The differential equation corresponding to the family of circles

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

Advertisement

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


A.

dydx = y2 - x22xy

Equation of family of circles, which touch the Y-axis at origin is(x - a)2 + y2 = a2 x2 + y2 - 2ax + y2 = a2 x2 + y2 = 2ax          ...iNow, on differentiating both sides of Eq. (i), we get2x + 2ydydx = 2a         ...iiOn substituting the value of 2a from Eq. (ii) m Eq. (i), we get      x2 + y2 = 2x + 2ydydxx x2 + y2 = 2x2 + 2xydydx       dydx = y2 - x22xy

which is the required differential equation.


Advertisement
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)


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


Advertisement

 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


Advertisement
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


Advertisement