12th Standard cbse -- Maths - Differential Equations

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Question - 1

The degree of differential equation
\({ \left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 2 }+3\frac { dy }{ dx } +\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } =4\), then the value of 2p – 3q is

  • A 7
  • B -7
  • C 3
  • D -3

Question - 2

The degree of the differential equation 
\({ \left( 1+\frac { dy }{ dx } \right) }^{ 3 }={ \left( \frac { dy }{ dx } \right) }^{ 2 }\) is

  • A 1
  • B 2
  • C 3
  • D 4

Question - 3

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

  • A 1
  • B 2
  • C 3
  • D not defined

Question - 4

The order of the differential equation of all the circles of given radius 4 is

  • A 1
  • B 2
  • C 3
  • D 4

Question - 5

The differential equation of the family of lines passing through ongrn is

  • A y = mx
  • B \(\frac{dy}{dx}=m\)
  • C x dy – y dx = 0
  • D \(\frac{dy}{dx}=0\)

Question - 6

The degree of the differential equation
\({ \left( \frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } \right) }^{ 3 }+ { \left( \frac { dy }{ dx } \right) }^{ 2 }+sin{ \left( \frac { dy }{ dx } \right) }+1=0\)

  • A 3
  • B 2
  • C 1
  • D not defined

Question - 7

The order of the differential equation \({ 2x }^{ 2 }\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -3\frac { dy }{ dx } +y=0\) is

  • A 2
  • B 1
  • C 0
  • D not defined

Question - 8

The number of arbitrary constants in the general solution of a differential equation of fourth order are:

  • A 0
  • B 2
  • C 3
  • D 4

Question - 9

The number of arbitrary constants in the particular solution of a differential equation of third order are:

  • A 3
  • B 2
  • C 1
  • D 0

Question - 10

Which of the following differential equations has y = c1 ex + c2 e–x as the general solution?

  • A \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +y=0\)
  • B \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -y=0\)
  • C \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +1=0\)
  • D \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -1=0\)
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