CBSE  /  Class 12  /  Maths  /  Differential Equations

  • 1. 
    Integration factor of differential equation \(\frac{dy}{dx}\) + py = Q, where P and IQ are functions of x is

  • ∫e
  • \(_{e}\)∫pdx
  • \(_{e}\)-∫pdx
  • None of these

  • 2. 
    The radius of a circle is increasing at the rate of 0.4 cm/ s. The rate of increasing of its circumference is

  • 0.4 π cm/s
  • 0.8 π cm/s
  • 0.8 cm/s
  • None of these

  • 3. 
    The solution of \(\frac{dy}{dx}\) = 1 + x + y + xy is

  • x – y = k(1 + xy)
  • log (1 + y) = x + \(\frac{x^2}{2}\) + k
  • log (1 + x) + y + \(\frac{y^2}{2}\) = k
  • None of these

  • 4. 
    The degree of the differential equation

  • 1
  • 2
  • 3
  • not defined

  • 5. 
    The degree of differential equation[1 + (\(\frac{dy}{dx}\))²]= \(\frac{d^2y}{dx^2}\) is

  • 4
  • \(\frac{3}{2}\)
  • 2
  • not defined

  • 6. 
    The order and degree of the differential equation \(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))+ x= 0 respectvely, are

  • 2 and not defined
  • 2 and 2
  • 2 and 3
  • 3 and 3

  • 7. 
    If y = e

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

  • 8. 
    The differential equation for y = A cos αx + B sin αx where A and B are arbitary constants is

  • \(\frac{d^2y}{dx^2}\) – α²y = 0
  • \(\frac{d^2y}{dx^2}\) + α²y = 0
  • \(\frac{d^2y}{dx^2}\) + αy = 0
  • \(\frac{d^2y}{dx^2}\) – αy = 0

  • 9. 
    Solution of differential equation xdy – ydx = Q represents

  • a rectangular hyperbola
  • parabola whose vertex is at origin
  • straight line passing through origin
  • a circle whose centre is at origin

  • 10. 
    Integrating factor of the differential equation cos x \(\frac{dy}{dx}\) + y sin x = 1 is

  • cos x
  • tan x
  • sec x
  • sin x
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