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12th Standard Business Maths Differential Equations English Medium Free Online Test One Mark Questions 2020 - 2021

12th Standard EM

    Reg.No. :
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Business Maths

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

    Answer all the questions

    10 x 1 = 10
  1. The degree of the differential equation \(\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3\)

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  2. The order and degree of the differential equation \({ \left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ \frac { 1 }{ 2 } }-\sqrt { \frac { dy }{ dx } } -4=0\) are respectively

    (a)

    2 and 6

    (b)

    3 and 6

    (c)

    1 and 4

    (d)

    2 and 4

  3. If y=cx + c− c3 then its differential equation is

    (a)

    \(y=\frac { dy }{ dx } +\frac { dy }{ dx } -{ \left( \frac { dy }{ dx } \right) }^{ 3 }\)

    (b)

    \(y={ \left( \frac { dy }{ dx } \right) }^{ 3 }=x\frac { dy }{ dx } -\frac { dy }{ dx } \)

    (c)

    \(\frac { dy }{ dx } +y={ \left( \frac { dy }{ dx } \right) }^{ 3 }-x\frac { dy }{ dx } \)

    (d)

    \(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } =0\)

  4. The differential equation of y = mx + c is (m and c are arbitrary constants)

    (a)

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

    (b)

    y = x \(\frac { dy }{ dx } \) + c

    (c)

    xdy + ydx = 0

    (d)

    ydx − xdy = 0

  5. Solution of \(\frac { dy }{ dx } \) + Px = 0

    (a)

    x=cepy

    (b)

    x=ce−py

    (c)

    x = py + c

    (d)

    x = cy

  6. The differential equation formed by eliminating A and B from y = e−2x(A cos x + B sin x) is

    (a)

    y− 4y+ 5 = 0

    (b)

    y2+ 4y – 5 = 0

    (c)

    y2−4y1−5= 0

    (d)

    y+ 4y+ 5 = 0

  7. A homogeneous differential equation of the form \(\frac { dy }{ dx } \) = f\(\left( \frac { y }{ x } \right) \) can be solved by making substitution,

    (a)

    y = v x

    (b)

    v = y x

    (c)

    x = v y

    (d)

    x = v

  8. The solution of the differential equation \(\frac { dy }{ dx } =\frac { y }{ x } +\frac { f\left( \frac { y }{ x } \right) }{ f'\left( \frac { y }{ x } \right) } \) is

    (a)

    \(f\left( \frac { y }{ x } \right) =k.x\)

    (b)

    \(xf\left( \frac { y }{ x } \right) =k\)

    (c)

    \(f\left( \frac { y }{ x } \right) =ky\)

    (d)

    \(yf\left( \frac { y }{ x } \right) =k\)

  9. The differential equation \(\left( \frac { dx }{ dy } \right) ^{ 2 }+5y^{ \frac { 1 }{ 3 } }\)=x is

    (a)

    order 2 degree 

    (b)

    order 1 degree 2

    (c)

    order 1 degree 6

    (d)

    order 1 degree 3

  10. The amount present in a radio active element disintegrates at a rate proportional to its amount. The differential equation corresponding to the above statement is (k is negative).

    (a)

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

    (b)

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

    (c)

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

    (d)

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

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