Differential Equations Test

Differential Equations

This is Differential Equations Test-01 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Differential equations are equations containing functions y = f(x), g(x) and
  • A
    minima of y
  • B
    derivatives of y
    Correct
  • C
    tangent of y at zero
  • D
    maxima of y
2
Order of a differential equation is defined as
  • A
    the number of derivative terms
  • B
    the number of constant terms
  • C
    the order of the lowest order derivative ofthe dependent variable
  • D
    the order of the highest order derivative ofthe dependent variable
    Correct
3
Degree of a differential equation, when the equation is polynomial equation in y′ is
  • A
    Highest power (positive integral index) of the highest order derivative in the given differential equation.
    Correct
  • B
    Lowest power (positive integral index) of the highest order derivative in the given differential equation.
  • C
    Highest (positive integral index) of the lowest order derivative in the given differential equation.
  • D
    Lowest power (positive integral index) of the lowest order derivative in the given differential equation.
4
The order of the equation \(\frac{{{d^2}y}}{{d{x^2}}} + \;y = 0\) is
  • A
    4
  • B
    2
    Correct
  • C
    1
  • D
    3
5
The order of the equation \(\frac{{{d^3}y}}{{d{x^3}}} + \;{x^2}\)\({(\frac{{{d^2}y}}{{d{x^2}}})^3}\)= 0 is
  • A
    1
  • B
    3
    Correct
  • C
    2
  • D
    4
6
The degree of the equation\({(\frac{{dy}}{{dx}})^2} + \;\frac{{dy}}{{dx}}--{\text{ }}si{n^2}y{\text{ }} = {\text{ }}0\) is
  • A
    3
  • B
    1
  • C
    0
  • D
    2
    Correct
7
Find the order and degree of \(y\prime \prime \prime + {\text{ }}{y^2} + {\text{ }}{e^{y{\text{ }}\prime }} = {\text{ }}0\) is
  • A
    4, degree undefined
  • B
    2, degree undefined
  • C
    3, degree undefined
    Correct
  • D
    1, degree undefined
8
Determine order and degree (if defined) of\(\frac{{{d^4}y}}{{d{x^4}}}\) +sin(y’’’) = 0
  • A
    1, degree undefined
  • B
    4, degree undefined
    Correct
  • C
    2, degree undefined
  • D
    3, degree undefined
9
Determine order and degree (if defined) of y’ + 5y = 0
  • A
    1,degree undefined
  • B
    1, 2
  • C
    1, 1
    Correct
  • D
    2, 1
10
Determine order and degree (if defined) of \({(\frac{{ds}}{{dt}})^4}\) + 3s\(\frac{{{d^2}s}}{{d{t^2}}}\) = 0
  • A
    2, 1
    Correct
  • B
    2, 2
  • C
    1,degree undefined
  • D
    1, 2
11
Determine order and degree (if defined) of\({(\frac{{{d^2}y}}{{d{x^2}}})^2} + \)cos(\(\frac{{dy}}{{dx}}\)) = 0
  • A
    0,degree undefined
  • B
    3,1
  • C
    2,degree undefined
    Correct
  • D
    1,degree undefined
12
Determine order and degree (if defined) of \(\frac{{{d^2}y}}{{d{x^2}}} = cos3x + sin3x\)
  • A
    2,1
    Correct
  • B
    3,1
  • C
    2,1
  • D
    1,1
13
What is the order of differential equation : \(\frac{{{d^3}y}}{{d{x^3}}} + \frac{{{d^2}y}}{{d{x^2}}} + {\left( {\frac{{dy}}{{dx}}} \right)^2} = {e^x}\)
  • A
    2
  • B
    3
    Correct
  • C
    0
  • D
    1
14
Function y = f(x) is said to satisfy a differential equation g (y, y’, y’’...) =h(x) if
  • A
    y and its derivatives substituted in equation g (y, y’, y’’...) =h(x) yield L.H.S. = R.H.S.
    Correct
  • B
    y and its derivatives substituted in equation g (y, y’, y’’...) =h(x) yield L.H.S. = 0
  • C
    y and its derivatives substituted in equation g (y, y’, y’’...) =h(x) yield L.H.S. \( \ne \) R.H.S.
  • D
    If h(x) = 0.
15
Function y = f(x) is said to be a solution differential equation g (y, y’, y’’...) =h(x) if
  • A
    Function y = f(x) does not satisfy the differential equation g (y, y’, y’’...) = h(x)
  • B
    Function y = f(x) satisfies the differential equation g (y, y’, y’’...) = 0
  • C
    Function y = f(x) 2 satisfies the differential equation g (y, y’, y’’...) = h(x)
  • D
    Function y = f(x) satisfies the differential equation g (y, y’, y’’...) = h(x)
    Correct