Differential Equations Class 12 Mcq Test (120901)

What is the order of a differential equation?

a) The highest power of the derivative in the equation

b) The lowest power of the derivative in the equation

c) The sum of all powers of the derivative in the equation

d) The degree of the polynomial in the equation

What is the order of the differential equation \(\frac{d^2y}{dx^2} + \frac{dy}{dx} + y = 0\)?

a) First order

b) Second order

c) Third order

d) Fourth order

What is the general solution of a differential equation?

a) A solution that satisfies the equation for any given initial condition

b) A solution that satisfies the equation for a specific initial condition

c) A solution that satisfies the equation for only certain values of the independent variable

d) A solution that satisfies the equation for all values of the independent variable

What is the degree of the differential equation \(\frac{dy}{dx} + p(x)y = q(x)\)?

a) Zero

b) One

c) Two

d) Undefined

Which method is used to solve homogeneous differential equations of first order and first degree?

a) Separation of variables

b) Method of undetermined coefficients

c) Variation of parameters

d) Substitution method

The Integrating Factor of differential equation of the form \(\frac{dy}{dx} + py = q\) is given by:

a) \(y = e^(-∫p dx)\)

b) \(y = e^(∫p dx)\)

c) \(y = e^(-∫p dy)\)

d) \(y = e^(∫p dy)\)

What does the constant "C" represent in the general solution of a linear differential equation?

a) The initial condition of the differential equation

b) The particular solution of the differential equation

c) The order of the differential equation

d) The degree of the differential equation

The degree of a differential equation is determined by:

a) The highest power of the derivative in the equation

b) The lowest power of the derivative in the equation

c) The sum of all powers of the derivative in the equation

d) The degree of the polynomial in the equation

What is the degree of the differential equation \(\frac{d^2y}{dx^2} + \frac{dy}{dx} + y = 0\)?

a) Zero

b) One

c) Two

d) Undefined

The method of separation of variables is used to solve which type of differential equations?

a) Homogeneous differential equations

b) Linear differential equations

c) Second-order differential equations

d) First-order differential equations