New ! Maths MCQ Practise Tests

12th Standard Maths Ordinary Differential Equations English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021

12th Standard

    Reg.No. :
  •  
  •  
  •  
  •  
  •  
  •  

Maths

Time : 00:10:00 Hrs
Total Marks : 10

    Answer all the questions

    10 x 1 = 10
  1. The differential equation representing the family of curves y = Acos(x + B), where A and B are parameters, is

    (a)

    \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -y=0\)

    (b)

    \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } }+y=0\)

    (c)

    \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } }=0\)

    (d)

    \(\frac { { d }^{ 2 }x }{ { dy }^{ 2 } }=0\)

  2. The general solution of the differential equation \(\frac { dy }{ dx } =\frac { y }{ x } \) is

    (a)

    xy = k

    (b)

    y = k log x

    (c)

    y = kx

    (d)

    log y = kx

  3. The solution of \(\frac{dy}{dx}+\)p(x)y=0 is

    (a)

    \(y={ ce }^{ \int { pdx } }\)

    (b)

    \(y={ ce }^{ -\int { pdx } }\)

    (c)

    \(x={ ce }^{ -\int { pdy } }\)

    (d)

    \(x={ce }^{ \int { pdy } }\)

  4. If p and q are the order and degree of the differential equation \(y=\frac { dy }{ dx } +{ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) +xy=cosx,\)When

    (a)

    p < q

    (b)

    p = q

    (c)

    p>q

    (d)

    p exists and q does not exist

  5. If sin x is the integrating factor of the linear differential equation \(\frac { dy }{ dx } +Pt=Q,\)Then P is

    (a)

    log sin x

    (b)

    cos x

    (c)

    tan x

    (d)

    cot x

  6. The solution of (x2-ay)dx=(ax-y2)dy is

    (a)

    y=x2+y2-a(x+y)

    (b)

    y=x2+y2-a(x+y)

    (c)

    x3+y2=3ayx+c

    (d)

    (x2-ay)(ax-y2)=0

  7. The general solution of \(4\frac{d^2 y}{dx^2}\)+y=0 is

    (a)

    \(y={ e }^{ \frac { x }{ 2 } }\left[ A\quad cos\frac { x }{ 2 } +B\quad sin\frac { x }{ 2 } \right] \)

    (b)

    \(y={ e }^{ \frac { x }{ 2 } }\left[ A\quad cos\frac { x }{ 2 } -B\quad sin\frac { x }{ 2 } \right] \)

    (c)

    \(y=Acos\frac { x }{ 2 } +Bsin\frac { x }{ 2 } \)

    (d)

    \(t={ Ae }^{ \frac { x }{ 2 } }+B{ e }^{ \frac { -x }{ 2 } }\)

  8. The population p of a certain bacteria decreases at a rate proportional to the population p. The differential equation corresponding to the above statement is __________.

    (a)

    \(\frac{dp}{dt}=\frac{k}{p}\)

    (b)

    \(\frac{dp}{dt}=kt\)

    (c)

    \(\frac{dp}{dt}=kp\)

    (d)

    \(\frac{dp}{dt}=-kp\)

  9. Using y = vx, the differential equation \(\frac { dy }{ dx } =\frac { y }{ x+\sqrt { xy } } \) is reduced to ________.

    (a)

    x(1+\(\sqrt{v}\))dv=v\(\sqrt{v}\)dx

    (b)

    x(1-\(\sqrt{v}\))dv=v\(\sqrt{v}\)dx

    (c)

    x(1+\(\sqrt{v}\))dv=-v\(\sqrt{v}\)dx

    (d)

    v(1+\(\sqrt{v}\))dx-v\(\sqrt{v}\)dv=0

  10. The differential equation associated with the family of concentric circles having their centres at the origin is _________.

    (a)

    \(\frac { dy }{ dx } =\frac { -x }{ y } \)

    (b)

    \(\frac { dy }{ dx } =\frac { -y }{ x } \)

    (c)

    \(\frac { dy }{ dx } =\frac { x }{ y } \)

    (d)

    \(\frac { dy }{ dx } =\frac { y }{ x } \)

*****************************************

TN 12th Standard Maths free Online practice tests

Reviews & Comments about 12th Standard Maths Ordinary Differential Equations English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021

Write your Comment