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Differential Equations Class 12 Multiple Choice Test

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Differential Equations Class 12 (120901)


General Instruction:

1. There are 10 MCQ’s in the Test.

2. Passing %age is 50.

3. After time gets over, test will be submitted itself.

1 / 10

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

2 / 10

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

3 / 10

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

a) First order

b) Second order

c) Third order

d) Higher order

4 / 10

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

5 / 10

The general solution of a homogeneous differential equation of the form \(\frac{dy}{dx} + p(x)y = 0\) is given by:

a) \(y = Ce^(∫p(x)dx)\)

b) \(y = Ce^(-∫p(x)dx)\)

c) \(y = C∫p(x)dx\)

d) \(y = \frac{C}{x}\)

6 / 10

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

7 / 10

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

8 / 10

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) \(y = e^(∫p dy)\)

9 / 10

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

10 / 10

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

a) Zero

b) One

c) Two

d) Undefined

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