + logx

  • y = C1 + logx


126.

The solution of the differential equation logxdydx + yx = sin2x is

  • ylogx = C - 12cosx

  • ylogx = C + 12cos2x

  • ylogx = C - 12cos2x

  • xylogx = C - 12cos2x


127.

If xy = A sin(x) + B cos(x) is the solution of  the differential equation xd2ydx2 - 5adydx + xy = 0, then the value of a is

  • 25

  • 52

  • - 25

  • - 52


128.

The solution of the differential equation dydx = 3e2x + 3e4xex + e- x is

  • y = e3x + C

  • y = 2e2x + C

  • y = ex + C

  • y = e4x + C


Advertisement
129.

The order and degree of the differential equation of the family of circles of fixed  radius r with centres on the y-axis, are respectively

  • 2, 2

  • 2, 3

  • 1, 1

  • 1, 2


130.

The solution of the differential equation (kx - y2 ) dy = (x2 - ky) dx is

  • x3 - y3 = 3kxy + C

  • x3 + y3 = 3kxy + C

  • x2 - y2 = 2kxy + C

  • x2 + y2 = 2kxy + C


Advertisement