If cos-1yb = 2logx2, where x >&n

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

361.

The solution of the differential equation dydx = sinx +ytanx + y - 1 is

  • cscx +y + tanx +y = x + c

  • x +cscx + y = c

  • x +tanx +y = c

  • x +secx +y = c


362.

The differential equation of the family  y = aex + bxex + cx2ex of curves, where a, b, c are arbitrary constants , is 

  • y''' + 3y'' + 3' + y = 0

  • y''' + 3y'' - 3' - y = 0

  • y''' - 3y'' - 3' + y = 0

  • y''' - 3y'' + 3' - y = 0


363.

The solution of tanydydx = sinx + y + sinx - y is

  • sec(y) = 2cos(x) + c

  • sec(y) = - 2cos(x) + c

  • tan(y) =  - 2cos(x) + c

  • sec2(y) = - 2cos(x) + c


364.

A family of curves has the differential equation xydydx = 2y2 - x2. Then, the family of curves is

  • y2 = cx2 + x3

  • y2 = cx4 + x3

  • y2 = x + cx4

  • y2 = x2 + cx4


Advertisement
365.

The solution of the differential equation dydx = yx + ϕyxϕ'yx is

  • yx = k

  • ϕyx = kx

  • yx = k

  • ϕyx = ky


366.

If y = y(x) is the solution of the differential equation 2 + sinxy + 1dydx + cosx = 0 then y(π2)is equal to

  • 13

  • 23

  • 1

  • 43


367.

If u = fr, where r2 = x2 + y2, thenux2 + 2uy2 = ?

  • f''(r)

  • f''(r) +f'(r)

  • f''(r) + 1rf'(r)

  • f''(r) + rf'(r)


368.

If dydx + 2xtanx - y = 1, then sinx - y = ?

  • Ae- x2

  • Ae2x

  • Aex2

  • Ae - 2x


Advertisement
369.

An integrating factor of the differential equation1 - x2dydx + xy = x41 + x51 - x23 is 

  • 1 - x2

  • x1 - x2

  • x21 - x2

  • 11 - x2


Advertisement

370.

If cos-1yb = 2logx2, where x > 0, thenx2d2ydx2 + xdydx = ?

  • 4y

  • - 4y

  • 0

  • - 8y


B.

- 4y

cos-1yb = 2logx2, where x > 0On differentiating w r t x we get- 11 - y2b2 . 1bdydx =  2 . 1x2 12 - 1b2 - y2 . dydx = 2x xdydx = - 2b2 - y2    ...iAgain, differentiating w r t. x we get,x2d2ydx2 + xdydx = - 2 . 12b2 - y2 - 12 - 2ydydxx2d2ydx2 + xdydx =  2y- x2 . dydx . dydx     from eq i x2d2ydx2 + xdydx = - 4y


Advertisement
Advertisement