Please refer to Differential Equations MCQ Questions Class 12 Mathematics below. These MCQ questions for Class 12 Mathematics with answers have been designed as per the latest NCERT, CBSE books, and syllabus issued for the current academic year. These objective questions for Differential Equations will help you to prepare for the exams and get more marks.

## Differential Equations MCQ Questions Class 12 Mathematics

Please see solved MCQ Questions for Differential Equations in Class 12 Mathematics. All questions and answers have been prepared by expert faculty of standard 12 based on the latest examination guidelines.

### MCQ Questions Class 12 Mathematics Differential Equations

**Question. The differential equation representing the family of curves y ^{2} = 2c ( x+√c) , where c > 0, is a parameter, is of order and degree as follows : **

(a) order 1, degree 2

(b) order 1, degree 1

(c) order 1, degree 3

(d) order 2, degree 2

**Answer**

C

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

**Answer**

A

**Question. Solution of the differential equation**

**Answer**

C

**Question. Solution of the differential equation**

**Answer**

B

**Question. Solution of the differential equation**

**Answer**

D

**Question. Solution of the differential equation**

**Answer**

C

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

**Answer**

C

**Question. Solution of the differential equation**

**Answer**

B

**Question. Solution of the differential equation**

**Answer**

C

**Question. Solution of the differential equation**

**Answer**

B

**Question. The general solution of**

**Answer**

C

**Question. Solution of the differential equation**

**Answer**

A

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

(a) hyperbolas

(b) parabolas

(c) ellipses

(d) circles

**Answer**

D

**Question. Solution of the differential equation**

**Answer**

B

**Question. The solution of the equation dy/dx=x(2log x+1)/sin y +y cos y is **

**Answer**

A

**Question. The solution of dy/dx + = xy= xy ^{2} is **

**Answer**

B

**Question. The solution of differential equation**

**Answer**

C

**Question. The general solution of dy/dx=2xe ^{x2-y} is**

**Answer**

C

**Question. The solution of x dy- y dx+ x ^{2} e^{x} dx=0 is**

**Answer**

A

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

**Answer**

A

**Question. The solution of differential equation**

**Answer**

C

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

**Answer**

B

**Question.**

**Answer**

B

**Question. The solution of differential equation**

**Answer**

A

**Question. The solution of ydx- xdy =xydx – = is**(a) y= Cxe

^{-x}

(b) 2y= Cxe

^{-x}

(c) y= 3Cxe

^{-x}

(d) y2 =Cxe

^{-x }

**Answer**

A

**Question. Consider the differential equation **

**Answer**

C

**Question. The equation of the curve through the point (1, 2) and whose slope is y-1/x ^{2}+x , is **

(a) (y – 1)(x +1) – 2x = 0

(b) 2x(y – 1) + x +1 = 0

(c) x(y -1)(x +1) + 2 = 0

(d) None of these

**Answer**

A

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

(a) 2, 2

(b) 2, 3

(c) 2, 1

(d) None of these

**Answer**

A

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

(a) d^{2}y/dx^{2}

(b) d^{2}x/dy^{2} = 0

(c) dy/dx = 0

(d) dx/dy = 0

**Answer**

B

**Question. If y(t) is a solution of(1+t)dy/dt – ty = 1 and y(0) = –1, then the value of y (1) is **

(a) 1/2

(b) -1/2

(c) 2

(d) 1

**Answer**

B

**Question. The order of the differential equation of a family of curves represented by an equation containing four arbitrary constants, will be **

(a) 2

(b) 4

(c) 6

(d) None of these

**Answer**

B

**Question. Consider the following statements **

I. The order of the differential equation dy/dx = e^{x} is 1.

II. The order of the differential equation d^{2}y/dx^{2} + y = 0 is 2.

III. The order of the differential equation (d^{3}y/dx^{3}) + x^{2} (d^{2}y/dx^{2})^{3} = 0 is 3.

Choose correct option.

(a) I and II are true

(b) II and III are true

(c) I and III are true

(d) All are true

**Answer**

D

**Question. The differential equation (1+ y ^{2} )x dx – (1+ x^{2} )ydy = 0 represents a family of : **

(a) ellipses of constant eccentricity

(b) ellipses of variable eccentricity

(c) hyperbolas of constant eccentricity

(d) hyperbolas of variable eccentricity

**Answer**

D

**Question. For the function y = Bx ^{2} to be the solution of differential equation (dy/dx)^{3} – 15x^{2} dy/dx – 2xy = 0, the value of B is __________, given that B ≠ 0. **

(a) 2

(b) 4

(c) 6

(d) 8

**Answer**

A

**Question. **

**Codes**

A B C D E F

(a) 2 1 4 3 6 5

(b) 2 1 4 6 5 3

(c) 5 6 1 4 3 2

(d) 3 5 1 6 4 2

**Answer**

D

**Question. Solution of the differential equation xdy – ydx = √x ^{2}+y^{2} dx is **

(a) y = cx

^{2}

(b) y = cx

^{2}+ √x

^{2}+ y

^{2}

(c) y + √x

^{2}+ y

^{2}= cx

^{2}

(d) y – √x

^{2}– y

^{2}= c

**Answer**

C

**Question. The particular solution of log dy/dx = 3x + 4y, y(0) = 0 is **

(a) e^{3x} + 3e^{–4y} = 4

(b) 4e^{3x} – 3^{–4y} = 3

(c) 3e^{3x} + 4e^{4y} = 7

(d) 4e^{3x} + 3e^{–4y} = 7

**Answer**

D

**Question. General solution of the differential equation dy/dx + y g’ (x) = g(x). g’ (x), where g(x) is a function of x is **

(a) g(x) – log[1- y – g(x)] = C

(b) g(x) – log[1+ y – g(x)] = C

(c) g(x) +[1+ y – logg(x)] = C

(d) g(x) + log[1+ y – g(x)] = C

**Answer**

D

**Question. The equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2x ^{2} + 1) dx (x ≠ 0) is **

(a) x

^{2}= y + log |x|

(b) y = x

^{2}+ log |x|

(c) y

^{2}= x + log |x|

(d) y = x + log |x|

**Answer**

B

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

(a) y^{2}y” – 2xy’ = 0

(b) y^{2} – 2xyy” = 0

(c) y^{2} – 2xyy’ = 0

(d) None of these

**Answer**

C

**Question. The order and degree of the differential equation y = x dy/dx + √a ^{2}(dy/dx)^{2} + b^{2} is **

(a) order = 1, degree = 2

(b) order = 2, degree = 1

(c) order = 2, degree = 2

(d) None of these

**Answer**

A

**Question. The order of the differential equation whose general solution is given by ****y = (C _{1} + C_{2}) cos (x +C_{3}) – C_{4}e^{x}+C_{5} where C_{1}, C_{2}, C_{3}, C_{4}, C_{5} are arbitrary constant, is**

(a) 5

(b) 4

(c) 3

(d) 2

**Answer**

C

**Question. If dx +dy = (x + y) (dx – dy), then log (x + y) is equal to **

(a) x + y + C

(b) x + 2y + C

(c) x – y + C

(d) 2x + y + C

**Answer**

C

**Question. A homogeneous differential equation of the dx/dy = h (x/y) can be solved by making the substitution **

(a) y = vx

(b) v = yx

(c) x = vy

(d) x = v

**Answer**

C

**Question. The differential equation representing the family of curves y = A cos (x + B), where A, B are parameters, is **

(a) d^{2}y/dx^{2} + y = 0

(b) d^{2}y/dx^{2} – y = 0

(c) d^{2}y/dx^{2} = dy/dx + y

(d) dy/dx + y = 0

**Answer**

A

**Question. The differential equation dy/dx = √1-y ^{2}/y determines a family of circle with **

(a) variable radii and fixed centre (0, 1)

(b) variable radii and fixed centre (0, –1)

(c) fixed radius 1 and variable centre on x-axis

(d) fixed radius 1 and variable centre on y-axis

**Answer**

C

**Question. The solution of differential equation **

(a) ye^{2√x} =2 √x + C

(b) ye √x = √x + C

(c) ye^{2√x} =√y + C

(d) ye^{2√x} =2√x + C

**Answer**

A

**Question. The order and degree of the differential equation d4y/dx4 + sin (y”) = 0 are respectively **

(a) 4 and 1

(b) 1 and 2

(c) 4 and 4

(d) 4 and not defined

**Answer**

D

**Question. The differential equation which represent the family of curves y = aebx, where a and b are arbitrary constants. **

(a) y’ = y^{2}

(b) y” = y y’

(c) y y” = y’

(d) y y” = (y’)^{2}

**Answer**

D

**Question. The order of the differential equation of all tangent lines to the parabola y = x ^{2}, is **

(a) 1

(b) 2

(c) 3

(d) 4

**Answer**

A

**Question. The differential equations of all conics whose axes coincide with the co-ordinate axis is **

**Answer**

C

**Question. The solution of the equation dy/dx = 3x-4y- 2/3x-4y- 3 is **

(a) (x – y^{2}) + c = log (3x – 4y + 1)

(b) x – y + c = log (3x – 4y + 4)

(c) (x – y + c) = log (3x – 4y – 3)

(d) x – y + c = log (3x – 4y + 1)

**Answer**

D

**Question. A differential equation of the form dy/dx = F(x, y) is said to be homogeneous, if F(x, y) is a homogeneous function of degree, **

(a) 0

(b) 1

(c) 2

(d) 3

**Answer**

A

**Question. If the I.F. of the differential equation dy/dx + 5y = cos x is ∫ e ^{Adx} , then A = **

(a) 0

(b) 1

(c) 3

(d) 5

**Answer**

D

**Question. If (1+e ^{x/y}) dx + (1-x/y)e^{x/y} dy = 0 , then **

(a) x – ye

^{x/y}= c

(b) y – xe

^{x/y}= c

(c) x + ye

^{x/y}= c

(d) y + xex/y = c

**Answer**

C

**Question. Solution of differential equation xdy – ydx = 0 represents: **

(a) rectangular hyperbola.

(b) parabola whose vertex is at origin.

(c) circle whose centre is at origin.

(d) straight line passing through origin.

**Answer**

D

**Question. Family y = Ax + A _{3} of curves will correspond to a differential equation of order **

(a) 3

(b) 2

(c) 1

(d) not infinite

**Answer**

B

**Question. The order and degree of the differential equation d ^{2}y/dx^{2} + (dy/dx)^{1/3} + x^{1/4} – 0 is **

(a) order = 3, degree = 2

(b) order = 2, degree = 3

(c) order = 2, degree = 2

(d) order = 3, degree = 3

**Answer**

B

**Question. If y = ex (sin x + cos x), then the value of d ^{2}y/dx^{2} – 2 dy/dx + 2y , is **

(a) 0

(b) 1

(c) 2

(d) 3

**Answer**

A

**Question. General solution of dy/dx + 2xy/1+x ^{2} = 1/(1+x^{2})^{2} is **

(a) y(1 + x

^{2}) = c + tan

^{–1}x

(b) y/1+x

^{2}+ c tan

^{-1}x

(c) y log (1 + x

^{2}) = c + tan

^{–1}x

(d) y (1 + x

^{2}) = c + sin

^{–1}x

**Answer**

A

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

(a) e

^{x}= y

^{3}/3 = e

^{y}+ c

(b) e

^{y}= x

^{2}/3 + e

^{x}+ c

(c) e

^{y}= x

^{3}/3 + e

^{x}+ c

(d) None of these

**Answer**

C

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

(a) y/4 + 1/x^{2} + y^{2} = c

(b) y/x – 1/x^{2}+y^{2} = c

(c) x/y – 1/x^{2}+y^{2} = c

(d) None of these

**Answer**

B

**Question. In the particular solution of differential equation dy/dx = 1/x(3y ^{2} – 1) , the value of constant term is ________, given that y = 2 when x = 1. **

(a) 2

(b) 4

(c) 6

(d) 8

**Answer**

C

**Question. The expression satisfying the differential equation (x ^{2}-1)dy/dx + 2xy = 1 is **

(a) x

^{2}y – xy

^{2}= c

(b) (y

^{2}-1)x = y + c

(c) (x

^{2}-1) y = x + c

(d) None of these

**Answer**

C

**Question. Which of the following differential equation has y = x as one of its particular solution ? **

**Answer**

C

**Assertion and Reason type Questions :**

(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.

(b) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion

(c) Assertion is correct, Reason is incorrect

(d) Assertion is incorrect, Reason is correct.

**Question. Assertion:** The degree of the differential equation d^{2}y/dx^{2} + 3(dy/dx)^{2} = x^{2} log (d^{2}y/dx^{2}) is not defined. **Reason :** If the differential equation is a polynomial in terms of its derivatives, then its degree is defined.

**Answer**

A

**Question. Assertion :** The number of arbitrary constants in the solution of differential equation d^{2}y/dx2 = 0 are 2. **Reason:** The solution of a differential equation contains as many arbitrary constants as is the order of differential equation.

**Answer**

A

**Question. Assertion :** The degree of the differential equation d^{3}y/dx^{3} + 2(d^{2}y/dx^{2})^{3/2} + 2y = 0 is zero **Reason:** The degree of a differential equation is not defined if it is not a polynomial eq in its derivatives.

**Answer**

D