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Ordinary Differential Equations 1 Mark Creative Question Paper With Answer Key

12th Standard

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Maths

Time : 00:15:00 Hrs
Total Marks : 15

    Multiple Choice Question

    15 x 1 = 15
  1. The order and degree of y'+(y")= (x + t")2 are _________.

    (a)

    1, 1

    (b)

    1, 2

    (c)

    2, 1

    (d)

    2, 2

  2. The differential equation corresponding to xy = c2 where c is an arbitrary constant is ________.

    (a)

    xy"+ x = 0

    (b)

    y" = 0

    (c)

    xy'+ y = 0

    (d)

    xy"-x = 0

  3. On finding the differential equation corresponding to y = emx where m is the arbitrary constant, then m is ________.

    (a)

    \(\frac { y }{ { y }^{ 1 } } \)

    (b)

    \(\frac { { y }^{ 1 } }{ y } \)

    (c)

    y'

    (d)

    y

  4. 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)

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

  5. The solution of log \(\left( \frac { dy }{ dx } \right) \) = ax + by is______.

    (a)

    \(\frac { { e }^{ ax } }{ a } +\frac { { e }^{ -by } }{ b } +c=0\)

    (b)

    aeax- be-by + c = 0

    (c)

    ae+ be= k

    (d)

    beax + ae-by = k

  6. The general solution of x \(\frac{dy}{dx}\) = y is _________.

    (a)

    y = cx

    (b)

    x2+ y= c

    (c)

    x2- y= c

    (d)

    y = cx

  7. The differential equation of x2y = k is _________.

    (a)

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

    (b)

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

    (c)

    \({ x }\frac { dy }{ dx } +2y=0\)

    (d)

    \(y\frac { dy }{ dx } +2x=0\)

  8. 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

  9. The I.F. of (1+y2) dx = (tan-1-t-x) dy is ________.

    (a)

    etan-1 y

    (b)

    etan-1 x

    (c)

    tan-1 y

    (d)

    tan-1x

  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)

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

  11. The solution of the differential equation \(\frac{d y}{d x}=e^{x+y}\) is __________

    (a)

    ex + ey = c

    (b)

    ex + e-y = c

    (c)

    ex - e-y = c

    (d)

    none of these

  12. The solution of the \(\operatorname{DE} \ y \frac{d x}{d y}=\cot x \text { is }\) __________

    (a)

    sec x = cy

    (b)

    sec y = cx

    (c)

    sec y = c

    (d)

    sec x = c

  13. The order and degree of the differential equation \(\frac{d^{3} y}{d x^{3}}+6 \frac{d y}{d x}+3 y=0 \text { is }\)__________

    (a)

    3, 1

    (b)

    1, 3

    (c)

    1, 1

    (d)

    none of these

  14. The order and degree of the differential equation \(e^{\frac{d^{3}y}{d x^{2}}}+\cos (x) \frac{d y}{d x}=4 \text { is }\)__________

    (a)

    3, not defined

    (b)

    not defined 1

    (c)

    3, 1

    (d)

    none of these

  15. If m, n are the order and degree of the differential equation \(\left(\frac{d^{4} y}{d x^{4}}+\frac{d^{2} y}{d x^{2}}\right)^{\frac{1}{2}}=a \frac{d^{3} y}{d x^{3}}\) respectively, then the value of 4m - n is __________

    (a)

    15

    (b)

    12

    (c)

    14

    (d)

    13

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