Differential Equations One Mark Question

12th Standard EM

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Business Maths

Time : 00:30:00 Hrs
Total Marks : 15
    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 differential equation formed by eliminating a and b from y=ae+ be−x is

    (a)

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

    (b)

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

    (c)

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

    (d)

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

  3. The complementary function of (D2+ 4)y = e2x is

    (a)

    (Ax +B)e2x

    (b)

    (Ax +B)e−2x

    (c)

    A cos 2x + B sin 2x

    (d)

    Ae−2x+ Be2x

  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. The differential equation satisfied by all the straight lines in xy plane is

    (a)

    \(\frac { dy }{ dx } \)=a constant

    (b)

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

    (c)

    y+ \(\frac { dy }{ dx } \) = 0

    (d)

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

  6. If y = k.eλx then its differential equation where k is arbitrary constant is

    (a)

    \(\frac { dy }{ dx } \)=λy

    (b)

    \(\frac { dy }{ dx } \)=ky

    (c)

    \(\frac { dy }{ dx } \)+ky=0

    (d)

    \(\frac { dy }{ dx } \)=eλx

  7. The differential equation obtained by eliminating a and b from y = a e3x + b e-3x is

    (a)

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

    (b)

    \(\frac { { d }^{ 2 }y }{ dx^{ 2 } } \)-9y=0

    (c)

    \(\frac { { d }^{ 2 }y }{ dx^{ 2 } } -9\frac { dy }{ dx } \)

    (d)

    \(\frac { { d }^{ 2 }y }{ dx^{ 2 } } \)+9x=0

  8. The differential equation formed by eliminating A and B from y = ex (A cos x + B sin x) is

    (a)

    y2+y1=0

    (b)

    y2-y1=0

    (c)

    y2-2y1+2y=0

    (d)

    y2-2y1-2y=0

  9. The degree of the differential equation \(\sqrt { 1+\left( \frac { { d }y }{ dx } \right) ^{ \frac { 1 }{ 3 } } } =\frac { { d }^{ 2 }y }{ dx^{ 2 } } \) is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    6

  10. The degree of c =\(\frac { \left[ 1+\left( \frac { dy }{ dx } \right) ^{ 3 } \right] ^{ 2/3 } }{ \frac { d^{ 3 }y }{ dx^{ 3 } } } \) where c is a constant is

    (a)

    1

    (b)

    3

    (c)

    -2

    (d)

    2

  11. 5 x 1 = 5
  12. y= mx

  13. (1)

    1

  14. Degree of linear differential equation

  15. (2)

    Family of lines

  16. General form of linear equation

  17. (3)

    \(\frac { dy }{ dx } \)+Py=Q

  18. I.F. of \(\frac { dy }{ dx } \)+Px=Q

  19. (4)

    \(e^{ \int { pdy } }\)

  20. I.F. of \(\frac { dy }{ dx } \)+Py=Q

  21. (5)

    \(e^{ \int { pdx } }\)

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