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12th Standard Business Maths Differential Equations English Medium Free Online Test One Mark Questions with Answer Key 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 order and degree of the differential equation \(\sqrt { \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } } =\sqrt { \frac { dy }{ dx } +5 } \) are respectively

    (a)

    2 and 3

    (b)

    3 and 2

    (c)

    2 and 1

    (d)

    2 and 2

  2. The integrating factor of the differential equation \(\frac{dx}{dy}+Px=Q\)

    (a)

    eഽPdx

    (b)

    eഽPdx

    (c)

    ഽPdy

    (d)

    eഽPdy

  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 particular integral of the differential equation f(D)y = eax where f(D) = (D−a)2

    (a)

    \(\frac { { x }^{ 2 } }{ 2 } { e }^{ ax }\)

    (b)

    xeax

    (c)

    \(\frac { x }{ 2 } \)eax

    (d)

    x2eax

  5. The differential equation of all circles with centre at the origin is

    (a)

    xdy +ydx = 0

    (b)

    xdy - ydx = 0

    (c)

    xdx + ydy = 0

    (d)

    xdx - ydy = 0

  6. 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

  7. The degree and order of \(\frac { { d }^{ 2 }y }{ dx^{ 2 } } -6\sqrt { \frac { dy }{ dx } } \)=0 are

    (a)

    2,1

    (b)

    1,2

    (c)

    2,2

    (d)

    1,1

  8. The integrating factor of (1+x2)\(\frac { dy }{ dx } \)+xy = (1+x2)3 is

    (a)

    \(\sqrt { 1+{ x }^{ 2 } } \)

    (b)

    log(1+x2)

    (c)

    etan-1x

    (d)

    log(tan-1x)

  9. The complementary function of the differential equations (D2-D)y=ex is

    (a)

    A+Bex

    (b)

    (Ax+B)ex

    (c)

    A+Be-x

    (d)

    (A+Bx)e-x

  10. The P.I. of \(\frac { d^{ 2 }y }{ { dx }^{ 2 } } -6\frac { dy }{ dx } +9y\)=e3x is ______

    (a)

    \(\frac { { e }^{ 3x } }{ 2! } \)

    (b)

    \(\frac { { x }^{ 2 }e^{ 3x } }{ 2! } \)

    (c)

    \(\frac { xe^{ 3x } }{ 2! } \)

    (d)

    9e3x

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