Please refer to the MCQ Questions for Class 12 Mathematics Chapter 9 Differential Equations with Answers. The following Differential Equations Class 12 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 12. Our experts have designed MCQ Questions for Class 12 Mathematics with Answers for all chapters in your NCERT Class 12 Mathematics book.

## Differential Equations Class 12 MCQ Questions with Answers

See below Differential Equations Class 12 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question.** The degree of the differential equation

(a) 4

(b) 3/2

(c) not defined

(d) 2

**Answer**

D

**Question.** The differential equation for y = A cos a x + B sin a x, where A and B are arbitrary constants is

**Answer**

B

**Question. The order of the differential equation of all circles of radiusr, having centre on y-axis and passing through the origin, is**

(a) 1

(b) 2

(c) 3

(d) 4

**Answer**

A

**Question. The differential equation whose solution is a circle centred at (h ,k) and radius a is (where, a is a constant)**

**Answer**

B

**Question.**

**Answer**

B

**Question. The solution of differential equation**

**Answer**

B

**Question. The solution of the differential equation dy/dx-x tan(y-x) ) 1is**

**Answer**

C

**Question. The solution of(x+ y+1) dy= dx**

**Answer**

A

**Question. The equation of the curve passing through the origin and satisfying the differential equation**

**Answer**

C

**Question.**

**Answer**

A

**Question. The solution of the differential equation x(dy/dx)+y=y ^{2}log x is**

(a) 1/y = log +1+Cx

(b) y = logx+1+Cx

(c) 1/y=log x -+C/x

(d) None of these

**Answer**

A

**Question.**

(a) touch each other

(b) are orthogonal

(c) are one and the same

(d) None of these

**Answer**

B

**Question. Order and degree of the differential equation**

(a) order = 2, degree = 1

(b) order = 2, degree = 4

(c) order = 1, degree = 4

(d) order = 1, degree= 1

**Answer**

A

**Question. The number of arbitrary constants in the general solution of a differential equation of fourth order is**

(a) zero

(b) 2

(c) 3

(d) 4

**Answer**

D

**Question. Order and degree of the differential equation**

(a) order = 1, degree = 1

(b) order = 1, degree = not defined

(c) order = 2, degree = 1

(d) order = 2, degree = not define

**Question. Order and degree of the differential equation**

(a) order = 4, degree = 1

(b) order = 3, degree= 1

(c) order = 4, degree = 0

(d) order = 4, degree = not defined

**Answer**

D

**Question. Family y =Ax+ A ^{3 }of curves is represented by the differential equation of degree **

(a) 1

(b) 2

(c) 3

(d) 4

**Answer**

C

**Question. The degree of the differential equation to of all tangent lines to the parabola y ^{2}=4ax is **

(a) 1

(b) 2

(c) 3

(d) 4

**Answer**

B

**Question. The number of arbitrary constants in the particular solution of a differential equation of third order is**

(a) 3

(b) 2

(c) 1

(d) zero

**Answer**

D

**Question. The order of the differential equation whose general**

(a) 5

(b) 6

(c) 3

(d) 2

**Answer**

C

**Question. The order of the differential equation whose general solution is given by**

** is**

(a) 5

(b) 4

(c) 3

(d) 2

**Answer**

C

**Question. The differential equation of the curve y2=a(b2-x ^{2})///10 representing the given family of curves, where a and b are constants, is**

**Answer**

B

**Question. The differential equation of the family of parabolas having vertex at origin and axis along positive y-axis is**

**Answer**

C

**Question. The differential equation of the curve y=e ^{x}(a coa x +b sin x) representing the given family of curves, where a and b are constants, is **

**Answer**

A

**Question. The differential equation of the family of hyperbolas having foci on x-axis and centre at origin is**

**Answer**

A

**Question. Which of the following differential equation has**

**Answer**

B

**Question. The differential equation of the family of circles inthe first quadrant which touch the coordinate axes is **

**Answer**

B

**Question.** The degree of the differential equation

(a) 1

(b) 2

(c) 3

(d) not defined

**Answer**

D

**Question.**

(a) y sec x = tan x + C

(b) y tan x = sec x + C

(c) tan x = y tan x + C

(d) x sec x = tan y + C

**Answer**

A

**Question.** The solution of differential equation

(a) x (y + cos x) = sin x + C

(b) x (y – cos x) = sin x + C

(c) xy cos x = sin x + C

(d) x (y + cos x) = cos x + C

**Answer**

A

**Question.****The solution of differential equation xdy – ydx = 0 represents**(a) a rectangular hyperbola

(b) parabola whose vertex is at origin

(c) straight line passing through origin

(d) a circle whose centre is at origin

**Answer**

C

**Question.** If y = e^{-x} ( A cos x + B sin x), then y is a solution of

**Answer**

C

**Question.** The solution of differential equation tan ysec^{2} xdx + tan x sec^{2} ydy = 0 is

**Answer**

D

**Question.** The integrating factor of differential equation cos x (dy/dx) y sin x = 1 is

(a) cos x

(b) tan x

(c) sec x

(d) sin x

**Answer**

C

**Question.** The order and degree of the differential equation

(a) 2 and 4

(b) 2 and 2

(c) 2 and 3

(d) 3 and 3

**Answer**

A

**Question.** The family y = Ax + A^{3 }of curves is represented by differential equation of degree

(a) 1

(b) 2

(c) 3

(d) 4

**Answer**

A

**Question.** The solution of (dy/dx) – y = 1, (0) = 1 is given by

(a) xy =^{ }-e^{x}

(b) xy = – e^{-x}

(c) xy = -1

(d) y = 2 e^{x} -1

**Answer**

B

**Question.** tan tan^{-1} x + tan^{-1} y = C is general solution of the differential equation

**Answer**

C

**Question.**

(a) none

(b) one

(c) two

(d) infinite

**Answer**

B

** Question. Which of the following is a second order differential equation?**(a) (y ‘)

^{2}+ x = y

^{2 }

(b) y ‘y ” + y = sin x

(c) y ”’ + (y “) + y = 2 0

(d) y ‘ = y

^{2}

**Answer**

B

**Question.** The integrating factor of differential equation

**Answer**

C

**Question.** The integrating factor of

(a) x (

b) log x

(c) 1/x

(d) – x

**Answer**

C

** Question. The differential equation y (dy/dx) + x = c represents**(a) family of hyperbolas

(b) family of parabolas

(c) family of ellipses

(d) family of circles

**Answer**

D

**Question.** The solution of (dy/dx) + y = e^{-x}, y(0) = 0 is

(a) y = e^{x} (x – 1)

(b) y = x^{e-x}

(c) y = x^{e-x} + 1

(d) y = (x + 1) e^{-x}

**Answer**

B

**Question.** Which of the following is the general solution of

(a) y = (Ax + B) e^{x}

(b) y = (Ax + B) e^{-x}

(c) y = Ae^{x }+ Be^{-x}

(d) y = A cos x + B sin x

**Answer**

A

**Question.** The general solution of differential equation**(ex + 1) ydy = (y + 1) ex dx is**

**Answer**

C

**Question.** The integrating factor of differential equation dy/dx + y tan x – sec x = 0 is

(a) cos x

(b) sec x

(c) e^{cos x}

(d) e^{sec x}

**Answer**

B

**Question.****The general solution of e ^{x} cos ydx – e^{x} sin ydy = 0 is**(a) e

^{x}cos y = k

(b) e

^{x}sin y = k

(c) e

^{x}= k cos y

(d) e

^{x}= k sin y

**Answer**

A

**Question.****The degree of differential equation**

(a) 1

(b) 2

(c) 3

(d) 5

**Answer**

A

**Question.** The solution of differential equation

(a) y = x tan^{-1} x

(b) y – x = k(1+ xy)

(c) x = y tan^{-1} y

(d) tan(xy) = k

**Answer**

B

**Question.** The solution of differential equation cos x sin ydx + sin x cos ydy = 0 is

**Answer**

B

**Question.**

**Answer**

A

**Question.** The differential equation of the family of curves x^{2} + y^{2} – 2ay = 0, where a is arbitrary constant, is

**Answer**

A

**Question.** The family Y = Ax + A^{3} of curves will correspond to a differential equation of order

(a) 3

(b) 2

(c) 1

(d) not defined

**Answer**

C

**Question.** The integrating factor of differential equation

(a) x/e^{x}

(b) e^{x}/x

(c) xe^{x}

(d) e^{x}

**Answer**

B

**Question.** y = ae^{mx} + be^{-mx} satisfies which of the following differential equation?

**Answer**

C

**Question.**

(a) e^{x2} – y = C

(b) e-y + e^{x2} = C

(c) ey = e^{x2} + C

(d) e^{x2} + y = C

**Answer**

C

**Question.** The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is

(a) an ellipse

(b) parabola

(c) circle

(d) rectangular hyperbola

**Answer**

D

**Question.** The general solution of differential equation

(a) y = Ce^{-x2/2}

(b) y = Ce^{x2/2}

(c) y = (x + c) e^{x2/2}

(d) y = (c – x)e^{x2/2}

**Answer**

C

**Question.** The solution of equation (2y – 1) dx – (2x + 3) dy = 0 is

**Answer**

C

**Question.** The differential equation for which y = a cos x + b sin x is a solution, is

**Answer**

A

**Question.**

(a) y = e^{-x} (x – 1)

(b) y = x^{e-x} + 1

(c) y = x^{ex}

(d) y = xe^{-x}

**Answer**

D

**Question.** The solution of differential equation dy/dx = e^{x-y }x^{2} e^{-y} is

**Answer**

B

**Question.** The solution of differential equation

**Answer**

A

**Question.** The order and degree of differential equation

(a) 1, 4

(b) 3, 4

(c) 2, 4

(d) 3, 2

**Answer**

D

**Question.** The order and degree of differential equation

(a) 2(3/2)

(b) 2, 3

(c) 2, 1

(d) 3, 4

**Answer**

C

**Question.** The differential equation of family of curves y^{2} = 4a (x + a) is

**Answer**

D

**State True or False for the following**

**Question.** Number of arbitrary constants in the particular solution of a differential equation of order two is two.

**Answer**

False

**Question.****The differential equation representing the family of circles x ^{2} + (y – a)^{2} = a^{2} will be of order two.**

**Answer**

False

**Question.**

**Answer**

True

**Question.** Correct substitution for the solution of the differential equation of the type**dy/dx = where f (x, y) is a homogeneous function of zero degree is y = vx.**

**Answer**

True

**Question.** Correct substitution for the solution of the differential equation of the type dy/dx = g (x, y) where g (x, y) is a homogeneous function of the degree zero is x = vy.

**Answer**

True

**Question.** Integrating factor of the differential of the form dy/dx + p_{1 }x = 0_{1} is given by e∫p_{1}/dy

**Answer**

True

**Question.****The differential equation of all non horizontal lines in a plane is**

**Answer**

True

**Question.** Differential equation representing the family of curves y = ex (A cos x + B sin x) is

**Answer**

True

**Question.** Solution of the differential equation of the type**dx/dy + p _{1}x = 0_{1 }is given by x · IF = ∫ (IF) x Q_{1} dy.**

**Answer**

True

**Question.**

**Answer**

True

**Question.** The solution of the differential equation

**Answer**

True